2024

enVision Mathematics

Publisher
Savvas Learning Company
Subject
Math
Grades
K-8
Report Release
10/09/2024
Review Tool Version
v1.5
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
Meets Expectations
Our Review Process

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Report for Kindergarten

Alignment Summary

The materials reviewed for enVision Mathematics Kindergarten meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

Kindergarten
Alignment (Gateway 1 & 2)
Meets Expectations
Gateway 3

Usability

25/27
0
17
24
27
Usability (Gateway 3)
Meets Expectations
Overview of Gateway 1

Focus & Coherence

The materials reviewed for enVision Mathematics Kindergarten meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

Criterion 1.1: Focus

06/06

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Indicator 1A
02/02

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment items are present but could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

The series is divided into topics that include a Topic Assessment, available for online and/or paper and pencil delivery, and a Topic Performance Task. Additional assessments include a Kindergarten Readiness Test; Basic-Facts Timed Tests; four Cumulative/Benchmark Assessments addressing Topics 1–4, 1–8, 1–11, and 1–14; and Progress Monitoring Assessments A–C. Assessments can be found in the digital teacher interface and the Assessment Sourcebook online or in print. The materials include an ExamView Test Generator allowing teachers to build customized tests.

Examples of items that assess grade-level content include:

  • Topic 8, Assessment, Problem 2, “Directions Have Students: count the fruits, draw counters to show how many more fruits are needed to make 10, and write the number that tells how many.” A picture of eight pears is provided. (K.OA.4)

  • Topic 10, Assessment, Problem 5, “Directions Have students: draw counters to make 14, and then complete the equation to match the picture.” Students engage with two ten-frames, with 10 counters in the top frame with the bottom frame empty, and the equation 14 = __+__ . (K.NBT.1)

  • Topic 12, Performance Task, Problem 1 presents images such as a basketball, a trash can, a crate, and a pennant. Students identify shapes by drawing circles around objects that look like cylinders and marking an “X” on other objects that look like spheres. Problem 1, “Directions Carnival Time! Say: Miguel and his friends go to a carnival. Have Students: 1 draw a circle around the objects that look like a cylinder. Then have them mark an X on the objects that look like a sphere.”  Students view images of a megaphone, soccer ball, crate, bottle, cone, empty cage,  trash can, and basketball. (K.G.2)

  • Topics 1–4, Cumulative/Benchmark Assessment, Problem 13, “Directions Say: Joanie has 2 toy bears and 4 toy lions. Color the cubes to show how many of each type of toy and then draw a circle around the cube train that is greater than the other cube train.” Students view images of two bears and four lions and engage with two five-cube trains. (K.CC.5 and K.CC.6)

Examples of above grade-level assessment items that could be modified or omitted include, but are not limited to:

  • Topic 11, Assessment, Problem 2, students count 78 beads and choose the correct answer from the following choices: 78, 79, 88, and 89. This question requires students to recognize the standard form of the number. (1.NBT.1)

  • Topics 1–14, Cumulative/Benchmark Assessment, Problem 15, “Directions Have students: mark all the objects that can be measured with the tool shown.” This question requires students to identify a tool to find an exact measurement. (2.MD.1)

Indicator 1B
04/04

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding. During Independent Practice, students work with problems in various formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

  • In Topic 3, Lessons 3-1 and 3-5 and Topic 9, Lessons 9-3 and 9-4, students engage in extensive work with grade-level problems to meet the full intent of K.CC.5 (Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects). In Lesson 3-1, Quick Check, students count out a specified number of objects. Problem 1 asks, “Which shows 6 muffins?” Pictured are four choices of rows of muffins. Problem 4 asks, “Which shows 7 balls?” Pictured are four choices of rows of balls. In Lesson 3-5, Enrichment, students count how many birds, nests, apples, flowers, bees, and skunks up to 10. “Directions Have children count each item in the nature picture and draw counters to show how many of each item.” Pictured is a nature scene with scattered images of the above-mentioned items. In Lesson 9-3, Guided Practice, Problems 1 and 2 students count two groups of piggy banks up to 16 and 17, respectively. “Directions 1 and 2 Have students count the piggy banks in each group; use cubes to show how many, and then practice writing the number that tells how many.” Provided is a picture of 16 piggy banks in a rectangular array and 17 piggy banks in a row. In Lesson 9-4, Reteach to Build Understanding, Problem 2, students count fish up to 19. “Directions Say: 2. Let’s count the fish. There are 19 fish. Practice writing the number 19.” Pictured are 19 fish arranged in a circle. 

  • In Topics 6 and 7, students engage in extensive work with grade-level problems to meet the full intent of K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations). In Topic 6, Lesson 6-1, Solve & Share, students look at pictures and use counters/fingers to represent addition. “Carlos is thinking about some flowers he picked. Use counters to show how many pink and purple flowers he picked. How many flowers did he pick in all? Think about the problem. Write the number that tells how many. Then use your fingers to show how you know.” In Lesson 6-4, Reteach to Build Understanding, Problem 1, students represent addition using equations. “Directions Say: 1. When you add two groups, you can write an addition sentence that tells how many in all. You can use the plus sign and equal sign to write an addition equation. 3 and 5 is 8 can be written as 3 + 5 = 8. Circle the plus sign and the equal sign.” In Topic 7, The Animated Math Story: Where’s My Fish?, students reason about subtraction given a story. “Zak has 4 fish. Maria wants a fish. So Zak gives her 1 fish. Now Zak has ___ fish.” In Lesson 7-7, Visual Learning Bridge, Problem 2, students use tools to solve subtraction problems posed with a story. “Directions Have students listen to each story, use a tool to help them solve the problem, and then write the equation. Then have them explain whether or not the tool they chose helped to solve the problem. 2. Marta sees 7 seagulls. 4 fly away. How many seagulls are left?

  • In Topics 6 and 7, students engage in extensive work with grade-level problems to meet the full intent of K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10). In Topic 6, Lesson 6-5, Guided Practice, Problems 3 and 4, students use or make pictures to represent word problems and to write addition equations that represent how many in all. “Directions Have students listen to the story, use counters to show the addition, look at or draw a picture, and then write an equation to tell how many in all. 3. 5 squirrels are looking for food. 4 more join them. How many squirrels are there in all? 4. There is 1 turtle on the beach. 5 more walk up. How many turtles are there in all?” Problem 3 provides pictures of the squirrels; Problem 4 provides blank space for student drawings. The worksheet includes a two-lined paper image to guide students' writing and circles to enclose the + and = symbols. In Topic 7, Lesson 7-5, Independent Practice, Problems 7 and 8, students use or make pictures to represent word problems and to write subtraction equations that represent how many are left. “Directions Have students listen to each story, draw a picture to show what is happening, and then write an equation. 7. There are 5 acorns under a tree. A squirrel takes 3 of them. How many acorns are left? 8. Higher Order Thinking Have students listen to the story, draw a circle around the picture that shows the story and tell why the other picture does NOT show the story, and then write an equation. There are 4 ducks in a pond. 1 leaves. How many ducks are left?” Problem 7 provides blank space for student drawings; Problem 8 provides pictures of 9 ducks with an X through 1 duck. The worksheet includes two-lined paper images to guide students’ writing and circles to enclose the + and = symbols.

  • In Topic 14, Lessons 14-1 through 14-3, and Lesson 14-5, students engage in extensive work with grade-level problems to meet the full intent of K.MD.1 (Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object). In Lesson 14-1, Independent Practice, Problems 7 and 8, students compare the lengths of two objects to determine which item is longer, shorter, or the same length. “Directions 7 and 8 Have students mark an X on the shorter object and draw a circle around the longer object, or underline the objects if they are the same length.” Provided is a picture of two wrenches and two sneakers. In Lesson 14-2, Additional Practice, Problem 1, students compare objects based on their capacity. “Directions Say: Which bowl holds more? How do you know? Draw a circle around it. Then mark an X on the bowl that holds less. 1. Have students draw a circle around each container that holds more and mark an X on each container that holds less, or underline the containers if they hold the same amount.” Provided is a picture of a room with two buckets below a table, two jars on a table, and two watering cans on a shelf above the table. In Lesson 14-3, Reteach to Build Understanding, Problem 1, students compare items based on weight. “Directions Say: 1. You can use the words same, lighter and heavier to compare how much objects weigh. Look at the apples. Do you think 1 apple is heavier than a basket of apples? Draw a circle around the object you think is heavier. Mark an X on the object that is lighter.” Pictured are a picture of a single apple and a basket of apples. In Lesson 14-5, Guided Practice, Problems 2 and 3, students describe attributes that can be measured. “Directions Have students look at the objects on the left and identify the attributes that can be measured. 2-3 Then have students mark an X on the object that holds less or underline both objects if they can hold the same amount. Say: Which tool can you use to tell about how much the objects hold? Circle this tool. ” Problem 2 shows a bucket and a yellow wagon on the left and a scale and a measuring cup on the right.

Criterion 1.2: Coherence

08/08

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

Indicator 1C
02/02

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for that, when implemented as designed the majority of the materials address the major clusters of each grade. The materials devote at least 65% of instructional time to the major clusters of the grade.

  • The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10 out of 14, which is 71%. 

  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 73 out of 96, which is approximately 76%.

  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 108 out of 145, which is approximately 74%.

A lesson-level analysis is most representative of the materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 76% of the materials focus on the major work of the grade.

Indicator 1D
02/02

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for enVision Mathematics Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher’s Edition, Lesson Overview, Coherence, Cross-Cluster Connections on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed in a document titled “Scope and Sequence.” Examples of connections include:

  • Topic 5, Lesson 5-2 connects the supporting work of K.MD.B (Classify objects and count the number of objects in each category) to the major work of K.CC.B (Count to tell the number of objects). In the Visual Learning Bridge, students count objects in a category and sort categories by count. Pictured are images of small creatures: bees, a ladybug, caterpillars, millipedes, and spiders. Classroom Conversation asks students the following questions: “A) What do you see? Which creature has 6 legs? Which has 8 legs? This creature has lots of legs. Does it have more than 6 legs? B) Which category does this show?” Guided Practice, “Directions 1 Have students draw lines in the chart as they count the animals that are in the pond and the animals that are NOT in the pond, and then write the numbers to tell how many in another chart.” A picture of a field is shown with various animals in and out of the pond.

  • Topic 12, Lesson 12-2 connects the supporting work of K.G.A (Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)) to the major work of K.CC.A (Know number names and the count sequence). In Solve & Share, students find objects that resemble circles and triangles. “Go on a shape hunt. Find objects in the classroom or outside that look like the shapes shown. Which objects did you find? How are they different? Draw the objects you find in the space below.” In the Visual Learning Bridge, students continue to distinguish between circles and triangles and describe the shapes by their attributes. In addition, students count the sides of the triangle and vertices of the triangle to determine the shape. The teacher asks students the Essential Question, “How do you tell the difference between a circle and a triangle?” Students are shown a visual picture of a girl tracing a circle (Picture A), holding a flying disc (Picture B), tracing a triangle (Picture C), and pointing to a sail on a sailboat (Picture D). Classroom Conversation asks students the following questions: “A) Emily is tracing a shape called a circle. What does a circle look like? B) What is Emily holding? What shape is the flying disc? C) Emily is tracing a shape called a triangle. What does a triangle look like? D) What shape is Emily pointing to on the sailboat? How do you know?” 

  • Topic 13, Lesson 13-4 connects the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and other attributes) to the major work of K.OA.4 (For any number from 1 to 9, find the number that makes 10 when added to the given number). In the Solve & Share, students are given images of ten two- and three-dimensional shapes of different sizes and orientations, students sort shapes into two categories: flat and solid. “ Directions Say: Jackson wants to put flat shapes behind Door 1 and solid figures behind Door 2. Draw a line from each shape to the correct door to show how he should sort the shapes. Count all the shapes on the shelves. Then cover one door. Count the number of shapes that are behind the door you can see. Without counting any shapes, tell how many you think are behind the other door. Then count to check your answer.”

Indicator 1E
02/02

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Topic Overview, Scope and Sequence, and Teacher Guides within each topic. Examples include:

  • In Topic 3, Lesson 3-7, Independent Practice, Problems 5 and 6, students write the number (0, 2 or 8, 10) that corresponds to dots shown on cards. “Directions Have students: 5 and 6 count to find the number that is 1 less than and 1 greater than the given number, and then write the numbers.” In Problem 7, students sequence numbers 7–10. Directions, “7 compare the number cards, write the smallest number, and then count forward and write the number that is 1 greater than the number before.” The materials show cards bearing the numbers 10, 8, 7, and 9 in that order. This connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects).  

  • In Topic 4, Lesson 4-1, Guided Practice, Problems 1–4, students compare the numbers. The materials show rows of chicks of different colors. “Directions 1 Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group. … 3 and 4 Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is less in number than the other group.” This connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.CC.C (Compare numbers).

  • In Topic 10, Lesson 10-3, Reteach to Build Understanding, Problem 2, students engage with counters organized in ten-frames and write an equation. “Say: How many counters are in the first ten-frame? Draw more counters in the second ten-frame to show how to make 19. How many counters did you draw? Now write an equation to match the picture. The picture and equation show one way to make 19 with 10 ones and some more ones.” This connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.NBT.A (Work with numbers 11–19 to gain foundations for place value). 

  • In Topic 12, Lesson 12-1, Independent Practice, Problem 6, students sort various shapes and real-world objects by indicating if they are flat (two-dimensional) or solid (three-dimensional). The directions state, “mark an X on the objects that are solid. Then have them draw a circle around the objects that are flat.” The materials show shapes (circle, square, rectangle, and triangle) and real-world objects (vase, can of beets, and a shoe box). This connects the supporting work of K.MD.B (Classify objects and count the number of objects in each category) to the supporting work of K.G.A (Identify and describe shapes).

Indicator 1F
02/02

Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for enVision Mathematics Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

Prior and Future connections are identified within the Teacher Edition Math Background: Focus, Math Background: Coherence, and Lesson Overview. Examples of connections to future grades include:

  • Topic 5, Lessons 5-1 - 5-3 connect K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count) to the work of future grades. “In Lesson 5-1, students classify objects into two categories. In Lesson 5-2, they count objects in each category and represent the counts with tally marks and numbers. In Lesson 5-3, they sort categories as defined by comparing or ordering the number of objects in the categories.” In Grade 1, Topic 6, students will “organize data into three categories and will use data to make a typical tally chart and picture-graph representation.”

  • Topic 6 connects K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations) to the work of future grades. In Topic 6, “the meaning of addition is illustrated with objects, fingers, claps, mental images, drawings, and acting out situations. Students progress from using addition sentences in Lesson 6-1, 6-2, and 6-3 to using equations in Lesson 6-4 to describe addition situations. In Grade 1, “Topics 1, 2, 3, and 5, students will work on addition within 20. The emphasis will be on strategies and building fluency. Grade 1 students will be expected to become fluent with adding within 10.”

  • Topic 10 connects K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones) to the work of future grades. ”In Lessons 10-1, 10-2, and 10-3, students make teen numbers by putting together 10 ones and some extra ones and then writing the related equation. In Lessons 10-4, 10-5, 10-6, students draw on these understandings to break apart teen numbers into 10 ones and some extra ones and then write the related equation.” In Grade 1, Topic 8, students will “determine how many tens and ones are in 2-digit numbers.”

Examples of connections to prior knowledge include:

  • Topic 1 connects K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20) to learning before entering school. “Before entering school … Most young children have memorized a part of the verbal sequence of counting numbers. Many can recite the sequence using numbers 1 to 10.”  In Lesson 1-1, “students count 1, 2, or 3 objects. In Lesson 1-2, students view 1,2, or 3 objects in different arrangements. Then, in Lesson 1-3, they represent these quantities using numerals. This sequencing is repeated in Lessons 1-4 through 1-6 for the quantities of 4 and 5. Students connect representing 0 in Lessons 1-7 and 1-8.”

  • Topic 2 connects K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group) to learning before entering school. “Before Entering School... Many students come to school with experiences using direct measurement to determine which object is longer or which child is taller. This helps students when they are using a matching strategy to determine which group has the greater number of objects. Students are also likely to have compared numbers when they tell which of two children is older." In this topic, “students use matching to determine whether groups of objects are equal in number. Students then apply the matching technique to help them determine if the number of objects in a given group is greater than, less than, or equal to the number of objects in another group.”

  • Topic 7, Lesson 7-5, connects K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10) to learning before entering school. Before entering school, “children understand simple subtraction situations. … (they) know that if one of their toys were taken away, or one of their sandwiches eaten, they would be left with fewer toys or sandwiches.” In this lesson, students “represent different subtraction word problems in multiple ways, including with equations.”

Indicator 1G
Read

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for enVision Mathematics Kindergarten foster coherence between grades and can be completed within a regular school year with little to no modification. 

As designed, the materials can be completed in 145 days. As indicated in the Teacher’s Edition Program Overview, “A Program Paced for Success,” “Each core lesson, including differentiation, takes 45-75 minutes.” 

Kindergarten consists of 14 topics. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment. For example: 

  • 96 days of content-focused lessons

  • 7 days of 3-Act Math activities

  • 14 days of Topic Centers

  • 28 days of Topic Reviews and Assessments

Additional Resources that are not counted in the program days include:

  • Math Diagnosis and Intervention System

  • 10 Step-Up Lessons to use after the last topic

  • Readiness Test; Review What You Know; four Cumulative/Benchmark Assessments; and Progress Monitoring Assessment Forms A, B, and C

Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for enVision Mathematics Kindergarten meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2.1: Rigor and Balance

08/08

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately.

Indicator 2A
02/02

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials develop conceptual understanding throughout the grade level. According to the Teacher’s Edition’s Program Overview, “conceptual understanding and problem solving are crucial aspects of the curriculum.” In the Topic Overview, Math Background: Rigor, “Conceptual Understanding Background information is provided so you can help students make sense of the fundamental concepts in the topic and understand why procedures work.” Each Topic Overview includes a description of key conceptual understandings developed throughout the topic. The 3-Act Math Task Overview indicates the conceptual understandings that students will use to complete the task. At the lesson level, Lesson Overview, Rigor, the materials indicate the Conceptual Understanding students will develop during the lesson.

Materials provide opportunities for students to develop conceptual understanding throughout the grade level. The Visual Learning Bridge and Guided Practice consistently provide these opportunities. Examples include: 

  • Topic 4, Lesson 4-1, Lesson Overview, Conceptual Understanding states, “Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number.” In the Visual Learning Bridge, the materials show two adjacent frames: A) contains scattered groups of yellow chicks and black chicks and B) contains a row of yellow chicks and another row of black chicks. Classroom Conversation asks students the following questions: “A) What do you see? Can you tell which group of chicks is greater in number than the other group just by looking at them? How can you compare the two groups? B) Construct Arguments Let’s count the chicks together. Is a group of 7 chicks greater in number or less in number than a group of 10 chicks? How do you know?” In Guided Practice, Problem 2, students compare two groups of chicks. Directions: “Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group.” The image for Problem 2 shows the two rows of chicks: three yellow and eight yellow. Students develop conceptual understanding by using strategies to identify whether one group is greater than, less than, or equal to another. (K.CC.6)

  • Topic 6, Lesson 6-3, Lesson Overview, Conceptual Understanding states, “Students explore addition as putting together. The addition problems continue in the format of addition sentences as students build understanding.” In the Visual Learning Bridge, the materials show three frames: A) has a column of two red tomatoes and a column of four yellow tomatoes, B) has a column of two red counters and a column of four yellow counters, and C) shows a boy drawing a circle around the two groups of tomatoes to put them together, indicating “2 and 4 is 6.” Classroom Conversation asks students the following questions: “A) What number story can you make up about the tomatoes in the box? B) What can you show with the counters? How many tomatoes are in the first group? In the second group? C) Reasoning What does the drawing show? What is one way to put together the 2 groups? What does the sentence tell? How many are there in all when you put together 2 and 4?”  In Guided Practice, Problem 3, students use counters to model putting together groups. Directions: “Have students use counters to model putting together the groups, draw a circle around the groups to put them together, and then write an addition sentence to tell how many in all.” The materials show a group of five yellow corns and a group of four blue corns with the sentence frame: and   is __. Students develop conceptual understanding as they represent addition using counters. (K.OA.1)

  • Topic 13, Lesson 13-2, Lesson Overview, Conceptual Understanding states, “Students learn to identify 3-D shapes based on common attributes. These include the attributes that allow solid figures to roll, stack, or slide.” In the Visual Learning Bridge, the materials show four frames: A) shows a cube, sphere, cone, and cylinder; students discuss which solid figure has two or more vertices and which figures have flat surfaces. B) shows three solid figures in motion, and students discuss what a solid object needs to look like to roll. C) focuses on student reasoning about why a cube and a cylinder can be stacked. D) shows three solids in motion, and students discuss what a solid object needs to look like to slide. Classroom Conversation asks students the following questions: “A) What solid figures do you see? Which solid figure has 2 or more vertices? Which solid figures have flat surfaces? B) Which solid figures do you see? What movement is each figure doing? What does an object have to look like to roll? C) Reasoning What do you see? Why can these solid figures be stacked? Can you stack a cone? D) Which solid figures slide? Which can stack, slide, and roll?” Students build on prior and emerging understandings as they identify which 3-D shapes can roll, stack, and slide. In Guided Practice, Problem 2, students compare shapes based on their attributes. Directions: “2 look at the rolling solid figure on the left, and then draw a circle around the other solid figures that roll.” The materials show a circle and the indication that it can roll, with three shapes next to it, a cube, a cone, and a cylinder. Students develop conceptual understanding as they analyze and compare three-dimensional shapes using their attributes. (K.G.4)

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. The Practice problems consistently provide these opportunities. Examples include:

  • Topic 1, Lesson 1-5, Lesson Overview, Conceptual Understanding states, “Students’ understanding of counting is deepened as they realize the arrangement of objects does not affect the number of objects.” In Independent Practice, Problem 11, students draw a circle around the group that matches a given number. Directions: “11 count the groups, and then draw a circle around the groups that show 4”. The materials show three groups of bees: a row of four bees, a random arrangement of four bees, and a random arrangement of three bees. Students independently demonstrate conceptual understanding by recognizing that the number of objects is the same regardless of their arrangement or the order in which they were counted. (K.CC.4b) 

  • Topic 10, Lesson 10-5, Lesson Overview, Conceptual Understanding states, “Students will build on the concept that a number can be shown as two parts. They focus on decomposing the numbers into a group of 10 ones and some more ones. Students expand their knowledge of an equation representing a quantitative relationship. They continue to establish a basic understanding of place value in our base-ten numeration system.” In Independent Practice, Problem 5, students draw counters to match an equation. Directions: “5 draw counters to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.” Students draw counters in two ten frames to match the equation 16 = 10 + 6. Students independently demonstrate conceptual understanding by composing and decomposing numbers from 11 to 19 into ten ones and some further ones. (K.NBT.1)  

  • Topic 14, Lesson 14-4, Lesson Overview, Conceptual Understanding states, “Previously students have been thinking of length, height, weight, and capacity individually when comparing. They now think of objects as being described by more than one of these attributes. This is an important step in understanding how attributes describe objects, focusing on what defines the object and understanding that not every object can necessarily be described by every attribute.” In Independent Practice, Problem 7, students identify the attributes that can be measured of an object. Directions: “Have students look at the object on the left, identify the attributes that can be measured, and then draw a circle around the tools that could be used to tell about those attributes.” A picture of a mug is on the left and the options of tools are the following measure length (cubes), weight (scale), and capacity (measuring cup). Students independently demonstrate conceptual understanding by describing measurable attributes of an object. (K.MD.1) 

Indicator 2B
02/02

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

The materials develop procedural skills and fluency throughout the grade level within various portions of lessons. The Teacher’s Edition Program Overview indicates, “Students perform better on procedural skills when the procedures make sense to them. So procedural skills are developed with conceptual understanding through careful learning progressions. … A wealth of resources is provided to ensure all students achieve success on the fluency expectations of Grades K-5.” Various portions of lessons that allow students to develop procedural skills include Solve & Share, Visual Learning Bridge, Convince Me!, Guided Practice, and 3-ACT MATH; in addition, the materials include Fluency Practice Activities. Examples include: 

  • Topic 1, Lesson 1-3, Lesson Overview, Procedural Skill states, “Students practice how to write 1, 2, and 3 to tell how many are in a group.” In Guided Practice, the materials show one star, then two stars, and finally three stars. In Problems 1-3, students develop procedural skills and fluency by writing the number of stars. “Directions. “Have students count the stars, and then write the number to tell how many.” Students write numerals 1, 2, and 3. (K.CC.3)

  • Topic 6, Lesson 6-4, Lesson Overview, Procedural Skill states, “Students write addition equations to show adding two groups to find a sum.” In the Visual Learning Bridge, the materials show three adjacent frames: A) includes a boy and five scattered drums; B) depicts the boy assigning the numbers 4 and 1 to groups of 4 and 1 drum, respectively; and in C) the boy translates “4 and 1 is 5” to the equation “4 + 1 = 5.” In Guided Practice, Problem 1, students develop procedural skills and fluency by translating “2 and 6 is 8” to the equation “2 + 6 = 8.” Directions: “Have students add the groups to find the sum, and then write an equation to show the addition.” The image for Problem 1 shows a group of 2 drums and a group of 6 drums. (K.OA.1)

  • Topic 13, Lesson 13-1, Lesson Overview, Procedural Skill, "Students identify shapes when given attributes as clues." In the Visual Learning Bridge, the materials show a triangle, a square, and a rectangle; students compare their attributes. In Convince Me!, students develop procedural skills and fluency by knowing that the number of sides and/or the number of vertices can help them identify the shape. “Which shape has 4 sides and 4 vertices: squares, rectangles, circles, or triangles?” (K.G.4)

Materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Independent Practice and Problem Solving consistently include these opportunities. When appropriate, teachers may use other portions of lessons for independent demonstration of procedural skill and fluency. Examples include:

  • Topic 3, Lesson 3-3, Lesson Overview, Procedural Skill states, “Students’ knowledge of the counting sequence builds as they extend their counting to groups of 8 and 9 objects.” In Independent Practice, Problem 8, students independently demonstrate procedural skills and fluency when they connect that the last number counted tells how many pieces of fruit there are. “Directions: “Have students count the pieces of fruit, and then draw counters to show how many.” The materials show eight strawberries and include a ten-frame. (K.CC.4a)

  • Topic 8, Lesson 8-1, Lesson Overview, Procedural Skill states, “Students work on the procedural skill of showing parts of a number and representing those parts in an equation as they solve word problems.” In Independent Practice, Problem 5, students independently demonstrate procedural skills and fluency when they draw pictures to create a representation of 5. “Directions: Higher Order Thinking Have students draw another way to break apart 4 with flowers, and then write an equation to match the story and show the parts that equal 5.” The materials show “5 = ___ + ___.” (K.OA.2)

  • Topic 14, Lesson 14-1, Lesson Overview, Procedural Skill states, “Students identify the longer/taller and shorter objects (or objects that are the same length) as they make comparisons throughout this lesson.” In Independent Practice, Problems 7 and 8, students independently demonstrate procedural skills and fluency as they tell which object is longer or shorter by sight. Directions: “Have students mark an X on the shorter object and draw a circle around the longer object, or underline the objects if they are the same length.” For Problem 7, the materials show a long wrench above a short wrench; for Problem 8, the materials show two sneakers that are the same length. (K.MD.2)

Indicator 2C
02/02

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials for enVision Mathematics Kindergarten meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Engaging applications—which include single and multi-step, routine and non-routine applications of the mathematics—appear throughout the grade level and allow for students to work with teacher support and independently. In each Topic Overview, Math Background: Rigor provides descriptions of the concepts and skills that students will apply to real-world situations. Each Topic is introduced with a STEM Project, whose theme is revisited in activities and practice problems in the lessons. Within each lesson, Application is previewed in the Lesson Overview. Practice & Problem Solving sections provide students with opportunities to apply new learning and prior knowledge.

Examples of routine applications of the math include:

  • In Topic 2, Lesson 2-5, Independent Practice, Problem 3, students independently represent a number of objects with a written numeral 0–20. “Directions Say: Carlos has 4 red blocks and 3 blue blocks. Which group of blocks is less in number than the other group? How can you use numbers to show your answer? Have students use a number to show and explain their answer.” (K.CC.3 and K.CC.6)

  • In Topic 8, Lesson 8-9, Independent Practice, Problem 10, students independently find the number that makes 10 when added to a given number. “Directions Higher Order Thinking Say: A child is holding up 3 fingers to show how old she is. What part of 10 is she showing? Use that number to write the missing numbers in the equation to tell the parts of 10. __ + __ = 10” (K.OA.4)

  • In Topic 10, Lesson 10-5, Solve & Share, students use counters and write an equation by decomposing 14 into two parts. “Directions Say: 14 students go to the zoo. The first bus takes 10 students. The rest of the students go on the second bus. Use counters to describe this situation. Then complete the equation to match the counters and tell how the counters and equation show 10 ones and some more ones. 14 = __ + __ ” The materials show two ten-frame counters shaped as buses. (K.NBT.1 and K.CC.5)

Examples of non-routine applications of the math include:

  • In Topic 5, Topic Performance Task, students classify objects into given categories as well as count the number of objects in each category and sort the categories by count. “Directions Works of Art Say: A kindergarten class uses paintbrushes and paint to draw pictures. Have students: 1 draw a circle around the little paintbrush, and then mark an X over the paintbrushes that are NOT little; 2 draw lines in the first chart as they count the paintbrushes that are little and the paintbrushes that are NOT little. Then have them write the number to tell how many are in each group in the second chart, and draw a circle around the number of the group that is less than the number of the other group. 3 Have students show one way to organize the jars of paint they see on the page before, and then explain how they sorted them. 4 Say: Tina says that the number of jars of paint is equal to the number of large jars of paint. Does her answer make sense? Have students look at the paint on the page before, draw a circle around yes or no, and then use the sorting and counting of each category to explain their reasoning.” The materials include a picture of a table with small and large paintbrushes and small and large jars of paint of various numbers on it. (K.MD.3)

  • In Topic 7, enVision STEM Project: Animal Needs, students independently add and subtract within 10 using drawings to represent the context of a non-routine problem. “Directions Read the character speech bubbles to students. Find Out! Have students find out about how plants, animals, and humans use their environment to meet basic needs such as food, water, nutrients, sunlight, space, and shelter. Say: Different organisms need different things. Talk to friends and relatives about the different needs of plants, animals, and humans, and how different organisms meet those needs. Journal: Make a Poster Have students make a poster. Ask them to draw as many as 5 pictures of a human’s needs and as many as 5 pictures of an animal’s needs. Have then cross out the needs that are the same for humans and animals, and then write how many are left.” One speech bubble says “Food” and the other says “Animals need food and water.” (K.OA.2)

  • In Topic 11, Topic Performance Task, Problem 5, students independently solve a non-routine problem by counting forward beginning from a given number within the number sequence. “Directions Say: Ty has 64 raisins in one bag. He has 18 raisins in another bag. Help Ty count his raisins. Have students start at 64 on the number chart and they make a path to show how to count up 18 in any way they choose. Then have them draw a circle around the number where they stopped, and then explain how they counted up.” Students are provided a number chart that ranges from 51 - 100. (K.CC.2)

Indicator 2D
02/02

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials for enVision Mathematics Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a topic contains opportunities for students to build conceptual understanding, procedural skills and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

The three aspects of rigor are present independently throughout the grade. For example:

  • Topic 2, Lesson 2-1, Solve & Share, students attend to conceptual understanding, explaining how they know whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. “Directions Say: Marta has some toy cars. Are there the same number of red cars as there are yellow cars on the rug? How do you know? Use counters to show your work.” The materials show Marta lying on a rug playing with cars: four yellow and four red. (K.CC.6)

  • Topic 8, Fluency Practice Activity, students attend to procedural skills and fluency as they practice fluently adding and subtracting within 5. “Directions Have students: 1 color each box that has a sum or difference that is equal to 3; 2 write the letter that they see.” The materials present two frames for student engagement: (1) a 5 by 5 worksheet of addition and subtraction problems (such as 1 + 2 and 5 - 2) and (2) blank space where the students write the letter. (K.OA.5)

  • Topic 14, Lesson 14-1, Solve & Share, students attend to application as they compare measurable attributes of two objects. “Directions Say: Marta makes a cube train with 4 cubes. Is her cube train bigger or smaller than the crayon? Is her cube train bigger or smaller than the pencil? How can you find out?” The materials show images of a crayon and a pencil. (K.MD.2)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the grade. For example:

  • Topic 3, Lesson 3-6, Independent Practice, Problems 6 and 7, students attend to conceptual understanding and procedural skills and fluency as they see that 10 can be made in different ways and practice how to write 10 to tell how many are in a group. “Directions Number Sense 6 and 7 Have students count the shells, and then write the number to tell how many.” The materials show for problem 6, 10 blue shells situated in one row and for problem 7, 10 red shells divided evenly into two rows of five and provide lines for students to write their answers. (K.CC.3 and K.CC.5)

  • Topic 6, Lesson 6-5, Guided Practice, Problem 5, students attend to conceptual understanding and application as they solve an addition word problem using drawings and an equation. “Directions Have students listen to the story, use counters to show the addition, look at or draw a picture, and then write an equation to tell how many in all. 5. 2 turtles swim in the water. 6 more join them. How many turtles are swimming in all?” Students draw in the provided space and write the equation 2 + 6 = 8. (K.OA.2)

  • Topic 11, Lesson 11-5, Independent Practice, Problem 5, students attend to procedural skills and application as they count forward from a beginning number by ones and complete the sequence by counting by tens. “Directions Have students count forward, and then draw a circle around the row that shows the missing set of numbers.” The materials show a three-row table: the first row shows numbers 31-39 with a blank cell for 40. The second and third rows similarly show 41-49 and 51-59, respectively, with blank cells for the 50 and 60. The materials provide students with three options for the missing set of numbers: 40, 50, 60 or 40, 41, 42 or 38, 39, 40. (K.CC.1 and K.CC.2)

Criterion 2.2: Math Practices

10/10

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for enVision Mathematics Kindergarten meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Indicator 2E
02/02

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices across the year, and they are explicitly identified for teachers within the Program Overview within the Topic Contents at the Lesson-level. The Math Practices and Problem Solving Handbook introduces each of the Math Practices with specific emphasis on making connections among representations to develop meaning and corresponding Thinking Habits. The Teacher’s Edition provides support for developing, connecting, and assessing each math practice. Topic Planners include the Math Practices at the lesson level; relevant practices are specified in Lesson Overviews. 

MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 2, Lesson 2-5, Problem Solving, Performance Task, Problem 4, students make sense of problems and persevere in solving them as they apply matching and counting strategies to identify whether a number of objects in one group is greater than a number of objects in another group. “Directions Read the problem aloud. Then have students use multiple problem-solving methods to solve the problem. Say: Marta has 2 stickers. Emily has a greater number of stickers than Marta. How many stickers could Emily have? Make Sense. What do you know about the problem? Can Emily have 1 sticker? Tell a partner why or why not?” 

  • Topic 8, Lesson 8-2, Convince Me!, students make sense of problems and persevere in solving them as they make sense of situations that involve addition and subtraction within five to solve problems. “Give students 2 red and 2 yellow cubes. Have them tell and act out an addition and subtraction story. Have students compare the stories (both use the same numbers but the actions are different).” 

  • Topic 14, Lesson 14-4, Solve & Share, students make sense of problems and persevere in solving them as they describe measurable attributes of objects, such as length or weight, or describe several measurable attributes of a single object. “Directions Say: These are 2 tools for measuring. What can you measure with the cup? What can you measure with the cube train? Draw an object you can measure with each tool. The materials show a cup and a train of six counting cubes. 

MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 4, Lesson 4-2, Guided Practice, Problem 2, students reason abstractly and quantitatively as they compare groups that contain different objects and represent quantities with written numerals. “Directions Have students count the vegetables in each group, write the number to tell how many, draw a line from each vegetable in the top group to each vegetable in the bottom group, and then mark an X on the number that is less than the other number.” The materials show a top row of four peppers and a bottom row of five ears of corn. 

  • Topic 9, Lesson 9-7, Solve & Share, students reason abstractly and quantitatively as they count forward beginning from a given number and write numbers 10 to the number 20 and identify possible answers to word problems that have more than one potential answer. “Directions Say: Carlos wants to put some or all of the eggs in the carton. Draw a circle around the numbers that tell how many eggs he could put in the carton. Explain why there could be more than one answer.” The materials show an empty egg carton, 14 scattered eggs, and the numbers 10 through 14. 

  • Topic 13, Lesson 13-3, Solve & Share, students reason abstractly and quantitatively as they analyze and compare two- and three-dimensional shapes, in different sizes and orientations, and relate the two-dimensional shapes to the shapes of the flat surfaces in the three-dimensional shapes, and vice versa. “Directions Say: Jackson needs to find a circle that is a flat surface of a solid figure. Which of these solids has a flat circle as part of the figure? Draw a circle around each solid figure that has a flat circle part. Mark an X on the solid figures that do NOT have a flat circle part. How many shapes in all are there on the page? How many shapes did you circle? Without counting, how many shapes have an X? Count the shapes with an X to check your answer.” The materials show scattered shapes: pyramid, shipping box, cone, tennis ball, sphere, cylindrical clock, tube of tennis balls, log, and cylinder. 

Indicator 2F
02/02

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices across the year, and they are explicitly identified for teachers within the Program Overview within the Topic Contents at the Lesson-level. The Math Practices and Problem Solving Handbook introduces each of the Math Practices with specific emphasis on making connections among representations to develop meaning and corresponding Thinking Habits. The Teacher’s Edition provides support for developing, connecting, and assessing each math practice. Topic Planners include the Math Practices at the lesson level; relevant practices are specified in Lesson Overviews.

Students construct viable arguments and critique the reasoning of others in connection to grade-level content as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 1, Lesson 1-2, Solve & Share, students construct viable arguments and critique the reasoning of others as they explain solutions to problems where they have to count and consider other students’ work. “Directions, Say: “Redbird and Bluebird each have 2 babies. Redbird and Bluebird get worms for their babies and put them in their nests. Bluebird’s worms moved around in the nest. Show and count how many worms with your counters. Color the boxes to show the worms in each nest. Tell how you know you are correct.” The teacher is prompted to, “choose which solutions to have students share and in what order. Focus on the idea that no extra counters were placed or taken away. If needed, show and discuss the student work at the right.” The student work at the right shows two worms in each nest accompanied by the teacher's statement, “Marlon says each bird found a different number of worms. Why might Marlon have thought the birds found a different number of worms?”

  • Topic 5, Lesson 5-4, Solve & Share, students construct viable arguments and critique the reasoning of others as they tell whether a given statement makes sense—providing reasons for their choice using numbers, pictures, or words to explain—and compare their answer to other student work.  “Directions Say: Carlos says that the number of blue cubes is equal to the number of cubes that are NOT blue. Does his answer make sense? Use numbers, pictures, or words to explain your answer.” The materials show ten blue cubes, five yellow cubes, and four green cubes as well as the statement, “I can tell whether the way objects have been sorted, counted, and compared makes sense. I can explain how I know.” Teachers are prompted to use questions and additional work to help students construct viable arguments and critique the reasoning of others such as: “Based on your [teacher] observations, choose which solutions to have students share and in what order…If needed, show and discuss the student work at the right.” There are two pieces of work displayed at the right one is labeled Kirsty’s Work and the other is labeled Tim’s Work. The following questions are asked: Kirsty says that Carlos’s answer does not make sense because 10 is greater than 9. Do you agree with Kirsty? Why? How did Kirsty show this? What mistake did Tim make? Why might this mistake make him think Carlos was correct?

  • Topic 9, Lesson 9-7, Problem Solving, Performance Task, Problems 6 and 7, students construct viable arguments and critique the reasoning of others as they identify possible answers to word problems that have more than one possible answer and compare their work with another student’s work. “Directions Read the problem to students. Then have them use multiple problem-solving methods to solve the problem. Say: Alex lives on a farm with so many cats that they are hard to count. Sometimes the cats are outside and sometimes they hide in the shed. Alex knows that the number of cats is greater than 11. There are less than 15 cats on the farm. How can Alex find out the number of cats that could be on his farm? 6. Model How can you show a word problem using pictures? Draw a picture of the cats on Alex’s farm. Remember that some may hide inside the shed. 7. Explain Is your drawing complete? Tell a friend how your drawing shows the number of cats on Alex’s farm. The materials suggest to teachers, “Students should explain how their drawing represents each part of the word problem.” Teachers say, “Think about how the drawing shows the problem, not whether your drawings are the same.”

  • Topic 12, Lesson 12-1, Guided Practice, Problem 2, students construct viable arguments and critique the reasoning of others as they identify an object as flat or solid, explaining how they distinguish between the two. “Directions “Have students: draw a circle around the objects that are flat, and mark an X on the objects that are solid.” The materials suggest “Have students compare their answers and explain their choices, telling why they think a particular shape was or was not flat or solid. Encourage students to state if they agree and tell why.”

Indicator 2G
02/02

Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices across the year, and they are explicitly identified for teachers within the Program Overview within the Topic Contents at the Lesson-level. The Math Practices and Problem Solving Handbook introduces each of the Math Practices with specific emphasis on making connections among representations to develop meaning and corresponding Thinking Habits. The Teacher’s Edition provides support for developing, connecting, and assessing each math practice. Topic Planners include the Math Practices at the lesson level; relevant practices are specified in Lesson Overviews. 

MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 2, Lesson 2-5, Solve & Share, students model with mathematics as they compare groups of objects, using models to show how they know those which are greater in number, less in number, and equal in number. “Directions Say: Work with your partner and take turns. Take 1 cube at a time from the bag and place it on your mat. Keep taking cubes until all the cubes are gone. Do you have a greater number of red cubes or blue cubes? How can you show your answer? Explain and show your work.”

  • Topic 6, Lesson 6-6, Independent Practice, Practice 9, students model with mathematics as they represent real-world word problems involving addition and subtraction in different ways and add and subtract within 10. “Directions Higher Order Thinking Have students listen to the story, circle the connecting cubes that show the story and tell why the other cubes do not show the story, and then write the number to tell how many in all. Say: Jimmy pics 5 raspberries. Then he picks 3 more. How many raspberries does he have in all?” A picture of two sets of connecting cubes is shown: the first set has five red cubes and three purple cubes; the second set has four red cubes and three purple cubes.

  • Topic 12, Lesson 12-5, Independent Practice, Problem 12, students model with mathematics as they use knowledge about specified shapes to draw objects to match the given shapes.   “Directions Higher Order Thinking Have students name the solid figure on the left, and they draw 2 more objects that look like that shape.” The materials show a sphere.

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 3, Lesson 3-4, Solve & Share, students use appropriate tools strategically as they use counters and draw pictures to make a group of 8 or 9 in different ways. “Directions Say: Jackson sees some turtle eggs. Draw a number card to tell how many. Count out that many counters and place them across the top of the workmat. What are some different ways to make the number? Draw two ways on the turtle shells. Are there different ways to count the number? Tell how you know.” The materials show a picture of two large turtles.

  • Topic 9, Lesson 9-4, Convince Me!, students use appropriate tools strategically as they use counters and a double ten-frame to represent and visualize numbers 18, 19, and 20. Teacher guidance: “Show a double ten-frame with 18 counters on it. Which number card shows how many? Have students hold up the number card for 18 and say the number. Repeat, placing additional counters in the double ten-frame for the numbers 19 and 20. Have students explain how the double ten-frame and counters help to show each number.”

  • Topic 14, Lesson 14-5, Visual Learning Bridge, students use appropriate tools strategically as they identify tools that can be used to tell about measurable attributes of objects. Teacher guidance: “Essential Question Ask How can you describe and compare attributes of objects?” In (B) “Use Appropriate Tools StrategicallyMarta is thinking about three tools she can use to describe attributes of the vases. Which tool would Marta use to tell about their heights? Their weights? How much do they hold? ” The materials show a girl with thought clouds: measuring cup, scale, and counting cubes.

Indicator 2H
02/02

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with MP6 across the year, and they are explicitly identified for teachers within the Program Overview within the Topic Contents at the Lesson-level. The Math Practices and Problem Solving Handbook introduces each of the Math Practices with specific emphasis on making connections among representations to develop meaning and corresponding Thinking Habits. Topic Planners include the Math Practices at the lesson level; relevant practices are specified in Lesson Overviews.

Students attend to precision in mathematics in connection to grade-level content as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 3, Lesson 3-2, Guided Practice, Problem 3, students attend to precision by counting objects and showing how to use a specific symbol to represent the total quantities.   identifying and writing the numbers 6. “Directions Have students count the objects, and then practice writing the number that tells how many.” The materials show 6 flip flops and space for a student to write the number 6 three times. 

  • Topic 8, Lesson 8-2, Guided Practice, Problem 3, students attend to precision by writing equations that distinguish between the appropriate use of a plus sign and a minus sign. “Directions Have students use cubes for these facts with 4. Have them decide whether the cubes show addition or subtraction. Encourage students to make up their own stories to match the cubes. Then have them write equations to tell the related facts.” Teacher guidance: “Be Precise … First, have students tell a take away story. Will you use a plus or minus sign for a take away story. Then have them tell an add to story. Will you use a plus or minus sign for an add to story? ” The materials show (i) two orange cubes adjoined to two blue cubes and (ii) two orange cubes separate from two blue cubes. Students write the equations 4 - 2 = 2 and 2 + 2 = 4.

  • Topic 13, Lesson 13-1, Solve & Share, students attend to precision by identifying examples of shapes and nonexamples of shapes, based on given clues. “Directions Say: “Emily wants to figure out which shapes are behind the door. The mystery shapes that are behind the door have only 4 vertices (corners). Use the shapes shown above the door to help you decide which shapes are behind the door. Draw the shapes that match the clue on the door. How many shapes did you draw? Write that number next to the door. Now mark an X on the shapes that are NOT behind the door. Count those shapes and write the number. Look at the two numbers you wrote. Circle the number that is greater than the other number. If the numbers are the same, circle both numbers. Name the shapes that are behind the door.” The materials show the following shapes above the door: circle, equilateral triangle, square, rectangle, isosceles right triangle, isosceles trapezoid, regular hexagon, and regular octagon. 

Students attend to the specialized language of mathematics in connection to grade-level content as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 2, Lesson 2-4, Guided Practice, Problem 4, students use specialized language when they count to compare two groups of objects. “Directions Have students count the stickers, write the numbers to tell how many, and then draw a circle around the number that is greater than the other number and mark an X on the number that is less than the other number, or draw a circle around the numbers if they are equal.” The materials show four beers and four caves. Teacher guidance: “Remind students that they can use the totals they have counted for the two groups to compare how many are in each group. If the numbers are the same, then the number of objects in the two groups is equal.”

  • Topic 5, Lesson 5-3, Independent Practice, Problem 4, students use specialized language when they count items in two groups and determine which group has the greater number of objects. “Directions Have Students: sort the balls into balls that are yellow and balls that are NOT yellow, count them and then write numbers in the chart to tell how many. Then have students draw a circle around the category that is greater in number than the other category and tell how they know.” The materials show two soccer balls, two baseballs, four basketballs, and five tennis balls. The chart asks students to quantify tennis balls and not tennis balls.

  • Topic 14, Lesson 14-4, Visual Learning Bridge, students use specialized language when they identify attributes to describe an object. Visual Learning Bridge,“Essential Question Ask “What attributes can you use to describe objects?” Teacher guidance: (A) “What words can you use to describe this water bottle? Which attributes do these words describe? What tools do you see?”

Indicator 2I
02/02

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices across the year, and they are explicitly identified for teachers within the Program Overview within the Topic Contents at the Lesson-level. The Math Practices and Problem Solving Handbook introduces each of the Math Practices with specific emphasis on making connections among representations to develop meaning as well as corresponding Thinking Habits. The Teacher’s Edition provides support for developing, connecting, and assessing each math practice. Topic Planners include the Math Practices at the lesson level; relevant practices are specified in Lesson Overviews. 

MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 1, Lesson 1-9, Guided Practice, Problem 1, students look for and make use of the structure as they work within the order of numbers 0-5, using objects to help them see the pattern that each number represents 1 more each time. “Directions Have students write the number that comes just before 1 and the number that comes just after 1. Then have them write the number that comes just before 4 when counting, and the number that comes just after 4 when counting. Have them say the numbers in order from 0 to 5.” The materials show ___ 1 ___ ___ 4 ___ and cube(s) above the spaces that correspond with the number.

  • Topic 9, Lesson 9-4, Independent Practice, Problem 7, students look for and make use of structure as they look at the arrangement of a group to help find out how many are in the group. “Directions Have students count the stickers in each group, and then practice writing the number that tells how many.” The materials show two rows of ten dog’s faces each.

  • Topic 13, Lesson 13-2, Solve & Share, students look for and make use of structure as they analyze 3-D shapes to determine if they will fit a given criteria. “Directions Say: Jackson wants to find a solid figure. The solid figure has more than one flat side and it rolls. Color the solid figures that match the description. Then count them. How many are there? How many shapes do you see in all?” The materials show twelve 3-D shapes: spheres, cones, cylinders, and prisms.

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Topics. Examples include:

  • Topic 4, Lesson 4-5, Independent Practice, Problem 2, students look for and express regularity in repeated reasoning when they find 1 more by counting on to find the total number rather than beginning counting from 1 each time, noticing how this is a general method that can be applied to different numbers in the same way. “Directions Say: Alex sees frogs at the pond. Then he sees 1 more. How many frogs are there now? Have students use repeated reasoning to find the number that is 1 greater than the number of frogs shown. Draw counters to show the answer, and then write the number. Have students explain their reasoning.” The materials show seven frogs. 

  • Topic 6, Lesson 6-3, Guided Practice, Problems 4-6, students look for and express regularity in repeated reasoning when they notice that they can approach problems with similar steps even though quantities and objects may be different. “Directions Have students use counters to model putting together the groups, draw a circle around the groups to put them together, and then write an addition sentence to tell how many in all. The materials show for Problem 4, six radishes and one cabbage, Problem 5, eight cabbages and one radish, and for Problem 6, two radishes and eight carrots. Students complete sentences such as “___ and ___ is ___.”

  • Topic 11, Lesson 11-4, Guided Practice, Problem 3, students look for and express regularity in repeated reasoning as they use a hundred chart to count forward by ones from a given number. “Directions Have students color the boxes of the numbers as they count aloud, starting at the yellow box and ending at the red box.” The materials show a hundred chart: its yellow box is at 34 and the red box is at 55.

Overview of Gateway 3

Usability

The materials reviewed for enVision Mathematics Kindergarten meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, and Criterion 2, Assessment, and partially meet expectations for Criterion 3, Student Supports.

Criterion 3.1: Teacher Supports

09/09

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, contain adult-level explanations and examples of the more complex grade-level concepts beyond the current grade so that teachers can improve their own knowledge of the subject, include standards correlation information that explains the role of the standards in the context of the overall series, provide explanations of the instructional approaches of the program and identification of the research-based strategies, and provide a comprehensive list of supplies needed to support instructional activities.

Indicator 3A
02/02

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. 

The Teacher’s Edition Program Overview provides comprehensive guidance to assist teachers in presenting the student and ancillary materials. It contains four major components: Overview of enVision Mathematics, User’s Guide, Correlation and Content Guide.

  • The Overview provides the table of contents for the course as well as a pacing guide for a traditional year long course as well as block/half year course. The authors provide the Program Goal and Organization, in addition to information about their attention to Focus, Coherence, Rigor, the Math Practices, and Assessment.

  • The User’s Guide introduces the components of the program and then proceeds to illustrate how to use a ‘lesson’: Lesson Overview, Problem-Based Learning, Visual Learning, and Assess and Differentiate. In this section, there is additional information that addresses more specific areas such as STEM, Building Mathematical Literacy, Routines, and Supporting English Language Learners.

  • The Correlation provides the correlation for the grade.

  • The Content Guide portion directs teachers to resources such as the Big Ideas in Mathematics, Scope and Sequence, Glossary, and Index.

Within the Teacher’s Edition, each Lesson is presented in a consistent format that opens with a  Lesson Overview, followed by probing questions to provide multiple entry points to the content, error intervention, supports for English Language Learners and ends with multiple Response to Intervention (RtI) differentiated instruction.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. The Teacher’s Edition includes numerous brief annotations and suggestions at the topic and lesson level organized around multiple mathematics education strategies and initiatives, including the CCSSM Shifts in Instructional Practice (i.e., focus, coherence, rigor), CCSSM practices, STEM projects, and 3-ACT Math Tasks, and Problem-Based Learning. Examples of these annotations and suggestions from the Teacher’s Edition include:

  • Topic 1, Lesson 1-1, Visual Learning Bridge, Essential Question, “Ask How can you count objects?” Teachers begin the Classroom Conversation by doing the following: “Model telling a story about the picture and then have volunteers tell their own stories to the class. [I see worms wiggling up from the ground. How many worms are there?]” 

  • Topic 4, Lesson 4-2, Independent Practice, Problem 5, Directions, “Higher Order Thinking Have students count the flowers in the group, draw a group of flowers that is less than the group shown, and then write the numbers to tell how many.” Teacher guidance: “Make Sense and Persevere Have students plan both their work and how they will explain it. Ask: How will you know that you have drawn a group that has fewer objects? Which group will have extra objects?[The top group will have extra objects]”

  • Topic 10, Lesson 10-1, Guided Practice, Problems 4 and 5, Directions, “draw blocks to match the equation. Then have them tell how the picture and equation show 10 ones and some more ones.” Teacher guidance: “Remind students to fill the ten-frame first. Explain that even though the entire ten-frame will be filled, it is important to fill it in the proper order: left to right and top to bottom. Model to students as needed.”

Indicator 3B
02/02

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for containing adult-level explanations and examples of the more complex grade concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. 

The materials provide professional development videos at two levels to help teachers improve their knowledge of the grade they are teaching.

  • Professional development topic videos are at SavvasRealize.com. In these Topic Overview Videos, an author highlights and gives helpful perspectives on important mathematics concepts and skills in the topic. The video is a quick, focused ‘Watch me first’ experience as you start your planning for the topic.

  • Professional development lesson videos are at SavvasRealize.com. These Listen and Look for Lesson Videos provide important information about the lesson.”

An example of the content of a Professional development video:

  • Topic 1: Professional Development (topic) Video, “Number is the most fundamental concept in all of mathematics. … The first critical skill that four or five year olds develop is rational counting. This means  they can take a set of objects, like counting cubes, move them one by one from an uncounted pile to a counted pile and as they move each one say the next number name. … In order to do this accurately, a child must be able to 

  1. Be able to recite the number names in order up to the target number.

  2. Establish a one-to-one correspondence between the action of moving one counter and saying one number name.

  3. Understand that order doesn’t matter. The cubes can be counted in any order and the number remains the same.

  4. Understand that the last number named is how many are in the set.

At yet a slightly more advanced level, a fifth understanding that students develop about this process is that

  1. Even if the objects are rearranged spatially, their number “remains the same”.

The Math Background: Coherence, Look Ahead section, provides adult-level explanations and examples of concepts beyond the current grade as it relates what students are learning currently to future learning.

An example of how the materials support teachers to develop their own knowledge beyond the current grade:

  • Topic 4, Math Background: Coherence, Look Ahead, the materials state, “Grade 1 Comparison Situations In Topic 1, students will understand that subtraction can be used to determine how many more or how many fewer. Compare Two-Digit Numbers In Topic 9, students will compare two-digit numbers. They will also learn the symbols for ‘greater than’ and ‘less than’ and use these to write inequallities.” An example of an inequality is shown.

Indicator 3C
02/02

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. 

Standards correlation information is indicated in the Teacher’s Edition Program Overview, the Topic Planner, the Lesson Overview, and throughout each lesson. Examples include:

  • The Teacher’s Edition Program Overview, Grade K Correlation to Standards For Mathematical Content organizes standards by their Domain and  Major Cluster and indicates those lessons and activities within the Student’s Edition and Teacher’s Edition that align with the standard. Lessons and activities with the most in-depth coverage of a standard are distinguished by boldface. The Correlation document also includes the Mathematical Practices. Although the application of the mathematical practices can be found throughout the program, the document indicates examples of lessons and activities within the Student’s Edition and Teacher’s Edition that align with each math practice.

  • The Teacher’s Edition Program Overview, Scope & Sequence organizes standards by their Domain, Major Cluster, and specific component. The document indicates those topics that align with the specific component of the standard.

  • The Teacher’s Edition, Topic Planner indicates the standards and Mathematical Practices that align to each lesson.

The Teacher’s Edition, Math Background: Coherence provides information that summarizes the content connections across grades. Examples of where explanations of the role of the specific grade-level mathematics are present in the context of the series include:

  • Topic 3, Math Background: Coherence, the materials highlights three of the learnings within the topics: “Counting Sequence, See Quantities as They Relate to 5 and 10, and Counting All and Counting Out” with a description provided for each learning, including which lesson(s) cover the learnings. The “Look Ahead” section asks the question, “How does Topic 3 connect to what students will learn later?” and provides Grade 1 connections, “Relate Counting to Addition In Topics 2, 3, and 4 students will use counting on and counting back as strategies for adding and subtracting within 20. Extend the Counting Sequence to 120 In Topic 7, students will count on from any number to 120, and read and write numbers to 120.” 

  • Topic 7, Math Background: Coherence, the materials highlight three of the learnings within the topics: “Representations, Solve Word Problems, and Fluency Development” with a description provided for each learning, including which lesson(s) cover the learnings. The “Look Ahead” section asks the question, “How does Topic 7 connect to what students will learn later?” and provides a Grade 1 connection, “Subtract Within 20  In Topics 1, 2, 4, and 5, students will work on subtraction within 20. The emphasis will be on strategies and building fluency, Students will also subtract to compare. Grade 1 students will be expected to become fluent with subtracting within 10.”

  • Topic 11, Math Background: Coherence, the materials highlight two of the learnings within the topics: “Extend the Count Sequence to Greater Numbers, and See Quantities as They Relate to 10” with a description provided for each learning, including which lesson(s) cover the learnings. The “Look Ahead” section asks the question, “How does Topic 11 connect to what students will learn later?” and provides Grade 1 connections, “Extend the Counting Sequence to 120 In Topic 7, students will begin at any number less than 120, count to 120, and read and write numbers to 120. Count by Tens and Ones In Topic 8, students will count with groups of tens and leftover ones. Count On to Add and Subtract In Topics 2, 3, and 4, students will count on and count back to add and subtract with 20. In Topics 10 and 11, students will count on and count back to add and subtract 2-digit numbers.”

Indicator 3D
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Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for enVision Mathematics Kindergarten provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement. All resources are provided in English and Spanish.

In the Teacher Resource section, a “Parent Letter” is provided for each topic. The “Parent Letter” describes what the student is learning in each topic, an example of a problem students will learn to solve, and a suggestion of an activity the family could try at home.

  • Home-School Connection, Topic 1, Numbers 0 to 5, “Dear Family, Your child is learning about numbers from 0 to 5, in this topic, he or she will learn to recognize numbers 0 through 5 in different arrangements, and then learn how to write them. Number Arrangements: Counting tells how many are in a set, regardless of the arrangement or order of the objects. The same number is shown in each arrangement.  Try this activity with your child to practice counting 1 to 5 objects in different arrangements. Arrange the Objects: Place 10 small objects on a table such as pennies or buttons. Say a number from 3 to 5 and have your child arrange the objects in two different ways to show that number. For example, he or she can show the number 4 as a row, a column, or in a square pattern.”

In the Grade K Family Engagement section, the materials state the following:

Welcome Thank you for working with your child’s teacher and with us, the authors of enVision Mathematics, to advance your child’s learning. This is important to us, and we know it is to you. enVision Mathematics was specifically designed to implement the Common Core State Standards for Mathematics and to foster your child’s success. enVision Mathematics was developed to help children see the math. And the program includes resources to help families see the math as well.” 

These resources are divided into the following areas:

  • Overview of Resources “enVision Mathematics offers a variety of digital resources to help your child see the math. Your child can access and utilize these resources at any time in their student login portal.”

  • Content and Standards “enVision Mathematics was specifically developed for the Common Core State Standards for Mathematics. Each lesson is correlated to one or more of the content standards and one or more of the math practice standards. To help you understand the standards and how they are applied in enVision Mathematics, family-friendly explanations and examples are provided. When helping your child with homework, reference this document to understand the mathematical expectations for each content standard and to see how your child might engage with each math practice standard.”

  • Topic/Lesson Support “View topic- and lesson-level support. Look for an overview of each topic’s content, sample worked problems, and related home activities.”

Indicator 3E
02/02

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. The Teacher’s Edition Program Overview provides detailed explanations behind the instructional approaches of the program and cites research-based strategies for the layout of the program. Unless otherwise noted all examples are found in the Teacher’s Edition Program Overview.

Examples where materials explain the instructional approaches of the program and describe research-based strategies include:

  • The Program Goal section states the following: “The major goal in developing enVision Mathematics was to create a program for which we can promise student success and higher achievement. We have achieved this goal. We know this for two reasons. 1. EFFICACY RESEARCH First, the development of enVision Mathematics started with a curriculum that research has shown to be highly effective: the original enVisionMATH program (PRES Associates, 2009; What Works Clearinghouse, 2013). 2. RESEARCH PRINCIPLES FOR TEACHING WITH UNDERSTANDING The second reason we can promise success is that enVision Mathematics fully embraces time-proven research principles for teaching mathematics with understanding. One understands an idea in mathematics when one can connect that idea to previously learned ideas (Hiebert et al., 1997). So, understanding is based on making connections, and enVision Mathematics was developed on this principle.”

  • The Instructional Model section states the following: “There has been more research in the past fifteen years showing the effectiveness of problem-based teaching and learning, part of the core instructional approach used in enVision Mathematics, than any other area of teaching and learning mathematics (see e.g., Lester and Charles, 2003). Furthermore, rigor in mathematics curriculum and instruction begins with problem-based teaching and learning. … there are two key steps to the core instructional model in enVision Mathematics. STEP 1 PROBLEM-BASED LEARNING Introduce concepts and procedures with a problem-solving experience. Research shows that conceptual understanding is developed when new mathematics is introduced in the context of solving a real problem in which ideas related to the new content are embedded (Kapur, 2010; Lester and Charles, 2003; Scott, 2014)... STEP 2 VISUAL LEARNING Make the important mathematics explicit with enhanced direct instruction connected to Step 1. The important mathematics is the new concept or procedure students should understand (Hiebert, 2003; Rasmussen, Yackel, and King, 2003). Quite often the important mathematics will come naturally from the classroom discussion around students’ thinking and solutions from the Solve and Share task…”

  • Other research includes the following:

    • Hiebert, J.; T. Carpenter; E. Fennema; K. Fuson; D. Wearne; H. Murray; A. Olivier; and P.Human. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, NH: Heinemann, 1997.

    • Hiebert, J. (2003). Signposts for teaching mathematics through problem solving. In F. Lester, Jr. and R. Charles, eds. Teaching mathematics through problem solving: Grades Pre-K–6 (pp. 53–61). Reston, VA: National Council of Teachers of Mathematics.

  • Throughout the Teacher’s Edition Program Overview references to research-based strategies are cited with some reference pages included at the end of some authors' work.

Indicator 3F
01/01

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

In the online Teacher Resources for each grade, a Materials List is provided in table format identifying the required materials and the topic(s) where they will be used. Additionally, the materials needed for each lesson can be found in the Topic Planner and the Lesson Overview. Example includes:

  • Topic 1, Topic Planner, Lesson 1-2, Materials, “Counters (or Teaching Tool 6), Crayons”

  • Topic 6, Lesson 6-1, Lesson Resources, Materials, “Two-color counters (or Teaching Tool 6)”

  • Teacher Resources, Grade K: Materials List, the table indicates that Topic 12 will require the following materials: “2-D and 3-D Shapes (or Teaching Tool 37), 3-D Shapes and Real-Life Objects (or Teaching Tool 39), Circles (or Teaching Tool 32), ...”

Indicator 3G
Read

This is not an assessed indicator in Mathematics.

Indicator 3H
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This is not an assessed indicator in Mathematics.

Criterion 3.2: Assessment

09/10

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for Assessment. The materials include an assessment system that provides multiple opportunities throughout the courses to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The materials also provide assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices. The materials partially include assessment information in the materials to indicate which standards are assessed.

Indicator 3I
01/02

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for enVision Mathematics Kindergarten partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. The materials do not identify practices for most of the assessment items.

The materials identify the following assessments in the Teacher’s Edition Program Overview:

  • Diagnostic Assessments are to be given at the start of the year and the start of a topic; they consist of a Readiness Test, Diagnostic Tests, and “Review What You Know.”

  • Formative Assessments are incorporated throughout each lesson. Some examples of formative assessments include: Guided Practice, Convince Me!, and Quick Check.

  • Summative Assessments, including Topic Assessments and Cumulative/Benchmark Assessments, are provided in multiple editable forms to assess student understanding after each topic and/or group of topics as well as at the end of the course.

The Teacher’s Edition maps content standards to items from Diagnostic and Summative Assessments and identifies Standards for Mathematical Practices only when the assessment is within the lesson. Examples of how the materials identify the standards include:

  • Topic 1, Topic Performance Task, Problem 1, “Flower Cart Say: Micheal’s family sells flowers from a flower cart. Have students count how many of each kind of flower, and then write the number to tell how many.” Four images of flowers in vases are shown with a space to write how many flower(s) are in each vase. Item Analysis for Diagnosis and Intervention indicates Standards K.CC.A.3, K.CC.B.4a, and MP.2.

  • Topic 2, Topic Assessment, Problem 1, “Directions Look at the group of baseballs. Which group of tennis balls is greater in number than the group of baseballs?” An image of three baseballs is shown. The choices for answers are pictures of the following: A. one tennis ball B. two tennis balls C. three tennis balls and D. four tennis balls. Item Analysis for Diagnosis and Intervention indicates Standard, K.CC.C.6.

  • Topic 5, Review What You Know, Problem 2, “Directions Have students: draw a circle around the group that has a number of birds that is less than 5.” A picture of eight purple birds and four yellow birds is shown. Item Analysis for Diagnosis and Intervention indicates Standard, K.CC.C.6. 

  • Topic 9, Lesson 9-1, Guided Practice, Problem 2, “Directions Have students count the cars in each group, and then practice writing the number that tells how many.” A picture of 12 cars is shown. The Lesson Overview indicates Standards, K.CC.A.3, K.CC.B.5, MP.2, MP.3, and MP.6.

Indicator 3J
04/04

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for including an assessment system that provides multiple opportunities throughout the grade  to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

The assessment system provides multiple opportunities to determine student’s learning throughout the lessons and topics. Answer keys and scoring guides are provided. In addition, teachers are given recommendations for Math Diagnosis and Intervention System (MDIS) lessons based on student scores. If assessments are given on the digital platform, students are automatically placed into intervention based on their responses.

Examples include:

  • Topic 1, Lesson 1-1, Independent Practice, Evaluate, Quick Check, Problems 7-9, “Check mark indicates items for prescribing differentiation on the next page. Items 7 and 8: each 1 point.  Item 9: up to 3 points.” “Directions 7-8 Have students color a box as they count each box to show how many.  9 Higher Order Thinking Have students draw 1, 2, or 3 nests, and then color a box as they draw each nest to show how many.” The following page, Step 3: Assess and Differentiate states, “Use the Quick Check on the previous page to prescribe differentiated instruction. I Intervention 0-3 points, O On-Level 4 points, A Advanced 5 points.” The materials provide follow-up activities—to be assigned at the teacher’s discretion—to students at each indicated level: Intervention Activity I, Technology Center I O A, Reteach to Build Understanding I,  Build Mathematical Literacy I O, Enrichment O A, Activity Centers I O A, and Additional Practice Leveled Assignment I Items 1-5, O Items 1-2, 4-6, and A Items 3-7.

  • Topic 7, Topic Assessment, Problem 4, “Directions Have students listen to the story and then complete the sentence to tell how many are left. Kyle sees 10 turtles at the zoo. 2 turtles crawl away. Write a number sentence that tells how many are left.” Item Analysis for Diagnosis and Intervention indicates: DOK 2, MDIS B8, Standards K.OA.A.1 and K.OA.A.2. Scoring Guide indicates: 1 point “Correct numbers are written.”

  • Topic 10, Topic Performance Task, Problem 5, “Directions Say: Mason put his striped marbles in a five-frame. Then he buys ten more striped marbles. Have students write the number to tell how many striped marbles Mason had at first, and then color the part of the number chart to show how many striped marbles he has now. Then have them write an equation and ask them to explain how the picture and equation show 10 ones and some more ones.” Item Analysis for Diagnosis and Intervention indicates: DOK 3, MDIS A10, Standards K.NBT.A.1 and MP.7. Scoring Guide indicates: 3 points “Number 4 is written, 14 is marked in chart, and correct equation written for 14”; 2 points “Number 4 is written and 14 is marked in chart, or written equation matches 14 marked in chart”; 1 point “Number 4 is written, or 14 is marked in chart, or correct equation written for 14.” 

  • Topics 1-14, Cumulative/Benchmark Assessment, Problem 9, “Directions Have students draw a circle below the book and a triangle beside the book.” Item Analysis for Diagnosis and Intervention indicates: DOK 3, MDIS D28, Standard K.G.A.1. Scoring Guide indicates: 2 points, “Draws a circle and a triangle in the correct positions relative to the book”; 1 point “Draws either a circle or a triangle in the correct position relative to the book.”

Indicator 3K
04/04

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

The materials provide formative and summative assessments throughout the grade as print and digital resources. As detailed in the Assessment Sourcebook, the formative assessments—observational tools, Convince Me!, Guided Practice, and Quick Checks—occur during and/or at the end of a lesson. The summative assessments—Topic Assessment, Topic Performance Task, and Cumulative/Benchmark Assessments—occur at the end of a topic, group of topics, and at the end of the year.  The four Cumulative/Benchmark Assessments address Topics 1-4, 1-8, 1-11, and 1-14. 

  • Observational Assessment Tools “Use Realize Scout Observational Assessment and/or the Solve & Share Observation Tool blackline master.”

  • Convince Me! “Assess students’ understanding of concepts and skills presented in each example; results can be used to modify instruction as needed.”

  • Guided Practice “Assess students’ conceptual understanding and procedural fluency with lesson content; results can be used to review or revisit content.”

  • Quick Check “Assess students’ conceptual understanding and procedural fluency with lesson content; results can be used to prescribe differentiated instruction.”

  • Topic Assessment “Assess students’ conceptual understanding and procedural fluency with topic content.” Additional Topic Assessments are available with ExamView.

  • Topic Performance Task “Assess students’ ability to apply concepts learned and proficiency with math practices.

  • Cumulative/Benchmark Assessments “Assess students’ understanding of and proficiency with concepts and skills taught throughout the school year.”

The formative and summative assessments allow students to demonstrate their conceptual understanding, procedural fluency, and ability to make application through a variety of item types. Examples include: 

  • Order; Categorize

  • Matching

  • Graphing

  • Yes or No; True or False

  • Number line

  • True or False

  • Multiple choice

  • Fill-in-the-blank

  • Technology-enhanced responses (e.g., drag and drop)

  • Constructed response (i.e., short and extended responses)

Indicator 3L
Read

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for enVision Mathematics Kindergarten partially provide assessments which offer accommodations that allow students to determine their knowledge and skills without changing the content of the assessment.

The Topic Online Assessment offers text-to-speech accommodation in English and Spanish for students. For the Topic Performance Task, students can draw, stamp (this allows various items including but not limited to: red/yellow counters, ten frames, part part whole diagrams, connecting cube of various colors, place value blocks, and money), place text, place a shape, place a number line, and add an image. Students also have access to additional Math Tools, and a English/Spanish Glossary.

According to the Teacher’s Edition Program Overview, “Types of Assessments Readiness assessments help you find out what students know. Formative assessments in lessons inform instruction. Various summative assessments help you determine what students have learned… Auto-scored online assessments can be customized.” In addition to customizing assessments, Teachers are able to alter an assessment—for one student or multiple students—but in ways that change the content of the assessment: by deleting items, by adding from item sets, or by creating/adding their own questions.

Criterion 3.3: Student Supports

07/08

The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for enVision Mathematics Kindergarten partially meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially provide extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Indicator 3M
02/02

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing strategies and support for students in special populations to support their regular and active participation in learning grade-level mathematics. 

The materials provide strategies and support for students in special populations via its 3-tier Response to Intervention (RtI) Differentiated Instruction plan.

  • Tier 1 offers Ongoing Intervention: “During the core lesson, monitor progress, reteach as needed, and extend students’ thinking.” 

    • Types of support include:

      • Guiding Questions -  In the Teacher’s Edition Guiding questions are used to monitor understanding during instruction. Online Guiding Questions Guiding questions are also in the online Visual Learning Animation Plus.

      • Preventing Misconceptions -  This feature in the Teacher’s Edition is embedded in the guiding questions.

      • Error Intervention: If… then… - This feature in the Teacher’s Edition is provided during Guided Practice. It spotlights common errors and gives suggestions for addressing them. 

      • Reteaching - Reteaching sets are at the end of the topic in the Student’s Edition. They provide additional examples, reminders, and practice. Use these sets as needed before students do the Independent Practice. 

      • Higher Order Thinking - These problems require students to think more deeply about the rich, conceptual knowledge developed in the lesson.

      • Practice Buddy Online - Online interactive practice is provided for most lessons.

  • Tier 2 offers Strategic Intervention: “At the end of the lesson, assess to identify students’ strengths and needs and then provide appropriate support.” The Quick Check (either in print or online) is used to prescribe differentiated instruction for Tier 2 interventions based on the following scale: I = Intervention 0-3 points, O = On-Level 4 points and A = Advanced 5 points. 

    • Types of support include:

      • Intervention Activity (I) - Teachers work with struggling students. 

      • Technology Center Activities (I, O, A) - Digital Math Tools Activities reinforce the lesson content or previously taught content using a suite of digital math tools. Online Games practice the lesson content or previously taught content.

      • Reteach to Build Understanding (I) - This is a page of guided reteaching.

      • Build Mathematical Literacy (I, O) - Help students read math problems.

      • Enrichment (O, A) - Enhances students’ thinking.

      • Activity Centers (I, O, A) - Pick a Project lets students choose from a variety of engaging, rich projects. enVision STEM Activity is related to the topic science theme introduced at the start of the topic. Problem-Solving Leveled Reading Mat is used with a lesson-specific activity.

      • Additional Practice (I, O, A) - Use the leveled assignment to provide differentiated practice.

  • Tier 3 offers Intensive Intervention: “As needed, provide more instruction that is on or below grade level for students who are struggling.”

    • Math Diagnosis and Intervention System (MDIS)

      • Diagnosis Use the diagnostic test in the system. Also, use the item analysis charts given with program assessments at the start of a grade or topic, or a the end of a topic, group of topics, or the year.

      • Intervention Lessons These two-page lessons include guided instruction followed by practice. The system includes lessons below, on, and above grade level, separated into five booklets.

      • Teacher Supports Teacher Notes provide the support needed to conduct a short lesson. The Lesson focuses on vocabulary, concept development, and practice. The Teacher’s Guide contains individual and class record forms, correlations to Student’s Edition lessons, and correlation of the Common Core State Standards to MDIS.

Examples of the materials providing strategies and support for students in special populations include: 

  • Topic 2, Lesson 2-2, RtI 1, “Prevent Misconceptions Students may think the balls cannot be compared as they are not lined up. Show how the balls are matched 1 to 1 like in Boxes A and B, and there is still 1 soccer ball that is left over.”

  • Topic 6, Lesson 6-6, RtI 2, “Use the QUICK CHECK on the previous page to prescribe differentiated instruction. Intervention Activity (I), Picture a Story, Materials Crayons, 

    • Tell this Put Together addition story: 2 students are hopping. 3 students are skipping. How many students are there in all? 

    • As you tell the story again, draw a group of 2 stick figures and say the number 2. Then draw a group of 3 stick figures and say the number 3. Have one student draw a circle around all the stick figures. Ask another student to tell how many figures there are in all. 

Tell a different number story and ask partners to draw a picture to solve it. Help students retell the story using in all.”

Indicator 3N
01/02

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for enVision Mathematics Kindergarten partially meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Within each topic, the Differentiated Instruction resource for teachers identifies activities intended for more advanced students such as Enrichment or Extensions. Enrichment is “higher order thinking work (that) helps students develop deeper understandings.” Extensions, which come in the form of Teacher Resource Masters (online and in print), include Pick a Project, an enVision STEM Activity, and Problem Solving Leveled Reading Mats—all grouped in Activity Centers—and Additional Practice. The Technology Center includes Digital Math Tools Activities and Online Games for advanced learners. Assignments are auto-assigned based on formative assessment scores in the online platform, however, there is no guidance on how to use these materials in the classroom in a way that would ensure advanced learners would not be completing more assignments than their peers.  

Examples of Enrichment and Extensions include:

  • Topic 6, Lesson 6-4, Enrichment, Problem 2, “Directions Have children count the buttons in each group, record the numbers, and write how many in all.” The materials show a group of 3 buttons and a group of 4 buttons. Students write the equation, “3 + 4 = 7.”

  • Topic 12, Pick a Project, Project 12A, “DirectionsLook at picture A. Think about this question: Where did all those bones come from? If you choose Project A, you will create dinosaur puzzles.Extensions: “Ask students to tell how they know they have made a square or a triangle when they have put the puzzle together. Ask students who worked on different puzzles to compare their puzzles and tell how the pieces they cut are similar and different.”

Indicator 3O
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Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for enVision Mathematics Kindergarten partially provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning. The materials provide a variety of approaches for students to learn the content over time but provide limited opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways within a consistent lesson structure. The Teacher’s Edition Program Overview indicates that the lesson structure incorporates both Problem-based Learning and Visual Learning within the 5Es instruction framework: Engage, Explore, Explain, Elaborate, and Evaluate. Examples of how the lesson structure allows for varied approaches to learning tasks and variety in how students demonstrate their learning include:

  • Problem-based Learning

    • Engage and Explore: Solve & Share begins the lesson instruction by asking students to solve a problem that embeds new ideas. Students will use concrete materials or pictorial representations and may solve these problems any way they choose.

  • Visual Learning

    • Explain: Visual Learning Bridge offers “explicit instruction that connects students’ work in Solve & Share to new ideas taught in the lesson. The Visual Learning Bridge at times shows pictures of concrete materials, drawing of concrete materials, and/or diagrams that are representations of mathematical concepts.” Convince Me! “checks for understanding right after the instruction.”

    • Elaborate: Guided Practice, which includes concepts and skills, checks for understanding before students progress to Independent Practice and allows for error intervention by the teacher. Independent Practice and Problem Solving are opportunities to build(s) proficiency as students work on their own. Problem types are varied throughout and vocabulary questions build understanding.

    • Evaluate: Quick Check varies depending on the source of student interaction: Students engage with three items if using the Student’s Edition and five items in a variety of lesson formats if using online. In both cases, a total of five points is possible and scores may be “used to prescribe intervention, on-level, or advanced resources.”

Indicator 3P
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Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for enVision Mathematics Kindergarten provide some opportunities for teachers to use a variety of grouping strategies. The Program Overview suggests using assessment data to group students, and the Teacher’s Edition routinely suggests using groups for different activities. While suggestions for the timing and size of groups are explicit within a structured instructional routine; suggestions do not always address how to form specific groups based on the needs of individual students. Examples of how the materials provide opportunities for teachers to use grouping in instruction include:

  • The Program Overview suggests, “Using Assessment Data You can use the assessment data to organize students into groups for purposes of making instructional decisions and assigning differentiation resources.” Teacher can choose the breakpoint for the assessment and students above and below the breakpoint will be put into two separate groups. 

  • The Teacher’s Edition indicates:

    • Pick a Project, “Grouping You might have students who work alone or with a partner or small group. … Project Sharing Students should share their completed projects with a partner, a small group, or the whole class.”

    • Vocabulary Activity: Frayer Model … you may wish to have students work in groups to complete Frayer models for different vocabulary words.”

    • 3-Act Math guidance indicates, “Develop A MODEL - small group - partners, … EXTEND THE TASK - individual, … and REVISE THE MODEL - individual.”

Indicator 3Q
02/02

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for enVision Mathematics Kindergarten meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The Teacher’s Edition Program Overview, Supporting English Language Learners section, list the following strategies and supports: 

  • Lesson Language Objective for each lesson indicates a way that students can demonstrate their understanding of the math content through language modalities.

  • Two ELL suggestions for every lesson are provided in the Teacher’s Edition. One suggestion is used with Solve & Share and the other is used with the Visual Learning Bridge.

  • Levels of English language proficiency are indicated, and they align with the following levels identified in WIDA (World-Class Instructional Design and Assessment): Entering, Emerging, Developing, Expanding, Bridging.

  • ELL consultants, Janice Corona from Dallas, Texas, and Jim Cummins from Toronto, Canada, ensured quality ELL instruction.

  • Language Support Handbook provides topic and lesson instructional support that promotes language development. Includes teaching support for Academic Vocabulary, Lesson Self-Assessment Recording Sheets, and more.

  • Visual Learning Animation Plus provides motion and sound to help lower language barriers to learning.

  • Visual Learning Bridge often has visual models to help give meaning to math language. Instruction is stepped out to visually organize important ideas.

  • Animated Glossary is always available to students and teachers while using digital resources. The glossary is in English and Spanish.

  • Pictures with a purpose appear in lesson practice to help communicate information related to math concepts or to real-world problems. You many want to display the Interactive Student Edition pages so you can point to specific pictures or words on the pages when discussing the practice”

Examples where the materials provide strategies and supports for students who read, write, and/or speak in a language other than English include:

  • Topic 3, Lesson 3-2, English Language Learners (Use with the Solve & Share), “Entering Have students compare work with a partner and count the counters. Ask students to point to each counter as they count. Then have them tell the total number.” This strategy/support falls under the Speaking category. 

  • Topic 7, Lesson 7-3, English Language Learners (Use with the Solve & Share), “Speaking Read the directions to students. Ask: How many lady bugs does Marta see at the start? What does it mean that some ladybugs then crawl away? Discuss a range of responses. For example, students may answer with actions, single words, sentences, or with reference to the picture on the page. Establish that some crawling away means some ladybugs have moved away from the group.” The teacher then has the choice between Entering, Emerging or Expanding, strategies and supports.

  • Topic 11, Lesson 11-4, English Language Learners (Use with the Visual Learning Bridge), “Bridging Ask students to tell the number in the yellow box. Say: This is the number you will start count at. Ask students to tell the number in the red box. Say: This is the number you will stop counting at. Have students count each number. Ask students to explain the steps they took.” This strategy/support falls under the Listening category.

A general support that the materials provide for students who read, write, and/or speak in a language other than English and Spanish include PDFs that may be downloaded and translated to meet individual student needs. 

Indicator 3R
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Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for enVision Mathematics Kindergarten provide a balance of images or information about people, representing various demographic and physical characteristics.

Materials represent a variety of genders, races, ethnicities, and physical characteristics. All are indicated with no bias and represent different populations. The Avatars that work with students throughout the grade represent various demographics and are named: Alex, Carlos, Daniel, Emily, Jackson, Jada, and Marta. When images of people are used they do represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Examples include:

  • Topic 1, Lesson 1-7, Guided Practice, Problems 3-8, “ Tell students to listen for the number in the sentence, and raise their hand when they hear the number word. Today I ate 2 bananas. Juwan has 0 sisters. Micah ate 4 grapes.”

  • Topic 5, Pick a Project, “Directions Say: You will choose one of these projects. Look at picture A. Think about this question: What would our class flag look like? If you choose Project A, you will design a flag. Look at picture B. Think about this question: How do you go? If you choose Project B, you will make a model. Look at picture C. Think about this question: How does an instrument make music? If you choose Project C, you will act out playing instruments and making music.” The materials include three pictures: A an array of international flags, B young children of multiple ethnicities on bikes, and C professional musicians of multiple ethnicities.

  • Topic 14, Topic Assessment, Answering the Topic Essential Question, “Rayanne has 2 pencils of different lengths. … Marcus has a number of different school supplies. … Paulie is using tools from his classroom to describe the attributes of different shapes.”

Indicator 3S
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Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for enVision Mathematics Kindergarten partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials include a Language Support Handbook and Spanish versions of the Interactive Student Edition, all online and print instructional resources (e.g., Glossary), and the Family Engagement materials (which entails an overview of Resources, Content and Standards, and Topic/Lesson Supports).

The Language Support Handbook makes clear the philosophy about drawing upon student home language to facilitate learning: “ … Over the years, new language is meaningful when it is connected to a variety of experiences, objects, pictures, abstract ideas, and previously-learned language.  … For meaningful learning, help students connect new ideas and languages to a variety of experiences, objects, pictures, abstract ideas, and previously-learned language. … Provide language support as needed, while giving all students full access to rich experiences that facilitate meaningful, engaging learning. Make math class a place that continues to nurture children’s natural love of learning.”

The Language Support Handbook provides Professional Reading: Language Support in Mathematics, Academic Vocabulary Resources, and Language Support Activities. Professional Reading focuses on supporting access to mathematical thinking; supporting productive struggle in mathematics; supporting reading, writing, speaking, and representing; supporting vocabulary and language in mathematics; supporting classroom conversations in mathematics; and scaffolding without overscaffolding. Additional Resources include WIDA proficiency level descriptors, types of math problems involving operations, academic vocabulary activities, academic vocabulary in six languages, and the Language Demands in Mathematics Lessons (LDML) Tool.

Materials can be accessed in different languages by highlighting any text in the Student Edition (not available in the interactive version) and pressing the translate button. The text that is highlighted will be translated with text only or with text and text to speech (audio support) depending on the language availability in the settings. All translations are done by Google and students are also able to control the speed of the voice. Languages that are available include but are not limited to the following: Afrikaans (audio support), Belarusian, Bosnian, Chinese Traditional (audio support), Finnish (audio support), Galician (audio support), Greek (audio support), Haitian Creole, Portuguese (audio support), Spanish (audio support)...etc.

While Language Supports are regularly embedded within lessons and support mathematical language development, they do not include specific suggestions for drawing on a student’s home language.

Indicator 3T
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Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for enVision Mathematics Kindergarten partially provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The Teacher’s Edition Program Overview, states the following about Pick a Project, “Student Choice Pick a Project offers students the opportunity to explore areas of interest and complete projects of their choosing. This kind of student choice has special benefits related to differentiation, motivation, and open-ended rich tasks…Varied contexts in the projects let students choose contexts related to everyday life as well as contexts with cross-curricular connections to social studies, science, art, and literacy.” Some of the project choices in the Pick a Project gives students opportunities to draw upon their cultural and social background. Additionally, enVision STEM Project extensions, sometimes include tasks that require students to draw on their everyday life.

Examples of the materials drawing upon students’ cultural and/or social backgrounds to facilitate learning include:

  • Topic 4, Pick a Project, “Directions Say: You will choose one of these projects. Look at picture A. Think about this question: How can you train to go into space? If you choose Project A, you will act out an exercise skit. Look at picture B. Think about this question: What kinds of fruit would you put into a fruit salad? If you choose Project B, you will create a fruit salad recipe. Directions Say: You will choose one of these projects. Look at picture C. Think about this question: What is the most exciting ride at a theme park? If you choose Project C, you will design a ride. Look at picture D. Think about this question: What do you like to do on a vacation? If you choose Project D, you will make a list.

  • Topic 8, enVision STEM Project, “Extension Show students the symbol that shows whether a material is recyclable. Have them look for that symbol on objects in the

Indicator 3U
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Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for enVision Mathematics Kindergarten provide supports for different reading levels to ensure accessibility for students. 

In the Teacher’s Edition Program Overview, Build Mathematical Literacy section, it  describes resources for aspects of building mathematical literacy.  “Math Vocabulary describes resources to enhance instruction, practice, and review of math vocabulary used in the topic. Math and Reading describes resources to support leveled reading, help students read and understanding problems in the lesson practice, and (in Grades K-2) introduce math concepts with interactive math stories.” 

The following are examples where materials provide supports for different reading levels to ensure accessibility to students: 

  • Examples of the supports that are offered in the Math Vocabulary section include the following:

    • “My Words Cards Write-on vocabulary cards are provided at SavvasRealize.com. Students use information on the front of the cards to complete the back of the card. Additional activities are suggested on the back of the sheet of cards.

    • Vocabulary Review At the back of each topic is a page of Vocabulary Review. It includes questions to reinforce understanding of the vocabulary used in the topic and asks students to use vocabulary in writing.”

    • Animated Glossary An animated glossary is available to student online. Students can click to hear the word and the definition read aloud.

  • Examples of the supports that are offered in the Math and Reading section are the following:

    • Build Mathematical Literacy Lesson Masters These masters provide support to help students read and understand a problem from the lesson. The support is given in a variety of ways to enhance a student’s ability to comprehend the kind of text and visual displays in a math lesson.” 

    • Problem-Solving Leveled Reading Mat and Activity A big, colorful mat filled with data is provided for each topic in the Quick-and-Easy Centers Kit for Differentiated Instruction. One side of the mat has on-level reading and the other side has below-level reading. A Problem-Solving Reading Activity master is provided for 2 lessons in a topic. The activity has problems that use a context similar to the context on the mat.

    • Interactive Math Stories, Grades K-2 Each topic beings with an interactive math story. It is available as an online story, as an animated story, and as a color-in, take-home story in the Teacher’s Resource Masters.”

  • An example of student support:

    • Topic 7, 3-Act Math, Task Planning, teachers are given the following guidance, “...For emerging readers and writers, you may wish to record student responses on the board in a numbered or color-coded list. Students could write the number that represents their response(s) or make a mark with the color that represents their answer(s). In some situations, it may be helpful to have each student in the class write their prediction on a sticky note, and use all of the sticky notes to create a chart or number line to represent the class predictions.”

Throughout the materials, students can enable a text-to-speech feature in both the interactive and non-interactive student editions.

Indicator 3V
02/02

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials for enVision Mathematics Kindergarten meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. 

In general, the manipulatives are visual images printed in the materials or virtual manipulatives found in the online materials. On occasion, students are prompted to use tools such as counters, cubes, place value blocks, ten frames, a ruler, a protractor, and grid paper. If and when the materials prompt students to use particular manipulatives, they are used appropriately. Examples of the overall use of manipulatives throughout the grade include:

  • Teacher’s Edition Program Overview, Program Components indicates that “Manipulative Kits” accompany Teacher Resource Masters (online and in print). 

  • Teacher’s Edition Program Overview, Using a Lesson, Assess and Differentiate, Quick-and-Easy Centers Kit for Differentiated Instruction includes “Holds mats, pages, and manipulatives for the Technology Center (Digital Math Tools Activities) and for the Activity Centers.”

  • Teacher’s Edition Program Overview, Routines, Quick and Easy Implementation, “Accessible Available in both English and Spanish, the routines require little preparation and few or no physical materials. When needed, common manipulatives are used to reinforce hands-on experiences.”

  • Teacher’s Edition Program Overview, Math Practices, MP.5, states, “Students become fluent in the use of a wide assortment of tools ranging from physical objects, including manipulatives, rulers, protractors, and even pencil and paper, to digital tools, such as Online Math Tools and computers.”

Examples of how manipulatives, both virtual and physical, are representations of the mathematical objects they represent and, when appropriate to written methods, include:

  • Topic 2, Lesson 2-5, Problem Solving, Performance Task, Problem 5, students use manipulatives to represent stickers in the problem and determine a number greater than two. “Directions Read the problem aloud. Then have students use multiple problem-solving methods to solve the problem. 5. Model Use cubes, draw a picture, or use numbers to show how many stickers Marta has and Emily could have.” Teacher guidance: “5. Model with Math Students have been using connecting cubes as tools for modeling in this lesson. Students can be encouraged to use alternative tools for models, such as counters or other small objects.”

  • Topic 6, Lesson 6-6, Solve & Share, students use cubes to represent the name rags in the problem and show how they know that the total is five. “Directions Say: Daniel’s teacher is making name tags for her students. She makes 3 name tags for boys. She makes 2 more for girls. Now she has 5 name tags. How does Daniel’s teacher know that she has made 5 name tags? Explain and then show how you know.” Teacher guidance: “BEFORE 1. Introduce the Solve & Share Problem Give each student 3 cubes of one color and 2 cubes of another color. .. DURING 3. Observe Students at Work To support productive struggle, observe and, if needed, ask guiding questions that elicit thinking. How do students represent the name tags to show how they know? Students might use cubes or draw a picture. Or they might use numbers. If needed, ask What tools do you have to help? What can you write?”

  • Topic 8, Interactive Math Story, During the Story, students use manipulatives to represent flowers in the problem and show that they know the total is three. “Sue gives 2 of her flowers to Ruby. Sue and Ruby are good pals! 1 + 2 = ___ Now Ruby has ___ flowers.” Teacher guidance: “SPEAK … Have students use plastic spoons, pencils, or another easily countable manipulative as flowers.”

Criterion 3.4: Intentional Design

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The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for enVision Mathematics Kindergarten integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

Indicator 3W
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Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for enVision Mathematics Kindergarten integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. The Teacher Edition Program Overview states, the “Interactive Student Edition K-5 consumable and online increase student engagement. Students develop deeper understanding of math ideas as they explain their thinking and solve rich problems.”

Examples of how the materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standard include:

  • Topic 4, Lesson 4-5, Solve & Share, “There are 7 fish in a bowl. Emily puts 1 more fish in the bowl. How many fish are in the bowl now? How can you solve this problem?” The materials show a fish bowl that contains seven different colored fish and a line on which to write how many. The option is given for the students to play a recording of someone reading the problem. Students use tools in DrawPad to add a counter (to represent the added fish) and to write the number 8.

  • Topic 8, Lesson 8-5, Independent Practice, Problem 6, “Directions Have students listen to the story, use and color cubes to show different ways you can break apart the flowers and put them in the vases, and then complete the equations to match each way. Say: Daniel has 6 flowers. He puts one in a red vase and some in a blue vase. How many flowers could he put in each vase?” The materials show a ten-block with six cubes. Students use tools from the DrawPad to add cubes and complete the equation “6 = ___ + ___.”

  • Topic 12, End of Topic 12, Vocabulary Review, “Directions Understand Vocabulary Have students (1) draw a circle around the two-dimensional shape; (2) draw a circle around the three-dimensional shape; (3) draw a circle around the vertices of the triangle; (4) draw a circle; (5) draw a shape that is NOT a square.” Students use tools from DrawPad to complete the task.

  • Under the Tools menu students also have access to additional tools and dynamic mathematics software including but not limited to the following:

    • Math Tools, these tools consist of the following: Counters, Money, Bar Diagrams, Fractions, Data and Graphs, Measuring Cylinders, Geometry, Number Line, Number Charts, Place-Value Blocks, Input-Output Machine, and Pan Balance.

    • Grade K: Game Center, which includes games about place-value relationships, fluency, and vocabulary.

Indicator 3X
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Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for enVision Mathematics Kindergarten partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable. The materials include digital technology that provides opportunities for student-to-teacher collaboration, and student-to-student collaboration but opportunities for teacher-to-teacher collaboration are not provided.

The digital system allows students and teachers to collaborate by commenting on assignments. The Savvas Realize help page states the following: “Realize Reader Comments Using the Realize Assignment Viewer, you can provide your student with feedback in their Realize Reader assignments by adding a comment to a highlight, annotation, or inline Notebook prompt response. When you or your student adds a comment, a comment thread is created that enables you to continue to communicate with each other in context.”

The digital system allows students to collaborate with other students and teachers through the Discussion Forums. The Savvas Realize help page states the following: “Discussion Forum Discussions enable you to facilitate class and group discussions on important academic and social topics. Students can reflect on learning, share ideas and opinions, or ask and answer questions. You can create, monitor, and reply to discussions, and students can participate in discussions you create. In addition, you can choose whether or not to score discussions.”

Indicator 3Y
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The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for enVision Mathematics Kindergarten have a visual design (whether print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within topics and lessons that support student understanding of mathematics. Examples include:

  • Each topic begins with the Math Background (Focus, Coherence, and Rigor), Math Practices and ETP (Effective Teaching Practices), Differentiated Instruction, Build Mathematical Literacy, enVision STEM Project, Review What You Know!, Pick a Project, and 3-Act Math (if applicable).

  • Each lesson follows a common format:

    • Math Anytime consists of Today’s Challenge and Daily Review.

    • Step 1: Problem-Based Learning focuses on Solve & Share.

    • Step 2: Visual Learning consists of Visual Learning, Convince Me!, and Practice & Problem Solving which includes  Student Edition Practice, Interactive Practice Buddy, and Interactive Additional Practice.

    • Step 3: Assess & Differentiate consists of Quick Check, Reteach to Build Understanding, Build Mathematical Literacy, Enrichment, Digital Math Tool Activity, Pick a Project, and Another Look.

  • Each topic ends with the Fluency Review Activity, Vocabulary Review, Reteaching, Topic Assessment, Topic Performance Task, and Cumulative/Benchmark Assessment (if applicable).

  • Student materials include appropriate font size and placement of direction. There is ample space in the printable Student Task Statements, Assessment PDFs, and workbooks for students to capture calculations and write answers.

  • When images, graphics, or models are included, they clearly communicate information supporting student understanding of topics, texts, or concepts.

Indicator 3Z
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Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for enVision Mathematics Kindergarten provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable. The materials provide teachers with multiple easy access points for technology and with specific guidance provided in the supplementary handouts.

Examples of teacher guidance for the use of embedded technology include:

  • Examples from the “Let’s Go Digital!” Handout,

    • Tools “Open the Tools menu anytime to find a variety of interactive tools that you and your students can use. Check out the Game Center and Math Tools.”

    • Planning a Topic “…Then, review the Today’s Challenge problems. Notice that each problem of the five-day challenge uses the same data with increasing difficulty each day. Consider displaying the problem at the beginning of the day and having students use the DrawPad tools to respond...”

    • Teaching a Lesson “...Start each lesson with the problem-based Solve & Share task. Display the problem from your computer and use the DrawPad tools to model your students’ ideas...”

  • An example from the Assessment Handout, “Additional Assessment Options On Savvas Realize, you can customize assessments to meet your instructional needs. To explore these options, click Customize under the assessment name. You can modify the title, the description, and whether the test should count toward mastery. To add questions, click Add items from test bank and search the bank of test items by standard or keyword. You can also add your own assessments. Select Create Content menu to upload files, add links, or build your own tests. Finally, check out ExamView test generator in the Tools menu.”

  • All of the above-mentioned handouts are also available as Tutorial Videos.

  • An example from the Savvas Realize help page, “Remove Students from a Realize Class You can remove students from a Realize class using the instructions in this topic. To remove a student that was imported from Google Classroom, see Remove Students Imported From Google Classroom. 1. Click Classes on the top menu bar, then select the class. 2. Click Students & groups on the left. 3. Click the 3-dot menu next to the student you want to remove, then click Remove Student.” Pictures are included with some steps to provide additional guidance.