Kindergarten - Gateway 1

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations that they assess grade-level content.

The series is divided into topics, and each topic has a topic assessment that can be given both online and/or paper and pencil and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-14. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator.

Examples of grade-level assessment items include:

• Topic 1, Topic Assessment, Problems 8 and 9, students count the number of objects and write the number 0-5. (K.CC.2)
• Topics 1-4 Cumulative/Benchmark Assessment, Problem 2, students solve, “Which number is less than the number shown? Which number is greater than the number shown?” (K.CC.3.7)
• Topic 5, Topic Assessment, Problem 3, students compare the number of animals inside of a circle to the number of animals outside of the circle. (K.CC.3.6)
• Topic 8, Topic Assessment, Problem 6, students look at pictures as they listen to a story, use connecting cubes to represent each story, choose an operation, and write the equations to show the related number facts. (K.OA.1.2)
• Topic 10, Topic Assessment, Problem 7, “Have students.... color 10 cubes blue to show 10 ones and then draw 10 blue cubes in the top ten-frame. Have them color in the remaining cubes in the train red to show more ones, count them, and then draw the same number of red cubes in the bottom ten-frame. Then have them write the equation to match the pictures.” (K.NBT.1.1)
• Topic 11, Topic Assessment, Problem 7, students count by ones to write the missing numbers in the top row and draw a circle around each of the missing numbers in the remaining rows. (K.CC.1)
• Topic 14, Topic Assessment, Problem 7, students compare objects and match the heavier object to the lower side of the scale and the lighter object to the higher side of the scale. (K.MD.1.2)

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 14, which is 50%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 89 out of 96, which is approximately 92%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 123 out of 145, which is approximately 85%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 92% of the instructional materials focus on major work of the grade.

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

The publishers identify connections between supporting content and major work on the Topic Planner pages in the Teacher Edition. For example:

• Topic 5 addresses supporting standard K.MD.2.3 (Classify objects and count the number of objects in a category) connected to major work, specifically clusters K.CC.2 (Count to tell the number of objects), and K.CC.3 (Compare numbers).
• Lesson 5-2, Independent Practice, Problems 4-6, students count and compare animals using tally marks and then write the number.
• Lesson 5-3, Guided Practice, Problem 1, students “Sort colors, count them and then write numbers in the chart to tell how many.” “Have students draw a circle around the category that is less in number than the other category.”  
• Lesson 5-4, Problem Solving and Critique Reasoning, students have multiple opportunities to engage in supporting standards connected to major work of the grade:
• In the Solve and Share, students solve, “Carol 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 and words to explain your answer.”
• During the Visual Learning Animation Plus, students solve, “Gabbi says the category of airplane is greater in number than the number that is not airplanes. Does her answer make sense? Have students draw a circle around yes or no then use the sorting and counting of each category to explain their reasoning.”
• In Independent Practice, students solve, “Have students listen to each problem. Draw a circle around yes or no. Then use the sorting and counting of each category to explain their reasoning. Question 2) Damon says, he counted 8 yellow train cars and 6 train cars that are not yellow. Does his answer make sense? Question 3) Malinda says that the category of yellow train cars is less than the category of train cars that are not yellow. Does her answer make sense?”
• Topic 13, addresses supporting cluster K.G.2 (Analyze, compare, create and compose shapes) and is connected to major clusters K.CC.3 (Compare numbers) and K.OA.1 (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from).
• Lesson 13-1, Guided Practice, students solve, “Have students listen to the clues, mark an “X” on the shapes that do NOT fit the clues, draw a circle around the shape that the clues describe, and then tell how the shapes they marked with an “X” are different than the shape they drew a circle around.”
• Lesson 13-2, Solve and Share, students count to solve, “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?”
• Lesson 13-4, Solve and Share, students solve, “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 behind the door you can see. Without counting, tell how many shapes are behind the other door. Then count to check your answer.”
• Lesson 13-5, Visual Learning Animation Plus, students solve, “Have students use the pattern block shown to cover the shape, draw the lines, and then write the number that tells how many pattern blocks to use.”

There are some missed opportunities connecting supporting work to major work in the Teacher’s Edition. For example:

• In Topic 11, the Topic Opener: Extension identifies major work cluster K.CC.1 (Know number names and the count sequence). There is a missed opportunity to connect to supporting cluster K.MD.2 (Classify objects and count the numbers of objects in categories). Students, “explain that some animals live alone or in small groups, like bears and jaguars, and others live in large groups, like schools of fish and colonies of bees. Then have students draw a picture of an animal that lives alone or in a small group and another animal that lives in a large group.” Students draw a picture of the animal, but do not draw and count certain numbers of animals.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades.

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 145 days.

Included are 14 topics in for the grade. Each Topic is broken down into lessons. Each Topic also includes additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22):

• There are 96 Content focused lessons.
• There are 14 days of Topic Centers
• There are 7 days for 3-Act Math activities
• There are 28 days of Topic Reviews and Assessments

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems.

Overall, the materials develop according to the grade-by-grade progressions in the standards. Typically, material related to prior and future grades is clearly identified and related to grade-level work. In the Teacher Edition Program Overview, all grade-level standards are present as noted in the Correlation to Florida Kindergarten Standards.

The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. Though explicit connections are made to prior and future mathematical content, no standards are listed in either Look Back or Look Ahead. For example, in the Topic 2 Overview, Coherence:

• The Look Back states, “Earlier in Kindergarten, Counting Principles - In Topic 1, students learned to use the counting numbers in standard order (the stable-order principle) and to count a group of objects by pairing each object with one and only one number (the one-to-one principle). They also learned that the final number they say in a number sequence tells the number of objects in the group (the cardinality principle). These important counting principles laid the foundation for students to be able to compare two groups of objects.”  
• The Look Ahead states, “Later in Kindergarten, Compare Quantities and Numbers 0 to 10 - In Topic 4, students will compare groups of objects and numbers from 0 to 10. Count and Compare Data - In Topic 5, students will classify objects into categories and the use counting to compare how many objects are in the categories. Compare Measurable Attributes - In Topic 14 students will compare lengths, capacities, and the weights of object.”
• The Look Ahead also states, “Grade 1, Comparison Situations - In Topic 1, students will compare two groups of objects in a variety of ways. They will come to understand that subtraction can be used to determine “how many more” or “how many fewer.”  Additional connections to “Interpret Data” in Topic 6 and “Compare Two-Digit Numbers” in Topic 9 are evident.

The instructional materials support the progressions of grade-level standards, for example:

• Counting and Cardinality is addressed in Topic 1: Numbers 0-5; Topic 2: Compare Numbers 0-5; Topic 3: Numbers 6-10; Topic 4: Compare Numbers 6-10; and Topic 5: Classify and Count Data.
• Operations and Algebraic Thinking is addressed in Topic 6: Understand Addition; Topic 7: Understand Subtraction; and Topic 8: More Addition and Subtraction.
• Number & Operations in Base Ten is addressed in Topic 9: Count Numbers to 20 and Topic 10: Compose and Decompose Numbers 11-19.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. For example:

• In Lesson 2-1, Equal Groups, students solve, “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.” (K.CC.3.6 and K.CC.2.5)
• In Lesson 2-2, Problem 3, students use a matching strategy to determine which of two groups is greater in number of objects. As students explain their work, the publisher provides some student responses such as, “I know that 4 is more than 3... Others might explain that one group is greater in number because it has at least one object.” (K.CC.3.6 and K.CC.2.5)
• In Lesson 2-4, Solve and Share, students solve, “Maria builds a tower with red and blue blocks. Count how many red blocks and how many blue blocks she uses. Write the numbers to show how many. Then draw a circle around the number that is less than the other.” (K.CC.3.6, K.CC.1.3, and K.CC.2.5)
• In Lesson 6-3, Independent Practice, Problems 7 through 10, students complete addition as putting together. For example, in Problem 8, students see a picture of 2 eggplants and six green peppers, "find _ and _ is _." (K.OA.1.1, K.CC.1.3, and K.OA.1.2)
• In Lesson 10-1, Visual Learning Bridge, students find, “How many?” Students have 13 cubes and use ten frames to find 10 + 3. (K.NBT.1.1 and K.CC.2.5)

Each topic also includes: digital practice, extra worksheets, reteach to build understanding, build mathematical literacy, enrichment activities, envision STEM activities, leveled reading, and problem solving.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• In Lessons 1-1 and 1-2, the objectives are, “Count 1, 2, and 3 objects” and “Count groups of 1, 2, and 3 objects shown in different ways,” respectively, and are shaped by K.CC.2, Count to tell the number of objects.
• In Lessons 6-4 and 6-5, the objectives are, “Write an equation to show addition” and “Solve addition problems,” respectively, and are shaped by K.OA.1, Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
• In Lessons 14-2 and 14-3, the objectives are, “Describe and compare objects by capacity” and “Describe and compare objects by weight,” respectively, and are shaped by K.MD.1, Describe and compare measurable attributes.

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important.

• Lesson 1-9, Solve & Share, connects K.CC.1, Know number names and the count sequence, and K.CC.2, Count to tell the number of objects. Students solve, “Marta is thinking of two numbers - one is the number that comes just before 4 when counting, and the other is the number that comes just after 4 when counting. Write the two numbers Marta is thinking of. Show how you know you are correct.”
• Lesson 2-4 connects K.CC.1, Know number names and the count sequence, and K.CC.3, Compare numbers. Students “count the stickers, write the number 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 both numbers if they are equal.”
• Lesson 10-2 connects K.NBT.1, Work with numbers 11-19 to gain foundations of place value, and K.CC.1, Know numbers and the count sequence. Using 10-frames, students “Count the objects in the 10 frame. 10 and 4 is 14. 6 and 10 is 16.”