6th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 85% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for focus and coherence. For focus, the materials assess grade-level content and spend at least 65% of class time on major work of the grade, and for coherence, the materials have supporting content that enhances focus and coherence and foster coherence through connections at a single grade.
Criterion 1.1: Focus
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.
Indicator 1a
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for assessing grade-level content. Overall, assessments are aligned to grade-level standards, and the instructional materials do not assess content from future grades. Each chapter has an End of Chapter Assessment in both Word and PDF formats.
Examples of End of Chapter Assessment items aligned to grade-level standards include:
- In Chapter 2, Item 3 states, “A basketball player makes 84 out of 100 free throw attempts. a. Find the percent of free throws that the player makes. b. At this rate, how many free throw attempts should it take to make 210 free throws?” (6.RP.3c)
- In Chapter 6, Item 1 states, “Write and evaluate: the sum of four to the third power and 35.” (6.EE.1)
- In Chapter 6, Item 4 states, “Use the numbers 48 and 30 to answer the following questions: a. What is the greatest common factor of the two numbers? b. Use the GCF to write the sum in the form __( __ + __ ).” (6.NS.4)
- In Chapter 7, Item 3 states, “Toby is driving 50 mph on the highway. He wants to know the relationship between how far he drives and how long it takes. a. What is the independent variable? What is the dependent variable? How do you know? b. Write an equation to represent the relationship between the two variables. Let x represent the independent variable and let y represent the dependent variable. c. Create a table and graph. How do the values in the table and graph relate to the equation?” (6.EE.9)
- In Chapter 10, Item 1a states, “You want to create a study about the diet of cats. Write a statistical question for your study. Explain why it is a statistical question.” (6.SP.1)
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for devoting the majority of class time to the major work of the grade. Overall, the materials spend at least 65% of class time on major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for spending a majority of class time on the major clusters of the grade.
- The approximate number of chapters devoted to major clusters of the grade is eight out of ten, which is approximately 80%.
- The number of lessons devoted to major clusters of the grade (including assessments and supporting clusters connected to the major clusters) is 79 out of 96, which is approximately 82%.
- The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 87 out of 107, which is approximately 81%.
A day-level analysis is most representative of the instructional materials because this calculation includes assessment days that represent major clusters. As a result, approximately 81% of the instructional materials focus on major clusters of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for coherence. The materials have supporting content that enhances focus and coherence and foster coherence through connections at a single grade. The materials are partially consistent with the progressions in the Standards, and they partially have an amount of content designated for one grade level that is viable for one school year.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for supporting work enhancing focus and coherence simultaneously by engaging students in the major work of the grade.
Supporting standards/clusters are connected to the major standards/clusters of the grade. Lessons in Grade 6 incorporate supporting standards in ways that support and/or maintain the focus on major work standards. Examples of the connections between supporting and major work include the following:
- Lesson 2.4 connects 6.RP.3 and 6.NS.3. Students divide whole numbers by decimals and use the rate to solve problems. For example, in Activity 3, students find and compare rates, “Usain Bolt also known as ‘Lightning Bolt’, is the fastest sprinter of all time. He ran 100 meters in 9.58 seconds and he ran 200 meters in 19.19 seconds. Which race was his fastest speed?”
- Lesson 6.9 connects 6.NS.B and 6.EE.4. Students factor expressions by finding a common factor and using the distributive property. For example, in Activity 3, Inline Question 5 states, “Look at the expression 12x + 20. Select the equivalent expression. a) 4(3x+5), b) 6x+10, c) 2(6x + 10), d) 3x+5.”
- In Lesson 9.2, students find the area by composing triangles into rectangles (6.G.1) and identifying what the formula would be with letters representing numbers (6.EE.2). In Activity 3, Inline Question 1 states, “In general, for a tangram with side length s, what is the area of all the pieces? a) 2s, b) 4s, c) 8s, d) $$s^2$$”.
- Lesson 9.3 connects 6.G.1 and 6.EE.2. Students use written formulas to find the areas of parallelograms or trapezoids. For example, “Area of a parallelogram = base x height, where height is the line that forms a right angle between the bases.”
- Lesson 9.10 connects 6.G.4 and 6.EE.2. Students find the surface area by evaluating expressions with a letter representing a number. For example, in Activity 2, Inline Question 4 states, “If a cube has a side length of s units, which expression could be used to represent the surface area? a) $$6s^2$$, b) $$(s^2)^6$$ c) $$6s$$, d) $$4s^2$$.”
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for the amount of content designated for one grade level being viable for one school year in order to foster the coherence between grades.
As described below, the lessons and assessments provided within the instructional materials can be completed in 107 days. Within each lesson, there is Related Content aligned to the lesson, but there are no instructions for teachers as to when, or how, to assign the Related Content to students. The materials also do not indicate how long completion of the Related Content might take. The suggested amount of time to complete the lessons and assessments is not viable for one school year, and although the Related Content would add to the suggested time, the lack of guidance for teachers regarding the Related Content would require modifications to be made to the materials to be viable for one school year.
- According to the Publisher’s Orientation Video, the average time for a lesson is approximately 50 minutes, and most lessons can be completed in one class period. For the majority of the lessons, the length ranges from 45 to 55 minutes, with one lesson being 95 minutes in length.
- There are 10 chapters. Each chapter ends with an assessment, and the chapters include varying amounts of lessons.
- No lessons are marked as supplementary or optional.
- There are 96 lessons altogether. All lessons are one day, except one lesson which is 95 minutes, or two days, for a total of 97 days. In addition, there are 10 days for 10 chapter assessments, for a total of 107 days.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for being consistent with the progressions in the Standards. The instructional materials give all students extensive work with grade-level problems. However, the instructional materials do not clearly identify content from prior or future grade-levels, and the materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
The instructional materials do not clearly identify content from prior or future grade-levels and relate it to grade-level work. Sixth grade standards are identified in a list at the beginning of each lesson and in the Curriculum Guide of the Teacher Edition, in which you can see Standards by Lesson, Lessons by Standard, and Focus Standards for Grade 6 standards.
Examples of grade-level standards at the beginning of the lesson include:
- Lesson 4.7, Decimals Divided by Decimals, lists 6.NS.3.
- Lesson 6.4, Order of Operations, lists 6.EE.1.
- Lesson 8.7, Inequality Solutions, lists 6.EE.5, and 6.EE.8 is listed as an additional standard.
In a few Chapters in the Teacher Edition, previous or future work from Grade 6 is listed, but there is no learning identified from prior or subsequent grade levels. Examples include:
- In Chapter 1.2, the Warm-Up states, “This is a review of the block sorting interactive from the lesson Introducing Ratios. Students should be able to quickly complete the activity and answer the included questions. Students will not all have the same number of blocks of each color.”
- In Chapter 3.6, the purple notes state, “Students should already be familiar with the idea of scaled images from some of the activities in, ‘Constructing Tables of Equivalent Ratios.'”
- In Chapter 5.6, the purple notes state, “This lesson focuses on the coordinate plane itself and the next lesson, Points on the Coordinate Plane, will introduce students to using coordinate points to describe an object location.”
The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All lessons contain a Warm-Up, two or more activities, Extension Activities, Inline Questions, and Review Questions that are at grade level. Inline Questions range in number, and lessons generally contain around 10, which are used throughout the lesson to check for understanding. Also, there are Supplemental Questions and Extension Activities. These questions and activities are only seen in the Teacher’s Edition. The Review Questions are mostly multiple choice, and there are approximately 10 per lesson. Examples include:
6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
- In Lesson 2.2, Activity 3 states, “Students can make up their own kind of sharks with a given number of rows and series of teeth. They can draw pictures of their sharks and give them names. In a small group, students can find the unit rates of teeth per shark and order the sharks from the greatest number of teeth to the least number of teeth.” (6.RP.2)
- In Lesson 2.9, Activity 1, Question 2 states, “A percent is a rate per 100. How would you write 95% and 105% as rates per 100?” (6.RP.3c)
6.NS.C, Apply and extend previous understandings of numbers to the system of rational numbers.
- In Lesson 5.4, Question 4 states, “ Find the distance between -23 and 13.” (6.NS.6a)
- In Lesson 5.10, Activity 2, Question 4 states, “Look at the points (3, 5) and (3, -5). The points have the same x-value, but they are located in different quadrants. How can you find the distance between the two points?” (6.NS.8)
- In Lesson 8.3, Warm Up states, “Which movement would take you farther left, a vertical movement of -2 or a vertical movement of +2?” (6.NS.7a)
6.EE.B, Reason about and solve one variable equations and inequalities.
- In Lesson 7.1, Activity 2 states, “What variable can we use to represent the distance from each planet to the Sun?” (6.EE.5)
- In Lesson 7.4, Activity 3 states, “If you have $$\frac{1}{4}$$ of a variable on one side and you add three more fourths to that side of the balance beam, what operation can be used to represent this?” (6.EE.7)
- In Lesson 8.6, Question 6 states, “Write the solution set for the inequality. Include at least three values in your solution set. y ≥ 3” (6.EE.8)
The full intent of the standards can be found in the progression of the chapters and lessons, for example:
- In Lesson 4.4, students are multiplying decimals using the standard algorithm. Activity 2 states, “Rachel has a motorized mini bike with a fuel tank that holds 0.32 gallons. The cost of gas in her neighborhood is $2.859 per gallon. Use the interactive to see how much it costs to fill Rachel's mini bike with gas.” (6.NS.2)
- In Chapter 9, there are multiple lessons on finding the area of various shapes, 9.3 Area of Quadrilaterals, Lesson 9.4 Area of Triangles, and Lesson 9.5 Area of Polygons. (6.G.1)
The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades, for example:
- In Lesson 2.2, Teacher Directions state, “Students will begin reviewing fractions within real-world contexts context and practice using diagrams.” There is no explicit relation to content from Grades 4 and 5.
- In Lesson 4.1, Teacher Directions state, “Students should be very familiar with adding numbers such as 100 + 20 + 4 or 800 + 50 + 4.” There is no explicit relation to content from Grade 2.
- In Lesson 9.1, Teacher Directions state, “To start, students will review the concept of area and what it is used for.” There is no explicit relation to content from Grade 3.
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The materials include learning objectives that are visibly shaped by CCSSM cluster headings, and the materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade.
Examples of learning objectives visibly shaped by CCSSM cluster headings include:
- In Lesson 1.1, one of the Learning Objectives is “Understand the concept of a ratio,” and in Lesson 1.3, one of the Learning Objectives is, “Use ratio reasoning to solve real-world problems.” These objectives are visibly shaped by 6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.
- In Lesson 3.4, one of the Learning Objectives is, “Solve word problems involving division of fractions by fractions using visual fraction models,” and in Lesson 3.8, one of the Learning Objectives is, “Find the quotient of two fractions by multiplying by the reciprocal of the divisor.” These objectives are visibly shaped by 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- In Lesson 7.2, one of the Learning Objectives is, “Understand that the process of solving an equation involves determining which values from a specified set, if any, make the equation true,” and this objective is visibly shaped by 6.EE.B, Reason about and solve one-variable equations and inequalities.
The materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, and examples include:
- Lesson 6.6 connects 6.EE.A with 6.EE.B as students evaluate expressions and examine how variables can be used in place of numbers. For example, in Activity 1, Inline Question 4, students use a variable in an expression, “Instead of writing out the number of reflected images, replace this phrase with r. Which expression can you use to find the measure between the two mirrors when there are r reflections? a. $$360+r$$, b. $$\frac{360}{r}$$, c. $$2r$$, d. $$\frac{r}{360}$$.”
- Lesson 7.9 connects 6.RP.A with 6.EE.C. Students solve problems involving ratios and identify how the variables are related. For example, in the Activity 3 Interactive, students see the ratio of the toys to actual size and determine what is the independent and dependent variable, “Use the interactive below and your knowledge of equivalent ratio equations to complete the interactive. Remember that the ratio of the height of toys to the height of the characters is 1:5.”
- Lesson 9.7 connects 6.G.A with 6.NS.B as students solve volume problems using decimal operations. For example, in Activity 3, Inline Question 2 states, “(Fill in the Blank) Recall that the volume of the sandbox is 37.5 cubic feet and one bag of sand that fills 0.5 cubic feet costs $4.50. It will cost the school ____________ to fill the entire sandbox.”
- Lesson 10.4 connects 6.SP.A with 6.SP.B. For example, in Activity 2, Inline Question 3 states, “Here is the test score data again (in ascending order): 77, 83, 83, 85, 87, 90, 93, 94, 99. The median of the test scores is 88.5, since the middle two values are 87 and 90, and the average of those two is 88.5. What is the mean of the whole set?”, and in Activity 3, Discussion Question 1 states, “How can you use measures of center to describe a data set?”
In the Grade 6 materials, there is not a connection between 6.NS.A and 6.EE.B. In Chapter 3, students multiply and divide fractions, but students do not solve equations with variables. For example, in Lesson 3.10, the Inline Questions for Activity 1 are: “1) If Anna has two bottles of polish and each holds 15 ml, how many total ml of polish does Anna have? 30 2) How can Anna find the total number of manicures she can give with all the nail polish she has? Anna can __ the total number of mL of nail polish by the fraction of a mL it took to give one manicure. Highlight the word that goes in the blank: Reciprocal, Multiply, Divide, Subtract 4) If Anna uses $$\frac{9}{10}$$ ml for one manicure and she has 30 ml nail polish, how many manicures can she give? a. $$\frac{3}{10}$$ b. 30 c. 27 d. $$\frac{100}{3}$$ 4) If Anna uses $$\frac{4}{5}$$ ml for one manicure and she has 60 ml nail polish, how many manicures can she give? a. 60 b. $$\frac{1}{75}$$ c. 75 d. 48.”