CK-12 Interactive Middle School Math for CCSS (2020)

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Report Overview

Summary of Alignment & Usability: CK-12 Interactive Middle School Math for CCSS | Math

Math 6-8

The instructional materials reviewed for CK-12 Interactive Middle School Math for CCSS partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials for Grades 6 and 7 meet expectations for focus and coherence by meeting expectations for focus and partially meeting expectations for coherence. In Gateway 1, the materials for Grade 8 meet expectations for focus and coherence by meeting expectations for focus and meeting expectations for coherence. In Gateway 2, the materials for Grades 6-8 partially meet expectations for rigor and practice-content connections by meeting expectations for rigor and partially meeting expectations for practice-content connections. Since the materials did not meet expectations for Alignment, Gateways 1 and 2, they were not reviewed for Usability in Gateway 3.

6th Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Partially Meets Expectations

Gateway 3

Usability

Not Rated

7th Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Partially Meets Expectations

Gateway 3

Usability

Not Rated

8th Grade

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Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Partially Meets Expectations

Gateway 3

Usability

Not Rated

Report for 6th Grade

Alignment Summary

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials for Grade 6 meet expectations for focus and coherence by meeting expectations for focus and partially meeting expectations for coherence. In Gateway 2, the materials for Grade 6 partially meet expectations for rigor and practice-content connections by meeting expectations for rigor and partially meeting expectations for practice-content connections.

6th Grade

Gateway 1

Focus & Coherence

Gateway 2

Rigor & Mathematical Practices

Alignment (Gateway 1 & 2)

Partially Meets Expectations

Gateway 3

Usability

Usability (Gateway 3)

Not Rated

Overview of Gateway 1

Focus & Coherence

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.

Gateway 1

v1.0

Gateway 1

Focus & Coherence

Criterion 1.1: Focus

Criterion 1.2: Coherence

Criterion 1.3: Coherence

Meets Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

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 material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

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 1.1: Focus

Indicator 1A

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 1.2: Coherence

Indicator 1B

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.”

Criterion 1.3: Coherence

Overview of Gateway 2

Rigor & Mathematical Practices

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for rigor and practice-content connections. The instructional materials meet expectations for rigor by developing conceptual understanding of key mathematical concepts, giving attention throughout the year to procedural skill and fluency, and balancing the three aspects of rigor. The materials partially meet expectations for practice-content connections as they explicitly attend to the specialized language of mathematics and partially meet expectations for the remainder of the indicators in practice-content connections.

Gateway 2

v1.0

Gateway 2

Rigor & Mathematical Practices

Criterion 2.1: Rigor

Criterion 2.2: Math Practices

Partially Meets Expectations

Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for rigor. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and do not always treat the three aspects of rigor together or separately. The materials are partially designed so that teachers and students spend sufficient time working with engaging applications of mathematics.

Indicator 2A

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

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include problems and questions that develop conceptual understanding throughout the grade-level.

Chapters 1 and 2 provide students with opportunities to develop conceptual understanding of understanding ratio concepts and use ratio reasoning to solve problems (6.RP.A) with the use of Interactives and Inline Questions. Examples include:

In Lesson 1.2, Activity 2: Tape Diagrams, students manipulate a tape diagram to build a conceptual understanding of how two quantities form a relationship in the form of ratios. The teacher notes describe what the students do independently by stating, “This gives students a chance to practice visualizing and identifying ratios.” (6.RP.1)
In Lesson 1.5, students complete tables of equivalent ratios and use values to answer questions (6.RP.3a). In Activity 2, students complete a table on beats in a sample song: “How many beats are there in this 12 second song sample? Use the table to find the total numbers of beats for 60 seconds of the song.” Once the table is completed, students answer the following inline questions: “1. What is the relationship between 24 seconds and 12 seconds? How can you use this to find the number of beats in 24 seconds? 2. For 12 seconds, the ratio of number beats to number of seconds is ___:12. 3. Since 48 seconds is four times 12 seconds, the number of beats in 48 seconds is ___times the number of beats in 12 seconds. There are ___ beats in 48 seconds. This works because the ratios 25:12 and _____are equivalent.” Examples of practice questions for students to complete are problem 2, “If there are six campers per tent, how many tents for 30 campers?” and problem 10, “Complete the table 72:48, 36:24, 24:16, ___:12, 12:8.”
In Lesson 2.8, Activity 2, students further develop their understanding of ratios by using a double number line to fill in the blanks based on a ratio and answering questions. For example, Item 2 states, “There are 4 thousand (4,000) pet tarantulas in the US. The number of turtles is 150% the number of tarantulas. How many pet turtles are there?” (6.RP.3)

Chapter 3 has multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of multiplication and division to divide fractions by fractions (6.NS.1) through the use of Interactives. Examples include:

In Lesson 3.3, Activity 3, students develop understanding of dividing a fraction by a fraction using a visual diagram. The teacher directions state how the students will use the interactive in the activity to build this conceptual understanding, “Students are given a tape diagram and slider and a fraction (starting at 1). Students can use the slider to divide the diagram and the resulting fraction will appear above the slider.” (6.NS.1)
In Lesson 3.6, Activity 1, students further develop their understanding of division of fractions through an interactive where students manipulate a scale of a map to connect division with fractions. The interactive introduces this to students by stating, “Pirate Captain Jim Hawkins designs a treasure map and draws out a 1 mile by 1 mile map of an island. He divides his map into smaller squares to make it easier to read.” (6.NS.1)
In Lesson 3.9, Warm-Up, students work with an interactive to divide fractions in the real world situation of a water gun fight. The directions for the students explain, “Use the interactive to see how many times you can reload the water gun before you have to run to fill the bucket up with more water. Through this lesson, you will use tape diagrams to model fraction division and find the quotients.” (6.NS.1)

Chapters 6 and 7 have multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of arithmetic to algebraic expressions and reasoning about and solving one-variable equations and inequalities (6.EE.A,B) through the use of Interactives. Examples include:

In Lesson 6.9, Activity 3, students factor expressions using the distributive property. Inline question 4 states, “Write an equivalent expression for $20x+30$ by dividing both terms by 5,” and question 5 states, “Look at the expression $12x+20$ . Select the equivalent expressions.” (6.EE.3)
In Lesson 7.4, Activity 1, students develop understanding of solving equations in the form of $20x+30$ through an interactive. In the interactive, students use numbers to try to isolate and solve for x. The student directions state, “Answering the question above will require knowledge of multiplication equations. Multiplication equations have many similarities with addition equations. Use the interactive below to explore these similarities and to practice solving multiplication equations visually.” (6.EE.7)

Indicator 2B

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for attending to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level, especially where called for by the standards (6.NS.2,3; 6.EE.1,2).

In Chapter 4, the materials develop and students independently demonstrate procedural skill and fluency in adding, subtracting, multiplying, and dividing multi-digit numbers and decimals with standard algorithms (6.NS.2,3). Examples include:

In Lesson 4.2, “there are widget interactives that will guide students through the standard method of adding and subtracting decimals. Students can work with an unlimited amount of times, so they should practice the method until they are comfortable before moving onto the real-world examples” (purple text). The first CK-12 Widget Interactive gives students step-by-step procedures on adding decimals, for example “8.153 + 1.535.” Students independently practice with numerous problems before moving onto the second part of the interactive where they now have to “carry over/borrow” a 1, for example “ $7.242+1.846$ ,” but the same step-by-step procedures are followed. Again, the student can practice independently as much as needed. The second CK-12 Widget Interactive focuses on subtracting decimals, again giving the same step-by-step procedures. The problems get increasingly more difficult, for example, “ $2.972 - 1.141$ ; $6.268 - 1.948$ ,” and students can practice independently with an unlimited amount of problems. (6.NS.3)
In Lesson 4.4, Activity 2 Interactive, students multiply multi-digit numbers. The teacher directions state, “This interactive gives students a walk through for multiplying two decimals. Use the text boxes to evaluate the product one step at a time, after a student has typed in their answer they should press the enter key to see if it is correct. If it is wrong, it will turn red and students can try again. Once a correct answer is entered it will turn black and a new text box will appear.” In Multiplying Decimals with the Standard Method, students independently demonstrate procedural skill with multiplying decimals in all of the Review Questions. For example, Review Question 7, “ $1.7 × 9.691 =$ ____.” (6.NS.3)
In Lesson 4.6, the Warm-Up: Practice Long Division “gives the student practice dividing with the standard method.” The interactive provides the student step-by-step procedures on long division with problems such as 679 divided by 7. In Activity 1, Practice More Difficult Long Division increases the level of difficulty, for example “9460 divided by 43,” but still gives the same step-by-step procedures. In Lesson 4.6, Activity 1 Interactive, students demonstrate fluency in dividing multi-digit numbers as students, “Use these interactives to practice some more challenging and advanced long division problems! Can you answer the most difficult ones? 180482 = ? and 8692505 = ?” (6.NS.2)

In Chapter 6, the materials develop and students independently demonstrate procedural skill in writing and evaluating numerical expressions (6.EE.1) and writing, reading, and evaluating expressions in which letters stand for numbers (6.EE.2). Examples include:

In Lesson 6.1, Activity 1: Can you make the math?, students write an expression from a word phrase, for example Inline Question 1 states, “Which of the following correctly displays ‘one-third of the sum of a number and 5’?” answer choices: a. $\frac{1}{3}(x+5)$ ; b. $\frac{1}{3}+x+5$ ; c. $\frac{1}{3}x+5$ ; d. $\frac{1}{3x}+5$ ,” and Practice Questions 2 states, “Choose an expression for the following phrase: Four less than a number.” (6.EE.2)
In Lesson 6.2, Activity 2 Interactive, students evaluate expressions involving whole-number exponents using sliders to see how the exponent is used to represent multiplication. The teacher directions state, “For this interactive, students can experiment with different values raised to an exponent and see the resulting expanded expression. Students can use the red and blue slider to adjust the values of the exponent.” (6.EE.1)
In Lesson 6.3, Activity 3 Interactive, students demonstrate fluency in writing expressions involving whole-number exponents using the interactive to determine how many lights are needed and identifying it as an expression with exponents. The directions for students state, “Use the interactive below to figure out how many strings of LED lights you would need to decorate the Christmas tree on an ugly Christmas sweater.” (6.EE.1)
In Lesson 6.4, Activity 3: What picture does connect the dots make? states, “This interactive helps students practice evaluating expressions using order of operations with an added bonus of drawing a picture. An expression is given and students can use the buttons at the bottom of the window to choose which operand that should be used next.” For example, Inline Question 1 states, “Which order of operations would you do FIRST in this type of problem? $2(4 + 3)2 ÷ 7$ .” (6.EE.1)

Indicator 2C

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. The materials include multiple opportunities for students to engage in routine application of grade-level skills and knowledge, within instruction and independently. The materials include one non-routine application problem within instruction, but students do not demonstrate independent application of mathematics in non-routine situations.

Examples of students engaging in routine application of grade-level skills and knowledge, within instruction and independently, include:

In Chapters 1 and 2, students engage in familiar real-world scenarios and demonstrate the application of ratio and rate reasoning through the use of questions and interactives (6.RP.3). For example, in Lesson 1.3, Activity 4, Inline Question 1 states, “You mix 12 cups of brown paint by using 3 cups of yellow paint to 4 cups of red paint to 5 cups of blue paint. After painting a portion of a fence you realize that you need more of the same color paint to finish the fence. This time you want to make 26 cups. How many cups of each color do you need?” The answers are multiple choice, and students can use the interactive to check each choice. Also, in Lesson 2.9, Activity 2 states, “1. What do you notice about the relationship between the decimal value and its percent? A. The percent is 10 times the decimal value. B. The percent is 100 times the decimal value. C. The percent is greater than the decimal value.”
In Chapter 7, students write and solve equations of the form $x + p = q$ and $px = q$ (6.EE.7) and use variables to represent two quantities in a real-world problem that change in relationship to one another through the use of interactives (6.EE.9). For example, In Lesson 7.3, Activity 1 Interactive states, “The typical lithium element has 3 protons and 7 total protons and neutrons. You can represent this relationship using an equation: Protons + Neutrons = Mass Number, $P + N = M$ . Substitute our known values to produce the following: $3 + N = 7$ . Use this equation in the interactive below to visually identify the number of neutrons in the lithium atom.” Also, Lesson 7.8, Activity 1 states, “This interactive gives students the chance to use the formula distance = rate x time. To start, select an animal from the drop down menu. The rate will be given at the top and below the students can fill out the table of values for the distance that the animal travels at certain times. If an incorrect value is entered, it will turn red. Once a correct value is entered it will turn black. Students can try different animals by clicking the reset button under the interactive window.” Inline Questions help to formulate an equation, for example, Inline Question 2 states, “Complete the table for the cheetah, The cheetah travels at 105 feet per second. Write an equation for the cheetah’s distance d over time t.”
In Lesson 9.4, Activity 2, students apply their knowledge of the area of a triangle in real-world contexts (6.G.1) as they answer, “Marielle wants to paint a triangular section of her house. One gallon of paint covers 400 square feet. Use the interactive below to find the dimensions of the triangle section.” Inline Question 4 includes, “If Marielle wants to use three layers of paint on the triangular section of her house, how many gallons will be needed?”
In Lesson 10.5, Activity 3, Inline Question 4, students use mean and median to analyze a set of data as they answer, “Look at Helena’s time again: 17.44, 17.5, 17.85, 17.99, 18.11, 18.25, 31.23, 35.55. Remember, the mean time is 21.74 seconds. The median time is 18.05 seconds. What can you conclude by comparing the mean (average) to median (middle)?”

The non-routine application problem within instruction is in Chapter 3. In Lesson 3.9, Activity 3 Interactive, the teacher's directions include, “In this interactive, students will create their own division of fractions problem and use a visual model to help solve the problem. To begin, students can type in the two fractions they want to divide. After the fractions are entered the tape diagrams will show the fraction represented as a diagram. Students can click and drag the red diagram over the blue diagram, then the division equation will appear. Click the Show divisions button to see how the division is represented on the diagram. Students can then type in their answer to the division statement in the textbox. Students will type in the value of the numerator, then the value for the denominator.” (6.NS.1)

Indicator 2D

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials. Examples include:

In Lesson 3.1, Activity 1, students develop conceptual understanding of division of fractions with the interactive, Can You Design a Flag?. The materials state, “Students are given an adjustable flag that measures $1\frac{1}{5}$ m. Students can change the thickness of each portion by clicking and dragging the red points at the bottom of the flag. As the sections are adjusted, the fractions at the bottom will change, showing how much of the flag that portion is taking up. Students can toggle between a flag with 6 stripes and 3 stripes by clicking the button at the bottom right hand corner of the screen.” (6.NS.1)
In Lesson 4.7, students demonstrate fluency with dividing decimals by decimals. For example, the practice problems include, “Find the quotient $31.93÷3.1$ . a) 10.3 b) 9.4 c) 12.6 d) 14.7.” (6.NS.3)
In Lesson 1.5, Activity 3, Inline Questions, students demonstrate application of ratios in the Interactive about bicycles. Some examples include: “1. What is the relationship between 16 teeth in the back gear with 8 teeth in the back gear? How can you use this to find the number of teeth in the front gear for every 8 teeth in back gear? A. Since 8 back teeth is half the number of 16 back teeth, you can divide 44 by 2 to get the number of front teeth associated with 8 back teeth. B. Since 16 back teeth is two times 8 back teeth, you can multiply 44 by 2 to get the number of front teeth associated with 8 back teeth. C. Since 8 back teeth is 16 back teeth minus 8, you can subtract 8 from 44 to get the number of front teeth associated with 8 back teeth. D. Since 16 back teeth divided by 2 is 8 back teeth, you can divide 44 by 2 to get the number of front teeth associated with 8 back teeth. 2. Since 12 is halfway between 8 and 16, the number of teeth in the front gear will be halfway between 55 and the number of teeth associated with 8 back teeth. True/False” (6.RP.3)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

In Lesson 1.3, students develop a conceptual understanding of equivalent ratios through tape diagrams. In the Warm Up: What does “miles per gallon” mean?, students use the interactive to adjust miles and gallons to create equivalent ratios. Inline Question 1 states, “Which ratio of miles to gallon would a person driving the truck like to have?” In Activity 4: How can you mix the color brown with paints?, students apply their understanding of equivalent ratios to mixing paint. Inline Question 1 states, “You mix 12 cups of brown paint by using 3 cups of yellow paint to 4 cups of red paint to 5 cups of blue paint. After painting a portion of a fence you realize that you need more of the same color paint to finish the fence. This time you want to make 26 cups. How many cups of each color do you need?”
In Lesson 2.6, students develop a conceptual understanding of percentages being a ratio per 100 in the interactive in Activity 1, How Much of a Century Have You Lived? The materials state, “To start, students are given a number line with dates from 200 to 2100 in ten year increments. Below there is a text box where students can input their birthday (must be between 2000 and the current date) and press the enter key. Students will see a red line on the timeline showing the imputed date to today, and above that, the percent.” Inline Question 5 states, “(Fill in the blank) When you are 20 years old you will have lived __% of a century. When you are 50 years old you will have lived __% of a century. When you are 100 years old you will have lived __% of a century. When you are 101 years old you will have lived __% of a century.” In Practice, students develop procedural skills as they independently determine percentages as numbers out of 100. The materials state, “Write the following percent as a ratio out of 100. 3% a) $\frac{4}{100}$ b) $\frac{3}{100}$ c) $\frac{2}{100}$ d) $\frac{1}{100}$ .”

Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for practice-content connections. The materials explicitly attend to the specialized language of mathematics. The materials partially: identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content; attend to the full meaning of each MP; provide opportunities for students to construct arguments and analyze the arguments of others; and assist teachers in engaging students to construct viable arguments and analyze the arguments of others.

Indicator 2E

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for identifying and using the Standards for Mathematical Practice (MPs) to enrich mathematics content within and throughout the grade-level. The materials state that teachers should use a few MPs in each lesson, but each lesson does not include guidance on which MPs to use. MPs are explicitly identified in the Teacher Notes, but MPs 7 and 8 are not identified in the materials. Also, no MPs are identified in Chapters 3 and 10, and they are only identified once in Chapters 6, 7, and 8.

Examples of the materials identifying and using the MPs to enrich the mathematics content include:

MP1: This was identified two times in the materials. Lesson 4.6 states, “Students will then work through some division problems within a context and work through a long division puzzle (MP1). If students are still not comfortable with long division, they can work through the widgets at the beginning as many times as they wish. For students who do not need to spend as much time practicing, encourage them to try to challenge problems at the end of the lesson.” Also, Lesson 4.9 states, “students will learn about least common multiples. Students will work through real-world examples and puzzles to practice finding the least common multiple of two or more numbers (MP1).”
MP2: Lesson 1.1 states, “In this lesson, students will learn that a ratio is used to describe the relationship between two quantities.Throughout the lesson it would be helpful to allow them to use the language. This will help them understand how they can use ratio language in everyday situations. With partners, they can compare the number of students, chairs, desks, windows, whiteboards, etc. using ratio language (MP2).”
MP4: Lesson 7.6 states, “As students write their equations, they should be thinking about the independent and dependent variables to help them understand that the equations represent the relationship between the two variables. Once students have written the equations, they should practice interpreting what each part means within the context of the situation (MP4).”
MP6: Lesson 2.3 states, “In this lesson, students will review long division and apply it to solving unit pricing problems. Students will be filling out tables, but it is important for them to practice using the language associated with unit rates. Students can practice reviewing their answers with a partner using ‘price per item’ phrases (MP6).”

There are some instances in which the Mathematical Practices are labeled but do not enrich the content. For example, in Lesson 4.4, MP5 is identified. Students use the Interactive to solve the equation, but they can type numbers into the Interactive until it shows the correct answer, which means students are not using tools strategically to enrich their work with dividing decimals using the standard algorithm. In Activity 2, this process is described in the Teacher Notes, “This interactive gives students a walk through for multiplying two decimals. Use the text boxes to evaluate the product one step at a time, after a student has typed in their answer they should press the enter key to see if it is correct. If it is wrong, it will turn red and students can try again. Once a correct answer is entered it will turn black and a new text box will appear. Students can use the text boxes above each number being multiplied to help with their calculation, but it is not necessary. Once students have multiplied and added all the numbers, they will be able to place the decimal by clicking and dragging the red point to one of the red circles in between each of the numbers in the final answer. Once the student has placed the decimal, click the Check button.”

Indicator 2F

Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of two MPs.

Examples of the materials not attending to the full meaning of MP5 include, but are not limited to:

In Lesson 4.4, the Introduction includes, “Students will continue practicing multiplying decimals; however, this lesson focused on the standard method. Students will begin working with an interactive similar to the ones found in the previous lesson, Multiplying Decimals with Diagrams. There is a widget interactive that will guide students through the standard method of multiplying decimals (MP5).” Students do not select which tools to use as they are provided.
In Lesson 5.4, Activity 2, “In the previous activity, we saw that numbers on both sides of the number line are related. The overlapping numbers in the interactive above are opposite numbers. The opposite of a number, also known as the additive inverse, comes from the additive inverse property. The additive inverse property states that for any real number n, there exists an additive inverse which is the same distance from zero in the opposite direction. Additionally, the sum of a number and its additive inverse will always be zero: n + (-n) = 0. A trick is to change the sign of the number, for example, the opposite of 7 is -7 and the opposite of -15 is 15. Use the interactive below to explore opposite numbers.” Students do not select a tool for this investigation.

Examples of the materials not attending to the full meaning of MP8 include, but are not limited to:

In Lesson 3.9, students use tape diagrams to practice dividing fractions. In the Warm-Up, students answer, “How many times can you reload the water gun?” The materials include, “Use the interactive to see how many times you can reload the water gun without having to run to fill the bucket up with more water. Through this lesson, you will use tape diagrams to model fraction division and solve for the quotients.” Students are given the tape diagram that represents the expression and the steps to solve it. Students do not generalize a pattern from this activity.
In Lesson 4.4, Activity 1, Inline question 3, students answer, “What pattern do you see when finding the number of Newtons? Remember that you multiply the number of kilograms by 10 to find the Newtons. Red Car: 0.454 kgs, 4.54 Newtons; Green Car: 0.681 kgs, 6.81 Newtons; Blue Car: 1.362 kgs, 13.62 Newtons. a) Multiplying by 10 adds a zero to the end of the number. b) Multiplying by 10 moves the decimal place over to the left by 1 place. c) Multiplying by 10 moves the decimal point over to the right by 2 places. d)Multiplying by 10 moves the decimal point over to the right by 1 place.” Students choose from a finite list, which they can do by guessing, instead of generalizing a pattern from repeated reasoning.

Indicator 2G

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

Indicator 2G.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The materials provide opportunities for the students to construct arguments about the content, and examples include:

In Lesson 1.3, Activity 4, Discussion Question, students construct an argument about how the ratio staying the same will impact the results of the paint mixing while taking equvalentance into account. The materials state, “When the total amount of paint increases and decreases but the ratio of paint colors remains equivalent, does the shade of brown change? Use the idea of equivalence to help explain why.”
In Lesson 2.2, Activity 3, Discussion Question, students construct an argument about the appropriate use of unit rates in relation to shark teeth. The materials state, “Use the unit rates to order the sharks from greatest number of teeth to least number of teeth. Did you need to find the unit rate to order the sharks? If not, think of an example of when you would need to find the unit rate to compare numbers of shark teeth.”
In Lesson 6.8, Activity 2, Discussion Question, students construct an argument to determine the appropriate time to substitute numbers in an expression. The question states, “You can only sometimes count the numbers of bumps on the spiral. When is it useful to substitute numbers into the expression to find the number of bumps?”

There are no opportunities for students to analyze the arguments of others, and examples include, but are not limited to:

In Lesson 1.4, Activity 1, Discussion Question, students discuss with the class but do not analyze the arguments of others. The question states, “What are the differences between a tape diagram and a number line? Discuss your answer with your class or in the CK-12 Cafe.”
In Lesson 3.6, Activity 2, Discussion Question, students use mathematics to explain their thinking but do not analyze other students’ reasoning. The question states, “The largest IMAX theater in the world is in Melbourne, Australia. It is 105 feet by 75 feet. Compare the area of the largest IMAX screen with the standard IMAX screen and the "local movie theater" screen from the example.”
In Lesson 10.5, Warm-Up, the Discussion Question states, “What is the difference between center and variability? Discuss in class or in the CK-12 Cafe. Answers may vary. Encourage students to point out that it is not guaranteed the 50% of the data values occur above or below the mean.”
In Lesson 10.8, Activity 3, Discussion Question, students describe which data set to use but do not analyze the arguments of others. The question states, “The mean of the dataset is 16.92 ounces and the mean absolute deviation is approximately 1.15 ounces. Which set of statistics do you feel better describes the data: the median and the interquartile range, or the mean and the mean absolute deviation (MAD)?”

Indicator 2G.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. The materials include some examples of assisting teachers in engaging students to construct viable arguments and analyze the arguments of others, but there are also multiple instances where the materials do not assist teachers.

Examples of the materials assisting teachers to engage students in constructing and/or analyzing the arguments of others include:

In Lesson 4.8, Activity 1, Interactive Plix: GCF Using Lists, the Teacher Notes state, “The last question prompts students to construct an argument for why the GCF is always a natural number and never a fraction. You can remind students that natural numbers are whole numbers not including the number 0 (1, 2, 3, 4, etc).”
In Lesson 5.1, Warm-Up: Sea Level, the Teacher Notes state, “Allow students to turn and talk and build off each other’s ideas in a whole class setting. By the end of the discourse, students should be able to articulate that the sea animals are below and the birds are above sea level, and that sea level represents 0 because it has no elevation, the other animals are located somewhere in relation to sea level.”
In Lesson 10.9, Activity 3, Discussion Question, the Teacher Notes state, “Answers may vary. Encourage students to use numerical evidence from the datasets to support their argument. One missing piece of information is the reason behind the two grades of 0. Perhaps the students did not know any answers or perhaps they were absent. Knowing this information would likely affect the students' stance on which side did better.”

Examples where the materials do not assist teachers to engage students in constructing and/or analyzing the arguments of others include:

In Lesson 3.8, Activity 2, Supplemental Questions, the Teacher Notes state, “Why is dividing by a fraction, the same as multiplying by the reciprocal of the fraction? Students will have different explanations. They may refer to the tape diagram and explain how many times a fraction can divide into a whole number. They may note that the number of parts the bars are divided into is the denominator and the groupings of the parts is the numerator.” The materials do not assist teachers in having students analyze the arguments of others.
In Lesson 5.3, Warm-Up, the Teacher Notes encourage students to discuss their answers to questions provided to the teachers. The Teacher Notes state, “Allow students to discuss and answer the questions. How does the use of a negative affect the meaning of the numbers above? The negative identifies whether the money is owned or owed. How does the distance from zero affect the meaning of the numbers above? The closer to zero, the smaller the debt or value. The farther from zero, the greater the debt or value.” The materials encourage discussion among students, but they do not assist teachers in having students analyze the arguments of others.
In Lesson 8.4, Warm-Up, Discussion Question, the Teacher Notes indicate that there may be different answers from students, but there is no assistance as to how students construct an argument about the weight. The Teacher Notes state, “Allow students to answer. Answers may vary. The beam must weigh either 18 tons or less. The beam could weigh 2 tons. The beam cannot weigh 20 tons.”

Indicator 2G.iii

Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for explicitly attending to the specialized language of mathematics. The materials provide instruction on communicating mathematical thinking using words, diagrams, and symbols. Examples include:

In Lesson 1.1, the Teacher’s Edition includes, “In this lesson, students will learn that a ratio is used to describe the relationship between two quantities. They will use ratio language to describe quantities involving recipes, colored blocks, and butterflies. Throughout the lesson it would be helpful to allow students the time to practice using ratio language to describe things in the classroom (MP6).”
In Lesson 5.6, at the beginning of the Lesson, the Teacher Notes state, “It would be helpful to define the terms horizontal and vertical, so students can use these terms throughout the lesson to describe an object's location on a coordinate plane.”
In Lesson 5.7, Warm-Up, “we can describe the position of an object by the location on the x-axis number line and the y-axis number line. The location of the object can be written using the coordinate (x, y) where x is the location of the object along the x-axis and y is the location of the object along the y-axis. Use the interactive below to practice using coordinate notation.”

The materials use precise and accurate terminology and definitions when describing mathematics, and the materials also support students in using the terminology and definitions. There is no separate glossary in these materials, but definitions are found within the units in which the terms are used. The vocabulary words are in bold print. Examples include:

In Lesson 1.1, Activity 1, Inline Questions, Example 2, “Angie wants to bake cookies for a bake sale. The recipe says “for every 1 cup of butter use 3 cups of flour.” You can use the word ratio to show the relationship between quantities. What is the ratio of butter to flour in one batch of cookies?”
In Lesson 5.5, Activity 1, “The absolute value of a number is the distance of that number from zero. The absolute value of 23 is 23 because it is 23 units from zero. The absolute value of -12 is 12 because it is 12 units from zero. The absolute value symbol is written using a straight vertical line on either side of the number or expression. The absolute value of 5 is written |5|.”
In Lesson 10.4, the Warm Up includes, “A measure of center is a single number used to describe a set of numeric data. It describes a typical value from the data set. Measures of center include the mean and the median. The mean (or what is more commonly referred to as the average) of a data set is the sum of the data values divided by the number of data values in the set. As you saw in the warm-up, the mean can be thought of as "evening out" the data values. The range is a measure of spread. You can find the range by taking the greatest data value and subtracting the least data value. In other words, it is the difference between the maximum and minimum data point.” Activity 2 includes, “The median represents the middle value of an ordered data set. It is another measure of center.”

Criterion 2.2: Math Practices

Overview of Gateway 3

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Gateway 3

v1.0

Gateway 3

Usability

Criterion 3.1: Use & Design

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

Criterion 3.5: Technology

Not Rated

Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3A

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

Indicator 3B

Design of assignments is not haphazard: exercises are given in intentional sequences.

Indicator 3C

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

Indicator 3D

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Indicator 3E

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Criterion 3.1: Use & Design

Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3F

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

Indicator 3G

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

Indicator 3H

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

Indicator 3I

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

Indicator 3J

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

Indicator 3K

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Indicator 3L

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

Criterion 3.2: Teacher Planning

Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3M

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

Indicator 3N

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Indicator 3O

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Indicator 3P

Materials offer ongoing formative and summative assessments:

Indicator 3P.i

Assessments clearly denote which standards are being emphasized.

Indicator 3P.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Indicator 3Q

Materials encourage students to monitor their own progress.

Criterion 3.3: Assessment

Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3R

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Indicator 3S

Materials provide teachers with strategies for meeting the needs of a range of learners.

Indicator 3T

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Indicator 3U

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

Indicator 3V

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Indicator 3W

Materials provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3X

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

Indicator 3Y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.4: Differentiation

Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3AA

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

Indicator 3AB

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Indicator 3AC

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

Indicator 3AD

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Indicator 3Z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Criterion 3.5: Technology

2020