Alignment: Overall Summary

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials for Grade 7 meet expectations for focus and coherence by meeting expectations for focus and partially meeting expectations for coherence. In Gateway 2, the materials for Grade 7 partially meet expectations for rigor and practice-content connections by meeting expectations for rigor and partially meeting expectations for practice-content connections.

See Rating Scale Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
12
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
14
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 1 states, “There is a wall in your living room that is 13 feet wide. Your TV is centered on the wall. You want to hang up two pictures on either side of the TV. Each picture should be 4.25 feet away from the center of the TV. a. Label where the center of the TV is on the number line above. b. Write two expressions to calculate where each picture will go. Then label their positions on the number line.” (7.NS.1)
  • In Chapter 3, Item 4 states, “Gary’s birthday is coming up! He wants to book the party room at his favorite restaurant. The restaurant requires him to spend a minimum of $200 in order to book the party room. Each person’s meal costs $12.50. He also plans to buy a cake from the restaurant for $45. a. Using the minimum requirement, write an inequality to represent the total amount he will spend at the restaurant for p people. b. Solve the inequality for p. Graph the solution on a number line. c. What is the least number of people you can have at your party? Show your Reasoning. Hint: remember that you can’t have a fraction of a person.” (7.EE.4b)
  • In Chapter 4, Item 2 states, “At a restaurant, a burger is $10.99 and a drink is $2.00. a. The tax rate is 8.5%. What is the cost of a burger and drink including tax? Round your answer to the nearest cent. b. If you want to tip your waiter 20% of the total cost, including tax, how much should you tip? Round your answer to the nearest cent.” (7.RP.3)
  • In Chapter 7, Item 2 states, “Jessie is playing a game where a red ball, a blue ball and a gold ball are each placed under a cup. Then the three cups are shuffled around. If Jessie correctly guesses which cup has a gold ball underneath it she wins the game. a. If Jessie has no idea which cup the ball is under, what is the probability that she guesses correctly? Write your answer as a fraction in simplest form. If Jessie plays the game 12 times, how many times would you expect her to guess correctly?” (7.SP.6,7)
  • In Chapter 8, Item 1a states, “A news reporter wants to estimate how many of the 900,000 registered voters in Rhode Island plan to vote for the candidate Fiona Rodriguez in the state senatorial race. The reporter goes to a mall in a major city and surveys 50 people. He finds that 35% of people plan to vote for Fiona Rodriguez. Why might this sample not be representative of the population?” (7.SP.1)

Criterion 1b

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.
4/4
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Criterion Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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.
4/4
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 four out of eight, which is approximately 50%.
  • The number of lessons devoted to major clusters of the grade (including supporting clusters connected to the major clusters) is 53 out of 80, which is approximately 66%.
  • The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 58 out of 88, which is approximately 66%. 

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 66% of the instructional materials focus on major clusters of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
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Criterion Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 7 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 1.9 connects 7.G.1 and 7.RP.A. Students work with scaled drawings and solve problems with the use of proportions. For example, in Activity 1, the Teacher’s Edition directions are, “Discuss with students why scale drawings are proportional relationships. Why are they included in this chapter?... Also we can write the scale factor into an equation of proportionality.” Also, in the Activity 2 Interactive, students use proportions to create a scaled drawing, “Tiana wants to rearrange the furniture in her bedroom. She knows that it is 12 feet by 10 feet, with a door and window on the opposite wall. In her bedroom, she needs her bed, a desk, bookshelf, dresser, and chair. She is drawing a scale mapping on graph paper and decides to make 1 foot = 2 squares (0.50 inch). Use the interactive to rearrange her furniture.”
  • Lesson 4.10 connects 7.G.1 and 7.RP.3. Students use proportional relationships to solve problems involving scale and percent. For example, in Activity 1, Inline Question 1 states, “Which methods correctly convert a scale factor of 45 to a percent?” In Activity 2, students scale an image, “A scale model of a car was built at 12.5% scale. If the width of the model car is 9.75 inches, what is the width of the real car?”
  • Lesson 7.6 connects 7.RP.2 and 7.SP.7. Students find the probability of possible outcomes with objects that have constant proportions. For example, in Activity 1 Interactive, students use the proportions of a dart board to predict probability, “Below is a very basic dartboard, without a bullseye. There are 20 sections on the dartboard, and you have an equal likelihood of hitting any of them. The numbers around the circle represent the point values for each section if you are keeping score. Find probabilities for different sets of numbers (numbers less than 8, multiples of 3, etc) by clicking on the sections. The fraction will adjust accordingly.”
  • Lesson 8.10 connects 7.SP.2 and 7.RP. Students examine samples to make generalizations using ratio understanding. The Warm Up states, “You will be using sample proportions to estimate the population proportions. A sample proportion is the ratio of members in the sample with a certain attribute to the total number of members in the sample.”

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 88 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 lessons can be completed in one class period. For the majority of the lessons, the length ranges from 40 to 50 minutes.
  • There are 8 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 80 lessons that would each last for one day, and there are 8 days for 8 chapter assessments, for a total of 88 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.
1/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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. Seventh 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 7 standards.

Examples of grade-level standards at the beginning of the lesson include:

  • Lesson 3.2, Rewriting Expressions Using the Distributive Property, lists 7.EE.1.
  • Lesson 5.4, Cross Sections of Prisms, lists 7.G.3.
  • Lesson 8.5, Introduction to Sampling, lists 7.SP.1.

In a few Chapters in the Teacher Edition, previous or future work from Grade 7 is listed, but there is no learning identified from prior or subsequent grade levels. Examples include:

  • In Chapter 2.1, the purple notes state, “We will start with integers and then apply the rules learned to fractions and decimals. Most of this should be a review for the students.” 
  • In Chapter 3.6, the purple notes state, “Students should know how to solve one-step equations, interpret expressions, and check solutions.” 
  • In Chapter 6.11, the purple notes state, “Even though the surface area of pyramids was explored earlier, the volume of one is not covered until 8th grade.”

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: 

7.RP.A, Analyze proportional relationships and use them to solve real-world and mathematical problems.

  • In Lesson 1.6, Activity 1, Question 2 states, “If $$c = 0.79s$$ is the equation that represents the proportional relationship in the interactive, what is k?” (7.RP.A)
  • In Lesson 4.2, Activity 2, Question 2 states, “Jake also has a monthly car note of $575. About what percent of his income is this?” (7.RP.3)

7.NS.1, Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. 

  • In Lesson 2.3, Warm Up states, “Think about the three cases of integer addition: when the addends (the two numbers that are being added) are both positive, both negative, or one of each. Discuss how you approach an addition problem differently in each of these cases and what sign the answer has.” (7.NS.1)
  • In Lesson 2.6, Question 7 states, “Solve $$-4 + 5 - 7$$” (7.NS.1)

7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  • In Lesson 3.10, Activity 2 states, “Are there any values of n such that + 1 < n?” (7.EE.4b)
  • In Lesson 6.7, Activity 1, Question 4 states, “If you are looking at a square pyramid that has a base length of x, a slant height of y, and the pyramid height of z, which of the following are true? a)The area of the base is $$4x$$. b) The area of the base is $$x^2$$. c) The area of a triangular face is $$12xy$$. d) The area of a triangular face is $$12xz$$.” (7.EE.4a)

The full intent of the standards can be found in the progressions of the chapters and lessons, for example:

  • In Lesson 4.2, students solve multiple word problems related to percentages. For example, in Activity 1, Question 1, students identify how percent is found, “Which of the following can be used to find 60% of 450 customers? A. $$450 - (45 + 45 + 45 + 45)$$ b. $$225 + 45$$ c. $$45 + 45 + 45 + 45 + 45 + 45$$ d. $$225 - 45$$”. In Activity 3, Question 1, students use ratios and percentages to solve the problems, “Jake pays $1625 per month in rent. He makes $6735 per month. Which equations can be used to correctly calculate the percent of Jake's salary on rent each month?” (7.RP.3)
  • In Lesson 7.10, students solve multiple problems involving probability. In Activity 2, Question 4, students reason about likelihood of probability by frequency, “The outcomes are not equally likely because the likelihood of getting a hit is less than 0.5. About one-third (0.333) of the time, the batter will hit the ball, and two-thirds of the time, he will not. Using a die roll to simulate an at-bat, what will the numbers 1 through 6 represent?” (7.SP.7)

The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades, for example: 

  • In Lesson 1.1, Teacher Directions state, “Unit rates are the constant theme throughout this chapter and should be a review from 6th grade.”
  • In lesson 2.1, Teacher Directions state, “We will start with integers and then apply the rules learned to fractions and decimals. Most of this should be a review for students.” There is no explicit relation to content from grade 6.
  • In Lesson 6.1, Teacher Directions state, “We will focus on triangles and quadrilaterals because students should be familiar with those formulas from 6th grade.”

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 1.4, one of the Learning Objectives is, “Decide whether two quantities are in a proportional relationship by graphing on a coordinate plane,” and in Lesson 4.2, one of the Learning Objectives is “Find the part given the whole and the percent in a real-world context.” These objectives are visibly shaped by 7.RP.A, Analyze proportional relationships and use them to solve real-world and mathematical problems.
  • In Lesson 2.3, one of the Learning Objectives is, “Understand that p+q is a distance |q| from p to the right if q is positive and to the left if q is negative,” and in Lesson 2.6, the Learning Objective is, “Apply properties of operations as strategies to add and subtract rational numbers.” These objectives are visibly shaped by 7.NS.A, Apply and extend previous understandings of operations with fractions, to add, subtract, multiply, and divide rational numbers.
  • In Lesson 3.5, one of the Learning Objectives is, “Solve real-world problems involving algebraic expressions with rational numbers,” and in Lesson 3.6, one of the Learning Objectives is, “Solve word problems leading to two-step equations with rational numbers.” These objectives are visibly shaped by 7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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 2.3 connects 7.NS.A with 7.EE.B. For example, in Activity 3, Stock Market states, “A particular stock started at $11.15 at the beginning of the day. After 3 hours, it was up $0.67 and at the end of the day it was down $2.25. What was the value of the stock at the end of the day? Use the number line interactive below to help you find the answer.” Also, Inline question 5 states, “On Monday, a stock rose $.50. On Tuesday, it dropped $.15. On Wednesday, it dropped $.12. Thursday it rose $.42. Friday it fell $.07. What was the overall loss?”
  • Lesson 3.4 connects 7.EE.A with 7.EE.B. Students rewrite expressions in different forms while using variables to represent numbers. For example, Activity 3 Interactive states, “Your math teacher, Miss Nomer, gives you an extra credit problem to figure out her age. Half of her age three years ago is equal to one-third of her age nine years from now. How old is she currently? All the pieces to figure out Miss Nomer's age are in the box below. Your job is to make two equivalent expressions from the clues above. Set them equal to each other so you can determine her age and get extra credit.”
  • Lesson 4.3 connects 7.NS.A with 7.RP.A. Students use operations to solve real-world problems involving percentages. For example, Warm-up Inline Question 1 states, “The original value of a house is $300,000. The house is now worth $600,000. Which of the following statements are true? a. The new price is 200% of the old price. b. The new price is 2 times the old price. C. The new price is 300% of the old price. d The amount of increase was $300,000.”
  • Lesson 4.6 connects 7.RP.A with 7.NS.A. Students interpret and calculate percent error and absolute error. In Activity 1, Inline Question 3 states, “Which of the following statements are true about the distance between -4 and 7?”, and Review Question 5 states, “A student determines the volume of a cube to be 4.6cm3. What is the percent error if the correct volume of the crystal is 4.3cm3?”

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

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Gateway Two Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content and explicitly attend to the specialized language of mathematics. The materials partially meet expectations for the remainder of the indicators in practice-content connections.

 

Criterion 2a - 2d

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.
7/8
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Criterion Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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.

Chapter 1 has multiple opportunities for students to work independently to develop conceptual understanding of analyzing proportional relationships and using them to solve real-world and mathematical problems (7.RP.A) through the use of interactives. Examples include:

  • In Lesson 1.6, Activity 1, students use the interactive to develop understanding of proportional relationships by manipulating numbers to see a total cost based on the amount being bought. The student directions state, “A website offers music downloads for $0.79 per song. Use the slider to see how the cost changes as you increase the number of songs you buy. Use the record button to mark different price points on the table below, then using the data given.” (7.RP.2)
  • In Lesson 1.8, Warm-up, students manipulate the sliders in the interactive to solve proportional relationships involving percents by finding out the discount on the amount being spent. The student directions state, “Use the interactive and slide the tape diagram to adjust for each fraction. This will help you determine the discount. Then, subtract the discount from the original price to get the sale price.” (7.RP.3)

Chapter 2 has multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of operations with fractions (7.NS.A) through the use of interactives. Examples include:

  • In Lesson 2.3, Activity 3, students develop a conceptual understanding of the distance between numbers by manipulating the sliders on the interactive activity and answering questions such as, “Which equation models the situation in the problem? A. $$11.15 + (-.67) + (-2.25)$$ B. $$11.15 + .67 + 2.25$$ C. $$11.15 + .67 + (-2.25) $$ D. $$11.15 + (-.67) + 2.25$$”. (7.NS.1)
  • In Lesson 2.7, students multiply rational numbers. In Activity 1, the context is owing friends money, and students answer, “Annie owes $6 to 3 friends. How much money does she owe? Remember owing money means you have a negative amount.” In Activity 2, the context is rewinding to the beginning of a TV show. Both of these contexts develop an understanding of multiplying signed rational numbers. (7.NS.2a) Practice questions at the end of the lesson in the student materials include problem 1, $$ (-9) × (+8)$$, and problem 2, $$(-5) ×(3)$$, and practice questions from the teacher materials include problem 1, $$(2)(-8)(-3)$$, and problem 4, $$4 ×(-50)$$.
  • In Lesson 2.10, Activity 2, students convert fractions to decimals in the interactive to develop understanding of multiplying and dividing rational numbers. The student directions state, “Use the interactive to match the fractions and decimals in the table. Then, select either T for terminating decimals or R for repeating decimals in the last column.” (7.NS.2)

Chapter 3 has multiple opportunities for students to work independently to build conceptual understanding of using properties of operations to generate equivalent expressions and solving real-life and mathematical problems using numerical and algebraic expressions and equations (7.EE) through the use of interactives. Examples include:

  • In Lesson 3.3, Activity 2, students manipulate the interactive to sort expressions that are equivalent to the given expression, which develops their understanding of equivalent expressions. The teacher notes describe how the students will be independently working by stating, “For this interactive, students practice matching equivalent expressions to the expression given at the top. Students can click and drag the expressions on the right into the yes or no column.” (7.EE.2)
  • In Lesson 3.7, Activity 1, students develop the conceptual understanding of solving multi-step problems with the interactive by balancing the equations to solve for x. The student directions state, “The interactive will tell you if it is not balanced and when the equation is solved correctly. Click on the buttons at the top of the interactive to add and subtract ones and x's. At the end, division buttons will appear, so that you can isolate x”. (7.EE.3)

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 (7.NS.1,2; 7.EE.1,4a).

In Chapter 2, the materials develop and students independently demonstrate procedural skill in adding and subtracting (7.NS.1) and multiplying and dividing (7.NS.2) rational numbers. Examples include:

  • In Lesson 2.3, Activity 2 Interactive, students demonstrate procedural skill in adding rational numbers written as decimals. The directions state, “You may remember adding decimals and fractions from last year. Adding decimals is not that much different than adding whole numbers, just make sure you line up the decimal point. As with integers, whichever rational number has the greater absolute value, the answer will have that sign. You may use the interactive below to brush up on adding decimals.” (7.NS.1)
  • In Lesson 2.4, the Warm-Up: Subtracting Integers states, “Subtraction is taking away a value from another. Adding -4 would mean moving 4 units to the left. With subtraction it is the opposite. Subtracting -4 would mean moving 4 units to the right. Therefore subtraction can also be defined as adding the opposite. $$2 - (-4) + 2 + 4$$. When doing subtraction problems change the problem to adding the opposite before starting.” Students complete practice problems, for example, Activity 1: Diving Depths, Inline Question 2 states, “If $$-5 - 12$$ models Fatima’s diving depth, what is another way to write this problem?” (7.NS.1)
  • In Lesson 2.7, students multiply rational numbers. In Activity 1: Annie’s Debt and Activity 2: TV Show Skip Back, students see the results of multiplying numbers with different signs. In Activity 3: Are you -8?, students determine which expressions are equal to -8. For example, Inline Question 1 states, “How would you multiply $$-\frac{2}{3}×2\frac{3}{4}$$?” The practice questions at the end of the lesson, such as “$$(-5) ×(3)$$,” give independent practice on multiplying integers. In Lesson 2.9, Review Questions, students demonstrate procedural skill in multiplying rational numbers, and some examples include “6. Multiply the following rational numbers. $$\frac{1}{11} ×\frac{22}{21} × \frac{7}{10}$$ and “9. Multiply: $$\frac{1}{3} ×\frac{4}{12} × \frac{2}{9}$$. (7.NS.2)

In Chapter 3, the materials develop and students independently demonstrate procedural skill in applying properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients (7.EE.1) and writing equations of the form $$px + q = r$$ and $$ p(x + q) = r$$ to solve word problems (7.EE.4a). Examples include:

  • In Lesson 3.2, Review Questions, students demonstrate procedural skill in applying properties of operations to expressions with multiple examples. Some examples include, “1. Simplify the expression using the distributive property and combining like terms until there are two terms. $$-5(6t-8)-6(t+3)$$” and “4. Use the distributive property to write an equivalent expression. $$(-x+4)$$.” (7.EE.1)
  • In Lesson 3.3, Activity 2: Are You Equivalent?, students develop procedural skill in applying properties of operations to determine equivalent expressions. The materials state, “Analyze the expression $$4(x-3) - 2(5x+6)+10.$$ In the box, there are several other expressions that may or may not be equivalent to it. Sort them depending on if they are equivalent or not to $$4(x-3) - 2(5x+6) +10$$.” Also, students develop skill in the practice questions at the end of the lesson, for example, “8. Simplify the expression $$\frac{4x}{2} - 2(x+13)-5^2$$.” (7.EE.1) 
  • In Lesson 3.7, students independently demonstrate procedural skill in solving two-step equations in the Review Questions, for example, “10. $$13 - 8x = -3$$.” (7.EE.4a)

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
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 Chapter 2, students solve problems using the four operations with rational numbers (7.NS.3). For example, In Lesson 2.4, Activity 2 Interactive states, “Gina has a savings account with $23.64 in it. She makes a withdrawal of $15.67 and then a deposit of $6.78. How much money is in her account?” Also, in Lesson 2.7, Activity 1 Interactive states, “Annie owes $6 to 3 friends: Lou, Sue, and Hugh. How much money does she owe in total? Use the interactive to drag the dollar bills from Annie's wallet into Lou, Sue, and Hugh's wallets. Remember that owing money means you have a negative amount.”
  • In Chapter 3, students solve multi-step problems posed with positive and negative rational numbers in any form (7.EE.3). For example, in Lesson 3.5, Activity 2 Interactive states, “A new skatepark, Sk8er L8er, is putting in two kickers, with a grind box in the middle, like the picture. To make the feature ready to skate on, the skatepark must also put a layer of Skatelite over the surface to make it smooth and perfect for tricks. The skatepark needs to figure out how many linear feet of Skatelite to buy for this feature. The ramp on each kicker is x feet long, and the grind box is $$\frac{3}{4}$$x feet long. The height is $$\frac{1}{2}$$x feet.” Also, in Lesson 3.8, Review Question 1 states, “1. Corey is taking a bus to her grandparent’s house, 58 miles away. The fee is $12.00 plus $0.12 per mile. If her parents send her $15.00, will she be able to make it all the way to her grandparent’s house?”
  • In Chapter 4, students use proportional relationships to solve multistep ratio and percent problems (7.RP.3). For example, in Lesson 4.2, Activity 2 Interactive states, “Jake is renting an apartment for $1,800 a month, and his monthly income is $5,625. What percent of Jake’s monthly income is his rent? Begin by using a tape diagram to estimate the percent of Jake’s monthly income that his rent is.” Also, in Lesson 4.6, Review Question 5 states, “A student determines the volume of a cube to be 4.6 cm$$^3$$. What is the percent error if the correct volume of the crystal is 4.3 cm$$^3$$?”
  • In Chapter 6, students use formulas related to circles to solve problems (7.G.4). For example, in Lesson 6.3, Activity 3, Inline Question 3 states, “Sherry wants to put some decorative tile around the pool (circular pool with a diameter of 20 feet). If each tile is 6 inches long, how would she determine how many tiles she needs?”

The non-routine application problem within instruction is in Chapter 3. In Lesson 3.6, Activity 3, Supplemental Question, the Teacher Notes state, “Come up with another word problem for this equation: 8x − 3 = 21.”

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 2, students develop conceptual understanding of combining like terms. Students sort different parts of expressions in the interactive activity. Teacher directions state, “This interactive is a visual example of combining like terms, given expressions with variables. The instructions mention the blue box on the graph represents 7x. Students will also see four yellow boxes each with their own values. Students can click and drag the red points at the corner of each of the boxes to move the boxes around. Students can add to the blue box by stacking the yellow boxes on top of the blue box ... Students can also visualize subtraction by placing the yellow boxes in the blue box.” (7.EE.2)
  • In Lesson 2.4, Interactive 3, students develop procedural skill by practicing subtraction with decimals. For example, Inline question 1 states, “Calculate: -56.902 - 12.45 - (-13.58) - (-27.9).  a) -41.567 b) -16.945 c) 33.124 d) -27.872.”  (7.NS.1)
  • In Lesson 1.6, Review Questions, students represent and solve proportional relationships presented through different real-world scenarios. For example, Question 5 states, “The amount of money Sebastian spends on shoes can be represented by the equation y = 50x , where x is the number of pairs of shoes he owns and y is the total cost. How many pairs of shoes does Sebastian own if he's spent $650?” (7.RP.2)

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 1.9, Activity 1, students develop understanding of the effects of scale factors in geometric shapes. The materials state, “Take Brainy’s photo and enlarge it and shrink it. See what sort of conclusions you can make about scale drawings. Determine what the scale factor would be if he started with an 8” by 8” photo and made a duplicate of 6” by 6”.” Later in the lesson, students build procedural skill in finding scale factors in the review questions. Review Question 4 states, “A map has a scale of 1 inch = 3 feet. What is the scale factor of the map?”
  • In Lesson 4.5, Activity 1: Mark Ups Interactive, students develop a conceptual understanding of using equations for percent problems. The materials state, “Use the interactive below to explore how markup rates affect the sale price of a product. In this interactive, students will get to experiment with markups and item prices, and see how that will affect the resulting purchase price.” Inline Question 3 states, “Change the markup rate to 160%. At this rate, what will you multiply each purchase price by to get the selling price?” In the review questions at the end of the lesson, students apply their knowledge of percents and equations to solving real-world problems. Review Question 2 states, “The marked price of a sweater at the clothing store was $24. During a sale a discount of 25% was given. A further 15% discount was given to the customers who have the store’s credit card. How much would a member customer need to pay for the sweater during the sale if the customer paid with the store's credit card? Round your answer to the nearest cent.”
  • In Lesson 6.3, students develop procedural skill in finding the circumference and area of circles. In Activity 2, students “Use 3.14 for ???? to determine the area and circumference of the circles in the interactive.” Inline Question 1 states, “The area of a circle is 81????. What are the steps to find the circumference?” In Activity 4: Room for pi?, students apply their understanding of circles to real-world situations. For example, Inline Question 3 states, “Sherry wants to put some decorative tile around the pool. If each tile is 6 inches long, how would she determine how many tiles she needs?”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
7/10
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Criterion Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for practice-content connections. The materials identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content and explicitly attend to the specialized language of mathematics. The materials partially attend to the full meaning of each practice standard, provide opportunities for students to construct arguments, and partially 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for identifying and using the Standards for Mathematical Practice (MPs) to enrich mathematics content within and throughout the grade-level. All MPs are explicitly identified in the Teacher Notes and used to enrich the content. 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.

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

  • MP1: Lesson 6.8 states, “In this lesson, students will be working with composite shapes, specifically finding their surface area. Students will use what they know about finding the surface area of rectangular and triangular prisms. Students will learn how to break apart composite solids into smaller shapes they are familiar with. They will need to determine which faces should be included in the total surface area (MP1).”
  • MP2: In Lesson 1.3, Activity 1, Interactive states, “This interactive works the same way as the previous one (three sliders and three equal numbers) however, the numerator for the first fraction increases by hundreds up to 4,000, and the denominators increase by ones up to 10. Students can use the questions below to reason quantitatively and contextualize the units within the house painting scenario (MP2).”
  • MP4: In Lesson 3.1, Activity 3, Discussion Question states, “Students may think it's silly to compare ordering fast food to combining like terms. However, it is a very useful thing in this scenario. There are several different items to order and it is much easier to order them if it is combined. It is also easier for the restaurant to receive the order in this way because there will be less room for error. Discuss why this is with your students to make the example more applicable (MP4).”
  • MP5: Lesson 5.3 states, “It may be helpful for students to try drawing various orientations of one of the triangles onto patty paper or a small piece of tracing paper (MP5). By flipping and rotating the tracing, they can see that the triangle still has the same angle measures and side lengths as the interactive.” 
  • MP6: In Lesson 6.2, Activity 3, Discussion Question states, “You just derived the formula for the area of a circle using orange segments! The area of any circle is A=pi r^2. Discuss what all the parts of the formula mean.” This Discussion Question encourages students to use precise mathematical language when discussing what each symbol in the formula represents.
  • MP7: In Lesson 3.9, Activity 1, Discussion Question states, “Much like equations, there are several different ways to write equivalent inequalities, in words and in symbols. Both of the phrases in #5 do represent the same inequality, but they will look very different. The first is $$5x + 6 < 9$$ whereas the second is $$9 > 6 + 5x$$. Discuss with students that these are the same (MP7).”
  • MP8: In Lesson 5.2, Activity 2 states, “Through the interactive and inline questions, students will use repeated reasoning to develop the general method for finding the range of the length of the third side given two sides (MP8).”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 2.4, Activity 3, Interactive, Teacher Notes, “In this interactive, students can model withdrawals and deposits on a number. Students can use the drop-down menu to choose whether they want to perform a withdrawal or deposit. Then they enter the dollar amount. After they click 'Enter' the transaction will appear on the vertical number line and as a "Bank Statement" showing the original amount, the amount change, and the resulting amount. Students can use this to help them answer the questions that follow (MP5).” Students do not select which tools to use as they are provided.
  • In Lesson 5.4, Activity 2, Part 2, the teacher’s edition states, “The main goal is for students to determine how to manipulate the interactive to produce the desired cross section (MP5). As an assignment, you could have students take screenshots of each of their cross sections.” Students do not select which tools to use as they are provided.
  • In Lesson 6.3, Activity 2, Teacher Notes below the Inline Questions, “The interactive has 10 different problems within it. Make sure students are comfortable with the formulas, by having them either take screenshots of their work or recording their answers in their notebooks. (MP5) The inline questions have the students work backward, so they need to be comfortable with solving for a variable. You may need to review what a square root is (or square number too).” Students do not select which tool to use as they are provided.

In the two lessons below, the materials attend to MP8. However, the materials do not attend to the full meaning of MP8 through these two lessons.

  • In Lesson 3.2, Activity 3, Part 2, Teacher Notes, “The last questions should lead to students realizing that they are doing the opposite (MP8). So, with a problem like $$6(2x + 5)$$, students know to multiply the 6 by the $$2x$$ and the 5. If they are given $$12x + 30$$, they now realize that they are dividing by 6 to pull out the GCF.”
  • In Lesson 7.11 Introduction in the Teacher Notes, “Much like the previous lesson, this lesson is about simulations. Now, students will represent compound events, The process is not that different, but how the results and probabilities are determined is (MP8).”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

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.
1/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 6.3, Activity 1, Discussion Question, students reflect on the steps needed to find square roots and the impact that has on the lesson. The question states, “Describe the steps you would take to find the square root of a number. Why would you need this in this lesson?”
  • In Lesson 7.7, Activity 2, Discussion Question, students construct an argument related to finding the probability based on the Activity. The question states, “Is finding the likelihood of the next marble picked the same when the outcomes are equally likely versus not equally likely?”
  • In Lesson 8.4, Activity 1, Discussion Question, students determine ways to prevent untrustworthy data and construct an argument supporting their determinations. The question states, “What are some things you can do to ensure that you are not tricked by untrustworthy data? What do you think?” 

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

  • In Lesson 2.11, Activity 2, Discussion Question, students reason about the distributive property but do not analyze the arguments of others. The question states, “Why is the Distributive Property true? What are some mistakes that someone could make when using the Distributive Property? Is it true for subtraction?”
  • In Lesson 3.9, Activity 1, Discussion Question, students determine if equations are the same but are not encouraged to analyze the arguments of others in the discussion. The question states, “Do you think that "5 times a number and 6 is less than 9" is the same as "9 is greater than 6 and 5 times a number"? Why or why not? Discuss in the CK-12 cafe!”
  • In Lesson 6.4, Activity 2, Discussion Question, students discuss changing the shape and what would happen to the area. The question states, “Could you separate the area of the field into a trapezoid and a triangle? Would you have gotten the same area? Discuss with your classmates or in the CK-12 cafe!”
  • In Lesson 7.2, the Introduction includes for students, “You will explore experimental probabilities and compare them to theoretical probabilities. Do you think they will always be the same? Why or why not?” In Activity 1, students “use the interactive to perform the experiment: flip a coin 10 times. Click on the coin in the interactive to simulate flipping it. The results will be recorded in the frequency table. Once you have completed the experiment (flipped the con 10 times) look over your data. Then repeat the experiment two more times. Do you get the expected (theoretical) outcome of 5 heads and 5 tails each?” 

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.
1/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 1.1, Activity 3, Discussion Question, the Teacher Notes state, “Discussion Question: Why is 50 miles per hour a unit rate, and 150 miles per 3 hours is not? As students construct viable arguments to answer this question, they should rely on the definition of unit rate (MP3). Ensure that students know that a unit rate must have a denominator of one. To find a unit rate, students may need to multiply or divide to make that denominator one.”
  • In Lesson 1.6, Activity 2, Discussion Question, the Teacher Notes state, “This discussion allows students to construct arguments and critique the reasoning of their peers (MP3). Discussion Question: A proportional relationship can be represented by a table of values, a graph, and an equation. Discuss how you can find one representation if you are given one of the other two.”
  • In Lesson 3.8, Activity 2, Inline Questions, Supplemental Question, the Teacher Notes provide a question to present to students about eliminating answers from questions. The Teacher Notes state, “Looking back at the answers for some of the inline questions, are any of the answers not possible? Could you automatically eliminate any? (MP3) The answer is, yes, some of the answers could definitely be eliminated. Ultimately, all students will have to take a standardized test at the end of the year, and it is always a good test-taking technique to learn how to eliminate answers that are not possible. In the case of 2, 3, and 5, seconds cannot be negative, so those "distractors" can automatically be eliminated, thus making the selection choice smaller and a greater likelihood of selecting the correct answer. For similar reasons, you could discuss with the class why some of the equations are incorrect in #1 and #5. For example, 160t cannot be positive in the equation because Alex is falling, meaning that 160 needs to be negative.”
  • In Lesson 5.2, Activity 2, Discussion Question, the Teacher Notes state, “It may be helpful for students to use tracing paper for question 2 (also called patty paper). They can trace the triangle on the screen (gently) and then rotate or flip the traced figure to see that the three lengths can only create one triangle. Then lead an informal discussion about whether any three lengths can create triangles. Students can come up with a conjecture and provide examples and counterexamples to support their arguments (MP3). Have students share their thinking out loud and compare with others' reasoning. This idea will be formally developed in the next activity. Discussion Question: Can any three lengths create a triangle?”
  • In Lesson 8.2, Activity 3, the Teacher Notes encourage the teacher to have students discuss mean and median in relation to visual data sets. The Teacher Notes state, “Based on the data taken, which angle do you believe produced the most solar energy? Allow students to discuss with a classmate and then share with the class. Encourage them to discuss how the mean, median, MAD and IQR influenced their conclusion. After several students have shared their results with the class, allow the groups to put all of their findings together to determine which angle produced the most solar energy.”

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

  • In Lesson 2.6, Activity 1, Supplemental Question, the Teacher Notes provide the teacher with instructions to have students discuss. The Teacher Notes state, “Which grouping was easier for you to add across? Discuss with your classmates why grouping different numbers together for an addition problem would be helpful or even easier in certain cases.” The materials encourage discussion among students, but they do not assist teachers in having students analyze the arguments of others.
  • In Lesson 7.4, Activity 3, Discussion Question, the Teacher Notes state, “All the numbers and face cards have an equal likelihood of being drawn because there are 4 of each in a deck. The same is true of drawing any suit over another because there are 13 cards in each suit. You could expand this discussion to the likelihood of drawing a face card (12/52), the likelihood of drawing an even card (20/52), drawing a red card (half), not drawing a numbered card (16/52), etc. See if students can connect the fractions to their reduced forms. For instance, show why 12/52 reduces to 3/13 (because there are 3 face cards out of 13 for each suit). Instead of discussing these, you could also play a game where students need to determine various probabilities as quickly as they can.” These notes do not assist teachers in having students construct an argument or analyze the arguments of others.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for CK-12 Interactive Middle School Math 7 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 3.2, Activity 1, Teacher Notes, “For questions #4 and #5, discuss what it means to be a factor. Students commonly get the words “factor and ‘multiple’ confused. It might be hard for students to see that a number with a + sign is a factor. If that’s the case, show them this example; if a = 2, b = 3 and c = 5, then 2 and 8, (b+c), are factors of their product, 16. Notice that 3 nor 5 are factors, but their sum is.”
  • In Lesson 5.1, the Teacher’s Edition at the beginning of the lesson includes, “Start by reviewing some important terminology: lines, line segments, types of angles, etc. Some of these terms may be new to students, like complementary and supplementary. If students are having difficulty with all the new vocabulary, you can provide them with a vocabulary toolkit or encourage them to make flash cards.”
  • In Lesson 6.2, Warm-Up, “A circle is a 2-dimensional figure such that all of the points are the same distance (the radius) from a fixed point (the center). The radius is a line segment where one endpoint is the center of the circle and the other is on the circle. The diameter of a circle is a line segment with both endpoints on the circle and also passes through the center. The length of the diameter is the same as two radii (plural for radius). In mathematical terms, this would be written d=2r. The distance around a circle is called the circumference. Place the vocabulary terms in the correct spot in the picture below.” 

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 3.3, Introduction, students read the definition of equivalent expressions, “Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.” In Activity 1 Interactive, students see an example of identifying equivalent expressions to help them understand the proper use. This is introduced to the students as, “In this interactive, there is a column of expressions and a box with other expressions. Your job is to drag the expressions in the box to its equivalent expression in the column. The first one is done for you.”
  • In Lesson 5.1, Activity 1, students read the exact definitions of terms relating to angles: “A line is composed of infinitely many points, but you only need two points to define a line. Three points are used to define an angle, where the middle point is always the vertex.” Students are supported in using the terms to answer Inline Questions where they must identify angle terms from a diagram: “1. (Highlight) Based on the data in the image, select the points collinear with point A. 2. (Drag and Drop) Sort the terms below into the correct categories using the image for reference. Remember multiple elements may use the same points. For example, points C and D could describe both a line segment and a ray. 3. Angles are labeled in the form A B C where the middle letter always describes the vertex. The other two letters may be in either order. Select all the correctly labeled angles below.”
  • In Lesson 8.5, Activity 1 includes, “Sampling is the practice of using data obtained from a group to represent a population. A population is a group of objects with a common characteristic. The group selected from the population is called a sample. By studying small groups of a larger population, you can identify trends that might apply to the entire population. Throughout this chapter, you will explore what makes a good sample and how it can be used to make estimates about large populations.”

Gateway Three

Usability

Not Rated

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

Criterion 3a - 3e

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.
N/A

Indicator 3b

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

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.
N/A

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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.
N/A

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.
N/A

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.
N/A

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.
N/A

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).
N/A

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.
N/A

Indicator 3l

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

Criterion 3m - 3q

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.
N/A

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

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.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

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.
N/A

Indicator 3s

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

Indicator 3t

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

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).
N/A

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

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.
N/A

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.
N/A

Indicator 3ab

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

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.
N/A

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.).
N/A
abc123

Additional Publication Details

Report Published Date: 10/22/2020

Report Edition: 2020

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Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
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Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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