Math Mammoth
2024

Math Mammoth

Publisher
Math Mammoth
Subject
Math
Grades
1-7
Report Release
04/04/2024
Review Tool Version
v1.5
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
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Showing:
7th Grade

About This Report

Report for 7th Grade

Alignment Summary

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for Alignment to the CCSSM. In Gateway 1, the materials partially meet expectations for focus and do not meet expectations for coherence, and in Gateway 2, the materials partially meet expectations for rigor and do not meet expectations for practice-content connections.

7th Grade
Gateway 1

Focus & Coherence
08/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
08/18
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Gateway 3

Usability
Usability (Gateway 3)
Not Rated
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1
Overview of Gateway 1

Focus & Coherence

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for focus and coherence. For focus, the materials do assess grade-level content, but they partially provide all students with extensive work with grade-level problems to meet the full intent of grade-level standards. The materials do not meet expectations for coherence and consistency with the CCSSM, as they do not address the major clusters of the grade and do not have content from prior and future grades connected to grade-level work. The materials do have supporting content connected to major work and make connections between clusters and domains.

Gateway 1
v1.5
Gateway 1

Focus & Coherence
08/14
0
7
12
14
Criterion 1.1: Focus
04/06
Criterion 1.2: Coherence
04/08
Partially Meets Expectations

Criterion 1.1: Focus
04/06

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for focus as they do assess grade-level content but partially provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Indicator 1A
02/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 7 Tests and Cumulative Reviews section which includes an End-of-Chapter test for each chapter, a Cumulative Review for every chapter after Chapter 1 and one End-of-the-Year test. There are assessment items that are aligned to above grade level skills, but these materials can be removed or modified without impacting the structure of the materials.

Examples of assessment items that assess grade-level content include:

  • Tests and Cumulative Reviews, Chapter 2 Test, Question 9, “a. Write an expression for the distance between -2 and -18. b. Write an expression for the distance between x and 5. c. Evaluate the expression from (b) when x = -2.” (7.NS.1c and 7.EE.1)

  • Tests and Cumulative Reviews, Chapter 5 Test, Question 2, “Ethan purchased 24 cookies and a loaf of bread for a total of $6.85\$6.85. He didn’t pay attention to the cost of the cookies but he remembered that the bread cost $3.25\$3.25. Find the cost of one cookie by writing an equation and solving it.” (7.EE.4)

  • Tests and Cumulative Reviews, Chapter 10 Test, Question 4, “Logan and Alex tossed two coins 400 times. a. List all the possible outcomes when two coins are tossed just one time. b. Here are Logan’s and Alex’s results. Calculate and fill in the table with the experimental and the theoretical probabilities to the nearest tenth of a percent. c. Suggest a reason for the large discrepancy between the experimental and theoretical probabilities.” (7.SP.7 and 7.SP.8 ) 

Examples of mathematically reasonable assessment items that align to above-grade-level standards that could be removed or modified without impacting the structure or intent of the materials include, but are not limited to:

  • Tests and Cumulative Reviews, Chapter 4 Test, Question 9, “Write the numbers in scientific notation. a. 25,600,000 b. 7,810,000,000” (8.EE.3)

  • Tests and Cumulative Reviews, Chapter 8 Test, Question 6, “Draw two lines that are perpendicular to each other using only a compass and a straightedge.” (G-CO.12)

  • Tests and Cumulative Reviews, End of Year Test, Question 45, “*a. Find the volume of the cylindrical part of the juicer, if its bottom diameter is 12 cm and its height is 4.5 cm. b.* Convert the volume to milliliters and to liters, considering that 1 ml = 1 cm3.” (G-GMD.3)

Indicator 1B
02/04

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide limited opportunities for all students to engage in extensive work with the grade-level-problems including but not limited to: 7.EE.3, 7.EE.4b and 7.G.5 . Some off-grade-level work negatively impacts students’ work with grade-level content.

The materials are divided into two Worktexts, 7-A and 7-B. Each Worktext is divided into chapters. Each chapter is divided into lessons that contain content instruction, mental math problems, puzzle corners, and practice problems, in addition to chapter reviews and a chapter test.

Examples of extensive work with grade-level problems to meet the full intent of some grade-level standards include:

  • Worktext 7-A, Chapter 1: The Language of Algebra,  Growing Patterns 1, Question 1, “a. Draw the next steps.  b. How do you see this pattern growing? (There is more than one way to look at it!) c. How many flowers will there be in step 39? d. What about step n?” Students are provided three steps, the first step has three flowers, the second step has six flowers, and the third step has nine flowers. In The Distributive Property, Question 13, “a. Sketch a rectangle with an area of 9x+15. b. Sketch a rectangle with an area of 9a +15b + 3.” In Chapter 5: Equations and Inequalities, Growing Patterns 2, Question 2, “a. How do you think this pattern is growing?  b. How many snowflakes will there be in step 39?  c. Write a formula for the number of snowflakes in step n. Check your answer with your teacher before going on to part (d). d. In which step will there be 301 snowflakes? Write an equation and solve it.” Students are provided three steps, the first step has five snowflakes, the second step has seven snowflakes, and the third step has nine snowflakes. In Worktext 7-B, Chapter 7: Percent, Percent Equations, Question 1, “Write an expression for the final price using a decimal for the percentage. c. Pizza sauce: price x, discounted by 17%\%. New price = _____  d. Sunglasses: price s, price increased by 6%\%. New price = _____” In Chapter 7 Review, Question 3, “A flashlight is discounted by 18%\%, and now costs $23.37\$23.37. Let p be its price before the discount. Find the equation that matches the statement above and solve it.” Students choose from:  p - 0.18 = $23.37\$23.37,  p - 18 = $23.37\$23.37, 0.82p = $23.37\$23.37, and 0.18p = $23.37\$23.37 . Students engage in extensive work with grade-level problems to meet the full intent of 7.EE.2 (Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities are related.)

  • Worktext 7-A, Chapter 2: Integers, Addition and Subtraction on the Number Line, Question 3, “Write an addition or a subtraction. a. You are at -3. You jump 6 to the right. You end up at ____. b. You are at -3. You jump 6 to the left. You end up at ____. c. You are at 2. You jump 7 to the left. You end up at _____. ” Next to each problem is an empty box with the heading of Addition/subtraction for the student to write the corresponding equation. Question 4, “Write an addition or subtraction to match the number line jumps. a. ____ b. ____ c. ____” Students are given a number line with four number line jumps and they are tasked with writing four equations. Question 7, “Draw a number line jump for each sum and complete the addition sentence. a. 2+(-5) = _____ b. -2+(-5)= _____ c. -1+(-4)= _____” Students are provided four numbers lines running from -10 to 3.  Students engage in extensive work with grade-level problems to meet the full intent of 7.NS.1(Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.) 

  • Worktext 7-B, Chapter 10: Probability, Counting the Possibilities, Question 1, “a, How many outcomes are there for rolling the same number on both dice (such as (5, 5))? b. What is the probability of rolling the same number on both dice?” Question 4, “a. Complete the tree diagram to show the outcomes when you first roll a die, then toss a coin. The bottom row lists the outcomes using number-letter combinations, such as 1H and 1T. Now find these probabilities: b. P(even number, heads). c. P(not 6, heads)” Question 10, “In tossing two distinct coins, one of the possible outcomes is HT: first coin heads, second coin tails. a. List all the possible outcomes. b. Each of the possible outcomes is equally likely. Therefore, what is the theoretical probability of each outcome? c. Now toss two coins 200 times and compare the experimental probabilities to the theoretical ones. Before you do, predict about how many times you would expect to see each outcome: _____ times d. Check whether the observed frequencies are fairly close to those predicted by the theoretical probabilities. Let’s say they were not. What could be the reason?”  Students engage in extensive work with grade-level problems to meet the full intent of 7.SP.7 (Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.)

The materials provide limited opportunities for all students to engage in extensive work with grade-level-problems for standards including, but not limited to:

  • Students do not have the opportunity to engage in extensive work with 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies). In Worktext 7-A, Chapter 5: Equations and Inequalities, Word Problems, Question 1, “Which equation matches the problem? Once you find it, solve the equation. a. Mrs. Hendrickson bought herself a cup of coffee that cost $3\$3. She also bought ice cream cones that cost $2.20\$2.20 each for each of her preschoolers. She paid for all of it with $25\$25. How many ice cream cones did she buy?” A box with the following four equations is provided: n(3+2.20)=25n(3+2.20)=25 3+2.20n=253+2.20n=25 3(n+2.20)=253(n+2.20)=25 3n+2.20=253n+2.20=25. “b. Mr. Sanchez spent about $35\$35 to treat some people in his bicycling club to a cup of coffee and an ice cream cone each. Each coffee cost $3\$3, and each ice cream cone cost $2.83\$2.83. How many people were treated to coffee and ice cream by Mr. Sanchez?” A box with with the following four equations is provided: n(3+2.83)=35n(3+2.83)=35 3+2.83n=353+2.83n=35 3(n+2.83)=353(n+2.83)=35 3n+2.83=353n+2.83=35. Students are provided with limited opportunities to solve multi-step real-life and mathematical problems posed with negative decimals.

  • Students do not have the opportunity to engage in extensive work with 7.EE.4b (Solve word problems leading to inequalities of the form px+q>rpx+q>r or px+q<rpx+q<r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem). In Worktext 7-A, Chapter 5: Equations and  Inequalities, Inequalities, the material states the following: “So solving inequalities works essentially the same way as solving equations, but there is one exception. That is, if you divide or multiply an inequality by a negative number, you need to reverse the sign of the inequality (from < to > , or ≤ to ≥ , and vice versa). For example, multiplying the inequality −7 < 7 by −1 yields the inequality 7 > −7. However, we will not be dealing with the exception in this course. You will be solving only inequalities where you multiply or divide the inequality by a positive number.” Students are provided with no opportunities to multiply or divide inequalities by negative numbers.

  • Students do not have the opportunity to engage in extensive work with 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure). In Worktext 7-B, Chapter 8: Geometry, Angle Relationships, Question 9, “a. Find a pair of vertical angles in the figure. b. Write an equation for α\alpha, and solve it. Hint: Look for angles that form a straight line. c. What is the measure of ∠γ\gamma?” A diagram with 5 angles is shown. The angles are labeled γ\gamma, 43°, α\alpha, 107°, and β\beta. Students are provided with limited opportunities to write and solve equations for unknown angles in a figure using facts about those angles.

The materials include some off-grade-level content that negatively impacts students’ work with the grade-level standards. Examples include, but are not limited to:  

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Using the Distributive Property, Question 4, “a. 2(x+7)=3(x−6)2(x+7)=3(x-6)… d. 3(w−12)3(w-\frac{1}{2}) = 6(w+12)6(w+\frac{1}{2})…”. Students are asked to engage in solving equation using the distributive property and collecting like terms, which does not align to a seventh grade standard. 

  • Worktext 7-B, Chapter 8: Geometry, Angle Relationships, Question 11, “In this figure, lines k and m are parallel and line l intersects them both. a. Mark all the pairs of vertical angles in the figure. b. Measure or calculate all the eight angles. Mark them in the figure. What do you notice?” Students are given a picture of two parallel lines cut by a transversal.  Students are asked to solve problems involving angles created when parallel lines are cut by a transversal, which does not align to a seventh grade standard.

Criterion 1.1: Focus
04/06
Indicator 1A
02/02
Indicator 1B
02/04

Criterion 1.2: Coherence
04/08

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for coherence. The majority of the materials, when implemented as designed, do not address the major clusters of the grade. The materials do include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade and do have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials do not include content from future grades that is identified and related to grade-level work and do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

Indicator 1C
00/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The materials do not devote at least 65%\% of instructional time to the major clusters of the grade: 

  • The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 10, approximately 60%\%. 

  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 66 out of 112, approximately 59%\%. 

  • The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 96 out of 188, approximately 51%\%. 

A day-level analysis is most representative of the instructional materials as the lessons typically cover multiple days that focus on major work of the grade. As a result, approximately 51%\% of the instructional materials focus on major work of the grade.  

Indicator 1D
02/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed to connect supporting standards/clusters to the grade’s major standards/clusters. The materials include a Common Core Alignment Document that does not provide guidance for connections between supporting and major work of the grade.

Examples of connections between supporting and major work include:

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Some Problem Solving, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.) to the major work of 7.EE.1(Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) For example, Question 8, “Four adjacent (side by side) angles form line l. a. Write an equation to solve for the unknown a. b. Find the measure of each of the four angles, rounded to the nearest 0.01 degree.” A diagram is provided of the four angles that form line l.  Students use facts about supplementary angles and apply properties of operations in order to write and solve an equation for unknown angles.

  • Worktext 7-B, Chapter 8: Geometry, Angle Relationships, connects the supporting work of  7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.). For Example, Question 4, “Write an equation for each of the unknown angles. Then solve it. Do not measure any angles.” Given a diagram in part  a. that shows a line with a ray extended from the center forming angle x on the left and a 78° angle on the right and a diagram for b that shows a right angle with a ray splitting it into two angles; the left angle is 76° and the right angle is labeled a. Students are asked to determine the equations and solutions, “a. Equation for x: _____ Solution: _____ b. Equation for a: _____ Solution: _____” Students use facts about supplementary and complementary angles to write equations using variables to represent quantities in a mathematical problem. 

  • Worktext 7-B, Chapter 10: Probability, Experimental Probability, connects the supporting work of 7.SP.7 (Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.) to the major work of 7.RP.2 (Recognize and represent proportional relationships between quantities.). For example, Question 2, “Through the marvels of automation, you will now ‘roll’ a dice more times than in Exercise 1. You can use this online dice roller: https://www.mathmammoth.com/practice/dice-roller Or you can use a spreadsheet file (#1) from the list at https://www.mathmammoth.com/lessons/probability_simulations a. Predict about how many times you expect to get each of the six possible numbers if you roll a die 1,000 times: About _____ times b. Now roll one die 1,000 times. If you use the virtual roller, ... Record in the table the frequencies of each outcome and calculate experimental probabilities. Observe how close each experimental probability is to the theoretical probability of 16\frac{1}{6} = 16.67%\%.“Students develop a probability model to make predictions and  use proportional relationships between quantities to record observed frequencies.   

Supporting work is not connected to the major work of the grade, but the separation is mathematically reasonable. For example:

  • 7.G.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

A connection between supporting work and major work of the grade that is entirely absent from the materials is the following:

  • No connections are made between the supporting work of 7.G.6 (Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.) and the major work of 7.EE.1(Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.)  In the lessons related to area, volume, and surface area, there are no questions that apply the properties of operations as strategies to determine the answers.

Indicator 1E
02/02

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

The materials reviewed for  Math Mammoth Grade 7, Light Blue Series, meet expectations for including problems  and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Included within the materials is a Common Core Alignment document, however, the document does not provide explicit guidance for connections between or among domains and clusters. . 

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Two-Step Equations: Practice, connects the major work of 7.NS.1d (Apply properties of operations as strategies to add and subtract rational numbers.) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.). For example, Question 1, “Write an equation to match the number line model and solve for the unknown.” For part a, students are given a labeled number line that goes from - 8 to 12, three segments of equal size are marked with x and one segment is labeled with a 5. Students solve mathematical problems by writing and solving equations using the properties of operations.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Floor Plans, connects the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems.) to the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions.). For example, Question 6, “A floor plan is drawn using the scale 5 cm: 1 m. a. Calculate the dimensions in the plan for a kitchen that measures 4.5 m by 3.8 m in reality. b. The living room measures 26 cm by 22.5 cm on the plan. What are its dimensions in reality?” Students use their understanding of proportional relationships to compute the dimensions of figures.

  • Worktext 7-B, Chapter 8: Geometry, Conversions Between Metric Units of Area, connects the supporting work of 7.G.A (Draw construct, and describe geometrical figures and describe the relationships between them.) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.). For example, Question 8, “Jerry’s favorite lake to fish in is roughly a rectangle that measures 1.5 cm by 0.8 cm on a map with a scale of 1:20,000. What is its approximate area in reality, to the nearest thousand square meters? To the nearest tenth of a hectare?”  Students use a scale to solve an area problem about a two-dimensional object.

Some connections are entirely absent from the materials. Examples include:

  • No connections are made between the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.).

Some clusters and domains are not connected, but the separation is mathematically reasonable. For example, the Geometry (7.G) and Statistics & Probability (7.SP) domains remain separate throughout the curriculum. This is mathematically reasonable, as their content does not typically overlap within the seventh grade content.

Indicator 1F
00/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. While some references to future or earlier grade work does occur in the introduction lesson, these references are limited, and are not always related to grade-level concepts or work. The materials include a Common Core Alignment Document that lists the grade-level standards addressed in each lesson, however, the document does not include information regarding the progression of the lesson standards between grade-level bands. 

There are some examples of references to future grade content, however these references are not always identified and/or related to grade-level work. Examples include, but are not limited to: 

  • Worktext 7-A, Foreword, states, “The curriculum meets and actually exceeds the Common Core Standards (CCS) for grade 7. The two main areas where it exceeds those standards are linear equations (chapter 5) and the Pythagorean Theorem (chapter 9). Linear equations are covered in more depth than the CCS requires, and the Pythagorean Theorem belongs to grade 8 in the CCS. You can access a document detailing the alignment information either on the Math Mammoth website or in the download of this curriculum.” 

  • Worktext 7-B, Chapter 8: Geometry, Introduction, “We also briefly study the proof for the formula for the area of a circle. I feel it is important that students encounter justifications for mathematical formulas and procedures and even read some proofs before high school. We don’t want students to think that mathematics is only a bag of magic tricks or formulas to memorize that seemingly came out of nowhere. Proofs and logical thinking are foundations to mathematics and school mathematics should not be left without them.”  

There are some examples of references to prior grade learning, however not all references relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include, but are not limited to: 

  • Worktext 7-A, Chapter 4: Rational Numbers, Introduction, “Obviously, students already know a lot about rational numbers and how to calculate with them. Our focus in this chapter is to extend that knowledge to negative fractions and negative decimals.” 

  • Worktext 7-B, Chapter 7: Percent, Introduction, “In this chapter we review the concept of percent as ‘per hundred’ or as hundredth parts and how to convert between fractions, decimals, and percents. The lesson Solving Basic Percentage Problems is intended for review of sixth grade topics, focusing on finding a known percentage of a number (such as 21%\% of 56) or finding a percentage when you know the part and the total.”

Indicator 1G
Read

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not foster coherence between grades and cannot be completed within a regular school year with little to no modification.  Materials are divided between two Worktexts, 7-A and 7-B, that include an introduction for each chapter, and the lessons. A separate assessment book or file (on digital) contains the Chapter tests, cumulative reviews (optional), and the End of the Year test. The materials include 10 chapters which can be completed in 188 days, including 175 days for lessons, chapter reviews and mixed reviews, 13 days for assessments. 

According to the User Guide, Pacing the Curriculum, “The lessons in Math Mammoth complete curriculum are not written for a single teaching session or class. It is common for the lessons to span 4-7 pages and take 2-4 days or classes to complete. Therefore, it is not possible to say exactly how many pages a student needs to do in one day. This will vary. However, you can calculate approximately how many pages the student should complete each week (or each day) in order to finish the curriculum in one school year. Use that number as a guideline, but do not become bound by it. I need to note at this point that Math Mammoth Grade 7 is, in a sense, a hybrid course — it can work as a complete 7th grade curriculum that meets the Common Core Standards, or as a traditional pre-algebra course. The difference between the two has to do with the chapter on the Pythagorean Theorem. If your student(s) will be tested based on the Common Core Standards or your student(s) will be going on to an 8th grade curriculum that is based on the CCS, then you can safely omit the chapter on the Pythagorean Theorem.” Based on the publisher’s recommendations Chapter 9: Pythagorean Theorem was omitted from this review. The materials also include a table to calculate the number of pages a student should finish each day to complete the curriculum in the chosen number of school days.

Additional pacing suggestions are provided in the introduction of some chapters. For example, Worktext 7-B, Chapter 6: Ratios and Proportions, Introduction, “Keep in mind that the specific lessons in the chapter can take several days to finish. They are not ‘daily lessons.’ Instead, use the general guideline that seventh graders should finish about 12 pages a week in order to finish the curriculum in about 40 weeks.” Using the guidance of 12 pages a week, the total number of pages (420) was divided by 12 pages a week, this computation resulted in approximately 35 weeks of instruction, which when multiplied by 5 gives 175 total days of instruction. There are 10 days for the 10 Chapter tests and 3 days for the End of the Year Test, for a total of 188 days.

Optional content if added would account for an additional 12 days. Three of these days would be for optional lessons and the other nine days would be for the cumulative reviews.

Each chapter introduction contains a link to a list of various free online games and activities. “These games can be used to supplement the math lessons, for learning math facts, or just for some fun."

Criterion 1.2: Coherence
04/08
Indicator 1C
00/02
Indicator 1D
02/02
Indicator 1E
02/02
Indicator 1F
00/02
Indicator 1G
Read
Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for rigor and balance and practice-content connections. For rigor and balance, the materials do help students develop procedural skills and fluency, but they partially develop conceptual understanding. The materials partially provide opportunities for students to engage with multiple applications and partially balance the three aspects of rigor within the grade. The materials do not make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Gateway 2
v1.5
Gateway 2

Rigor & Mathematical Practices
08/18
0
10
16
18
Criterion 2.1: Rigor and Balance
05/08
Criterion 2.2: Math Practices
03/10
Does Not Meet Expectations

Criterion 2.1: Rigor and Balance
05/08

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for rigor. The materials give attention throughout the year to procedural skills and fluency. The materials partially develop conceptual understanding of key mathematical concepts, partially meet expectations for spending sufficient time working with engaging applications of mathematics, and partially balance the three aspects of rigor within the grade.

Indicator 2A
01/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.  The materials do not provide opportunities to develop conceptual understanding throughout the grade level as students are provided the procedure to solve problems during the introduction of conceptual understanding. 

The materials do not provide opportunities for students to develop conceptual understanding throughout the grade level. Examples include, but are not limited to:

  • Worktext 7-A, Chapter 1: The Language of Algebra, Properties of the Four Operations, Question 1, students compare expressions to find which ones are equivalent. “Are the two expressions in each box equivalent?  That is so they have the same value for any value of x?  Give c some test values to check.”The following expressions are given: a. c+5c+5, 5+c5+c b. c−5c-5, 5−c5-c c. c÷6c÷6, 6÷c6÷c d. 5c5c, c⋅5c⋅5 . This question does not provide an opportunity for students to build a conceptual understanding of 7.EE.1(Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) as students are guided to check different solutions to determine if expressions are equivalent. 

  • Worktext 7-A, Chapter 2: Integers, Addition and Subtraction on the Number Line, a box is provided with the following information. “What about subtracting a negative number? Here is a way to think about 3 − (−2) on the number line. Imagine you are standing at 3. Because of the subtraction sign, you turn to the left and get ready to take two steps. However, because of the additional minus sign in front of the 2, you have to take those steps BACKWARDS—to the right! So, because you ended up taking those 2 steps to the right, in effect you have just performed 3 + 2! Quite surprising, but true: that double minus sign in 3 − (−2) turns into a plus!” Question 16, “Draw a number line jump for each subtraction, using the method just explained. a. 1-(-2) = ___” This question does not provide an opportunity for students to build a conceptual understanding of 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.)as students are directed to use the method previously mentioned to get the correct answer.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Why Cross-multiplying Works, Instructional box, “Recall that if we multiply both sides of an equation by the same number, the two sides are equal.  In a proportion, we have two different numbers in the denominators, we can first multiply both sides of the proportion by the one denominator and then by the other, or we can cross-multiply. Cross-multiplying is in reality just a shortcut for doing those two separate multiplications at the same time.  Let’s solve the proportion below by multiplying both sides first by the one denominator, then by the other.  Cross-multiplying is not a ‘magic trick’, but simply a shortcut based on mathematical principles.” Students are then shown a demonstration of how to solve a proportion without cross-multiplying. This instruction does not provide an opportunity for students to build a conceptual understanding of 7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers) as students are explained why cross-multiplying works.

Indicator 2B
02/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Materials develop procedural skills and fluency throughout the grade level. Examples include:

  • Worktext 7-A, Chapter 4: Rational Numbers, Rational Numbers, Question 16, students convert fractions to decimals using long division. “Write as decimals, using a line over the repeating part (if any). Use long division. d. 2716\frac{7}{16}“ . This activity provides students with an opportunity to develop procedural skills and fluency with 7.NS.2d (Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats).

  • Worktext 7-B, Chapter 7: Percent, Percent Equations, Question 2, students select the correct equation for a world problem and then solve it. “A computer is discounted by 25%\%, and now it costs $576\$576. Let p be its price before the discount. Select the equation that matches the statement above and solve it.” The equations given are the following: p+0.25p=576p+0.25p=576, p−0.25p=576p-0.25p=576, 0.25p=5760.25p=576. This activity provides students with an opportunity to develop procedural skills and fluency with 7.EE.4a (Solve word problems leading to equations of the form px+q=rpx + q = r and p(x+q)=rp(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach).

  • Worktext 7-B, Chapter 8: Geometry, Chapter 8 Mixed Review, Question 8, students simplify several expressions. “Simplify the expressions. a. 2+w+11+w+2w2+w+11+w+2w” This activity provides students with an opportunity to develop procedural skills and fluency with 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).

The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include: 

  • Worktext 7-A, Chapter 1: The Language of Algebra,  Simplifying Expressions, Question 8, students simplify several expressions. “Simplify the expressions. a. 5p+8p−p5p+8p-p". This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Two-Step Equations: Practice, Question 4, students solve two-step equations. “Solve. Check your solutions (as always!) a. 20−3y=6520-3y=65". This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations).

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Chapter 6 Mixed Review, Question 4, students solve mathematical problems using the four operations. “Find the value of the expressions using the correct order of operations. a. 5⋅2−105⋅\frac{2}{-10} b. −12−4+7-\frac{12}{-4}+7” This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers).

Indicator 2C
01/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. The materials include multiple opportunities for students to engage with and independently demonstrate routine applications of the mathematics throughout the grade level. However, the materials include few opportunities for students to engage with and independently demonstrate non-routine applications of the mathematics throughout the grade level.

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

  • Worktext 7-A, Chapter 1: The Language of Algebra, The Distributive Property, Question 16, students solve a multi-step real-life problem with rational numbers and construct a simple equation by reasoning about quantities. “The Larson family are planning their new house. It is going to be 25 ft on one side and have a garage that is 15 ft wide, but they have not decided on the length of the house yet. a. If the total area of the house + garage is limited to 1200 square feet, how long can the house be?  b. Write a single equation for the question above. Write it in the form ‘(formula of area) = 1200.’ You do not have to solve the equation–just write it.” Students are provided a diagram of a rectangle split in two vertically, one section is labeled garage the other is labeled house. One side of the rectangle is labeled 25ft and the other side is labeled 15ft and x. This problem allows students to apply the mathematics of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.) in a routine application problem independently.

  • Worktext 7-A, Chapter 3: Solving One-Step Equations, Multiplication and Division Equations, Question 6, students write an equation for a word problem and then solve it. “Write an equation for each situation. Then solve it. Do not write the answer only, as the main purpose of this exercise is to practice writing equations. a. A submarine was located at a depth of 500 ft. There was a shark swimming at 1/6 of that depth. At what depth is the shark?” This problem allows students to apply the mathematics of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities) in a routine application problem independently.

  • Worktext 7-B, Chapter 8: Geometry, Chapter 8 Mixed Review, Question 11, students find the area of a rectangle after it is enlarged. “A rectangle with sides of 2 1/4 in. and 3 in. is enlarged by a scale factor of 3.5. Find the area of the resulting rectangle to the tenth of a square inch.” This problem allows students to apply the mathematics of 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.) in a routine application problem independently.

The materials provide few opportunities for students to engage with and independently demonstrate non-routine applications throughout the grade level. An example where a student would engage in a non-routine application is shown below. 

  • Worktext 7-A, Chapter 2: Integers, Adding or Subtracting Several Integers, Question 8,  students create a story based on an expression. “Write a story about money to match the expression -2 - (-10) + (-7) - 4. “ This problem allows students to apply the mathematics of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers) in a non-routine application problem.

Indicator 2D
01/02

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

The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. The materials do not balance all three aspects of rigor, as there is an over-emphasis on procedural skills and fluency. 

The materials provide some opportunities for students to develop conceptual understanding, procedural skills and fluency, and application separately throughout the grade and some opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. However, there are multiple lessons where one aspect of rigor is emphasized.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

  • Worktext 7-A, Chapter 2: Integers, Subtraction of Integers, Question 1, students develop conceptual understanding of adding and subtracting integers by using counters. “Model Subtraction with counters.  You may need to add positive-negative pairs before subtracting. a.  -4 - (-2)  = _____” Students are shown four negative counters. This activity provides students with an opportunity to develop a conceptual understanding with 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers).

  • Worktext 7-B, Chapter 6: Ratio and Proportions, Unit Rates, Question 3, students find the unit rate based on given situations. “Write the unit rate as a complex fraction, and then simplify it. a. Lisa can make three skirts out of 5 ½ yards of material. Find the unit rate for one skirt.” This problem allows students to apply the mathematics of 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.) in a routine application problem independently.

  • Worktext 7-B, Chapter 7: Percent, Solving Basic Percentage Problems, Question 7, students solve a series of percent tax problems. “Find the final price when the base price and sales tax rate are given. This is a mental math workout, so do not use a calculator! a. Bicycle: $100\$100; 7%\% sales tax. Tax to add: $____ Price after tax: $____” This activity provides students with an opportunity to develop procedural skills and fluency with 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems).

Examples of students having opportunities to engage in problems that use two or more aspects of rigor include:

  • Worktext 7-A, Chapter 1: The Language of Algebra, Properties of the Four Operations, Question 9, students write and simplify an expression based on an illustration. “Write an expression from the illustration and simplify it.” The illustration shows a line divided into five equal parts with an x under each part. Students develop conceptual understanding and build procedural skills and fluency for 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients) as they form expressions based on the illustration and simply them.

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Word Problems, Question 2, students solve for the width of a rectangle knowing only the length and the perimeter. “Write an equation for the following problem and solve it. The perimeter of a rectangle is 144 cm. Its length is 28 cm. What is its width?” Students develop conceptual understanding and application of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.) as they solve a word problem for an unknown based on their understanding of perimeter.

Criterion 2.1: Rigor and Balance
05/08
Indicator 2A
01/02
Indicator 2B
02/02
Indicator 2C
01/02
Indicator 2D
01/02

Criterion 2.2: Math Practices
03/10

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for practice-content connections. The materials support the intentional development of MP6 (attend to precision) and attend to the specialized language of mathematics. The materials partially support the intentional development of MP3 (Construct viable arguments and critique the reasoning of others). The materials do not support the intentional development of MPs 1, 2, 4, 5, 7, and 8. Additionally, the materials do not explicitly identify the mathematical practices in the context of individual lessons, so one point is deducted from the score in indicator 2e to reflect the lack of identification.

Indicator 2E
00/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. There is no intentional development of MP1 to meet its full intent in connection to grade-level content. The Standards of Mathematical Practice are not explicitly identified in the context of the individual lessons for teachers or students. As a result of this one point is deducted from the scoring of this indicator.

MP1 is not intentionally developed to meet its full intent as students have limited opportunities to make sense of problems and persevere in solving them. Examples include, but are not limited to:

  • Worktext 7-A, Chapter 1: The Language of Algebra, The Order of Operations, Question 8, “Rewrite each expression using a fraction line, then simplify. Compare the expression in the top row with the one below it. Hint: Only what comes right after the “÷” sign goes into the denominator. a. 2<em>÷5</em>⋅42<em>÷5</em>⋅4 “ This problem does not provide students with an opportunity to make sense of problems and persevere in solving them, since hints are provided to help students.

  • Worktext 7-A, Chapter 2: Integers, Distance and More Practice, Question 6, students determine if the order of numbers is important when considering distance. “What happens if you calculate the distance between two numbers m and n as ∣n−m∣|n-m| instead of ∣m−n∣|m-n|? In other words, what happens if you reverse the order of the numbers in the subtraction? Investigate this by checking several pairs of numbers. For example, what happens if you calculate the distance between 18 and 11 as ∣11−18∣|11-18| instead of ∣18−11∣|18-11|? Try some pairs of negative numbers, as well. Then try some pairs where one number is positive and the other is negative. Does the formula still work?” This problem does not provide students with an opportunity to make sense of problems and persevere, since it explains to students strategies to investigate.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Proportional Relationships, Question 3, students are asked to consider how proportional relationships are represented in tables, graphs and equations. “Now consider the plots, the equations, and the tables of values of the six items in the previous exercise. How do the equations and plots of the variables that are in proportion differ from those that aren’t? If you cannot tell, check the next page.” This problem does not provide students with an opportunity to make sense of problems and persevere, since it tells students they can check the next page for the answer.

MP2 is connected to grade-level content, and intentionally developed to meet its full intent. Students reason abstractly and quantitatively as they work independently throughout the units. Examples include:

  • Worktext 7-A, Chapter 2: Integers, Dividing Integers, Question 4, students must write an equation developed from an understanding of positive and negative numbers. “In a math game, you get a negative point for every wrong answer and a positive point for every correct answer. Additionally, if you answer in 1 second, your negative points from the past get slashed in half! Angie had accumulated 14 negative points and 25 positive points in the game. Then she answered a question correctly in 1 second. Write an equation for her current ‘point balance.’”This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students write an equation about the current point balance of a game.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Chapter 6 Review, Question 10, students reason quantitatively to determine if quantities are proportional. “Using a pre-paid internet service you get a certain amount of bandwidth to use for the amount you pay. The table shows the prices for certain amounts of bandwidth. a. Are these two quantities in proportion?  Explain how you can tell that. b. If so, write an equation relating the two and state the constant of proportionality.” Students are provided a table of the bandwidth ranging from 1G to 25G and the price ranging from $10\$10 to $50\$50. This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students use the information from the table to explain if the two quantities are in proportion and to write an equation that relates the two quantities.

  • Worktext 7-B, Chapter 7: Percent, Percentage of Change: Applications, Question 3, students answer questions about the side length and area of a square after the sides increase by a scale factor. “The sides of a square are increased by a scale factor of 1.15. a. By what percentage does the length of each side increase? b. What is the percentage of increase in area? Hint: Make up a square using an easy number for the length of side. c. (Challenge) Would your answers to (a) and (b) change if the shape were a rectangle? A triangle?” This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students reason about how an increase in side length, increases the area percentage.

Indicator 2F
01/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, partially meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Although support for the intentional development of constructing viable arguments are found throughout the materials, support for the intentional development of critiquing the reasoning of others is limited to certain chapters. 

Materials provide support for the intentional development of MP3 by providing opportunities for students to construct viable arguments in connection to grade-level content. Examples include:

  • Worktext 7-A, Chapter 4: Rational Numbers, Adding and Subtracting Rational Numbers, Question 11, students construct viable arguments as they explain a real-life situation based on an expression. “Explain a real-life situation for the sum −$50+(−$12.90) -\$50+(-\$12.90).” This question attends to MP3, constructing viable arguments as students explain a real-life situation based on the sum.

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Word Problems and Inequalities, Question 2, students explain their solution set to a word problem using their own words. “Jeannie earns $350\$350 per week plus $18\$18 for each hour of overtime that she works. How many hours of overtime does she need to work if she wants to earn at least $500\$500? Write an inequality and solve it. Plot the solution set on a number line. Lastly, explain the solution set in words.” This question attends to MP3, constructing viable arguments as students explain the solution set to an inequality that they wrote and solved.

  • Worktext 7-B, Chapter 8: Geometry, Area and Perimeter Problems, Question 5, students justify their answer for whether or not a unique trapezoid is formed from given conditions. “The two parallel sides of a trapezoid measure 12 cm and 9 cm, and its altitude is 7 cm. a. Draw a trapezoid using this information, either on paper or in drawing software. b. Do the specified dimensions determine a single, unique trapezoid, or is it possible to draw more than one shape of trapezoid that satisfies those dimensions? Justify your answer.” This question attends to MP3, constructing viable arguments as students justify their answer about what kind of trapezoid could be created based on the dimensions given.

Materials provide some support for the intentional development of MP3 by providing limited opportunities for students to critique the reasoning of others in connection to grade-level content. 

Examples include, but are not limited to:

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Solving Proportions: Cross Multiplying, Question 7, students perform error analysis as they explain what is wrong with a proportion. “Jane wrote a proportion to solve the following problem. Explain what is wrong with her proportion and correct it. Then solve the corrected proportion. Also, check that your answer is reasonable. Twenty kilograms of premium dog food cost $51. How much would 17kg cost?” An image labeled Jane’s proportion is provided for students. This question attends to MP3, critiquing the reasoning of others as students correct another person's error.

  • Worktext 7-B, Chapter 11: Statistics, Comparing Two Populations, Question 7, students critique the reasoning of others as they explain if an organization's way of selecting a sample is good. “An organization that helps teenagers with drug problems has set up a telephone hot line for teens to call in to discuss their problems. After a few months of operations, the organization wants to evaluate the effectiveness of their service. Since they don’t usually get as many calls on Tuesdays, they decide to choose a particular Tuesday to ask each teen at the end of the call to answer a few questions about how the service has helped. Is this a good method for selecting a sample? Explain.” This question attends to MP3, critiquing the reasoning of others as students explain if an organization's way of selecting sample is good or not.

  • Worktext 7-B, Chapter 11: Statistics, Chapter 11 Mixed Review, Question 13, students critique the reasoning of others as they explain why a sampling method is biased. “Sam is studying how well the people in his city like the paintings of the Romantic era. He is planning to stand on a certain street corner near his home and ask passersby if they would like to take part in his study. Explain why his sampling method is biased.” This question attends to MP3, critiquing the reasoning of others as students explain why another person's sampling method is biased.

Indicator 2G
00/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. There is no intentional development of MP4 and MP5 to meet its full intent in connection to grade-level content.

MP4 is not intentionally developed to meet its full intent as students have limited opportunities to model with mathematics. Examples include, but are not limited to:

  • Worktext 7-A, Chapter 1: The Language of Algebra, Expressions and Equations, Question 5,  students write an expression and pick an equation based on a real-world scenario. “a. Ann is 5 years older than Tess, and Tess is n years old. Write an expression for Ann’s age.  b. Let A be Alice’s age and B be Betty’s age.  Find the equation that matches the sentence ‘Alice is 8 years younger than Betty.’ Hint: give the variables some test values.” The equation choices are the following: A=8−BA=8-B, A=B−8A=B-8, and B=A−8B=A-8. This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are told to write an expression, with the variables given and to find the equation that matches the sentence. 

  • Worktext 7-A, Chapter 2: Integers, Addition of Integers, Question 4, students fill in a sentence to compare how an expression is modeled with two different methods. “4. Compare how −8+6−8 + 6 is modeled on the number line and with counters. a. On the number line, −8+6−8 + 6 is like starting at _____, and moving _____steps to the _____________, ending at _____. b. With counters, −8+6−8 + 6 is like _____ negatives and _____ positives added together. We can form _____ negative-positive pairs that cancel each other out, and what is left is ____ negatives.” This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are filling in blanks instead of modeling to explain how the number line compares to counters when used to solve addition problems with integers.

  • Worktext 7-A, Chapter 4: Rational Numbers, Multiply and Divide Rational Numbers 2,  Question 10, students create a written problem for each multiplication expressions and then solve them. “Give a real-life context for each multiplication. Then solve. I have already done the first two for you. Hint: The area of a rectangle, the length resulting from stretching or shrinking a dimension, a fractional part, and a percentage of a quantity are all calculated by multiplying. c. (9/10)⋅2,100m(9/10)· 2,100m  d. 0.65⋅19.900.65 · 19.90” This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are given hints and examples that they could use.

MP5 is not intentionally developed to meet its full intent as students have limited opportunities to choose tools strategically. Examples include, but are not limited to:

  • Worktext 7-A, Chapter 1: The Language of Algebra, Simplifying Expressions, Puzzle Corner, students write an expression and make a table to figure out how many coins a person has. “a. What is the total value, in cents, if Ashley has n dimes and m quarters? Write an expression. b. The total value of Ashley’s coins is 495 cents. How many dimes and quarters can she have? Hint: make a table to organize the possibilities.” This problem does not provide students with an opportunity to choose tools strategically as the problem gives students the hint of making a table and does not allow them to consider the tools available.

  • Worktext 7-A, Chapter 4: Rational Numbers, Adding and Subtracting Rational Numbers, Question 6, students find the distance between two numbers. “Find the distance between the two numbers. The number lines above can help. a. -0.8 and -2.2 b. 0.9 and -1.3” This problem does not provide students with an opportunity to choose tools strategically as the problem provides students with the tool they can use to help (number line), and does not allow them to consider the tools available.

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Using the Distributive Property, Question 2, students solve a two-step equation. “Solve in two ways: (i) by dividing first and (ii) by distributing the multiplication over the parentheses first. a. 6(x−7)=726(x-7)=72” This problem does not provide students with an opportunity to choose the method of solving as the problem recommends the ways for students to solve it. 

Indicator 2H
02/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Materials provide support for the intentional development of MP6 by providing opportunities for students to attend to precision in connection to grade-level content. Examples include:

  • Worktext 7-A, Chapter 3: Solving One-Step Equations, Constant Speed, Question 8, students find the average speed for several scenarios in the given units. “Find the average speed in the given units. a. A duck flies 3 miles in 6 minutes. Give your answer in miles per hour. b. A lion runs 900 meters in 1 minute. Give your answer in kilometrs per hour.” This problem intentionally develops MP6 as it requires students to accurately calculate the average speed in the units given.

  • Worktext 7-A, Chapter 4: Rational Numbers , Rational Numbers, Question 3, students convert fraction to decimals. “Form a fraction from the two given integers. Then convert it into a decimal. a. 8 and 5 b. -4 and 10 c. 89 and -100” This problem intentionally develops MP6 as it requires students to be precise in their calculation in order to convert the fraction to decimals correctly.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Floor Plans, Questions 1, 2, and 3, students use a scale drawing to answer questions about items' dimensions in reality. “1. This room is drawn at a scale of 1in : 4ft. Measure dimensions asked below from the picture and then calculate the actual (real) dimensions. a. the bed b. the desk 2. What is the area of this room in reality? 3. In the middle of the plan for the room, draw a table that in reality measure 3.5 ft x 2.5 ft.” This problem intentionally develops MP6 as it requires students to express the length of objects with a degree of precision.

Materials provide support for attending to the specialized language of mathematics. Examples include:

  • Worktext 7-A, Chapter 2: Integers, Integers, Question 7, students are tasked with writing an expression for a word or phrase using symbols. “Write using symbols, and simplify if possible. a. the opposite of 6 b. the opposite of -11 c. the opposite of the absolute value of 12 d. the absolute value of negative 12 e. the opposite of the sum 6+86 + 8 f. the opposite of the difference 9−79 - 7 g. the absolute value of the opposite of 8 h. the absolute value of the opposite of -2”. This problem attends to the specialized language of mathematics as students translate written phrases into written expressions and simplify (if possible) those expressions. 

  • Worktext 7-A, Chapter 5: Equations and Inequalities, Two-Step Equations: Practice, Question 5, students solve a word problem involving a quadrilateral. “Solve each problem below in two ways: write an equation, and use logical reasoning/mental math. a. A quadrilateral has three congruent sides. The fourth side measures 1.4 m. If the perimeter of the quadrilateral is 7.1 meters, what is the length of each congruent side? This problem attends to the specialized language of mathematics as students use the definition of congruency to solve the problem.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Scaling Figures, Question 6, students develop an understanding of the scale factor and scale ratio in a specific situation. Notes within the lesson define scaling and scale ratio, it also says the following: “Here is a way to keep the two very similar-sounding terms straight: The scale ratio is a ratio of two numbers (like 3:1), but the scale factor is a single number (such as 3).” Question 6, “a.  Find the scale factor from the smaller to the larger parallelogram.  b. What is the scale ratio?” A picture of two parallelograms of different sizes is provided. The larger parallelogram has side lengths of 19 cm and 14 cm. The smaller parallelogram has 6 cm on the shorter side. This problem attends to the specialized language of mathematics as students use the definition of scale factor and ratio to provide a correct solution.

Indicator 2I
00/02

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

The materials reviewed for Math Mammoth Grade 7, Light Blue Series, do not meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. The materials provide opportunities for students to engage with structure and repeated reasoning, but do not allow students to use the structure or the repeated reasoning to formulate their ideas. 

MP7 and MP8 are not intentionally developed to meet their full intent in connection to grade-level content as students have limited opportunities to look for and make use of structure and look for and express regularity in repeated reasoning. Examples include, but are not limited to: 

  • Worktext 7-A, Chapter 1: The Language of Algebra, The Distributive Property, Question 1, students use the structure of a line segment to recognize the repeated pattern involved in the distributive property. “Write an expression for the repeated pattern in the model. Then multiply the expression using the distributive property.” In part b, students are provided a line segment with four s’s under the blue portion of the line segment each s is followed by the number 11 which is under the red portion of the line segment. Above Question 1 in an instructional box, students are provided a model of how to write and multiply an expression using line segments. “Here is a way to model the distributive property using line segments. The model shows a pattern of line segments of length x and 1 repeated four times. In symbols, we write 4⋅(x+1)4⋅(x+1). However, it is easy to see that the total length can also be written as 4x+44x+4. Therefore, 4⋅(x+1)=4x+44⋅(x+1)=4x+4. Students are not provided with the opportunity to make use of the structure of the line segment or the repeated reasoning it provides since the problem was modeled for them before they attempted it.

  • Worktext 7-A, Chapter 2: Integers, Multiplying Integers, Question 5, students use the structure of a series of equations to complete a pattern. “Complete the patterns. …b. −5⋅3=-5⋅3=____ −5⋅2=-5⋅2=____ −5⋅1=-5⋅1=____ −5⋅0=-5⋅0=____ −5⋅(−1)=-5⋅(-1)=____ −5⋅(−2)=-5⋅(-2)=____ −5⋅(−3)=-5⋅(-3)=____ −5⋅(−4)=-5⋅(-4)=____ In the pattern above, the product (answers) increase by ____  in each step! … The patterns in the products show that to be consistent, a negative times a negative must be a positive.” Students are not provided with the opportunity to share their thinking about what they notice while continuing the pattern through repeated reasoning and comparing the columns.

  • Worktext 7-B, Chapter 6: Ratios and Proportions, Proportional Relationships, Question 1, students fill in a table to determine whether two variables are in direct variation or not. “Fill in the table of values and determine whether the two variables are in direct variation. a. y=3xy=3x” Students are given a table with the x values ranging from -3 to 4 increasing by increments of 1, and the y values of the table are blank. Above Question 1 in an instructional box, students are provided a model of how to check to see if two variables are in direct variation. “You can check to see if two variables are in direct variation in several different ways. Here is one way. (1) Check to see if the values of the variables are in direct variation. If you double the value of one, does the value of the other double also? If one quantity increases by 5 times, does the other do the same?” This question is followed by an example of a relationship presented in a table that is not in direct variation accompanied by an explanation of why the values in the table do not work. Students are not provided with the opportunity to make use of the structure of the table to make their own generalizations about direct variation.

Criterion 2.2: Math Practices
03/10
Indicator 2E
00/02
Indicator 2F
01/02
Indicator 2G
00/02
Indicator 2H
02/02
Indicator 2I
00/02
Overview of Gateway 3

Usability

Gateway 3
v1.5
Gateway 3

Usability
NE = Not Eligible. Product did not meet the threshold for review.
NE
0
17
24
27
Criterion 3.1: Teacher Supports
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.2: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.3: Student Supports
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.4: Intentional Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Not Rated

Criterion 3.1: Teacher Supports

NE = Not Eligible. Product did not meet the threshold for review.
NE

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

Indicator 3A
00/02

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

Indicator 3B
00/02

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

Indicator 3C
00/02

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

Indicator 3D
Read

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

Indicator 3E
00/02

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

Indicator 3F
00/01

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

Indicator 3G
Read

This is not an assessed indicator in Mathematics.

Indicator 3H
Read

This is not an assessed indicator in Mathematics.

Criterion 3.1: Teacher Supports
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3A
00/02
Indicator 3B
00/02
Indicator 3C
00/02
Indicator 3D
Read
Indicator 3E
00/02
Indicator 3F
00/01
Indicator 3G
Read
Indicator 3H
Read

Criterion 3.2: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE

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

Indicator 3I
00/02

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

Indicator 3J
00/04

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

Indicator 3K
00/04

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

Indicator 3L
Read

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

Criterion 3.2: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3I
00/02
Indicator 3J
00/04
Indicator 3K
00/04
Indicator 3L
Read

Criterion 3.3: Student Supports

NE = Not Eligible. Product did not meet the threshold for review.
NE

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

Indicator 3M
00/02

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

Indicator 3N
00/02

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

Indicator 3O
Read

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

Indicator 3P
Read

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

Indicator 3Q
00/02

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

Indicator 3R
Read

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

Indicator 3S
Read

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

Indicator 3T
Read

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

Indicator 3U
Read

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

Indicator 3V
00/02

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

Criterion 3.3: Student Supports
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3M
00/02
Indicator 3N
00/02
Indicator 3O
Read
Indicator 3P
Read
Indicator 3Q
00/02
Indicator 3R
Read
Indicator 3S
Read
Indicator 3T
Read
Indicator 3U
Read
Indicator 3V
00/02

Criterion 3.4: Intentional Design

NE = Not Eligible. Product did not meet the threshold for review.
NE

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

Indicator 3W
Read

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

Indicator 3X
Read

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

Indicator 3Y
Read

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

Indicator 3Z
Read

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

Criterion 3.4: Intentional Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3W
Read
Indicator 3X
Read
Indicator 3Y
Read
Indicator 3Z
Read
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