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:
2nd Grade

About This Report

Report for 2nd Grade

Alignment Summary

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

2nd Grade
Gateway 1

Focus & Coherence
09/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
06/18
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 2, 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 partially meet expectations for coherence and consistency with the CCSSM, as they do not have content from prior and future grades connected to grade-level work. The materials partially meet expectations for making connections between clusters and domains. The materials do address the major clusters of the grade and have supporting content connected to major work.

Gateway 1
v1.5
Gateway 1

Focus & Coherence
09/14
0
7
12
14
Criterion 1.1: Focus
04/06
Criterion 1.2: Coherence
05/08
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 2, Light Blue Series, partially meet expectations for focus as they do assess grade-level content, but they 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 2, Light Blue Series, meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 2 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.  

Note: The user guide identifies the tests as optional; however, the publisher orientation session identified these assessments as a required component for school use. Therefore, the tests are included in this review.

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

  • Tests and Cumulative Reviews, Chapter 1 Test, Question 4, “You read 23 pages in a story book. Your friend Sally read double that many pages.  How many pages did Sally read?” (2.OA.1)

  • Tests and Cumulative Reviews, Chapter 5 Test, Question 5, “Divide these shapes. Then color as you are asked to. d. Divide this into fourths. Color 34\frac{3}{4} . ” (2.G.3)

  • Tests and Cumulative Reviews, End of Year Test, Question 18, “Jennifer bought two vacuum cleaners for $152 each. What was the total cost?” (2.NBT.7)

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 3 Test, Question 3, “Write <, >, or =. c.  12\frac{1}{2} of 20 ______ 12\frac{1}{2} of 18” (3.NF.1)

  • Tests and Cumulative Reviews, Chapter 5 Test, Question 4, “Write the fraction.” Part a has a picture of a circle divided into five equal parts, one of which is colored green. Part b has a picture of a circle divided into six equal parts, five of which are colored green. (3.NF.1) 

  • Tests and Cumulative Reviews, Chapter 10 Test, Question 5, “Multiply. a 4 x 3 =, 3 x 10 =” (3.OA.1)

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 2, 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 meet the full intent with grade-level-problems for the following standards including but not limited to: 2.OA.1, 2.MD.7, and  2.G.3 . The materials provide limited opportunities for all students to engage in extensive work with the following standards: 2.NBT.1a and 2.NBT.6 . and some off-grade-level work negatively impacts students’ work with grade-level content.

The materials are divided into two Worktexts, 2-A and 2-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 2-A, Chapter 4: Regrouping in Addition, Regrouping with Tens, Question 1, students use representations of tens and ones to add with regrouping. “Circle ten cubes to make a new ten. Count the tens, including the new one. Count the ones. Write the tens and ones in their own columns. You can use manipulatives.” a. Shows a picture of three tens and three ones and a group of 9 ones. The problem is given vertically as 33 + 9, in boxes to show the place values of tens and ones. Question 2, students use more abstract representations of tens and ones to add with regrouping. “Circle ten ones to make a new ten. Add the tens and ones in columns.” Drawings of ten sticks and ones are shown, along with columns for showing addion with place value. c. A picture of three tens and five ones, and a group of nine ones and one ten is provided. The problem 35 + 19 is given in vertical format with place value names of ten and one above the place value boxes. A 1 is above the tens box to show the regrouping. Question 5. “Show the additions on the number line by drawing lines that are that long. a.  13 +9 + 11= ___.” Students use drawings, number lines, and mental strategies to add within 1000. Students engage in extensive work with grade-level problems to meet the full intent of 2.NBT.7 (Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.) 

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Which Number is Greater?, Question 1, “Can you tell which number is more?  Try! Write < or > between the numbers.”  Students are shown a picture of 5 hundreds, 1 ten, 3 ones and 3 hundreds, 1 ten, and 5 ones, “d. 513 _____ 315”. Question 2, students are asked to draw hundreds, tens, and ones for the numbers.  Then compare and write < or >.  “a. 120 ______ 130”  Question 4, “Write either < or > in between the numbers. f. 600 ___ 860”  Students engage in extensive work with grade-level problems to meet the full intent of 2.NBT.4 (Compare two three-digit numbers based on meanings of hundreds, tens, and ones digits using >,=, and < symbols to record the results of comparisons.)  

  • Worktext 2-B, Chapter 10: Exploring Multiplication, Multiplication and Addition, Question 1, students are shown an array with 3 groups of two dots, “Write an addition and multiplication sentence for each problem. a.   _____ + ____ + _____ = _____  _____ x ____ = ______ Question 2, “Draw groups to match the sum.  Then write a multiplication sentence. c.  5 + 5 + 5 = _____ x ____ = ______”  Question 3, students are asked to fill in the blanks using the picture to solve.  The problem shows 2 groups of 4 carrots, “d.  ______ groups, _____ carrots in each.  _____ x ______ carrots = _______ carrots _____ + ______ “  Students engage in extensive work with grade-level problems to meet the full intent of 2.OA.4 (Use additions to find the total number of objects arranged in rectangular arrays with up to 5 rows and and up to 5 columns; write an equation to express the total as a sum of equal addends.)

The materials do not provide opportunities for students to meet the full intent of most of the standards. Examples include, but are not limited to: 

  • Students are not provided the opportunity to engage with the full intent of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.). Throughout the materials students do not tell and write time from digital clocks to the nearest five minutes, using a.m. and p.m. 

The materials provide limited opportunities for all students to engage in extensive work with the following standards:

  • Students do not have the opportunity to engage in extensive work with 2.NBT.1a (100 can be thought of as a bundle of ten tens — called a "hundred."). In Worktext 2-B, Chapter 6: Three-Digit Numbers, Three-Digit Numbers, students are told that “Ten ten-pillars make ONE HUNDRED:” A picture of ten ten-pillars is set equal to one hundred flat and the equation 10 tens = 100 is written under it. Question 5, “The dots are ones, the pillars are tens. Group together 10 ten-pillars to make a hundred. b. ______ “An image is provided with 15 pillars and four dots. These are the only problems in the lesson that allow students to bundle the ten tens to make a hundred. All other problems in the lesson, which is the only lesson that addresses this standard, have students using one hundred flats. Students are provided with limited opportunities to understand that 100 can be thought of as a bundle of ten tens.

  • Students do not have the opportunity to engage in extensive work with 2.NBT.6 (Add up to four two-digit numbers using strategies based on place value and the properties of operations.). In Worktext 2-A, Chapter 4: Regrouping in Addition, Adding Three or Four Numbers Mentally, Question 7, “Add mentally. Think, what would the easiest order to add the numbers!”a. 30 + 2 + 40 + 8 = ______ … d. 20 +10 + 8 + 9 = ______” Students are provided with limited opportunities to use strategies based on the properties of operations.

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 2-A, Chapter 2: Clock, How Many Hours Pass?, Question 6, “a. Dad’s workday starts at 8:00 in the morning, and ends at 5PM. How many hours is Dad at work?” Students are asked to engage in solving problems involving elapsed time, which does not align to a second grade standard.

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Comparing Fractions, Question 5, “Color. Then compare and write <, >, or =. Which is more ‘pie’ to eat?” “b. 34\frac{3}{4} 35\frac{3}{5}”  This question displays two circles. One is partitioned into 4 equal parts, one into 5 equal parts.  Students are asked to engage in solving problems involving comparing fractions, which does not align to a second grade standard. 

  • Worktext 2-B, Chapter 7: Measuring, Weigh in Kilograms, Question 7, “d. Weigh yourself with and without a heavy book. I weigh ___ kg. I weigh ___ kg with a heavy book. What is the difference? ___kg. So, the book weighs ___kg.” Students are asked to engage in solving problems involving measurement with kilograms, which does not align to a second grade standard.

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

Criterion 1.2: Coherence
05/08

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

The materials reviewed for Math Mammoth Grade 2, Light Blue Series, partially meet expectations for coherence. The majority of the materials, when implemented as designed, address the major clusters of the grade and have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials partially 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 do not have 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
02/02

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

The materials reviewed for Math Mammoth Grade 2, Light Blue Series, meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The materials devote at least 65%\% of instructional time to the major clusters of the grade: 

  • The 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 78 out of 118, approximately 66%\%.

  • The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 118.5 out of 168, approximately 70%\%. 

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 70%\% 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 2, 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 2-A, Chapter 2: Clock, The Minutes, connects the supporting work of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.) to the major work of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s.) For example, Question 3, e. students are shown an analog clock showing 9:25,  “Write the time using the normal clock. Remember, the numbers for the minute hand are not shown, and they go by fives!” Students skip count and write time to the nearest five minutes. 

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Graphs and Problems, connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.) to the major work of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) For example, Question 1, “The table lists the eye colors of some children. Draw the bars for the bar graph. a. How many children have either brown or hazel eyes?” Students add to find the total number of children from the bar graph data.

  • Worktext 2-B, Chapter 9: Money, Adding Money Amounts, connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ symbols appropriately.) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions) For example, Question 3, “Find the total cost in each case. b. Judy bought hot chocolate and a side of pizza.” Students solve a word problem involving the addition of dollar bills based on the information provided in a menu that a hot chocolate costs $1.05\$1.05 and a slice of pizza cost $2.75\$2.75.

Indicator 1E
01/02

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 2, Light Blue Series, partially 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. Materials contain multiple connections of major work to major work throughout, however, multiple connections from supporting work to supporting work are entirely absent from the grade-level materials. 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. 

Materials provide connections from major work to major work throughout the grade-level when appropriate. Examples include:

  • Worktext 2-A, Chapter 1: Some Old, Some New, Adding with Whole Tens, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction.) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract.)  For example, Question 2, “Add. Break the second number into tens and ones first. Then add the tens. b.  10 + 28 = ______  (10 + _____ + _______)” Students use place value understanding to find the sum of an addition problem. 

  • Worktext 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Subtract to Ten, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction.) to the major work of 2.OA.B (Add and subtract within 20.) For example, Question 1, “Subtract the ‘ones’ that are not in the ten group. You should only have ten left! d. 13 - _____ = 10” Students solve subtraction problems within 20. 

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Practice with Whole Hundreds, connects the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract.) to the major work of 2.MD.B (Relate addition and subtraction to length.) For example, Question 7, “a. John’s family is driving to Grandma’s place, and from there they are going to a zoo. Dad says, ‘To Grandma’s is 150 km, and from there to the zoo is 100 km.’ How far will the family drive from their home to the zoo?” Students use mental math and place value strategies to solve word problems involving lengths that are given in the same unit.

The following connections are entirely absent from the materials:

  • No connections are made between the supporting work of 2.OA.C (Work with equal groups of objects to gain foundations for multiplication.), the supporting work of 2.MD.C (Work with time and money), the supporting work of 2.MD.D (Represent and interpret data.) and/or the supporting work of 2.G.A (Reason with shapes and their attributes.).

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 2, 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 2-B, Chapter 7: Measuring, Introduction, “The concrete activities we do in second grade are laying an important foundation for familiarizing the children with measuring units. In third grade, the study of measuring turns toward conversions between the different units. In case you wonder about volume, we will study that in third grade and onward.”

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Introduction, “After this, it is time to study regrouping in subtraction with three-digit numbers. There are four cases: 1. Regrouping one ten as 10 ones, such as necessary in 546 - 229. 2. Regrouping one hundred as 10 tens, such as is necessary in 728 - 441. 3. Regrouping two times (on ten as 10 ones, and one hundred as 10 tens), such as 725 - 448. 4. Regrouping with zero tens, such as necessary in 405 - 278. In second grade, we only study cases (1) and (2) from the list above. The other two cases are left for third grade.” 

The materials do not reference prior grade learning, so they do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

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 2, Light Blue Series, foster coherence between grades and can be completed within a regular school year with little to no modification. Materials are divided between two Worktexts, 2-A and 2-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 169 days, including 156 days for lessons, chapter reviews and mixed reviews, and 13 days for assessments. 

According to the User Guide, Pacing the Curriculum, “Most lessons are 2 or 3 pages long, intended for one to two days. Some lessons are 4 pages and can be covered in two days. There are also some optional lessons (not included in the tables on the right). It can also be helpful to calculate a general guideline as to how many pages per week the student should cover in order to go through the curriculum in one school year.” 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 2-A, Chapter 1: Some Old, Some New, Introduction, “Please add one day to the pacing for the test if you will use it. Note that the specific lessons in the chapter can take several days to finish. They are not ‘daily lessons.’ As a general guideline, second graders should finish 1.5-2 pages daily or 8-10 pages a week.” Each chapter introduction contains a suggested pacing guide for that chapter based on this criteria. Using the criteria we arrive at 156 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 169 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
05/08
Indicator 1C
02/02
Indicator 1D
02/02
Indicator 1E
01/02
Indicator 1F
00/02
Indicator 1G
Read
Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for Math Mammoth Grade 2, 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 also 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
06/18
0
10
16
18
Criterion 2.1: Rigor and Balance
05/08
Criterion 2.2: Math Practices
01/10
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 2, 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 2, 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 2-A, Chapter 4: Regrouping in Addition, Going Over to the Next Ten, Question 1, students write the answer for problems that require them to add within 100. “Circle ten little cubes to make a ten. Count the tens and ones. Write the answer. a. 13 + 9 = _____”  Students are shown a picture of one tens stick, with three ones block next to it and a group of nine ones box together. Before the question students are provided with a box that says, “Sums that go over to the next ten”, and then provide students with two different procedures of how to add a sum over ten.  This question does not provide an opportunity for students to build a conceptual understanding of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.), as students are provided with the procedure to solve the problems.

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Adding Whole Tens, Question 1, students write the answer for problems that require them to add within 1000.  “Add whole tens. a. 160 + 30 = _____”  A picture is shown of one hundreds block, 6 ten sticks and 3 ten sticks. Three similar questions b - d are provided. Students are then shown a box that states, “651 + 20 = ??  Add 50 and 20, or the tens. That is 70.  The answer is then 671.  Notice: Only the TENS digit will change!  The ‘6’ of the hundreds does not change, nor the “1” of the ones.” Students then work on Question 2 questions a - f to show their understanding. An example: Question 2, “Add whole tens. You can draw illustrations to help. Underline the tens digits to help. b. 412 + 70 = _______”  This question does not provide an opportunity for students to build a conceptual understanding of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.), as students are provided with the procedure to solve the problems. 

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Regrouping in Subtraction, Part 1, a box is provided with the following information, “We will now study regrouping (‘borrowing’) in subtraction. As a first step, we study breaking a ten-pillar into ten little cubes. This is called regrouping, because one ten ‘changes groups’ from the tens group into the ones.” Question 1, “Break apart a ten into 10 ones. What do you get? Draw or use manipulatives to help.” d. Five tens and five ones are pictured with an arrow indicating the space for the student to draw the broken apart ten. “____tens____ones→\rarr ____tens____ones.” This question does not provide an opportunity for students to build a conceptual understanding of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds), as students are given a procedure to solve the problems. 

There is a cluster and/or standards that specifically relate to conceptual understanding that is/are not developed. For example, there is no evidence of how conceptual understanding is developed for 2.MD.6 (Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.)

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 2, 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 2-A, Chapter 1: Some Old, Some New, Adding with Whole Tens, Question 3, students fluently add within 100 to solve equations. “Add. Break the first number into tens and ones first. Then add the tens. b. 27 + 20 =_____ (____+____+ 20)” This activity provides students with an opportunity to develop procedural skills and fluency with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction).

  • Worktext 2-A, Chapter 4: Regrouping in Addition, Mental Addition of Two-Digit Numbers, Question 1, students fluently add within 100 to solve equations. “Add in parts, breaking the second number into its tens and ones.  20 + 34 = ______  20 + _____ + _____”  This activity provides students with an opportunity to develop procedural skills and fluency with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.)

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Skip-Counting by Tens, Question 5, students mentally subtract and add 10 from a given number. “Write the number that is 10 less and 10 more than the given number. d.  _______, 606, ______” This activity provides students with an opportunity to develop procedural skills and fluency with 2.NBT.8 (Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900). 

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

  • Worktext 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Fact Families with 12, Question 2, students solve equations by subtracting within 20. “Check! Can you subtract quickly from 12 and from 11 without looking above? a. 12 - 4 = ______  11 - 9 = ______  12 - 8 = ______  11 - 6 = ______”  This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 2.OA.2 (Fluently add and subtract within 20 using mental strategies).

  • Worktext 2-A, Chapter 4: Regrouping in Addition, Add with Two-Digit Numbers Ending in 9, Question 4, students solve equations by adding within 20. “These problems review the basic facts with 9 and 8. By this time you should already remember these addition facts. Try to remember what number will fit without counting. d. 7 + 8 = ___ 5 + 8 = ___ 6 + 8 = ___ 3 + 8 = ___ 9 + 8 = ___ 4 + 8 = ___” This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 2.OA.2 (Fluently add and subtract within 20 using mental strategies).

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Regrouping 10 Tens as a Hundred, Question 3, students add within 1000 using strategies based on place value. “Add mentally. Compare the problems. Notice you get a NEW hundred from the tens! a. 70 + 40 = ___ 170 + 40 = ___  270 + 40 = ___ ” This activity provides students with an opportunity to independently demonstrate the procedural skill and fluency of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds).

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 2, 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 2-A, Chapter 1: Some Old, Some New,  Subtracting Whole Tens, Question 5, students add the weight of items together to solve for total weight. “Solve a. Three suitcases weigh 30kg, 18kg, and 20kg. How much is their total weight?” This problem allows students to apply the mathematics of 2.OA.A (Represent and solve problems involving addition and subtraction) in a routine application problem independently.

  • Worktext 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Review: Going Over Ten, Question 6, students solve world problems and write an addition or subtraction sentence depending on the situation. “Solve the word problems. ALSO, write an addition & subtraction sentence for them! a. You have $8\$8 and you buy a toy for $5\$5 and candy for $2\$2. How much money do you have now?” This problem allows students to apply the mathematics of 2.OA.A (Represent and solve problems involving addition and subtraction) in a routine application problem independently.

  • Worktext 2-B, Chapter 9: Money, Review Chapter 9, Question 6, student  “Lily has $1.26\$1.26. Alex has two dimes, two quarters, and seven pennies in his piggy bank. How much money does Alex have? How much money do the children have together?” This problem allows students to apply the mathematics of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately) 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. Examples include: 

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Making Shapes, Question 1, students combine different shapes to create new shapes that match given pictures. “Cut out the shapes on the next page. What shapes can you use to make the given shapes? There may be several possible solutions.”  Students are tasked to cut out triangles, squares, and parallelograms and combine them to match the given shapes a - f. This problem allows students to apply the mathematics of 2.G.A (Reason with shapes and their attributes) in a non-routine application problem.

  • Worktext 2-B, Chapter 7: Measuring, Mixed Review Chapter 7, Puzzle Corner, students find different numbers that fit a given criteria. “The DIGITS of the number 467 are 4, 6, and 7. The sum of its digits is 4 + 6 + 7 = 17 (just add its digits). Find a number that… 

    • is more than 100 but less than 200;

    • the sum of its digits is 11.

    There are actually 9 different numbers like that. Can you find all of them?” This problem allows students to apply the mathematics of 2.NBT.B (Use place value understanding and properties of operations to add and subtract) 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 skill 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 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Adding with 9, Question 2, students add doubles of numbers within 20. “It is good to memorize the doubles, also. Fill in.  2 + 2 = _____  3 + 3 = _____  4 + 4 = ____”  This activity provides students with an opportunity to develop procedural skills and fluency with 2.OA.2 (Fluently add and subtract within 20 using mental strategies).

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Some Fractions, Question 2, students divide a rectangle into fourth to answer questions about the number of squares.  “Complete. d. Divide this into fourths.  Color 14\frac{1}{4}____ little squares in one fourth.  ____little squares in the whole rectangle.” Students are shown an outline of a rectangle on a grid. This activity provides students with an opportunity to develop a conceptual understanding with 2.G.3 (Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape).

  • Worktext 2-B, Chapter 7: Measuring, Meters and Kilometers, Question 5, students solve a word problem about the distance traveled between bases in Finnish baseball. “The picture shows the field for Finnish baseball game (‘pesäpallo’). How many meters do you run with these ‘routes’? a. You run from the home base to the 1st base and then return to the home base. b. You run from the home base to the 1st base and on to the 2nd base, plus one meter over, because you cannot stop in time. c. (Challenge) You run all the way around the field.” Students are provided with a diagram of the field with “Home base”, “1st base”, “2nd base”, and “3rd base” labeled and the distance between the paths in meters. This problem allows students to apply the mathematics of 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units) in a routine application problem independently. 

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

  • Worktext 2-A, Chapter 1: Some Old, Some New, Adding with Whole Tens, Question 1, students write an addition problem to solve using ten-sticks and one-dots. “The numbers are shown with ten-sticks and one-dots. Write the sums. d. ___ + ___ = ___” The problem shows two ten-sticks plus one ten-stick and three one-dots. Students develop conceptual understanding and build procedural skills and fluency for 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) as they use the visual images of ten-sticks and one-dots to write the equation and find the sum.

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Add in Columns: Regrouping Twice, Question 6, students solve addition word problems that require various strategies. “Solve the word problems. a. From Flowertown to Princetown is 148 miles. You travel from Flowertown to Princetown and back to Flowertown. How many miles is that?”  Students are given a 3-column grid to write the equation in.  Students develop conceptual understanding and application of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.) as they solve word problems.

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
01/10

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

The materials reviewed for Math Mammoth Grade 2, Light Blue Series, do not meet expectations for practice-content connections. The materials attend to the specialized language of mathematics. The materials do not support the intentional development of MPs 1, 2, 3, 4, 5, 6, 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 2, 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 2-A, Chapter 4: Regrouping in Addition, Add a Two-Digit Number and a Single-Digit Number Mentally, Question 4, students add two-digit numbers using strategies based on place value. “Add and compare! The top problem is a helping problem for the bottom one.  a.  7 + 6 = ______    27 + 6 = ______  (three more than the next ten)” 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 2-A, Chapter 5: Geometry and Fractions, Solids, Question 3, students write down things that are in the shape of a cone or a part of them is a cone. “You might have seen safety cones on the street. They are used to mark off areas where people are not supposed to go. Can you think of other things in real life that are in the shape of a cone, or a part of them is a cone? (Hint: One thing that is cone-shaped tastes really yummy!)(Hint: Another thing you might see in birthday parties.) A picture of a safety cone is provided, as well as a picture of a building with a cone-shaped roof. 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 2-B, Chapter 6: Three-Digit Numbers, Practice with Whole Hundreds, Question 7, students solve word problems involving driving to and from multiple destinations. “b. How far will they drive if they make a round trip? (from home to Grandma’s, then to the zoo, then back to Grandma’s, and back home)” 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.

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 2-A, Chapter 4: Regrouping in Addition, Going Over to the Next Ten, Question 4, students use a number line to add double-digit numbers with grouping. “Show these additions on the number line by drawing two lines. b. 14 + 18 = ____”   This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students use a number line provided to demonstrate addition.

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Rectangles and Squares, Question 3, students draw rectangles with a specified area on a grid. “Draw rectangles so they have a certain number of little squares inside.  Guess and check! a. 10 little squares b. 15 little squares” This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students draw rectangles to fit the given parameters.

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Bar Graphs and Pictographs, Question 3, students reason quantitatively as they solve problems about a pictograph. “The pictograph shows how many people visited the fairgrounds on different days. Each symbol means 100 people. Half a symbol means 50 people. Draw a bar graph.” A space is provided for students to draw the bar graph with the x and y axis labeled. A pictograph is pictured with symbols to represent the quantities and days. “a. What was the most popular day of the fair? How many people visited on that day?  b. How many more people visited on Sunday than on Friday? c. What was the total number of visitors on Thursday and Friday? d. Which day would you have gone,  if you didn’t like to be in a crowd? Which day would you have gone, if you liked to be in a crowd?” This question attends to the full intent of MP2, reasoning abstractly and quantitatively as students use the information from the pictograph to create the bar graph and answer questions about the information.

Indicator 2F
00/02

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 2, Light Blue Series, do not 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. Opportunities for students to construct viable arguments and critique the reasoning of others are not intentionally developed in connection to grade-level content.

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

  • Worktext 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Fact Families with 15, Question 3, students construct viable arguments as they explain how a student could solve an expression using an alternate method. “Alice does not remember the answer to 15 - 9. Explain how she can solve it using addition.” This question attends to MP3, constructing viable arguments as students explain how to solve a subtraction problem using addition.

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Subtract Whole Tens, Question 5, students explain how to subtract an expression. “Explain in your own words how to subtract 683 - 50.” This question attends to MP3, constructing viable arguments as students explain in their own words how to subtract an expression.

  • Worktext 2-B, Chapter 8: Regrouping in Addition and Subtraction, Mental Subtraction Part 2, Question 8, students explain how a subtraction method they created works. “Devise your own method for these subtractions. Explain how your method works. a. 52 - 36 b. 81 - 47 ” This question attends to MP3, constructing viable arguments as students create their own method and explain how their method works.

There is no opportunity throughout the materials for students to critique the reasoning of others.

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 2, 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 2-A, Chapter 1: Some Old, Some New, Subtracting Whole Tens, Question 1, students solve subtraction problems by crossing out ten-pillars. “Cross out as many ten-pillars as the problem indicates. What is left? c. 46 - 20 =___ Notice: The amount of ONES does not change in these subtractions. You can just think of the TENS.” This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are told to use the ten-pillars to solve the problem. 

  • Worktext 2-A, Chapter 4: Regrouping in Addition, Going Over to the Next Ten, Question 4, students use a number line to add double-digit numbers with grouping. “Show these additions on the number line by drawing two lines. a. 19 + 7 = ____” This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are told to use the number line to solve the problem.  

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Bar Graphs and Pictographs, Question 4, students make a pictograph based on the given information. “Joe practiced basketball. Make a pictograph showing how many baskets he made each day. Draw a picture and decide how many baskets that picture represents.” A chart is provided with two columns, one labeled “Day” and the other labeled “Baskets”. This problem does not provide students with an opportunity to model the situation with an appropriate representation as students are told how to create the model and what it represents.

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 2-A, Chapter 3: Addition and Subtraction Facts Within 0-18, Difference and How Many More, Question 1, students solve problems about difference using a number line. “Find the differences between these numbers using the number line above. a. difference between 10 and 6: ____” This problem does not provide students with an opportunity to choose tools strategically as the problem provides students with the tool they should use (number line), and does not allow them to consider the tools available.

  • Worktext 2-B, Chapter 7: Measuring, Feet and Miles, Question 1, students measure things around them with a tape measure and record the results in a table. “Use the tape measure to find distances in feet, or feet and inches. Let an adult help you.” This problem does not provide students with an opportunity to choose tools strategically as the problem provides students with the tool they should use (tape measure), and does not allow them to consider the tools available.

  • Worktext 2-B, Chapter 10: Exploring Multiplication, Review Chapter 10, Question 2, students solve a multiplication problem by using a number line. “Draw number line jumps to illustrate these multiplication sentences. a. 3 x 6 = ____” This problem does not provide students with an opportunity to choose tools strategically as the problem provides students with the tool they should use (number line), and does not allow them to consider the tools available.

Indicator 2H
01/02

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 2, Light Blue Series, partially 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. Although the materials attend to the specialized language of mathematics, there is limited evidence of the intentional development of MP6 to meet its full intent in connection to the grade-level content.

The materials has limited evidence of intentional development of MP6 throughout the grade level. Examples include, but are not limited to:

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Which Number is Greater?, Instructional box, states “Remember, the open end (open mouth) of the symbol < and > ALWAYS opens towards the bigger number.” Question 4, students compare if a number is greater than or less than another number. “Write either < or > in between the numbers. e. 200 ___ 190“ Although the symbols < (less than) and (greater than)  > are frequently used in comparison problems throughout the materials, the materials do not call them by those names, and students do not have to explain the meaning of the symbols.

  • Worktext 2-B, Chapter 6: Three-Digit Numbers, Bar Graphs and Pictographs, Question 2, students fill out a chart and then use a bar graph created by that chart to answer questions. “Below, you see page counts for 14 different second grade math books.” The book's page counts are the following numbers: 217, 388,  365, 290, 304, 315, 243, 352, 289, 392, 346, 308, 329, and 323. “Count how many books have between 200 and 249 pages. Count how many books have between 250 and 299 pages. Continue. Write the total pages in the chart. After that, draw a bar graph using the numbers in the above chart. a. How many books have a page count between 350 and 399 pages? b. How many books had 300 pages or more? c. How many books had less than 250 pages? d. What was the lowest page count?” A chart is provided with the labels “Page count” and “Number of books”. A bar graph is provided with the title “Page count of 2nd grade math books” and the labels “number of books” and “pages”. The scales on the bar graphs are also filled in. This problem does not allow students to attend to precision as they do not have the opportunity to label the chart and graph appropriately.

  • Worktext 2-B, Chapter 7: Measuring, students are tasked with answering questions dealing with different units of measurement (centimeters, inches, feet, miles, meters, kilometers, pounds, and kilograms). Throughout the chapter, there are examples of the units of measurement being specified for the students by the problem. For example: Some More Measuring, Question 5, students are tasked with measuring some items and recording the results in a table. “Measure some things in your classroom or at home two times. First measure them in inches, to the nearest half-inch. Them measure them in centimeters, to the nearest whole centimeter. Remember to write “about” if the thing is not exactly so many inches or centimeters. Write your results in the table below.” A table is provided with three columns labeled “Item”, “in inches”, and “in centimeters”. This problem does not allow students to attend to precision as they do not have the opportunity to measure items and then specify the unit of measure.

The materials attend to the specialized language of mathematics. Examples include:

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Shapes Review, Question 4, students draw shapes to answer questions about vertices and sides. “Draw FIVE dots on the right.  Connect the dots with straight lines.  You have drawn a pentagon (penta means five).  It has ______ vertices and ____ sides.  Draw one more pentagon in the space.” This problem attends to the specialized language of mathematics as students use the name and drawing of the shape to find the number of vertices and sides. 

  • Worktext 2-A, Chapter 5: Geometry and Fractions, Solids, Question 2, students answer questions about the face of various objects. “a. A face is any of the flat sides of a solid. Count how many faces a cube has. ____ faces. What shapes are they? b. Count how many faces a box has. ____ faces What shapes are they?  c. Count how many faces a pyramid has. ____ faces What shapes are they?”A picture of a pyramid is provided. This problem attends to the specialized language of mathematics as students apply the definition of the geometric term “face” to answer questions.  

  • Worktext 2-B, Chapter 7: Measuring, Some More Measuring, Question 6, students draw a shape and then find the perimeter of that shape. “Draw three dots on a blank paper so you can join them and make a triangle. Then, measure its sides BOTH in inches (to the nearest half-inch) and in centimeters (to the nearest centimeter). Write your results in the table. How many centimeters is the perimeter (all the way around the shape)? _____ cm. How many inches is the perimeter (all the way around the shape)? _____ in.” This problem attends to the specialized language of mathematics as students apply the definition of the geometric term “perimeter” to answer questions. 

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 2, 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 2-A, Chapter 1: Some Old, Some New, The 100-Chart and More Review, Question 5, students color in a 100-chart to reveal a pattern. “Skip-count by fours starting at 4. Color these numbers yellow. It makes an interesting pattern!” Students are provided with a 100-chart. Students are not provided with the opportunity to share their thinking about the pattern.

  • Worktext 2-A, Chapter 4: Regrouping in Addition, Going Over to the Next Ten, Question 6, students continue a pattern of similar addition problems. “Continue the patterns. COMPARE the columns, and NOTICE what is the same. “a. 8 +1= ____ 8 + 2 = ____ 8 + 3 = ____ 8 + 4 = ____ 8 +____ =____ 8 +____ = ____ b. 28 +1= ____ 28 + 2 = ____ 28 + 3 = ____ 28 + 4 = ____ 28 +____ =____ 28 +____ = ____…”  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 2-B, Chapter 6: Three-Digit Numbers, Patterns and Problems, Question 5, students continue a pattern of similar subtraction and addition problems. “Continue the patterns! a. 590 - 60 = ____ 590 - 70 = ____ 590 - 80 = ____ 590 - ____ = ____ 590 - ____ = ____  590 - ____ = ____  …” Students are not provided with the opportunity to share their thinking about how the structure of the problem helps them complete the pattern, and what generalization can be formed due to the repeated calculations.

Criterion 2.2: Math Practices
01/10
Indicator 2E
00/02
Indicator 2F
00/02
Indicator 2G
00/02
Indicator 2H
01/02
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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