About This Report
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Report Overview
Summary of Alignment & Usability: Math Mammoth | Math
Math K-2
The materials reviewed for Math Mammoth Grades 1 and 2, Light Blue Series, do not meet expectations for Alignment to the CCSSM. For Grade 1, the materials do not meet expectations for focus and coherence in Gateway 1. For Grade 2, the materials partially meet expectations for focus and coherence in Gateway 1 and do not meet expectations for rigor and practice-content connections in Gateway 2.
1st Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
The materials reviewed for Math Mammoth Grades 3-5, Light Blue Series, do not meet expectations for Alignment to the CCSSM. In Gateway 1, the materials do not meet expectations for focus and partially meet expectations for coherence.
3rd Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 6-8
The materials reviewed for Math Mammoth Grades 6 and 7, Light Blue Series, do not meet expectations for Alignment to the CCSSM. For Grade 6, the materials do not meet expectations for focus and coherence in Gateway 1. For Grade 7, the materials partially meet expectations for focus and coherence in Gateway 1 and do not meet expectations for rigor and practice-content connections in Gateway 2.
6th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports 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)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 3rd Grade
Alignment Summary
The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not meet expectations for Alignment to the CCSSM. In Gateway 1, the materials do not meet expectations for focus and coherence.
3rd Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not meet expectations for focus and coherence. For focus, the materials do assess grade-level content, but they do not 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
Criterion 1.1: Focus
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 3, Light Blue Series, do not meet expectations for focus as they do assess grade-level content and do not provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1A
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Math Mammoth Grade 3, Light Blue Series, meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum has a Grade 3 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. In addition, there is one chapter, Chapter 5, that is aligned to above grade level standards that could be omitted without impacting the other 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 8, “One year has 365 days. Of those, 206 are school days. How many days in a year are not school days?” (3.NBT.2)
Tests and Cumulative Reviews, Chapter 2 Test, Question 3, “Write a number sentence for each problem and solve. a. Each basket holds 12 apples. How many apples are in three baskets?” (3.OA.1)
Tests and Cumulative Reviews, Chapter 4 Test, Question 6, “A soccer game started at 1:30 PM, and ended 50 minutes later. What time was it then?” (3.MD.1)
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 2 Test, Question 4, “Calculate. c. 0 x (10 + 2) x 3 d. (8 - 3) x 1 + 6 ” (5.OA.1)
Tests and Cumulative Reviews, Chapter 5 Test, Question 3, “Solve in your head a. You bought stamps for , a pen for , and a notebook for . What was the total cost?” (5.NBT.7)
Tests and Cumulative Reviews, End of Year Test, Question 16, “Each table in a restaurant seats four people. How many tables do you need to reserve for a party of 31 people?” (4.NBT.6)
The materials also include content that is not aligned to CCSS, an example includes:
Tests and Cumulative Reviews, Chapter 1 Test, Questions 3, “Write the Roman numerals using normal numbers. a. IV … f. XCVIII ” These items do not align to CCSS.
Indicator 1B
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 3, Light Blue Series, do not 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 and/or do not provide opportunities for students to meet the full intent with grade-level-problems for standards including but not limited to: 3.OA.3, 3.OA.8, 3.OA.9, 3.MD.3, and 3.MD.6 . Some off-grade-level work negatively impacts students’ work with grade-level content.
The materials are divided into two Worktexts, 3-A and 3-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 3-A, Chapter 2: Multiplication Concept, Many Times the Same Group, Question 1, “Write the multiplication.” Pictures showing equal groups are shown, for example, e. shows five groups of two blue dots. “_____ x _____” Question 2, “Now it is your turn to draw! Notice the symbol x which is read ‘times’. c. 1 times 7 1 x 7” Students engage in extensive work with grade-level problems to meet the full intent of 3.OA.1 (Interpret products of whole numbers)
Worktext 3-A, Chapter 3: Multiplication Tables, Multiplication Table of 2, Question 4, “Don’t write the answers down. Use these problems for random drill practice. _ x 2 = 14, _ x 2 = 12 , ___ x 2 = 6 …” Students fill in the missing number to make the equation true. In subsequent lessons, students solve similar problems with different factors. In the lesson, Multiplication Table of 5, Question 4, “Don’t write the answers down. Use these problems for random drill practice _ x 5 = 35, _ x 5 = 20 , ___ x 5 = 55 …” In Chapter 3: Multiplication Tables, lessons are available for Multiplication Tables 2 -12, with similar questions. Students engage in extensive work with grade-level problems to meet the full intent of 3.OA.4 (Determine the unknown whole number in a multiplication or division equation relating three whole numbers.)
Worktext 3-B, Chapter 10: Fractions, Fractions on a Number Line, Question 1, “Fill in. You can also color a rectangle that goes up to the arrow, to help you. a. The number line from 0 to 1 is divided into _____ parts. The arrow marks the fraction .” Question 5, “Divide the number line from 0 to 1 into equal parts. Then mark the fraction on it.” There are ten problems where students are shown a number line from 0 to 1 and they identify where a fraction is on the line, for example e. asks them to find . Question 6, “Write all the fractions under the tick marks.” A number line from 0 to 3 is shown. There are dots at each . Students engage in extensive work with grade-level problems to meet the full intent of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram.)
The materials provide limited opportunities for all students to engage in extensive work with grade-level problems and/or do not provide opportunities for students to meet the full intent of most of the standards. Examples include, but are not limited to:
Students do not have the opportunity to engage in extensive work with 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). In Worktext 3-A, Chapter 3: Multiplication Tables, Multiplication Table of 7, Question 4, “Solve. Write a number sentence for each problem, not just the answer! a. Jenny packed pretty stones in boxes. She put seven stones in each box. How many boxes did Jenny need to pack 28 stones?” The material does not provide extensive work in solving word problems involving arrays.
Students are not provided the opportunity to engage with the full intent of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs). In Worktext 3-A, Chapter 1: Addition and Subtraction, Graphs, Question 1, “The graph shows the number of books some children read during a vacation reading assignment. Read the graph and fill in the blanks. c. How many more books did Jack read than Jake? ___ books f. Did the girls or the boys read more books? ___ How many more? ___ ” Students are not provided the opportunity to draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
Students do not have the opportunity to engage in extensive work with 3.MD.6 (Measure area by counting square units). In Worktext 3-B, Chapter 7: Geometry, Getting Started with Area, Question 1, “How many square units is the area of these figures? a. The area is ___ square units. b. The area is ___ square units.” Students are provided four figures with colored squares to count and find the area. The material does not provide extensive work in measuring area by counting square units.
Students do not have the opportunity to engage in extensive work with 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.) In Worktext 2-B, Chapter 7: Geometry, Some Special Quadrilaterals. Question 2, “Draw three quadrilaterals that are NOT squares nor rectangles.”A square or a rhombus? The material does not provide extensive work in drawing examples of quadrilaterals that do not belong to the subcategories of rhombuses, rectangles, and squares.
Students are not provided the opportunity to engage with the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.). In Worktext 3-B, Chapter 10: Fractions, Understand Fractions, Question 7, “ Divide the shapes into equal parts. Shade ONE part. Write the area of that part as a fraction of the whole area. b. Divide the shape into three equal parts. shaded area = of the whole area” Students are provided a picture of 3 by 4 rectangle on a grid. Students are not provided an opportunity to express the area of each part as a unit fraction of the whole.
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 3-B, Chapter 6: Place Value with Thousands, Add 4-Digit Numbers with Regrouping, Question 2, “Add. Be careful to line up the ones, tens, hundreds, and thousands. a. 34 + 2,382 +, 391 + 77 + 3,409 ” Throughout the lesson students are tasked to add numbers beyond 1000, which does not align to a third grade standard.
Worktext 3-B, Chapter 6: Place Value with Thousands, Subtract 4-Digit Numbers with Regrouping, Question 3, “ a. 4,908 - 203 - 1,420 ”. Throughout the lesson students are tasked to subtract numbers beyond 1000, which does not align to a third grade standard.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Math Mammoth Grade 3, Light Blue Series, do not meet expectations for coherence. 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 majority of the materials, when implemented as designed, do not address the major clusters 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
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Math Mammoth Grade 3, 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 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 79 out of 127, approximately 62
The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 103.5 out of 173, approximately 60.
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 60 of the instructional materials focus on major work of the grade.
Indicator 1D
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Math Mammoth Grade 3, 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 3-B, Chapter 6: Place Value with Thousands, Word Problems, connects the supporting work of 3.MD.B (Represent and interpret data.) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic.) For example, Question 7, “Alex checked the price of a certain TV in four different stores. a. Draw a bar graph from his results. b. How much is the difference between the most and the least expensive TV?” Students represent data on a bar graph and solve to find the difference.
Worktext 3-B, Chapter 7: Geometry, Multiplying by Whole Tens, connects the supporting work of 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range of 10-90 using strategies based on place value and properties of operations) to the major work of 3.OA.5, (Apply properties of operations as strategies to multiply and divide.) For example, Question 6, “Break each multiplication into another where you multiply three numbers, one of them being 10. Multiply and fill in. b. 4 x 80 = ____ x _____ x 10, = ______ x 10 = _____” Students use the associative property to multiply one-digit numbers by multiples of ten.
Worktext 3-B, Chapter 10: Fractions, Understanding Fractions, connects the supporting work of 3.G.A (Reason with shapes and their attributes) to the major work of 3.NF.A (Develop understanding of fractions as numbers.) For example, Question 7, “Divide the shapes into equal parts. Shade ONE part. Write the area of that part as a fraction of the whole area. c. Divide the shape into six equal parts. shaded area = of the whole area.” Students divide the shape and represent the value of the shaded portion as a fraction.
Indicator 1E
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 3, 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 3-A, Chapter 1: Addition and Subtraction, Graphs, connects the supporting work of 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic.) to the supporting work of 3.MD.B (Rrepresent and interpret data.). For example, Question 2, “Below you see a pictogram that shows how many vegetables were used in certain places.” Each carrot symbol represents 5 kilograms. “d. How many kilograms of vegetables did the two restaurants use in all? __ kg.” Students interpret data on a pictograph in order to perform multi-digit arithmetic.add and subtract while answering questions about a pictographs and bar graphs.
Worktext 3-A, Chapter 2: Multiplication Concept, Multiplication in Two Ways, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division.) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division.). For example, Question 3, “Draw X’s and group them in two ways to illustrate the two ways to multiply. a. ___ x ____ = _____ nine groups of 2 ____ x _____= _____ two groups of 9.” Students draw groups of X’s and write both multiplication equations using the commutative property to match a given scenario.
Worktext 3-B, Chapter 7: Geometry, More about Area, connects the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division.) to the major work of 3.MD.C (Geometric measurement: understand concepts of area and relate area to multiplication and to addition.). For example, Question 2, “Write a number sentence for the total area, thinking of one rectangle or two. a. ___ x ( ___ + ___ ) area of whole rectangle = ____ x ____ area of the first part + ____ x ____ area of the second part.” Students are provided a grid with squares colored in that corresponds to the first part and the second part of the area. Students use the distributive property to solve area problems.
Worktext 3-B, Chapter 8: Measuring, Line Plots and More Measuring, connects the supporting work of 3.MD.B (Represent and interpret data.) to the supporting work of 3.G.A (Reason with shapes and their attributes.). For example, Question 2, “Draw three dots and join them to get a triangle. Measure its sides to the nearest quarter inch. Write the measurement next to each side. If you can, figure out the perimeter. (all the way around the shape) It is _______inches.” Students create a triangle and measure the sides to find the perimeter.
Indicator 1F
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 3, 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 3-A, Chapter 4: Telling Time, Introduction, "We review the topic of reading the clock to the five-minute intervals, first using numbers in telling the time, such as 6:45 or 12:15. Then, children learn about quarter hours, such as a quarter till 6 or a quarter past 9. We also review the topic of using “past” and “till”, such as in 20 till 6 or 10 past 11. Next, we study elapsed time in the lessons How Many Minutes Pass and More on Elapsed Time. These lessons provide lots of visual aids (clock faces) for the children to be able to figure out how much time passes. You can also use a practice clock. The lessons don't yet cover the situation where we would need to figure out the elapsed time in several parts (such as, how much time passes from 9:13 AM to 1:45 PM?). That is studied in 4th grade."
Worktext 3-B, Chapter 9: Division, Introduction, “...the student finds the remainder by using visual models (you could also use manipulatives), and then by calculating. This concept will be studied again in fourth grade.”
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 3-A, Chapter 1: Addition and Subtraction, Introduction, “I have included several lessons on mental math, including review of many of the strategies from second grade,”
Worktext 3-A, Chapter 4: Telling Time, Introduction, “ … The lesson Clock to the Minute completes the topic (begun in earlier grades) of reading the clock, because the student will now be able to tell the complete time.”
Indicator 1G
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 3, 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, 3-A and 3-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 173 days, including 160 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 intended to be done in a single teaching session or class. Sometimes you might be able to go through a whole lesson in one day, but more often, a lesson might span 3-5 pages and take 2-3 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, it is helpful to calculate a general guideline as to how many pages per week should be covered in order to get through the curriculum in one school year (or whatever span of time you are allotting to it).” 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 3-A, Chapter 1: Addition and Subtraction, 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 third graders should finish 1.5-2 pages daily or 8-10 pages a week.” Using the guidance of 10 pages a week, the total number of pages (318) was divided by 10 pages a week, this computation resulted in approximately 32 weeks of instruction, which when mutiple by 5 gives 160 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 173 days.
Optional content if added would account for an additional nine days. Nine days would be for the cumulative reviews, there are no optional lessons in the material.
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."
Overview of Gateway 2
Rigor & the Mathematical Practices
Gateway 2
v1.5
Criterion 2.1: Rigor and Balance
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.
Indicator 2A
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
Indicator 2B
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
Indicator 2C
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
Indicator 2D
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.
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
Indicator 2E
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.
Indicator 2F
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.
Indicator 2G
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.
Indicator 2H
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.
Indicator 2I
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.
Overview of Gateway 3
Usability
Criterion 3.1: Teacher Supports
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
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
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
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
Indicator 3D
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
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
Indicator 3F
Materials provide a comprehensive list of supplies needed to support instructional activities.
Indicator 3G
This is not an assessed indicator in Mathematics.
Indicator 3H
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
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
Assessment information is included in the materials to indicate which standards are assessed.
Indicator 3J
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
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
Indicator 3L
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
Indicator 3M
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
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
Indicator 3O
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
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Q
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
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
Indicator 3S
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
Indicator 3T
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
Indicator 3U
Materials provide supports for different reading levels to ensure accessibility for students.
Indicator 3V
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
Indicator 3W
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
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
Indicator 3Y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
Indicator 3Z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.