Kindergarten Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Kindergarten Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time in kindergarten should be devoted to number than to other topics.”
Units | Focus |
Classroom Routines & Materials | Counting and representing quantities |
Counting & Measurement I | Counting and representing quantities, comparing and ordering quantities, understanding length |
2D Geometry | Describing, identifying, and comparing 2D shapes |
Counting & Measurement II | Counting and representing sets of objects, using multiple units to measure and compare lengths, decomposing numbers, beginning to understand addition and subtraction |
3D Geometry | Describing, identifying, comparing, composing, and decomposing 3D shapes |
Addition, Subtraction, & the Number System I | Counting sets of objects, decomposing numbers, using notation, and solving addition and subtraction problems |
Modeling with Data | Sorting, classifying, counting, ordering, comparing, and representing data; using data to model real-world problems |
Addition, Subtraction, & the Number System II | Extending the counting sequence, adding and subtracting in a variety of contexts |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 1 Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Grade 1 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.”
Units | Focus |
Addition, Subtraction, & the Number System I | Understanding, representing, and solving problems involving addition and subtraction |
2D Geometry | Describing, identifying, comparing, composing, and decomposing 2D shapes |
Addition, Subtraction, & the Number System II | Understanding, representing, and solving problems involving addition and subtraction |
Measurement & Fractions | Understanding length and linear units |
Addition, Subtraction, & the Number System III | Developing fluency with addition and subtraction, finding an unknown addend or change, understanding the equals sign, composing and decomposing numbers |
Modeling with Data | Collecting, representing, describing, and interpreting data |
Addition, Subtraction, & the Number System IV | Counting, adding, and subtracting with multiples; representing adding and subtracting with models |
3D Geometry | Describing, identifying, comparing, composing, and decomposing 3D shapes |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 2 Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Grade 2 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.”
Units | Focus |
Addition, Subtraction, & the Number System I | Representing and solving problems involving addition and subtraction; understanding and using place value |
Geometry & Fractions | Describing, identifying, and comparing attributes of 2D and 3D shapes; understanding parts of a whole |
Addition, Subtraction, & the Number System II | Using place value and properties to add and subtract |
Modeling with Data | Sorting, classifying, describing, and interpreting data |
Addition, Subtraction, & the Number System III | Understanding, representing, and solving problems involving addition and subtraction; understanding and extending the counting sequence |
Linear Measurement | Measuring with nonstandard and standard units and tools |
Foundations of Multiplication | Examining groups in the structure of arrays; describing and representing equal groups |
Addition, Subtraction, & the Number System IV | Understanding, representing, and solving problems involving addition and subtraction |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 3 Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Grade 3 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes. ”
Units | Focus |
Multiplication & Division I | Understanding the properties of, representing, and solving problems with multiplication and division |
Modeling with Data | Describing, summarizing, and comparing data |
Addition, Subtraction, & the Number System I | Solving problems with operations fluently |
2D Geometry & Measurement | Finding perimeter and area, and classifying figures |
Multiplication & Division II | Solving multi-step problems with multiplication and division |
Fractions | Understanding the meaning of, reasoning about equivalence, comparing, and using notation to model fractions |
Addition, Subtraction, & the Number System II | Solving multi-step problems with operations fluently |
Multiplication & Division III | Solving multi-step problems with operations fluently |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 4 Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Grade 4 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.”
Units | Focus |
Multiplication & Division I | Reasoning about numbers, factors, and multiples; solving multiplicative comparison problems |
Modeling with Data | Representing, describing, summarizing, comparing, analyzing, and interpreting data |
Multiplication & Division II | Representing and solving multiplication and division problems |
2D Geometry & Measurement | Describing and classifying figures and angles; understanding and determining area |
Addition, Subtraction, & the Number System | Extending the number system; describing, analyzing, and comparing strategies to add and subtract fluently |
Fractions & Decimals | Comparing fractions and decimals and finding equivalents; using visual models to add, subtract, and multiply fractions |
Multiplication & Division III | Solving multi-step problems with operations fluently |
Analyzing Patterns & Rules | Generating and analyzing patterns; solving multi-step problems fluently |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 5 Math utilizes Investigations as its core program. Investigations has as its guiding principles that students have mathematical ideas, teachers are engaged in ongoing learning about student learning, and teachers make decisions based on their observations of student learning. The three pillars of Investigations are the routines, the classroom discourse, and the games. | |
Grade 5 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 5, instructional time should focus on four critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases; (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; (3) developing understanding of measurement systems and determining volumes to solve problems; and (4) solving problems using the coordinate plane.”
Units | Focus |
Multiplication & Division I | Performing operations with multi-digit whole numbers |
3D Geometry & Measurement | Understand concepts of and solve problems involving volume |
Rational Numbers I: Addition & Subtraction | Solving problems involving addition and subtraction of fractions |
Multiplication & Division II | Solving multi-step problems with multiplication and division efficiently |
Analyzing Patterns & Rules | Modeling situations with ordered pairs, table, and symbols; reading and constructing graphs; analyzing and comparing relationships |
Rational Numbers II: Addition & Subtraction | Solving problems involving addition and subtraction of decimals |
Rational Numbers III: Multiplication & Division | Solving problems involving multiplication and division of fractions and decimals |
2D Geometry & Measurement | Classifying triangles and quadrilaterals based on their properties |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 6 Math utilizes the Desmos version of the Illustrative Mathematics curriculum as its core program. | |
Grade 6 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 6, instructional time should focus on five critical areas: (1) connecting ratio and rate to whole number multiplication and division, and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; (4) developing understanding of statistical thinking; and (5) reasoning about geometric shapes and their measurements.”
Units | Progression of Understanding (adapted from https://im.kendallhunt.com/ and https://hub.illustrativemathematics.org/) |
Area & Surface Area | Area of Shapes Composed of Rectangles ➡ Area of Shapes Composed of Triangles How can we find the area of figures? How can we cut and rearrange irregular polygons in order to find their area? |
Introducing Ratios | Concrete Representations ➡ Abstract Representations What do we mean by “ratio reasoning” and how do different representations support students’ reasoning about how quantities are associated? |
Unit Rates & Percentages |
Rate ➡ Percentage as a Rate How do rates per 1 and rates per 100 help students understand percentages? |
Dividing Fractions | Meaning/Interpretations of DIvision ➡ Algorithm How can building understanding for division situations support making sense of the fraction division algorithm? |
Arithmetic in Base Ten | Diagrams ➡ Algorithms How does using diagrams to represent operations with decimals build understanding of algorithms? |
Expressions & Equations | Arithmetic ➡ Algebra How can we use our ideas about arithmetic to make sense of expressions and equations? |
Rational Numbers | Rational numbers as points on a line ➡ Aspects of rational numbers in contexts How does the use of number line models and context build understanding for aspects of rational numbers? |
Data Sets & Distributions | Informally Explore Distributions of Data ➡ Summarize Distributions of Data How can understanding distributions of data help us to both summarize data and use it to make decisions? |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 7 Math utilizes the Desmos version of the Illustrative Mathematics curriculum as its core program. | |
Grade 7 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.”
Units | Progression of Understanding (adapted from https://im.kendallhunt.com/ and https://hub.illustrativemathematics.org/) |
Scale Drawings | Scale Factor ➡ Scale Copies; Scale Factor ➡ Scale Drawings How does scaling affect lengths, angles, and areas in scaled copies? How can students represent distances in the world using scales and scale drawings? |
Introducing Proportional Relationships | Sets of Equivalent Ratios ➡ Proportional relationships How do students reason algebraically about proportions using the form y=kx in contrast to the more familiar a/b = c/d? |
Measuring Circles |
Proportional relationships ➡ Formulas for Circumference and Area How do proportional relationships support the understanding of the relationship between radius and diameter of a circle? |
Proportional Relationships & Percentages | Proportional Relationships ➡ Percent increase or decrease How do proportional relationships support the understanding of percent and percent increase or decrease? |
Operations with Positive & Negative Numbers | Representing Operations on Signed Numbers ➡ Evaluating Expressions with Signed Numbers How does the use of the number line support students’ sense-making of the rules of signed number arithmetic? |
Expressions, Equations, & Inequalities | Structure of Equations ➡ Algebraic Fluency How does noticing the structure of an equation help us make decisions about the steps we might take to solve the equation? |
Angles, Triangles, & Prisms | Geometry ➡ Algebra How does Grade 7 geometry applications, Angle relationships, Drawing Triangles and Solid Geometry, support students’ use and understanding of Algebra? |
Probability & Sampling | Quantifying Probability Through Random Sampling ➡ Sampling From a Population How do you quantifying probability and random sampling support making inferences from sampling a population? |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE
Grade 8 Math utilizes the Desmos version of the Illustrative Mathematics curriculum as its core program. | |
Grade 8 Mathematics
As noted in the MA 2017 Curriculum Framework for Math: “In grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; and (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.”
Units | Progression of Understanding (adapted from https://im.kendallhunt.com/ and https://hub.illustrativemathematics.org/) |
Rigid Transformations & Congruence | Rigid Transformations ➡ Understanding Congruence Why does precise work with rigid transformations help students reason carefully about congruence? |
Dilations, Symmetry, & Introducing Slope | Dilations ➡ Similarity ➡ Slope Why is slope well-defined? How does similarity help answer that? |
Proportional & Linear Relationships |
Proportional Relationships ➡ Linear Relationships How does understanding of proportional relationships and multiple representations extend to linear relationships? |
Linear Equations & Linear Systems | What is a solution to an equation ➡ Solutions to an equation with one variable ➡ Solutions to an equation with two variables How do structures of 1-variable equations support the reasoning about structure and solutions of and solutions of 2 equations in 2-variables? |
Functions & Volume | Defining Function ➡ Seeing Volume Formulas as Functions What is a function? How does the understanding of functions extend to volume formulas? |
Associations in Data | Organize and Display Data ➡ Describe Patterns and Associations How do data displays help us describe how variables are associated? What if variables are categorical? |
Exponents & Scientific Notation | Seeing Structure ➡ Language of Scientific Notation How do number lines and patterns help us conceptualize very large and very small numbers and make sense of scientific notation? |
Pythagorean Theorem & Irrational Numbers | Understanding Square Roots ➡ Understanding Pythagorean Theorem How does reasoning about the relationship between area of squares and side lengths prepare for understanding the Pythagorean theorem? |
All students engage in the STANDARDS FOR MATHEMATICAL PRACTICE