Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.

In Module 1, students used their existing understanding of multiplication and division as they began their study of ratios and rates.  In Module 2, students complete their understanding of the four operations as they study division of whole numbers, division by a fraction and operations on multi-digit decimals.  This expanded understanding serves to complete their study of the four operations with positive rational numbers, thereby preparing students for understanding, locating, and ordering negative rational numbers (Module 3) and algebraic expressions (Module 4).

Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers from previous grades. Students extend the number line (both horizontally and vertically) in Module 3 to include the opposites of whole numbers. The number line serves as a model to relate integers and other rational numbers to statements of order in real-world contexts. In this module's final topic, the number line model is extended to two-dimensions, as students use the coordinate plane to model and solve real-world problems involving rational numbers.

In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers. Students explore operations in terms of verbal expressions and determine that arithmetic properties hold true with expressions because nothing has changed—they are still doing arithmetic with numbers. Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers. They understand the relationships of operations and use them to generate equivalent expressions, ultimately extending arithmetic properties from manipulating numbers to manipulating expressions. Students read, write and evaluate expressions in order to develop and evaluate formulas. From there, they move to the study of true and false number sentences, where students conclude that solving an equation is the process of determining the number(s) that, when substituted for the variable, result in a true sentence. They conclude the module using arithmetic properties, identities, bar models, and finally algebra to solve one-step, two-step, and multi-step equations.

In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area.  Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons.  Extending skills from Module 3 where they used coordinates and absolute value to find distances between points on a coordinate plane, students determine distance, perimeter, and area on the coordinate plane in real-world contexts.  Next in the module comes real-life application of the volume formula where students extend the notion that volume is additive and find the volume of composite solid figures.  They apply volume formulas and use their previous experience with solving equations to find missing volumes and missing dimensions.  The final topic includes deconstructing the faces of solid figures to determine surface area.  To wrap up the module, students apply the surface area formula to real-life contexts and distinguish between the need to find surface area or volume within contextual situations.

In this module, students move from simply representing data into analysis of data.  Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data.  Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape.  Throughout the module, students see and represent data distributions using dot plots and histograms.  They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution.  As the module ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project.

In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in P-12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes. The full year of Grade 7 Mathematics curriculum is available from the module links.

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality.  Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions.  Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.

In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers. This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module.  Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation.

This module consolidates and expands upon students’ understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form.  They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers.  Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities.  They interpret solutions within the context of problems.  Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms.

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to “the whole” serves as a foundation for students.  Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.  Material in early lessons is designed to reinforce students’ understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on their earlier work with these.  As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction.

In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings.  They also learn how to estimate probabilities empirically.  Probability provides a foundation for the inferential reasoning developed in the second half of this module.  Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples.

In Module 6, students delve further into several geometry topics they have been developing over the years.  Grade 7 presents some of these topics, (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet.  Module 6 assumes students understand the basics.  The goal is to build a fluency in these difficult problems.  The remaining topics, (i.e., working on constructing triangles and taking slices (or cross-sections) of three-dimensional figures) are new to students.

This site teaches Statistics and Probability to 7th graders through a series of 475 questions and interactive activities aligned to 10 Common Core mathematics skills.

This site teaches Expressions and Equations to 8th graders through a series of 4712 questions and interactive activities aligned to 32 Common Core mathematics skills.

This site teaches Functions to 8th graders through a series of 1920 questions and interactive activities aligned to 17 Common Core mathematics skills.

This site teaches Geometry to 8th graders through a series of 2398 questions and interactive activities aligned to 19 Common Core mathematics skills.

In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for any integer exponent.  Next, students work with numbers in the form of an integer multiplied by a power of 10 to express how many times as much one is than the other.  This leads into an explanation of scientific notation and continued work performing operations on numbers written in this form.

In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.