# 7th Grade Math

**Relevant Brilliant Courses (Online Content)**

The four courses below are the foundations for all of the mathematics offered on Brilliant. If you’re an educator with a group of 10 or more students you want to give full access to these courses, contact pricing@brilliant.org to learn more about Brilliant’s discounts for school groups.

**Deep Diving Math Enrichment Problem Sets (Printable Content)**

Too often, school math is all about “racing to finish” instead of diving deep to understand and explore creative, tangential lines of inquiry. These sets were written to inspire deep diving exploration that extends and enriches the core mathematical topics and skills introduced in the 7th grade common core curriculum.

Each of the “Practice-Challenge-Culmination” problem sets listed below takes some foundational skill in the common core curriculum for that grade and, after a few practice problems, extends the concept to more creative challenges, and then to a single, deep-dive question.

#### Contents

## Patterns and Number Sense

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentSEEING PATTERNS [Printable PDF] CCSS.MATH.CONTENT.7.G.B.6. CCSS.MATH.PRACTICE.MP7 Mathematics is sometimes described as "the science of patterns," and being able to recognize patterns is very important in the development of algebraic thinking. It is good to encourage students to describe how they were able to find the missing terms in these pattern puzzles - how would they describe the rule that creates each pattern? Several of these patterns are based on square numbers. For many learners, linking geometry or physical models to the numbers helps students visualize the patterns. Mathematical Fundamentals: Seeing Patterns DESCRIBING PATTERNS [Printable PDF] CCSS.MATH.CONTENT.7.EE.A.2 CCSS.MATH.CONTENT.7.EE.B.4 While students are beginning to express mathematical relationships using the language of algebra, it is important that they continue to practice describing mathematical relationships using words and natural language sentences. In these problems, students begin by predicting terms in sequences, and then move on to describing sequences and patterns using words. Often there are different, but equally valid, ways of describing a given sequence. These problems will cumulate with one where students will contrast the recursiveandexplicitmethods of describing a sequence.Mathematical Fundamentals: Seeing Patterns DIVISIBILITY BY 9 [Printable PDF] CCSS.MATH.PRACTICE.MP7 There are many "divisibility rules” that allow us to determine whether one number is divisible by another without actually doing the division. For example, a number is divisible by 2 if its last digit is even. When is a number divisible by 9? Precisely when the sum of its digits is divisible by 9. These problems guide students toward the discovery of this fact, as well as an understanding of why it is true. Mathematical Fundamentals: Last Digits Part 2

## Integers, Fractions, and Decimals

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentON THE LINE [Printable PDF] CCSS.MATH.CONTENT.7.NS.A.1 CCSS.MATH.CONTENT.7.NS.A.2 CCSS.MATH.PRACTICE.MP2 These questions use number lines to build on prior knowledge of integer representations and operations. Mathematical Fundamentals: Using Variables FRACTION ACTION [Printable PDF] CCSS.MATH.CONTENT.7.RP.A.2 CCSS.MATH.CONTENT.7.NS.A.1 CCSS.MATH.CONTENT.7.NS.A.2 These questions cover some important parts of working with fractions: ordering fractions, equivalent fractions, converting between fractions and mixed numbers, and adding and subtracting fractions. Mathematical Fundamentals: Seeing Patterns TERMINATING DECIMALS [Printable PDF] CCSS.MATH.CONTENT.7.NS.A.2.D These problems guide students toward an understanding of how to tell whether a fraction's decimal representation terminates. In particular, a fraction has a terminating decimal representation if and only if there is an equivalent fraction whose denominator is a power of 10. Mathematical Fundamentals: Divisibility

## Algebraic Reasoning

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentIN SEARCH OF THE UNKNOWN [Printable PDF] CCSS.MATH.CONTENT.7.EE.B.4 Algebra is often used as a tool to find an unknown value. In these puzzles, a relationship is described and students must apply algebraic thinking to solve the puzzle and find the missing value. This problem set includes cryptogram puzzles, which build on student's knowledge of arithmetic to identify the value of a hidden digit. Problems and puzzles that are playful help students experience the fun of using algebra. While introducing more formal algebraic language, it is good to continue to return to pictographic algebra puzzles, and unusual problems like cryptograms, to make sure students don't loose sight of algebra's more whimsical applications. Mathematical Fundamentals: Cryptogram Algebra

## Ratios, Proportions, and Percents

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPERCENTAGES [Printable PDF] CCSS.MATH.CONTENT.7.RP.A.3 Percentages are part of everyday language. However, even though they are familiar, people often have misconceptions about them. These questions try to address some of the key misconceptions that students may have from their informal knowledge of percents. Mathematical Fundamentals: Seeing Patterns

## Geometry

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentCIRCLES [Printable PDF] CCSS.MATH.CONTENT.7.G.B.4 This set begins by leading students through one derivation for the formula for the area of a circle. Students then dive into some interesting problems applying both area and circumference. Mathematical Fundamentals: Perimeters CROSS SECTIONS [Printable PDF] CCSS.MATH.CONTENT.7.G.A.3 This set explores the different cross sections of a cube, and culminates in a proof regarding the number of sides possible in a cross-sectional shape. Joy of Problem Solving: Slicing Cubes

## Probability and Statistics

Coming Soon