# 8th 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 8th 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

## Finding Patterns

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentEXPLORATIONS IN NUMBER THEORY [Printable PDF] CCSS.MATH.PRACTICE.MP7 This introductory number theory set is designed to increase a student’s ability to reason and problem solve logically. These problems build upon traditional number theory learned in middle school, including primes, composites, evens, odds, factors and multiples. Students apply what they know about relationships between integers to solve these problems as they culminate into the classic scenario of finding patterns among opening and closing doors. Number Theory: Additional Challenges DIVISIBILITY RULES [Printable PDF] CCSS.MATH.PRACTICE.MP1 CCSS.MATH.PRACTICE.MP7 While familiarity with divisibility rules can provide time savings and short-cuts for problem solving, it also helps foster a deep understanding of our number system. In these problems, students review divisibility rules, and then apply them to number puzzles. Math Fundamentals: Divisibility CURIOUS CRYPTOGRAMS [Printable PDF] CCSS.MATH.PRACTICE.MP7 Cryptograms are puzzles where capital letters stand in for one or more digits of a number. In these cryptogram puzzles, students apply their knowledge of number patterns and divisibility rules. Math Fundamentals: Cryptogram Variety Pack

## Ratios and Proportionality

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPERCENTS MEET VARIABLES [Printable PDF] CCSS.MATH.CONTENT.8.EE.B.5 CCSS.MATH.CONTENT.8.EE.C.7 CCSS.MATH.PRACTICE.MP2 It’s time to move beyond typical percent calculations and into the world of percent intuition. In these percent problems, students move beyond simple calculations to complex problems that require applying algebraic reasoning and developing intuition about percents and percent change. The culmination question pushes students to reason through percent change as it pertains to halving and doubling times. Algebra Through Puzzles: Mixing Problems PRICKLY PROPORTIONS [Printable PDF] CCSS.MATH.CONTENT.8.EE.B.5 CCSS.MATH.CONTENT.8.EE.C.7 CCSS.MATH.PRACTICE.MP1 Proportional reasoning is one of the essential building blocks for algebraic thinking and higher level problem solving. These proportions problems encourage students to think intuitively about proportions and how quantities change in relation to one another. The red fish, blue fish culmination question wraps it all up with a ratio-filled, proportional reasoning challenge. Algebra Through Puzzles: Proportionality RATIOS MEET ALGEBRA [Printable PDF] CCSS.MATH.CONTENT.8.EE.C.7 CCSS.MATH.PRACTICE.MP1 CCSS.MATH.PRACTICE.MP7 Not just your standard ratio problems, these questions challenge students to deepen their understanding of ratios and proportions. From geometric scenarios to mixing problems to multi-part ratios, students are expected to apply algebraic strategies to make problem solving easier and more efficient. Algebra Through Puzzles: Mixing Problems

## The Rules of Algebra

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentARITHMETIC PUZZLES [Printable PDF] CCSS.MATH.PRACTICE.MP1 CCSS.MATH.PRACTICE.MP2 These arithmetic puzzles, ranging from magic squares to magic triangles, are designed to help broaden a student’s problem solving skills. These methods of strategic thinking lay a strong foundation for Algebra. Algebra Through Puzzles: Magic Rectangles 1 ARITHMETIC MEETS ALGEBRA [Printable PDF] CCSS.MATH.CONTENT.8.F.B.4 CCSS.MATH.PRACTICE.MP8 Students take their many years of experience with exploring number patterns to the next level in this series of problems. By examining sums and square, pentagonal, and hexagonal numbers, students identify patterns, make predictions, and generalize patterns using variables. Algebra Through Puzzles: The Gauss Trick EXPRESSIONS AND IDENTITIES [Printable PDF] CCSS.MATH.CONTENT.8.EE.C.7 CCSS.MATH.PRACTICE.MP7 Manipulation of algebraic expressions is one of the most basic and important skills in a problem solver's repertoire, as without it a problem solver would hopelessly be stuck on innumerable problems. Algebraic manipulation often involves changing an expression into a simpler form or a form which is more easily handled and dealt with. In this series of problems, students have the opportunity to simplify, manipulate, and compare a wide variety of algebraic expressions. Mathematical Fundamentals: Always-Sometimes-Never ALGEBRA PUZZLES [Printable PDF] CCSS.MATH.CONTENT.8.EE.C.7 CCSS.MATH.PRACTICE.MP7 Variable equations are one of the most generally applicable problem-solving tools in all of mathematics. In this series of problems, students explore how algebra's symbolic language can be experimented with and manipulated as a problem-solving tool. Students also learn various ways to approach problems strategically. Mathematical Fundamentals: Using Variables

## Systems of Equations

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## Exponents and Exponential Growth

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## Statistics and Probability

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## Transformations, Congruence, and Similarity

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## Angles and the Pythagorean Theorem

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## Angles, Surface Area, and Volume

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