# 6th 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 6th 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

## Exploring Patterns

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPATTERN HUNTING [Printable PDF] CCSS.MATH.CONTENT.6.EE.B.6 CCSS.MATH.PRACTICE.MP2 Searching for and analyzing patterns are core critical thinking skills that span all disciplines of mathematics. This set of problems requires students to identify a wide variety of patterns and use them to make predictions. Students may take the approach of writing and solving equations, or they may choose to apply their intuition and number sense skills. Mathematical Fundamentals: Seeing Patterns DESCRIBING PATTERNS [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6 CCSS.MATH.CONTENT.6.EE.B.7 CCSS.MATH.CONTENT.6.EE.C.9 This examination of patterns requires students to use variables to generalize about patterns. It is ideal for students who are beginning to express mathematical relationships using the language of algebra, as it encourages them to practice describing mathematical relationships using both words and algebraic symbols. Mathematical Fundamentals: Describing Patterns

## Working with Integers

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentBEYOND BASIC REMAINDERS [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6 CCSS.MATH.PRACTICE.MP7 Number theory is number magic. It's how mathemagicians seemingly "solve" difficult problems in their head. This activity pertains to remainders and involves the most fundamental number theory tools and concepts. The problems give students the chance to extend their understanding of remainders beyond what is traditionally taught in school. Students begin by exploring remainders in simple situations before diving into a series of challenging remainder puzzles. Number Theory: Arithmetic with Remainders DIVISIBILITY [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6 CCSS.MATH.PRACTICE.MP7 In this application of number theory, students combine their understanding of remainders with divisibility rules. Students begin by applying some common divisibility rules. Then, students move on to a puzzle that requires the application of several divisibility rules and a puzzle involving divisibility by 11. Finally, the culmination question requires a nifty combination of several different divisibility rules to determine the largest possible number that meets certain criteria. Number Theory: Arithmetic with Remainders DIVISIBILITY PUZZLES [Printable PDF] CCSS.MATH.CONTENT.6.NS.B.2 CCSS.MATH.PRACTICE.MP8 In cryptogram puzzles, students put their understanding of addition, subtraction, multiplication, and division to the test to determine the values of missing numbers. Each of the cryptogram puzzles in this activity requires using one or more divisibility rules and some strategic problem solving to solve. Students begin with divisibility rules of 4, 5, and 6 before moving on to more challenging cryptograms and a culmination question that involves only letters as clues. Mathematical Fundamentals: Cryptograms Solved By Divisibility DIVISIBILITY PUZZLES (2, 5, and 10) [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6CCSS.MATH.PRACTICE.MP7 In this application of number theory, students combine their understanding of remainders with divisibility rules while using variables. Students begin with divisibility puzzles pertaining to even and odd numbers. Then, students extend their thinking to divisibility puzzles involving the numbers 5 and 10. Finally, the culmination question requires some creative thinking involving how operations using even numbers can yield odd numbers. Mathematical Fundamentals: Cryptograms Solved By Divisibility DIVISIBILITY PUZZLES (4 and 8) [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6CCSS.MATH.PRACTICE.MP7 In this application of number theory, students combine their understanding of remainders with divisibility rules while using variables. Students begin with divisibility puzzles pertaining to the number 4. Then, students extend their thinking to more complicated divisibility puzzles and those involving the number 8. Finally, students explore how remainders relate to divisibility rules in a variety of cases involving unknowns. Mathematical Fundamentals: Last Digits Part 1

## Fractions, Ratios, Rates, and Proportions

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentFRACTION SENSE [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2. CCSS.MATH.CONTENT.6.NS.C.7 CCSS.MATH.CONTENT.6.EE.B.6 This deep dive into the world of fractions aims to improve students’ conceptual ability to reason with fractions. Students begin by comparing and ordering numerical fractions. Then, students have a chance to explore algebraic fractions and how fractions compare when their numerators and/or denominators increase or decrease by 1. Finally, students apply their fraction intuition to comparing some very large fractions. Mathematical Fundamentals: Comparing Ratios FRACTION FRENZY [Printable PDF] CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.NS.A.1 CCSS.MATH.CONTENT.6.EE.B.6 This fraction frenzy is designed to promote a deeper understanding of fraction operations. Students begin with some outside-of-the-box fraction operations practice. Then, students must use their fraction operation to solve some challenging puzzles. The culmination question weaves variables into a complex fraction equation that requires the application of a deep, conceptual understanding about fractions. Mathematical Fundamentals: Fraction Sense REASONING WITH RATIOS [Printable PDF] CCSS.MATH.CONTENT.6.RP.A.3 CCSS.MATH.CONTENT.6.EE.A.2 CCSS.MATH.CONTENT.6.EE.B.6 Beginning with two-part ratios and moving up to multi-part ratios, these problems build upon a student's ability to compare quantities and work simultaneously with ratios, fractions, and percents. The culminating puzzle involves a pile of money, multi-part ratios, and just one hint. Mathematical Fundamentals: Exploring Ratios RATES [Printable PDF] CCSS.MATH.CONTENT.6.RP.A.2 CCSS.MATH.CONTENT.6.RP.A.3.B CCSS.MATH.CONTENT.6.RP.A.3 From filling bathtubs with water to runners making passes to trains crossing bridges, these problems explore a wide variety of scenarios involving rates. And they can all be done without the use of variables! The early problems involve making estimates and performing straightforward calculations using rates. Then, the questions move into tricky scenarios where a deep understanding of rates leads to efficient and elegant problem solving. Algebra Through Puzzles: Rates & Ratios PRICKLY PERCENTS [Printable PDF] CCSS.MATH.CONTENT.6.RP.A.3.C This activity aims to increase a student’s conceptual understanding of percentages. The problems begin by asking students to compare percentages and perform percentage arithmetic. Then, questions dive into percent applications and percent puzzles. The culmination puzzle requires determining how to remove people from a room to meet some tricky requirements. Mathematical Fundamentals: Percent Applications

## Algebraic Reasoning

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## Statistics and Probability

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## Geometry

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