# Algebra One

**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 algebra 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 ContentDESCRIBING PATTERNS [Printable PDF] CCSS.MATH.CONTENT.HSA.SSE.A.1 CCSS.MATH.CONTENT.HSA.CED.A.1 CCSS.MATH.CONTENT.HSA.REI.B.3 Math isn't about memorizing formulas, it's about problem solving. It's about looking at patterns and predicting the future of those patterns. This examination of patterns requires students to use variables to generalize about several different types of growth patterns. Algebra Through Puzzles: Describing Sequences FIND THE FORMULA [Printable PDF] CCSS.MATH.CONTENT.HSA.SSE.A.1 CCSS.MATH.CONTENT.HSA.SSE.B.3 CCSS.MATH.CONTENT.HSA.CED.A.1 CCSS.MATH.CONTENT.HSA.REI.B.3 Math isn't about memorizing formulas, it's about problem solving. It's about looking at patterns and making predictions using those patterns. This examination of patterns requires students to use variables to generalize about several different types of patterns. Algebra Through Puzzles: Describing Sequences

## Algebraic Reasoning

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentALGEBRAIC ARITHMETIC [Printable PDF] CCSS.MATH.CONTENT.HSA.SSE.A.2 CCSS.MATH.CONTENT.HSA.SSE.B.3 In this set of problems, students use arithmetic properties to write, simplify, and compare algebraic expressions. While most problems could be solved with some long and drawn out arithmetic, they are solved far more elegantly and efficiently with the properties. Algebra Through Puzzles: Variables ALGEBRA RIDDLES [Printable PDF] CCSS.MATH.CONTENT.HSA.CED.A.1 CCSS.MATH.CONTENT.HSA.REI.A.1 CCSS.MATH.CONTENT.HSA.REI.B.3 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 practice various ways to approach problems strategically. Algebra Through Puzzles: Equations MAGIC PERIMETERS [Printable PDF] CCSS.MATH.CONTENT.HSA.SSE.A.1 CCSS.MATH.PRACTICE.MP8 CCSS.MATH.PRACTICE.MP7 It's possible to solve these puzzles by brute force, but, especially as they get more complex, it's better to use algebra. In particular, it's useful to set up equations relating the sum of the corner numbers to the magic sum to determine which magic sums are and are not possible. This will allow students to provethat certain results are true rather than exhaustively searching through all possible arrangements.Algebra Through Puzzles: Magic Perimeters CALCDOKU [Printable PDF] CCSS.MATH.PRACTICE.MP8 Calcdoku puzzles involve logical thinking about arithmetic relationships between numbers. These puzzles are simultaneously a review of basic arithmetic and a preview of algebra — using given information to determine unknown quantities. These problems first walk students through the basic logic and strategy of solving Calcdoku puzzles and then give them the opportunity to solve these puzzles from scratch. Algebra Through Puzzles: Learn Calcdoku CAN IT BE SOLVED? [Printable PDF] CCSS.MATH.CONTENT.HSA.SSE.A.1 CCSS.MATH.CONTENT.HSA.SSE.B.3 CCSS.MATH.CONTENT.HSA.CED.A.1 CCSS.MATH.CONTENT.HSA.REI.B.3 Sometimes x is unknown, and sometimes it’s unknowable. In these algebra puzzles involving combination locks, students must determine which is which. When do they have enough information to figure out the combination, when do they need more information, and when is the information they have logically inconsistent? These problems serve as a gentle introduction to systems of equations. Algebra Through Puzzles: Combination Locks

## Systems of Equations

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentARRAY PUZZLES [Printable PDF] CCSS.MATH.CONTENT.HSA.REI.C.5 CCSS.MATH.CONTENT.HSA.REI.C.6 CCSS.MATH.CONTENT.HSA.CED.A.2 In these array puzzles, logic meets algebra. Students have the opportunity to solve the visual puzzles, or determine if a solution is even possible, by applying logic and writing and solving systems of equations. The culmination question asks students to determine the maximum possible number of objects that can be used for a given array size. Algebra Through Puzzles: Array Puzzles MAKE IT BALANCE [Printable PDF] CCSS.MATH.CONTENT.HSA.REI.C.5 CCSS.MATH.CONTENT.HSA.REI.C.6 CCSS.MATH.CONTENT.HSA.CED.A.2 In these balance puzzles, logic meets algebra. Students work through systems of equations that are presented pictorially using balances rather than with variables and numbers. Algebra Through Puzzles: Balancing Scales SYSTEMS PROBLEM SOLVING [Printable PDF] CCSS.MATH.CONTENT.HSA.REI.C.5 CCSS.MATH.CONTENT.HSA.REI.C.6 CCSS.MATH.CONTENT.HSA.CED.A.2 In these problems students apply their understanding of what systems are and what their solutions, or lack thereof, represent. Students move beyond two-variable equations to simpler, conceptual cases of multi-variable systems. Algebra Through Puzzles: Problem Solving

## Inequalities

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## Quadratics

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## Exponents, Radicals, and Exponential Models

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## Modeling with Functions

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## Proportions and Rational Equations

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## Statistics and Probability

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