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 firstname.lastname@example.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.
Printable PDFs Common Core Standards Description Related Course Content SEEING 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 crucial for the development of algebraic thinking. These problems help students visualize patterns by linking them to physical models. After examining how several different types of patterns grow, students analyze a numerical pattern and a 3D geometric pattern. Encourage students to describe how they are able to find the missing values in these patterns and how they could describe the rule that creates each pattern. Mathematical Fundamentals: Seeing Patterns DESCRIBING PATTERNS [Printable PDF] CCSS.MATH.CONTENT.7.EE.A.2 CCSS.MATH.CONTENT.7.EE.B.4 This task 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. 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 culminate with students contrasting recursive and explicit methods of describing a sequence. Mathematical Fundamentals: Seeing Patterns
Printable PDFs Common Core Standards Description Related Course Content 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. The problems in this activity guide students toward a discovery of which numbers are divisible by 9 and why. Then, students put their new understanding of the 9 divisibility rule to the test as they tackle a variety of puzzles. Mathematical Fundamentals: Last Digits Part 2 ON 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. Students begin by applying the concept of scaling to find missing values, including negative ones, on a number line. Then, students move on to more complex number line puzzles involving exponents and proportions. 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 In this activity students dive into many important aspects of working with fractions: ordering and comparing fractions, writing equivalent fractions, converting between fractions and mixed numbers, and performing arithmetic with fractions. From there, students extend their thinking to learn some nifty shortcuts for working with 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 determine whether or not a fraction's decimal representation terminates. In particular, students learn that a fraction has a terminating decimal representation if and only if there is an equivalent fraction whose denominator is a power of 10. The culmination asks students to examine the denominator of 35. Mathematical Fundamentals: Divisibility
Printable PDFs Common Core Standards Description Related Course Content IN SEARCH OF THE UNKNOWN [Printable PDF] CCSS.MATH.CONTENT.7.EE.B.4 In these puzzles, students must apply algebraic thinking to solve the puzzles and find the missing values. This problem set begins with pictorial representations of algebraic scenarios. Then, students move on to cryptogram puzzles, which build upon logic and application of arithmetic to identify the value of a hidden digit. Mathematical Fundamentals: Cryptogram Algebra INEQUALITIES [Printable PDF] CCSS.MATH.CONTENT.7.EE.B.4 CCSS.MATH.CONTENT.7.EE.B.4.b In this activity, students deepen their understanding about inequalities. Moving beyond solving inequalities, these problems aim to improve inequality intuition. After examining one-variable inequalities, students apply reasoning skills to work through multi-variable scenarios. In the culmination, students examine an unbalanced mobile to determine the relative weights of various shapes. Algebra Through Puzzles: Balancing Scales
Printable PDFs Common Core Standards Description Related Course Content PERCENTAGES [Printable PDF] CCSS.MATH.CONTENT.7.RP.A.3 Although percentages are part of everyday language, people often have misconceptions about them. These questions aim to address some of the key misconceptions that students may have in their understanding of percentages. Students begin by calculating and comparing percentages. Then students move on to a set of challenge questions involving percent change, including the culmination question that also weaves in some intuition, logic, and algebraic reasoning. Mathematical Fundamentals: Seeing Patterns RATES [Printable PDF] CCSS.MATH.CONTENT.7.RP.A.1 CCSS.MATH.CONTENT.7.RP.A.2 CCSS.MATH.CONTENT.7.RP.A.3 In this proportional reasoning exploration, students explore several different applications of rates. The sequence is designed to help hone intuition and strategic thinking skills. Students begin by using rates to estimate the distance to a lightning strike. Then, they examine several situations involving multiple rates. Finally, students determine when collisions will happen between motorists moving at different speeds in different directions on a circular track. Algebra Through Puzzles: Distance, Rate, and Time
Printable PDFs Common Core Standards Description Related Course Content LINES & ANGLE HUNTING [Printable PDF] CCSS.MATH.CONTENT.7.G.B.5 In this problem set, students explore angles created by intersecting lines and line segments. Through the series of angle hunts, they apply their knowledge of vertical, complementary, and supplementary angles, linear pairs, and the triangle sum theorem. In addition, each problem involves at least one variable. In the culmination, students examine a figure with many triangles and congruent angles to determine the unknown measure of an angle. Outside the Box Geometry: Angle Hunting Axioms TRIANGLES & ANGLE HUNTING [Printable PDF] CCSS.MATH.CONTENT.7.G.B.5 This problem set is designed to guide students through some of the magic of geometry, revealing the thought processes that lead to clever solutions to basic angle hunting problems. Through the series of angle hunts, students apply their knowledge of vertical, complementary, and supplementary angles, linear pairs, and the triangle sum theorem. In the culmination, students determine the sum of a set of angles without being given a single angle measure. Outside the Box Geometry: Angle Hunting Axioms CIRCLES [Printable PDF] CCSS.MATH.CONTENT.7.G.B.4 This set covers applications of areas and circumferences of circles. Questions begin by leading students through derivations for the circumference and area formulas of a circle. Students then dive into a series of composite figures that address both area and circumference. Mathematical Fundamentals: Perimeters PRISM CROSS SECTIONS [Printable PDF] CCSS.MATH.CONTENT.7.G.A.3 In this problem set, students explore possible cross sections of prisms. Students explore conceptual aspects of cross sections before diving into ways to obtain different cross sections of a cube. The culmination problem explores the maximum number of sides that the cross section of a cube can have. Joy of Problem Solving: Slicing Cubes