Math at the Core: Middle School
Expand/Collapse Math at the Core: Middle School
Find engaging media and integrated activities, all aligned with the Common Core State Standards in Mathematics. Designed for middle school students of diverse learning styles and backgrounds. Produced by a collaborative of public media stations and producers with funding from the Corporation for Public Broadcasting.
Watch an introductory video about the Collection.

Additive Inverse
This animated Math Shorts video from the Utah Education Network explains the term additive inverse and provides several examples that demonstrate the concept. In the accompanying classroom activity, students create equations and solve problems that involve adding groups of negative and positive integers that sum to zero. To get the most out of this activity, students should be familiar with plotting positive and negative integers on a number line. This resource is part of the Math at the Core: Middle School collection.
Grades: 7 
Patterns of Factors
In this interactive activity from Annenberg Learner’s Learning Math, students sort numbers from 2 to 36 into categories based on the number of factors and number of prime factors. The accompanying classroom activity engages students in discussing strategies for finding factors. To get the most out of this activity, students should be familiar with factor pairs of numbers to 36.
Grades: 6 
Harry Makes a Big Splash with Positive and Negative Numbers
In this Cyberchase video, Harry, his friend, and his cousin Harley form a swim relay team. They get timed in three different strokes to see who should swim which one in a relay. They look at the results and try to find the combination of times which will yield the lowest overall relay time. In the accompanying classroom activity, students pair up and play a game that gives them practice adding positive and negative numbers on a number line.
Grades: 56 
Repeating Decimal Rings
In this interactive from Annenberg Learner’s Learning Math, investigate the repeating patterns that emerge when you expand sevenths and thirteenths fractions into decimals. In the accompanying classroom activity, students investigate patterns in a sequence of terminating decimals: fifths converted to decimal form. They then use the interactive to explore patterns that emerge from the decimal expansion of sevenths. To get the most out of this activity, students should have had experience converting fractions to decimals via division. They should also be familiar with the notion that decimal forms of rational numbers eventually terminate or repeat.
Grades: 78 
Building a Number Line
In this interactive from Annenberg Learner’s Learning Math, examine different number sets, including counting numbers, integers, rational numbers, and real numbers, on a number line. In the accompanying classroom activity, students answer questions about these number sets and describe the properties of each in a graphic organizer.
Grades: 8 
Addition and Subtraction of Integers
In this video, learn about the addition of integers during a card game in which negative and positive numbers are added together. In the accompanying classroom activity, students have the opportunity to play the card game using both addition and subtraction. They apply their skills by solving a word problem and then creating their own word problems that they share with the class. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
Grades: 67 
Fractions, Mixed Numbers, and Decimals on the Number Line
In this interactive, students use logic to solve three riddles involving a frog jumping contest and then place the contestants’ jumps at the correct points on the number line. Numbers are randomized so that the frogs’ placements on the number line are different each time one of the three riddles appears. The accompanying classroom activity provides a review of equivalent values of fractions and decimals and a response sheet to help students work with the interactive.
Grades: 67 
Approximating Square Roots of Nonperfect Squares
In this video, visualize a strategy for approximating the square roots of nonperfect squares. In the accompanying classroom activity, students estimate the value of irrational square roots and compare the estimate to the actual value.
This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
Grades: 8 
Distributive Property with Variables
This video demonstrates how algebra tiles are used to generate equivalent expressions using the distributive property. In the accompanying classroom activity, students explore the distributive property. They use algebra tiles to solve problems involving equivalent expressions and compare their solution strategies with the approach demonstrated in the video. Students then solve story problems in which they generate equivalent expressions. To get the most out of the activity, students should be comfortable using the distributive property to evaluate whole number expressions, and they should have prior exposure to expressions of the form ax + b.
This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
Grades: 6 
Keep, Change, Flip
In this video, educational hiphop artist Flocabulary presents a song that explains the “keep, change, flip” mnemonic, an approach to dividing fractions. In the accompanying classroom activity, students solve problems that involve dividing one fraction by another in a money context. They explain their solution strategies and represent them with words and equations. Then, they solve another problem, compare their solution strategies with the approach demonstrated in the video, and create story contexts for related problems. To get the most out of the activity, students should be comfortable multiplying two fractions and dividing a whole number by a unit fraction.
This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
Grades: 6 
Adding Fractions and Decimals from 0 to 1 on the Vertical Number Line
In this interactive, use logic to solve riddles involving flea circus high jumps. Then, add two consecutive jumps and place them on a vertical number line. This often requires you to find equivalent fractions with common denominators. Numbers are randomized so that you can answer riddles and place fleas on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to support the online work.
Grades: 67 
Fractions and Decimals from 0 to 1 on the Vertical Number Line
In this interactive, use logic to solve riddles involving a fleajumping contest. Place each contestant’s jump, represented by either a fraction or a decimal in both feet and inches, at the correct point on the vertical number line. Numbers are randomized so that riddles can be solved and fleas placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work.
Grades: 67 
Adding Rational Numbers on the Number Line
In this interactive, use logic to solve riddles involving a wallaby jumping contest. Add two consecutive jumps and place them on a number line, finding equivalent fractions and common denominators to do so. Backward jumps represent negative numbers, and forward jumps represent positive numbers. Numbers are randomized so that riddles can be answered and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet handout to support the online work.
Grades: 67 
Rational Numbers on the Number Line
In this interactive, use logic to solve riddles involving a wallaby jumping contest. Then, place each contestant’s jump—a fraction, mixed number, or decimal between –5 and +5—at the correct point on the number line. Backward jumps are represented by negative numbers and forward jumps by positive numbers. Numbers are randomized so that riddles can be solved and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work.
Grades: 6 
Adding Fractions, Mixed Numbers, and Decimals on the Number Line
In this interactive, use logic to solve riddles involving a jumping frog contest. Add two consecutive jumps by one frog and place the jumps on the number line, finding equivalent fractions with common denominators to do so. Numbers are randomized so that riddles can be answered and frogs placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and two response sheets to support the online work.
Grades: 67 
Graphing Inequalities: Rational Numbers
In this interactive, use logic to solve three riddles involving a jumping wallaby competition. Then, using knowledge of inequalities and rational numbers, place the wallabies on the correct range from –5 to 5 on the number line. Numbers are randomized so that the range on the number line is different each time the riddles appear. The accompanying classroom activity includes a concept review and response sheets to support the online work.
Grades: 6 
Graphing Inequalities: Fractions, Mixed Numbers, and Decimals
In this interactive, use logic to solve three riddles involving a jumping frog competition. Then, using knowledge of inequalities and rational numbers, place the frogs in the correct range from 0 to 5 on a number line. The fractions, mixed numbers, and decimals (in feet and inches) are randomized so that the range on the number line is different each time the riddles appear. The accompanying classroom activity includes a concept review and a response sheet handout to support the online work.
Grades: 6 
Graphing Inequalities: Fractions and Decimals from 0 to 1
In this interactive, use logic to solve three riddles involving highjump performers in a flea circus. Then, using knowledge of inequalities, place the fleas in the appropriate range on a vertical number line. Numbers are randomized so that the range on the vertical number line is different each time one of the three riddles appears. The accompanying classroom activity includes a fraction/decimal concept review and response sheets to support the online work.
Grades: 6 
Greatest Common Factor
In this video, learn how to find the greatest common factor of two numbers. Then, see how this can be used to solve problems with large numbers. In the accompanying classroom activity, students learn to find prime factors using factor trees. They then learn how prime factors, a Venn diagram, and simple multiplication can help them find the greatest common factor of two numbers. The lesson challenges students to find the greatest common factor of increasingly large numbers. It also pushes them to think about how prime factors are the building blocks of composite numbers.
Grades: 6 
Modeling Fraction Division Using Comparison, Group Number Unknown
This animated video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to use fractions to compare the spring weight of a hedgehog with its weight just before hibernation. In the accompanying classroom activity, students use visual models to work through the challenge problem presented at the end of the video, which also involves the division of fractions and comparison.
Grades: 67