## The Number System

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.

• ## Patterns of Factors

Demonstrate your grasp of patterns and factors by sorting the numbers into the correct columns. This interactive table focuses on factor pairs and prime factors for the numbers 2 to 36.

This resource is part of the Math at the Core: Middle School collection.

• ## 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.

• ## Repeating Decimal Rings

Investigate what happens when you convert certain fractions to decimals. This interactive exercise focuses on repeating decimals, specifically those calculated when you change sevenths and thirteenths to decimal form.
• ## Building a Number Line

Recall the definitions of four different sets of numbers. This interactive illustration focuses on displaying counting numbers, integers, rational numbers, and real numbers on a number line, providing the opportunity to visualize number sets in multiple ways.

• ## Addition of Positive and Negative Integers

Introducing a card game that your students can play in small groups to develop their addition skills. This video focuses on addition of positive and negative numbers and briefly touches on subtraction of integers.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Approximating Square Roots of Nonperfect Squares

Visualize a strategy for approximating the square roots of nonperfect squares through modeling. This video focuses on a ratio, the number of extra tiles over the number of tiles for the next square that will give you a fractional approximation of the square root of a number. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers. This resource is part of the Math at the Core: Middle School collection.

• ## Distributive Property with Variables

Model with algebra tiles to generate equivalent expressions. This video focuses on visualizing the distributive property.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

• ## Keep, Change, Flip

Watch and listen to an approach to dividing fractions set to hip-hop music. This video focuses on showing why when dividing fractions you should multiply by the inverse of the second fraction.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | Fractions and Decimals from 0 to 1 on the Vertical Number Line

In this interactive, use logic to solve riddles involving a flea-jumping 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.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | 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. This resource is part of the Math at the Core: Middle School Collection.

• ## Logical Leaps | Graphing Inequalities: Fractions and Decimals from 0 to 1

In this interactive, use logic to solve three riddles involving high-jump 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. This resource is part of the Math at the Core: Middle School Collection.