The Number System


  • Modeling Fraction and Mixed Number Division Using Arrays

    This video illustrates how to use an array as a visual model for solving a word problem involving the division of fractions and mixed numbers. The problem asks students to determine the width of a rectangular fennec fox den based on its length and area. In the accompanying classroom activity, students get additional practice solving another more difficult area problem featuring the division of fractions and mixed numbers. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Locating Points on the Cartesian Graph

    In this interactive, students use clues and logic to plot the location of aquatic animals on a Cartesian graph that represents the four cardinal directions. The three riddles in the interactive, including one that requires students to understand rate, have randomized values so that students can practice placing points at different locations on the graph. The accompanying classroom activity provides students with a review of locating points on a Cartesian graph. A response sheet helps students work with the interactive. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-6
  • Equivalent Expressions with the Distributive Property

    This animated Math Shorts video explains how the distributive property can help students model and create equivalent expressions. In the accompanying classroom activity, students play a quick game where they identify common factors within an expression and work on a series of problems that expand their understanding of how to apply the distributive property. While the problems begin with whole number expressions, students soon work toward algebraic notation and eventually develop the idea that ax + bx can be rewritten as x(a + b). This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Horizontal and Vertical Distances on the Cartesian Graph

    In this interactive, students use logic and mathematical skill to place aquatic animals at locations on a Cartesian graph with cardinal directions. Then, they determine both the vertical and horizontal distances between points. The riddles in the interactive, including one that requires an understanding of rate, have randomized values so that students can practice placing points at different locations and calculating different distances. The accompanying classroom activity provides a review of concepts related to determining the distances between points on a Cartesian graph and a response sheet to help students work with the interactive. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-6
  • Using the Pythagorean Theorem on the Cartesian Graph

    In this interactive, students use logic and mathematical skill to place animals at the correct points on a Cartesian graph representing the cardinal directions. Then, they use the Pythagorean theorem to determine the distances between points. The riddles in the interactive, including one requiring an understanding of rate, have randomized values so that students can place points at different locations and calculate different distances. The activity provides a review of concepts related to determining the distances between points on a Cartesian graph using the Pythagorean theorem and a response sheet to help students work with the interactive. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-8
  • Modeling Fraction Division, Equal Groups, Number of Groups Unknown

    This animated video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to determine how many equal-sized narwhals are within a whole pod. In the accompanying classroom activity, students work through a similar but more difficult problem with the help of bar models and other visual representations. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Modeling Fraction Division, Equal Groups, Group Size Unknown

    This animated video illustrates a word problem that requires dividing two fractions with equal groups, group size unknown. Students are presented with a problem that asks how long it takes a sloth to climb down a tree trunk at an even rate and given a solution to the problem that uses visual modeling. In the accompanying classroom activity, students solve a second problem using their own visual models.This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Absolute Value

    This animated Math Shorts video explains absolute value, as demonstrated on the number line and through a real-life example. In the accompanying classroom activity, students watch the video and then play a game in which they move a penny along a number line in positive and negative directions. As they play, they use absolute value to track the total distance that the penny moves. To get the most from the lesson, students should be comfortable determining distance between positive and negative numbers on a number line. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Manipulating Graphs

    Watch how a graph is altered when key elements of the equation change. This lesson focuses on how to manipulate the equation of a line in slope intercept form to match the graphs provided deepening the understanding of both the slope and y intercept's role in the expression. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
    Grades: 6-8
  • Converting Rational Numbers

    In this video, learn how to use division and place value to convert fractions to decimals. In the accompanying classroom activity, students watch the video to help them learn how to convert a fraction to a decimal using division. Then, they turn their attention to placing rational numbers on a number line. Practicing the placement of these numbers reinforces students’ number sense. It also gives them practice converting among the different representations of a single rational number. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7
  • Relationship of Division and Fractions

    Explore the connection between division and fractions while dividing up cookies. This video focuses on recognizing patterns when modeling dividing up cookies to share with people.

    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.

    Grades: 3-7
  • XY Flyer

    Explore the behavior of lines by composing equations to launch a toy airplane through a series of hoops. This interactive exercise focuses on working in the coordinate plane and deepening the understanding of how slope and y-intercept effect the appearance of linear equations.

    Grades: 6-8
  • Modeling Fraction Multiplication with Equal Groups

    This video presents a visual model for solving a word problem involving the multiplication of fractions. The problem asks students to use the amount of bamboo that a panda eats in an hour to determine how much he eats in a quarter of an hour if he eats at a steady rate. The video ends with a challenge problem for students to model themselves. In the accompanying classroom activity, students use visual models to work through the challenge problem. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Modeling Fraction Division Using Comparison, Group Size Unknown

    This video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to determine the length of a losing frog's jump in a jumping frog contest based on a comparison with the length of the winning jump. The accompanying classroom activity requires students to 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. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Modeling Fraction Division Using Arrays

    This video illustrates a visual model for solving a word problem involving the division of fractions. The problem asks students to determine the width of a rectangular platypus burrow based on its length and area. In the accompanying classroom activity, students use arrays to estimate and/or solve the challenge problem presented at the end of the video. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Practicing Fraction Division Using Arrays

    In this interactive game, students use an array to solve word problems involving the division of fractions. Specifically, they determine the width of a rectangular fennec fox tunnel based on its length and area. The game, which can be played in English or Spanish, includes a randomization feature that allows students to practice solving the same problem using different values. The accompanying classroom activity suggests ways that teachers can integrate this game into the classroom. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Practicing Fraction Division with Equal Groups, Group Size Unknown

    In this interactive game, students use a bar model to solve fraction division word problems. Specifically, they determine how long it takes a sloth to climb down a tree, assuming a steady rate of descent. The game, which can be played in English or Spanish, includes a randomization feature that allows students to practice solving the same problem using different values. The accompanying classroom activity suggests ways that teachers can integrate this game into the classroom. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Practicing Fraction Division, Equal Groups, Number of Groups Unknown

    In this interactive game, students use a model to solve word problems involving the division of fractions. Specifically, they determine how many equal-sized narwhals are within a whole pod. The game, which can be played in English or Spanish, includes a randomization feature that allows students to practice solving problems with different fractions. The accompanying classroom activity suggests ways that teachers can integrate this game into the classroom. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7
  • Opposites On a Number Line

    In this interactive from APT, learn to identify opposite numbers on a number line and explore the opposite of the opposite of a number. In the accompanying classroom activity, students use the interactive and then play a game in which they randomly generate positive and negative integers, including opposites of opposites, place them on the number line, and compare to find which is larger. To get the most from the lesson, students should be comfortable positioning and comparing integers on the number line. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-7,13+
  • Division of Fractions: Using Fraction Strips

    Model division by a fraction using fraction strips. This video focuses on modeling division of a whole number by fractions.

    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.

    Grades: 5-7

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