# Math

Math (X)

## Decimals on a Number Line: Positive and Negative Decimals

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Interpret a number line in order to locate where our positive and negative decimals should be placed.

## Volume of Shapes Composed of Right Rectangular Prisms

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Use unit cubes to determine the volume of an irregular 3D figure. This video focuses on breaking a complex figure up into two rectangular prisms and then finding the volume of the parts before adding them together to get the whole figure. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

## Exploring Scale and Proportion at the Holiday Train Show | Treasures of New York: "Holiday Train Show"

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Explore scale and proportion with this media gallery from Treasures of New York that offers a behind-the-scenes look at the design and installation of the annual Holiday Train Show at the New York Botanical Garden.

This annual event features more than 150 replicas of iconic New York landmarks made entirely of natural materials, such as bark, twigs, seeds and pine cones. Unlike an architectural model, which is a perfect replica of a building, botanical architecture model is scaled down to a size that takes into account the 3D landscape. Traversing through the New York City landscape are more than 20 large-scale G-gauge model trains, which is the largest available scale in model train.

## Equivalent Expressions with the Distributive Property

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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.

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In this video, examine strategies to identify the properties of quadrilaterals—specifically, parallelograms. Students will compare and contrast squares, rectangles, and rhombuses, which are all parallelograms. In the accompanying classroom activity, students create posters identifying the properties of various quadrilaterals. They explore how these shapes compare and contrast and then analyze the ways that parallelograms distinguish themselves from other quadrilaterals.

## Recognize and Represent Proportional Relationships Between Quantities: Ratio, Proportion, Cross Multiply, and Divide

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In this Cyberchase media gallery, learn about ratio and proportion and how to use an algebraic shortcut to solve proportion problems. In the accompanying classroom activity, students play a game called the "Pom-Pom Nose Push," in which they collect data and determine the ratio of time to distance. This resource is part of the Math at the Core: Middle School Collection.

## Definition of Integers | PBS Math Club: InstaCram

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Defining integers in 15 seconds using positive and negative numbers on a number line and discussing numbers that aren't integers with InstaCram from the Math Club.

## Value | PBS Math Club: InstaCram

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Discussing the value of integers in 15 seconds using a number line and exploring how to determine increasing and decreasing value of positive and negative numbers on a number line with InstaCram from the Math Club.

## NOVA: Making Stuff Faster | The Math Behind Package Delivery

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Learn how UPS, a global package delivery company, has developed an algorithm to schedule routes for its delivery trucks in this video from NOVA: Making Stuff Faster. Host and technology columnist David Pogue examines how difficult it is to find the most efficient way to visit multiple locations—a mathematical challenge known as the "traveling salesman problem." UPS has developed a system that breaks the problem down into smaller problems so that a computer can approximate the best solution without having to do an astronomical amount of calculations.

This video is available in both English and Spanish audio, along with corresponding closed captions.

## Understanding Concepts of Volume and Measurement: Bianca’s Babysitting Blues

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In this video from Cyberchase, Bianca is babysitting infant twins. As she tries to give each twin the same amount of liquid baby formula, she discovers that all the baby bottles are different shapes. Learn how she finds two that hold the same amount. In the accompanying classroom activity, students estimate which of four empty containers has the greatest capacity and then determine which one does by measuring actual volume. This resource is part of the Math at the Core: Middle School Collection.

## Numbers on a Number Line | PBS Math Club: InstaCram

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Illustrating the rules of addition of positive and negative numbers with a number line in 15 seconds with InstaCram from the Math Club.

## Distributive Property with Variables

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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.

## Dependent and Independent Variables Exercise: Express the Graph as an Equation

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This module shows how graphs are expressed as equations.

## Getting a Feel for Equations and Inequalities: Dependent and Independent Variables - Graphing

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It's helpful to express an equation on a graph where we plot at least 2 points. Watch and we'll show you.

## Box-and-Whisker Plots: Finding the Range and Mid-Range in a Series of Numbers

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Range is the difference between the largest and smallest numbers; and midrange is the average of the largest and smallest number. Practice with this problem.