• ## Organ Function Grinder

Watch as the organ function grinder from the National Museum of Mathematics solves a quadratic function for a specific input. This video focuses on converting an input into an output and challenges you to calculate the value for a given input before the function machine does.

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.

• ## Congruent vs Similar Triangles

Learn about the characteristics required for congruent or similar figures. This video focuses on the variety of ways you can use the side and angle measurements of two triangles to check for congruence and also briefly discusses how that differs from similar figures. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
• ## Representing Functions

Watch as the organ function grinder from the National Museum of Mathematics represents a quadratic function in a variety of ways. This video focuses on converting a verbal expression into an algebraic representation. 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.

• ## Understanding Slope with Similar Triangles

In this video, learn how similar triangles can be used to help explain the concept of slope. In the accompanying classroom activity, students apply the concept of similar triangles to explore the slope between different points on the coordinate plane. Students may already know that two points make a line. In the activity, they use similar right triangles to explore why the slope of a line is constant between any two points on that line. The activity begins with a review of two concepts: similar triangles and slope. Students then watch the video, which relating the two ideas, and break into partner groups to develop mathematical arguments relating slope and similarity. This resource is part of the Math at the Core: Middle School collection.

• ## Solving Simultaneous Linear Equations

In this video, learn the elimination method for solving two simultaneous linear equations in a real-world context. In the accompanying classroom activity, students watch the video, solve a pair of simultaneous linear equations, and write a word problem to fit the equations. In order to facilitate introduction to and practice with the elimination method, students work with simple linear equations. To get the most from this lesson, students should be comfortable solving linear equations in one variable, presented as real-world and algebraic problems.

• ## Understanding Solutions to Linear Equations

In this video, explore linear equations in one variable with one solution, infinitely many solutions, or no solutions. In the accompanying classroom activity, students watch the video and then write and solve three equations: one with one solution, one with infinitely many solutions, and one with no solutions. They trade with a partner and solve each other’s equations. To get the most from this lesson, students should be comfortable solving linear equations in one variable with one solution.

• ## Understanding Dilations

In this video, learn how photographers use dilations to print the same photograph in larger or smaller sizes. In the accompanying classroom activity, students consider how dilation is a geometric application of scale factor. After a brief refresher on scale, students watch the video. Then, they apply what they have learned by creating larger and smaller dilations of a picture, using the coordinate plane as their canvas. Students consider how both scale factor and the center of dilation influence the size and placement of the drawings they make.

• ## Thinkport | Systems of Equations

Learn about the role of math in architecture in this media gallery from MPT. In the accompanying classroom activity, students design a triangular roof and find equations for the lines that include the sides of the triangle. They verify that the point at which the two lines intersect satisfy both equations. To get the most from the lesson, students should be comfortable finding the equation of a line from two points and graphing linear equations, and they should be familiar with slope and y-intercept. For a longer self-paced student tutorial using this media, see "Systems of Equations" on Thinkport from Maryland Public Television.

• ## Thinkport | Two-Way Tables and Associations

Explore possible associations between students’ grade level and their preferences for using land behind a middle school with this interactive from MPT. They display frequencies and relative frequencies in a two-way table and interpret the results. Next, they apply what they learned as they use an interactive from MPT to explore possible associations between students’ grade and their preferences for using land behind a middle school. To get the most from the lesson, students would benefit from prior exposure to bivariate data. For a longer self-paced student tutorial using this media, see "Identifying Associations" on Thinkport from Maryland Public Television.

• ## Solving Linear Equations

In this interactive from APT, learn to transform linear equations into simpler forms to show whether the equation has one, infinitely many, or no solutions. In the accompanying classroom activity, students use the interactive and then write three equations: one with one solution, one with infinitely many, and one with no solutions. To get the most from this lesson, students should be comfortable using properties of operations to generate equivalent linear expressions and solving linear equations with one solution. This resource is part of the Math at the Core: Middle School Collection.

• ## Thinkport | Proportional Relationships and Slope: Part 2

Explore the role that proportions play in the design of cakes composed of several tiers in this video from MPT. In the accompanying classroom activity, students watch the video. Next, they examine photographs of tiered cakes, taking measurements to determine if the tiers are in proportion. They conclude by reflecting on the cake photographs and considering why the cake designer maintains that cakes in proportion are pleasing to the eye. To get the most from the lesson, students should have some familiarity with ratio and related tables of values. For a longer self-paced student tutorial using this media, see "Proportional Relationships and Slope" on Thinkport from Maryland Public Television.

• ## Thinkport | Solving Linear Equations

Learn how an architect uses scale drawing and other mathematics to represent floor plans of buildings under construction in this video from MPT. In the accompanying classroom activity, students watch the video and then create a scale drawing of a rectangular area in or near the classroom, choosing an appropriate scale and explaining their strategies for calculating scaled measurements. In the process, they are exposed to an algebraic strategy for calculating dimensions to scale. To get the most from the lesson, students should have experience solving equations of the form ax = b. For a longer self-paced student tutorial using this media, see "Solving Linear Equations" on Thinkport from Maryland Public Television.

• ## Thinkport | Proportional Relationships and Slope: Part 1

Generate unit rates, ratio tables, and graphs in order to determine which baker wins a cupcake bakeoff in this interactive from MPT. In the accompanying classroom activity, students use the interactive and then solve a similar real-life problem. They share their strategies with the class and then conclude by considering ways that unit rates can facilitate comparing rates. To get the most from the lesson, students should be comfortable graphing points in the first quadrant of the coordinate plane and converting between fractions and decimals. For a longer self-paced student tutorial using this media, see "Unit Rates and Slope" on Thinkport from Maryland Public Television.

• ## Ski Jumping: Understanding Proportional Relationships

Investigate the slopes involved in ski jumping. This video focuses on defining slope, showing how to calculate slope on a graph, with an expression, and positive and negative slopes. MIT ARTEMiS takes math out of the classroom and into the real world.
• ## What Is an Inclined Plane?

This interactive lesson from APT invites students to explore the mathematical concepts of slope, force, work, and inclined planes. Students learn that the work a person does equals the effort — the force exerted — multiplied by the distance over which the effort is maintained. They also recognize that what is gained in applying less effort is paid in distance, and vice versa. In the accompanying classroom activity, students work with real-world examples of force and inverse relationships.

• ## The Pythagorean Theorem: The Magic of Slope

In this interactive from APT, help a group of friends figure out why loading one person’s all-terrain vehicle into her truck at the end of a fun day of riding was easier for her than for the others. In the accompanying classroom activity, students use the interactive to calculate the slope of each friend’s inclined planes, recommend which one the friends should use to load the trucks, and explain their answers based on mathematical data.

• ## Calculating Force: Moving an ATV Up an Inclined Plane

In this interactive lesson from APT, Haylee and her friends spend the afternoon riding their all-terrain vehicles. When they are ready to go home at the end of the day, they have to load their ATVs onto their trucks. Use your knowledge of slope, force, and inclined planes to help Haylee and her friends solve the problem of getting their vehicles loaded. In the accompanying classroom activity, students complete the interactive and then discuss which solution is best for Haylee and her friends, offering evidence for their suggestions.

• ## String Product: Finding the Y-Intercept

Examine how a giant piece of art at the National Museum of Mathematics reveals some unexpected relationships between coordinates on a parabola. This video focuses on the relationship between negative and positive points on the parabola and their y-intercept.

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.

• ## String Product: y = x^2

Examine how a giant sculpture at the National Museum of Mathematics represents the solutions to the equation y=x^2. This video focuses on the basics of graphing quadratic functions and the relationship between x and y values along the parabola.

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