## 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.

• ## Area of a Parallelogram

Learn about the characteristics of a parallelogram and how to find its area in this video from KCPT. In the accompanying classroom activity, students develop and apply the formula for the area of a parallelogram. This resource is part of the Math at the Core: Middle School Collection.

• ## Prisms with Quadrilateral Faces

In this video from KCPT, watch an animated demonstration of finding the surface area of rectangular and trapezoidal prisms. In the accompanying classroom activity, students do two hands-on activities: they calculate the surface area of an object in the shape of a rectangular or trapezoidal prism and design and construct a rectangular or trapezoidal prism with a surface area of 24 square inches. To get the most from this lesson, students should be comfortable calculating the area of parallelograms. Prior exposure to rectangular and trapezoidal prisms and to surface area is helpful.

• ## Rotation and Dilation

In this video from KCPT, watch an animated demonstration of rotating and dilating a triangle on the coordinate plane. In the accompanying classroom activity, students watch the video; draw rotations and dilations of a triangle; and identify center of rotation, angle of rotation, and scale factors in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane and reproducing a drawing of a geometric shape at a different scale. Prior exposure to rotation and dilation is helpful.

Learn about the characteristics of different kinds of quadrilaterals, including parallelograms and rhombuses, in this video from KCPT. In the accompanying classroom activity, students classify quadrilaterals._

• ## Volume of a 3D Figure Composed of Quadrilaterals

Learn to use formulas and unit cubes to model the formula for volume of 3D figures composed of quadrilaterals in this video from KCPT.

• ## Nets

Learn how you can use a net to form a three-dimensional (3D) shape and to find the surface area of the shape in this video from KCPT.

• ## Finding the Volume of a Triangular Prism

An animation demonstrates how to find the volume of triangular prisms in this video from KCPT. In the accompanying classroom activity, students do two hands-on activities: they calculate the volume of an object in the shape of a triangular prism and design and construct a model of a roof in the shape of a triangular prism. To get the most from this lesson, students should be comfortable calculating the area of a triangle and finding the volume of a rectangular prism.

• ## Volume of a Polyhedron

In this video, learn how to calculate the volume of a polyhedron by determining the base and then watching the space inside fill in order to determine the height. In the accompanying classroom activity, students calculate the volume of mini cereal boxes, in this video from KCPT.

• ## Area of a Triangle

Watch Geometry Gal explain how to find the area of a triangle, comparing the formula for the area of this two-dimensional shape to that of a quadrilateral, in this video from KCPT.

• ## Volume of a Cone

Watch an animated demonstration of finding the volume of a cone and cylinder with the same base and height in this video from KCPT. In the accompanying classroom activity, students estimate the relative volume of a cone and cylinder with the same base and height. They test their estimates by filling the cone and pouring the contents into the cylinder and then use the cylinder volume formula as a basis for predicting the cone volume formula. To get the most from the lesson, students should know the formulas for the area of a circle and volume of a cylinder.

• ## Area of a Trapezoid

Learn about the characteristics of a trapezoid and how to find its area in this video from KCPT. In the accompanying classroom activity, students develop the formula for the area of a trapezoid by decomposing it into smaller, more familiar shapes.

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

• ## Translations and Reflections

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Watch an animated demonstration of translating and reflecting a triangle on the coordinate plane in this video from KCPT. In the accompanying classroom activity, students watch the video and then consider the effect of translating and reflecting on the coordinates of the vertices of the triangle. Next, they draw translations and reflections of a triangle and identify the number of units and direction of translation as well as the lines of reflection in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane. Prior exposure to reflection is helpful.

• ## Analyze the Data: Big Bay

Learn why sea urchins are taking over Big Bay in this interactive from WNET. In the accompanying classroom activity, students watch a series of Cyberchase videos and then work together in groups of two to complete an associated activity. As they use the interactive, students will represent the data that they collect in a double bar graph in order to make comparisons with a healthy bay and analyze the factors leading to the problem. This resource is part of the Math at the Core: Middle School Collection.

• ## Real-World Ratio and Rate Reasoning: How to Power the Skate Park

The CyberSquad works with area to figure out how to power a skate park using solar panels in this interactive from WNET. In the accompanying classroom activity, students view and analyze a series of video clips from Cyberchase and complete an activity using area and ratio. Students take what they’ve learned and put it to the test by designing their own solar power dream house. This resource is part of the Math at the Core: Middle School Collection.

• ## Solving Fraction Problems in Ecotopia

Solve problems using addition, subtraction, and multiplication of fractions in this interactive from WNET. In the accompanying classroom activity, students work in groups of two and watch a series of Cyberchase videos; answer associated discussion questions; and complete an activity that uses fraction knowledge, proportion, addition, and multiplication.

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

• ## Using Sampling and Statistics to Get Rid of the Trash in Perfectamundo

Learn how the CyberSquad uses sampling and data analysis to help solve a city's trash problem in this interactive from WNET. In the accompanying classroom activity, students watch a series of video clips in which the CyberSquad works to get rid of a mountain of trash by reducing, reusing, and recycling. Students use sampling, multiplication, and fractions to help determine the amount of trash for each method of removal and then complete a sampling and data analysis activity of their own design. This resource is part of the Math at the Core: Middle School Collection.

• ## Math with Jake: Frequencies & Pitch

In this video, musician Jake Shimabukuro uses the pitch of musical notes and vibrations in hertz to illustrate the concept of ratios. This clip is from Center for Asian American Media. In the accompanying classroom activity, students watch a portion of the video in which Shimabukuro explains the 3/4 time signature. After a brief introduction to musical pitch, students watch the rest of the video. They then use a chart listing the frequency of musical notes to identify ratios among notes that are one or more octaves apart. To get the most from the activity, students should have some familiarity with physics of sound. This resource is part of the Math at the Core: Middle School Collection.

• ## Math in Fencing: Strategy & Connectivity

Learn about the competitive sport of fencing along with the resulting mathematical problems and equivalent expressions that help determine the number of matches played per tournament in this video from the Center for Asian American Media. This resource is part of the Math at the Core: Middle School Collection.