Math at the Core: Middle School

Geometry


  • Rotational Symmetry

    Visualize how objects behave when they are rotated around a centrally located rotation point. This interactive exercise looks at angles of rotation and rotational symmetry of a variety of figures.

    Grades: 7-8
  • Classifying Polygons

    Exhibit your knowledge of 2D shapes and search for similar characteristics. This interactive diagram focuses on sorting polygons by common properties and then you select the correct label for each section of the Venn Diagram. This resource is part of the Math at the Core: Middle School collection.

    Grades: 4-5
  • Are These Shapes Congruent?

    Use your spatial awareness skills to make predictions about similar shapes. This interactive exercise focuses on whether or not two shapes are congruent and rotating, reflecting, and translating shapes.
    Grades: 7-8
  • Constructing Quadrilaterals

    Attempt to build a variety of different quadrilaterals using virtual linkage strips. This interactive exercise focuses on the appearance and manipulation of quadrilaterals.
    Grades: 1-7
  • Three-Dimensional Printing

    Discover how design software runs three-dimensional printers by translating 3D shapes into triangles. This video focuses on the composition of 3D polygons and introduces the idea of printing in three dimensions as stacking thin layers of material, taking math out of the classroom and into real world problem solving.
    Grades: 5-8
  • Reflection

    In this animated Math Shorts video from the Utah Education Network, learn about reflection, one type of movement for geometric shapes. The animation relates the geometric meaning of reflection to its more common understanding—a mirror image—and then displays geometric shapes on a coordinate plane reflecting through the x-axis and y-axis. In the accompanying classroom activity, students design a geometric figure in one quadrant and then reflect it into at least one other quadrant. They earn points by designing more complicated shapes or reflecting a shape into more quadrants. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-9
  • Rotation

    In this animated Math Shorts video from the Utah Education Network, learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. When a geometric shape rotates on a coordinate plane, it stays exactly the same distance from the center of rotation. In the accompanying classroom activity, students are given two rotations from a handout and work in pairs to try to determine whether one figure is a rotation of the other figure around the given point. If the figure is a rotation, the student pair must add one more rotation to the grid. If the figure is not a rotation, the student pair must add one accurate rotation to the grid. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-9
  • Translation

    In this animated Math Shorts video from the Utah Education Network, learn about translation, which occurs when a geometric shape slides from one location to another on a coordinate plane. The shape itself doesn’t change, just its location. The animation also explains mapping notations, which designate how far and in what direction a shape moves. In the accompanying classroom activity, students solve a series of practice translation problems and explain to one another what they did to solve them. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 7-9
  • Geometry and Classification of 2D Figures: Bianca Busts a Move

    In this video from Cyberchase, Bianca breaks her friend’s tabletop when she’s practicing dance moves in his living room. She uses measurement and geometry to get a new piece of wood that will fit the table exactly. The accompanying classroom activity helps students advance their understanding of perimeter and area by creating their own tabletop designs. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-6
  • Surface Area , Area and Volume: The Big Sleep

    In this video from Cyberchase, Bianca is planning a sleepover birthday party. To figure out the maximum number of friends she can invite, she decides to count how many sleeping bags she can fit over the area of her living room floor. In the accompanying classroom activity, students use the concepts presented in the video to determine the area of multiple shapes. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 5-6
  • Formulas for Circle Area and Circumference: Simple as Pie

    In this video from Cyberchase, Bianca and her friend team up to sell pies. Bianca learns that pie-pan sizes are the measured diameter of the pan, but that there is a mathematical relationship between the diameter of the pan and the circumference of the pan. In the accompanying classroom activity, students calculate the circumference of a variety of wheels. This resource is part of the Math at the Core: Middle School Collection.

    Grades: 6-7
  • Finding Pentominos

    Use your spatial visualization skills to create pentominos. This interactive exercise focuses on using reasoning skills to find all the different pentominos without duplicating them, factoring in reflections and rotations. This resource is part of the Math at the Core: Middle School collection.

    Grades: 7-8
  • 2D Nets for 3D Decorative Boxes

    Figure out how to make the most of your materials and budget when buying decorative paper to cover a given box. This interactive exercise focuses on surface area, measurement, and problem solving skills to compare alternate solutions to the same problem, taking math out of the classroom and into the real world.

    Grades: 6-8
  • The Largest Container: Problems Using Volume and Shape

    Maximize the volume of each solid if it is to be constructed from a single sheet of paper. This interactive exercise focuses on volume equations, measurement, and problem solving skills to compare the volume of 3D figures constructed from similar amounts of construction materials.

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

    Grades: 6-8
  • Constructing Triangles

    Attempt to build a variety of different triangles using virtual linkage strips. This interactive exercise focuses on the appearance and manipulation of triangles.
    Grades: 1-7
  • Calculating Distance Using the Pythagorean Theorem

    Determine the distance between any two points on the coordinate plane. This interactive exercise focuses on using the Pythagorean Theorem to calculate distance and plotting points on a Cartesian grid. This resource is part of the Math at the Core: Middle School collection.

    Grades: 7-8
  • Scaling

    Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.

    Grades: 5-8
  • Comparing Volumes of Cylinders, Spheres, and Cones

    Squash cones and spheres to compare their volumes to similar cylinders and look for patterns. This interactive exercise focuses on comparing volumes between figures that have the same height and diameter and drawing conclusions based on the ratios of the sizes. This resource is part of the Math at the Core: Middle School collection.

    Grades: 7-8
  • Cross Sections of a Cube

    Cut through a cube with a virtual sword and observe the resulting cross sections. This interactive exercise focuses on discovering the relationships between two and three-dimensional shapes. This resource is part of the Math at the Core: Middle School collection.

    Grades: 5-7
  • Classifying Triangles by Angles and Sides

    In this video, a middle school student explains how to classify triangles according to angle measurements and side lengths. In the accompanying classroom activity, students find and discuss triangular shapes around the classroom.

    Grades: 5

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