Classroom Resource

Square-Wheeled Tricycle: Radius and Circumference

Subject Area

Mathematics

Grade(s)

7, 8

Overview

Uncover the secret behind how a square-wheeled tricycle can work at the National Museum of Mathematics. This interactive exercise focuses on working with the radius of various circles to find the circumference and area as well as challenging you to find the distance a square wheel travels around the track.

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

Mathematics (2019) Grade(s): 7

MA19.7.20

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

Unpacked Content

UP:MA19.7.20

Vocabulary

  • Diameter
  • Radius
  • Circle
  • Area
  • Circumference
  • π

Knowledge

Students know:
  • that the ratio of the circumference of a circle and its diameter is always π.
  • The formulas for area and circumference of a circle.

Skills

Students are able to:
  • use the formula for area of a circle to solve problems.
  • Use the formula(s) for circumference of a circle to solve problems.
  • Give an informal derivation of the relationship between the circumference and area of a circle.

Understanding

Students understand that:
  • area is the number of square units needed to cover a two-dimensional figure.
  • Circumference is the number of linear units needed to surround a circle.
  • The circumference of a circle is related to its diameter (and also its radius).
Mathematics (2019) Grade(s): 7

MA19.7.22

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Unpacked Content

UP:MA19.7.22

Vocabulary

  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubes
  • Right rectangular prisms

Knowledge

Students know:
  • that volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Skills

Students are able to:
  • find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Understanding

Students understand that:
  • two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • the volume of a pyramid is 1/3 the volume of a prism with the same base.
Mathematics (2019) Grade(s): 8

MA19.8.30

Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

Unpacked Content

UP:MA19.8.30

Vocabulary

  • Radius
  • Pi
  • Volume
  • Cylinder
  • Cone
  • Sphere

Knowledge

Students know:
  • The volume formulas for cylinders, cones, and spheres.
  • That 3.14 is an approximation of pi commonly used in these volume formulas.
  • That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Skills

Students are able to:
  • Calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
  • Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
  • Combine the results of calculations to find volume for real-world composite figures.

Understanding

Students understand that:
  • the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.36

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

Unpacked Content

UP:MA19.7A.36

Vocabulary

  • Diameter
  • Radius
  • Circle
  • Area
  • Circumference
  • π

Knowledge

Students know:
  • the ratio of the circumference of a circle and its diameter is always π.
  • The formulas for area and circumference of a circle.

Skills

Students are able to:
  • use the formula for area of a circle to solve problems.
  • Use the formula(s) for circumference of a circle to solve problems.
  • Give an informal derivation of the relationship between the circumference and area of a circle.

Understanding

Students understand that:
  • area is the number of square units needed to cover a two-dimensional figure.
  • Circumference is the number of linear units needed to surround a circle.
  • The circumference of a circle is related to its diameter (and also its radius).
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.39

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. [Grade 7, 22]

Unpacked Content

UP:MA19.7A.39

Vocabulary

  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubs
  • Right rectangular prisms

Knowledge

Students know:
  • That volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Skills

Students are able to:
  • Find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Understanding

Students understand that:
  • Two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • The area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • The volume of a pyramid is 1/3 the volume of a prism with the same base.
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.41

Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems. [Grade 8, 30]

Unpacked Content

UP:MA19.7A.41

Vocabulary

  • Radius
  • Pi
  • Volume
  • Cylinder
  • Cone
  • Sphere

Knowledge

Students know:
  • the volume formulas for cylinders, cones, and spheres.
  • That 3.14 is an approximation of pi commonly used in these volume formulas.
  • That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Skills

Students are able to:
  • calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
  • Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
  • Combine the results of calculations to find volume for real-world composite figures.

Understanding

Students understand that:
  • the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.
Link to Resource
https://aptv.pbslearningmedia.org/resource/mgbh-math-g-squarewheel/square-wheel…

CR Resource Type

Interactive/Game

Resource Provider

PBS
Accessibility
License

License Type

Custom

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Approved Date

habradley
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