ALEX Classroom Resource

  

Square-Wheeled Tricycle: Radius and Circumference

  Classroom Resource Information  

Title:

 Square-Wheeled Tricycle: Radius and Circumference

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh-math-g-squarewheel/square-wheeled-tricycle-radius-and-circumference/

Content Source:

 PBS
Type: Interactive/Game

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 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.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve problems with the circumference and area of a circle.
Teacher 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).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.20.1: Define diameter, radius, circumference, area of a circle, and formula.
M.7.20.2: Identify and label parts of a circle.
M.7.20.3: Recognize the attributes of a circle.
M.7.20.4: Apply the formula of area and circumference to real-world mathematical situations.

Prior Knowledge Skills:
  • Define center, radius, and diameter of a circle.
  • Identify real-world examples of radius and diameter.
    Examples: bicycle wheel, pizza, pie.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.20 Identify the radius, diameter, and circumference of a circle.
Mathematics
MA2019 (2019)
Grade: 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
Evidence Of Student Attainment:
Students:
  • Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
  • Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
  • Use the formula for volume to find missing measurements of a prism.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.22.1: Define volume, surface area, triangles, quadrilaterals, polygons, cubes, and right prisms.
M.7.22.2: Discuss strategies for solving real-world mathematical problems.
M.7.22.3: Recall formulas for calculating volume and surface area.
M.7.22.4: Identify the attributes of triangles, quadrilaterals, polygons, cubes, and right prisms.

Prior Knowledge Skills:
  • Recognize the formula for volume.
  • Define volume, rectangular prism, edge, and formula.
  • Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
  • Set up V=lwh and V=Bh to find volumes in the context of solving real-world and mathematical problems.
  • Discover the volume of a rectangular prism using manipulatives.
  • Define three-dimensional figures, surface area, and nets.
  • Evaluate how to apply using surface area of a three-dimensional figure to solving real-world and mathematical problems.
  • Draw nets to find the surface area of a given three-dimensional figure.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.22 Determine the area regular, two-dimensional figures. Determine the volume of rectangular prisms, limited to whole numbers.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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.

a. Informally derive the formula for area of a circle.

b. Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve problems with the circumference and area of a circle.
Teacher 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).
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
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
Evidence Of Student Attainment:
Students:
  • Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
  • Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
  • Use the formula for volume to find missing measurements of a prism.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
41. Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems. [Grade 8, 30]
Unpacked Content
Evidence Of Student Attainment:
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.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 8
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
Unpacked Content
Evidence Of Student Attainment:
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.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.30.1: Define formula, volume, cone, cylinders, spheres, and height.
M.8.30.2: Discuss the measure of volume and give examples.
M.8.30.3: Solve problems with exponents, with or without a calculator.
M.8.30.4: Recall how to find circumference of a circle, with or without a calculator.
M.8.30.5: Identify parts of a circle.
M.8.30.6: Calculate the volume of three-dimensional figures.
M.8.30.7: Solve real-world problems using the volume formulas for three-dimensional figures, with or without a calculator.

Prior Knowledge Skills:
  • Define volume, surface area, triangles, quadrilaterals, polygons, cubes, and right prisms.
  • Discuss strategies for solving real-world mathematical problems.
  • Recall formulas for calculating volume and surface area.
  • Identify the attributes of triangles, quadrilaterals, polygons, cubes, and right prisms.
  • Define diameter, radius, circumference, area of a circle, and formula.
  • Identify and label parts of a circle.
  • Recognize the attributes of a circle.
  • Apply the formula of area and circumference to real-world mathematical situations.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.30 Use the formulas for perimeter, area, and volume to solve real-world and mathematical problems (where volume problems are limited to finding the volume of cylinders and rectangular prisms).

Tags: area, circle, circumference, formula, radius, realworld, sphere
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Author: Hannah Bradley
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