ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 39 :

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]

[MA2019] ACC-7 (7) 41 :

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

[MA2019] REG-8 (8) 30 :

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

[MA2019] GEO-19 (9-12) 17 :

17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.

Experiment with the volume of two cylinders made from the same size paper. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

   View Standards     Standard(s): [MA2019] (6) 26 :

26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

[MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 39 :

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]

To find area, you must figure out how many square units will fit inside the shape. Patricia Wilkins, a landscape designer, explains how she calculated square feet for a project in her yard.

   View Standards     Standard(s): [MA2019] (5) 18 :

18. Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.

a. Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.

[MA2019] (6) 28 :

28. Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

a. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

[MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 39 :

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]

Estimate the volume you get when you fill 3D shapes with candy. This video focuses on estimating volume using nonstandard units, using the volume equation to get a more reliable estimate, and checking your estimate by counting the nonstandard units. 

   View Standards     Standard(s): [MA2019] REG-7 (7) 20 :

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.

[MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 36 :

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]

[MA2019] ACC-7 (7) 39 :

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]

[MA2019] ACC-7 (7) 41 :

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

[MA2019] REG-8 (8) 30 :

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

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.

   View Standards     Standard(s): [MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 39 :

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]

In this interactive activity, students will be led through steps to calculate the surface area of solid figures. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.

   View Standards     Standard(s): [MA2019] (6) 26 :

26. Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

a. Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

[MA2019] REG-7 (7) 22 :

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.

[MA2019] ACC-7 (7) 39 :

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]

In this interactive activity, students will be led through steps to calculate the area of a triangle. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the interactive is available to be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.