Learning Activity

Sugar Cubes Lab

Subject Area

Mathematics

Grade(s)

5

Overview

This activity is a hands-on inquiry math lesson where students are asked to prove how many sugar cubes are in a box.  They will measure the volume of a rectangular prism by counting non-standard units and make a connection to multiplying the three edge lengths in the standard formula.

Mathematics (2019) Grade(s): 5

MA19.5.18

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.

Unpacked Content

UP:MA19.5.18

Vocabulary

  • Volume
  • Cube
  • Cubic unit
  • Unit cube
  • Space
  • Three-dimensional
  • Attribute

Knowledge

Students know:
  • strategies or the formula to find the area of a rectangle.

Skills

Students are able to:
  • Count unit cubes to find volume.
  • Demonstrate volume by packing a solid figure with unit cubes.

Understanding

Students understand that:
  • volume represents the amount of space enclosed in a three-dimensional figure and is measured by the number of same-size cubes that exactly fill the interior space of the object.
Mathematics (2019) Grade(s): 5

MA19.5.19

Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

Unpacked Content

UP:MA19.5.19

Vocabulary

  • Volume
  • Unit cube
  • Rectangular prism
  • Base
  • Base-area
  • Dimensions
  • Face
  • Length
  • Width
  • Height
  • Layers
  • Edge
  • Equivalent
  • Conservation of volume
  • Attribute
  • Composition
  • Decomposition
  • Formula

Knowledge

Students know:
  • Measurable attributes of area and how it relates to finding the volume of objects.
  • Units of measurement for volume, specifically unit cubes.

Skills

Students are able to:
  • Solve word problems involving volume.
  • Use associative property of multiplication to find volume.
  • Relate operations of multiplication and addition to finding volume.
  • Apply formulas to find volume of right rectangular prisms.
  • Find volume of solid figures composed of two rectangular prisms.

Understanding

Students understand that:
  • Volume is a derived attribute based on a length unit and can be computed as the product of three length measurements or as the product of one base area and one length measurement.
  • Volume is an extension of area and can be found as the area of the base being repeated for a given number of layers.

Phase

During/Explore/Explain
Learning Objectives

Learning Objectives

Students will be able to identify volume as an attribute of solid figures and measure volume by counting unit cubes. 

Students will be able to use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Students will be able to show that volume can be determined by multiplying the three edge lengths of a rectangular prism.

Activity Details

  • Begin the lesson by putting students into groups of 2-5.  This is an inquiry-based lesson, so mixed ability groups will be helpful.
  • Display the slideshow. Show students the slide with the picture of the box of sugar cubes.  (Students might be unfamiliar with sugar cubes and will need some extra information about how they are used.)  Explain that the box claims there are exactly 198 sugar cubes in the box, but that seems to be an odd number.  Why 198 and not an even 200?  How can we be sure there are exactly 198 cubes in the box?
  • Go to the next slide and explain that the students' task for today is to figure out a way to use math to prove that the box has exactly 198 cubes.  Give students a few moments to turn-&-talk before sharing out ideas.  Students might suggest counting each cube, but that would take a long time and would be difficult to get the count exactly right.  It would work, but it would be an inefficient mathematical solution.
  • When students are ready for the hint, reveal the picture showing how the cubes are arranged at the top of the box.  Describe the layout as an array and have a student share a multiplication equation to represent the array (3x6).
  • Give each group a box of cubes and set a timer.  Students should find a way to prove how many cubes are in the box (without counting each one).  If students are struggling, ask them to think about the top layer they can see -- how many layers of 18 are in the box?
  • Have students share their solutions.  After a class discussion, show students the last slide to help make the connection between counting unit cubes and multiplying the three edge lengths to find the volume. 
  • Note: The solution slide has been hidden in the presentation view to avoid accidentally revealing the answer; to display it, right-click the thumbnail and uncheck the option "skip slide."
  • Give each student an exit ticket to wrap up the lesson.
Assessment Strategies

Assessment Strategies

Observe to see if students are able to solve the real-world volume problem by counting unit cubes. 

Evaluate the exit tickets to see if students can explain how to prove the number of cubes by using the three dimensions of the box as measured in sugar cubes.

Variation Tips

Students can use a digital or printed image of the sugar cube box rather than being provided with the actual item.

 

Related Learning Activities

Learning Activity (Before)

Volume Warm-Up

Learning Activity (During)

Sugar Cubes Lab

Learning Activity (After)

Locker Design Challenge

Background and Preparation

Background / Preparation

Sort students into mixed-ability groups with 2-5 students per group.

Preview the slideshow and prepare to display it for the class.

Each group will need a box of sugar cubes.  (Butcher paper on the desks/tables will make it easier to clean up any sugar crumbs.)

Make enough copies of the exit ticket to give one to each student. (There are two on each page.)

Digital Tools / Resources

Sugar Cubes Lab Slideshow
https://docs.google.com/presentation/d/1naqPv_YAsNUUOMm9nwusdEMHcZ99RELm5zS_FoF…

Approved Date

Owner (Author)

seasley
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