ALEX Learning Activity

  

Locker Design Challenge

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2830
Title:
Locker Design Challenge
Digital Tool/Resource:
Locker Design Challenge sheet
Web Address – URL:
Overview:

This activity is a performance task where students design a locker with a specific volume.  They must create two different rectangular prisms with the same volume and record the length, width, and height of each one.  They must also choose which dimensions are the most appropriate for a locker and use reasoning to support their choice.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 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.

a. Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Measure volume of rectangular solids by packing the figure and counting the number of same-sized unit cubes needed to completely fill the figure.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.18.1: Define volume including the formulas V = L × W x h, and V = B x h.
M.5.18.2: Define solid figures.
M.5.18.3: Define unit cube.
M.5.18.4: Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
M.5.18.5: Describe attributes of three-dimensional figures.
M.5.18.6: Describe attributes of two-dimensional figures.
M.5.18.7: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.18.8: Define cubic inches, cubic centimeters, and cubic feet.
M.5.18.9: Compare the unit size of volume/capacity in the customary system including fluid ounces, cups, pints, quarts, gallons.
M.5.18.10: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
M.5.18.11: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
M.5.18.12: Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
M.5.18.13: Recall basic multiplication facts.
M.5.18.14: Fluently add.

Prior Knowledge Skills:
  • Count unit cubes to find volume.
  • Demonstrate volume by packing a solid figure with unit cubes.
  • 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.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.18 Using vocalization, sign language, augmentative communication, or assistive technology, identify cubes, cylinders, and spheres as three-dimensional shapes.
Mathematics
MA2019 (2019)
Grade: 5
19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

a. 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. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given right rectangular prisms with whole number edge lengths,
  • Use associative property of multiplication to find volume and relate it to packing a solid with unit cubes.
  • Apply formula V = l × w × h, where V represents volume and l, w, and h represent the three dimensions of the prism (length, width, height) and relate the formula to a unit cube filled model.
  • Apply formula V = B × h, where V represents volume, B is the base-area, and h represents the height (number of layers of the base-area) and relate the formula to a unit cube filled model.

  • Given a solid figure composed of two or more right rectangular prisms in real-world or mathematical contexts, find the total volume by decomposing the figure into non-overlapping rectangular prisms and find the sum of the volumes.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.19.1: Define volume.
M.5.19.2: Recognize angle measure as additive.
M.5.19.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
M.5.19.4: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
M.5.19.5: Recognize the formula for volume.
M.5.19.6: Recall the attributes of three-dimensional solids.
M.5.19.7: Recall basic multiplication facts.
M.5.19.8: Fluently add.
M.5.19.9: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.10: Measure and estimate liquid volumes.
M.5.19.11: Recall basic multiplication facts.
M.5.19.12: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.13: Recognize the formula for volume.
M.5.19.14: Recall basic multiplication facts.
M.5.19.15: Describe attributes of three-dimensional figures.
M.5.19.16: Describe attributes of two-dimensional figures.
M.5.19.17: Identify solid figures.

Prior Knowledge Skills:
  • Count unit cubes to find volume.
  • Demonstrate volume by packing a solid figure with unit cubes.
  • Convert measurement units.
  • Solve mulit-step word problems involving measurement conversions.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.19 Determine the volume of a rectangular prism by counting units of measurement (e.g., unit cubes).

Learning Objectives:

Students will solve a real-world problem involving volume by creating two different rectangular prisms with a given volume.

Students will make a connection between packing a prism with unit cubes and multiplying the three edge lengths to determine volume.

 
  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

  • Give students the Locker Design Challenge sheet.

  • Students can use centimeter cubes, unifix cubes, or digital cubes.

  • Students are tasked with designing two different rectangular prisms with the same volume.  Go over the task with the students and make sure they understand the problem.

  • Students record their designs and the dimensions on the sheet.

  • The final question asks students to choose which dimensions are most appropriate for a locker and support their choice.
Assessment Strategies:

Evaluate student responses to determine if they were able to solve a real-world problem involving volume; students should have created two different rectangular prisms with the given volume.

Use questioning, formative assessment strategies, and students' written responses to determine if students were able to make connections between counting unit cubes to find the volume and multiplying the three edge lengths.
Advanced Preparation:

Each student will need a copy of the Locker Design Challenge sheet and a set of at least 36 cubes (or access to digital equivalents).
Variation Tips (optional):

For struggling students, you can provide support by creating one of the designs so that students have to find a new shape with the same volume.  Students may also work in pairs for extra support.

For enrichment, the volume requirements can be adjusted.  For example, the lockers could be 60 in3 or 150,000 cm3 (to make connections with measurement conversion standards).
Notes or Recommendations (optional):

This activity can be used as a stand-alone activity or together with the following activities as a complete lesson:

Volume Warm-Up

Sugar Cubes Lab
  Keywords and Search Tags  
Keywords and Search Tags: cubes, dimensions, measurement, solid figures, unit, volume