5.MD.5 - About the Math, Learning Targets, and Rigor

Grade 5 Measurement

5.MD.5

About the Math

Full Standard

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

  1. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes (e.g., to represent the associative property of multiplication).
  2. Apply the formulas V = l × w × h and  V = b × 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.
  3. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

5th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

 

Report Card Measurement Topic: Demonstrates understanding of measurement, data and statistics.
4th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

 

Report Card Measurement Topic: Demonstrates understanding of measurement and geometry.

 

Learning Targets (I can)

  • Determine the volume of a rectangular prism.
  • Explain multiplication of the area of the base x the height will result in the volume.
  • Relate finding the product of three numbers to finding volume.
  • Explain how the associative property can be applied to finding volume.
  • Use a formula for finding the volume of a rectangular prism.
  • Decompose irregular figures into rectangular prisms.

 

 

About the Math

This standard builds on the ideas of volume established in grade 5. Essential vocabulary for this standard includes: volume, unit, cube, cubic units, rectangular prism, and additive. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

 

 

 

 

 

Progression of Standard within Grade 5

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
   
  • Determine the volume of a rectangular prism.
  • Explain multiplication of the area of the base x the height will result in the volume.
  • Relate finding the product of three numbers to finding volume.
  • Explain how the associative property can be applied to finding volume.
  • Use a formula for finding the volume of a rectangular prism.
  • Decompose irregular figures into rectangular prisms.

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 4 Grade 6
  • Apply the area formula for rectangles in real world and mathematical problems (4.MD.3)
  • Find the volume of prisms with formula and fractional edge lengths (6.G.2)

 

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • Students can explore volume with different containers and different sized units to see how it affects the total volume. This recording sheet Links to an external site. can be used.
  • How can you measure the volume of a container that is 5 ½ units x 2 ⅓ units x 1 ¾ units? What is the approximate volume of this container?
  • A cereal box has a volume of 128.8 cubic centimeters. What could the dimensions be?
  • Looking at the dimensions of two different boxes with identical volumes, what do you notice about multiples and factors?

                8 in x 2 in x 2 in
                4 in x 2 in x 4 in

  • Can you use the relationship from the previous question to find a container with the same volume, but different dimensions? For example, one prism has the dimensions of 6 x 8 x 2 with a volume of 96 cubic units. Will halving and doubling of factors help you find a container with a volume of 96 cubic units, but different dimensions?
  • A box 2 centimeters high, 3 centimeters wide, and 5 centimeters long can hold 40 grams of clay. A second box has twice the height, three times the width, and the same length as the first box. How many grams of clay can it hold? (Volume increases 6 times, so the second box should hold 40 x 6 = 240 grams of clay.)

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 11 • Measurement: Volume and Conversions

Finding Volume, Volume is Additive:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics

3-5

 Box Comparison - Cubic Units, Activity 9.10, Page 267
Groundworks: Algebraic Thinking 5 110 "Find the Dimensions"

Math In Practice

Teaching Fifth-Grade Math

 5 Module 13

 

 

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

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Assessment

Learning Targets

rubric

  • Determine the volume of a rectangular prism.
  • Explain multiplication of the area of the base x the height will result in the volume.
  • Relate finding the product of three numbers to finding volume.
  • Explain how the associative property can be applied to finding volume.
  • Use a formula for finding the volume of a rectangular prism.
  • Decompose irregular figures into rectangular prisms.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.