### Clarifications

*Clarification 1:*Instruction emphasizes the conceptual understanding that volume is an attribute that can be measured for a three-dimensional figure. The measurement unit for volume is the volume of a unit cube, which is a cube with edge length of 1 unit.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**5

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- NA

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

- This benchmark introduces volume to students. Their prior experiences with volume were restricted to liquid volume (also called capacity). The concept of volume should be extended from the understanding of area starting in Grade 3 (MA.3.GR.2.1), with the idea that a layer (such as the bottom of cube) can be built up by adding more layers of unit cubes. In Grade 6, (MA.6.GR.2.3) students solve volume problems involving rectangular prisms with fraction and decimal side lengths.
- As students develop their understanding of volume, they recognize that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. This cube has a length of 1 unit, a width of 1 unit and a height of 1 unit and is called a cubic unit. This cubic unit is written with an exponent of 3 (e.g., in
^{3}, 3^{3}). Students connect this notation to their understanding of powers of 10 in our place value system (MTR.5.1).

### Common Misconceptions or Errors

- Students may incorrectly fill figures to find volume with cubes. Students need to ensure there is no empty space included and that unit cubes are equally-sized and packed tightly in without overlaps.

### Strategies to Support Tiered Instruction

- Instruction includes providing unit cubes and having students build rectangular prisms with specific dimensions and then calculating the volume.
- For example, the teacher provides students with unit cubes and the following dimensions: length is 8 units, width is 4 units, and height is 5 units. Students stack equally sized unit cubes and ensure that the cubes are packed tightly with no gaps or overlaps to create a solid three-dimensional figure. Students begin building the figure as shown below, continuing to fill it in until complete. Students calculate the volume by multiplying 8 × 4 × 5 and then decompose the figure and count the cubes to determine if their calculation is correct.

- Instruction includes providing rectangular prisms filled with cubes. Some are filled correctly with no gaps or overlaps, and others have the cubes filling the rectangular prism, but with gaps left between them. Students identify which are stacked correctly to find volume and which are not stacked correctly and record the dimensions of the number of cubes for the height, length, and width, counting the total to determine the volume.

### Instructional Tasks

*Instructional Task 1* (MTR.6.1)

- Part A. Will all of Molly’s blocks fit in the storage container? Explain how you know using drawings and equations.
- Part B. If there is enough room, determine how many more blocks Molly could fit in the storage container. If there is not enough room, determine how many blocks will not fit be able to fit in the storage container.

### Instructional Items

*Instructional Item 1 *

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Expert

## Problem-Solving Tasks

## Teaching Idea

## Tutorials

## Unit/Lesson Sequence

## MFAS Formative Assessments

Students analyze a rectangular prism that contains one layer of unit cubes and are asked to explain how to determine the volume of the entire prism using only the information given.

Students are asked to determine how a unit cube can be used to measure the volume of a rectangular prism.

Students discuss the volume of a prism measured in cubic units with gaps between the unit cubes used to measure its volume.

Students are asked to determine the volume of a rectangular prism in cubic units.

Students determine how many improvised units of volume will fill a large box.

## Original Student Tutorials Mathematics - Grades K-5

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume, in this interactive tutorial.

## Student Resources

## Original Student Tutorials

Build on your previous knowledge of area and learn how to calculate volume in cubic units with this interactive tutorial.

Type: Original Student Tutorial

Demonstrate how a rectangular prism can be carefully filled without gaps or overlaps using the same size unit cubes and then use this model to determine its volume, in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Task

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Type: Problem-Solving Task

## Tutorials

This Khan Academy tutorial video illustrates measuring volume by counting unit cubes. Models in this video include composite figure of rectangular prisms although only counting is used to find volume, not an equation.

Type: Tutorial

This Khan Academy tutorial video describes measurement in one, two, and three dimensions.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

Students are asked to determine the number of unit cubes needed to construct cubes with given dimensions.

Type: Problem-Solving Task