Volume of rectangular prisms – Grade 5 math lesson

Lesson 16 of 18 in the Grade 5 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 5 (ages 10–11) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 5 (ages 10–11)
You need: Paper, a pencil and this page
Graded: Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

Read what your child will learn and the big ideas together.
Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
Finish with the exit ticket and the talk question: “Can two different boxes have the same volume?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Adding the lengths instead of multiplying. Build a layer of cubes: rows times columns, times layers.
Using square units (cm²) for volume. Volume is three-dimensional: cubic units, cm³.

Tip for home: Estimate then work out the volume of cereal or shoe boxes.

What your child will learn

Learning goal: find the volume of rectangular prisms by counting cubes and by using length × width × height.

Success looks like

I can count cubes to find volume.
I can use length × width × height.
I can find a missing length.

Key words

volume: space taken up by a solid
cubic centimeter: a cube 1 cm on each side (cm³)
rectangular prism: a box shape with rectangle faces
dimensions: length, width and height

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Fill a small box with cubes or sugar lumps, count one layer and the number of layers, then multiply.

The big ideas (for the adult)

Volume is the amount of space a solid takes up. It is measured in cubic units such as cm³.

For a rectangular prism, find how many cubes fit in one layer (length × width), then multiply by the number of layers (height).

If you know the volume and two lengths, divide to find the missing length.

The lesson, step by step

45 minutes in 5 parts
Part	Time	How it is checked
Starter: quick recall	5 min	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

All Grade 5 math lessons and tests · Math Department

More Grade 5 math lessons

Curriculum

Common Core State Standards 5.MD.C.3.a: “A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.”

Common Core State Standards 5.MD.C.3.b: “A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.”

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