This is an activity based on the picture book *The Emperor’s Army*

Students will be able to model their understanding of volume through creating models and calculating volume using a formula.

The volume of cuboids is found by multiplying the length by the height by the width. This is expressed in cubic units.

The Emperor’s Army by Virginia Walton Pilegard

Lego Units

This activity is based on the picture book: *The Emperor’s Army *

Author: Virginia Walton Pilegard

Illustrator: Adrian Tans

Publisher: Pelican (2010)

ISBN: 978-1-58980-690-0

**Summary: **

This is another “mathematical adventure” in the Warlord series that takes place in ancient China. After being forced to flee the palace, the young apprentice discovers the terra-cotta army being built. He calculates the size of the army based on his measurements of the clay hole being dug.

**Lesson Sequence:**

- Prior to reading, explore your students’ understanding of volume and seek out examples from their own lives when volume needs to be calculated or considered (filling drink bottles, packaging, pumping up sports balls etc). Compare and contrast the concept with those of perimeter and area. Create a chart to remind students about the measures
**Feature****dimensions****expressed as***perimeter**length (fence line: 1-D)**units: u**area**length and width (carpet coverage: 2-D)**units squared: u*^{2}*volume**length and width and height (box: 3-D)**units cubed: u*^{3} - Share the book with your students. As you read the story, emphasise how the apprentice calculates the volume of clay used for the soldiers and how he knows there must be more than the first ones they find. Explain that the units being used as imperial based on the old measure of the “foot”.
- Discuss the formula used for calculating the volume of cuboids.
*How would you find the volume of a wedge?*

What about a triangular prism? - Issue the following challenges to be completed as independent activities in small groups.

Lego is your building material and 1 block cube block is the base unit. Thus an “eight” block has a volume of 1x4x2 = 8 Lego^{3}and a “two” block would have a volume of 1x 2x 1 = 2 Lego^{3}

a. Create as many different objects as you can that have exactly a volume of 1000 Lego^{3}.

b. Create a hollow tower with walls that have a volume of 1000 Lego^{3}.

Calculate the volume of the hollow space inside your tower in Lego^{3}.