The Warlord's Kites
This is a measurement activity based on the picture book The Warlord's Kites
About this resource
This activity, Kite squares, is based on the picture book The Warlord’s Kites (words by Virginia Walton Pilegard and illustrations by Nicholas Debon).
Specific learning outcomes:
- Derive a formula for finding the area of a triangle based on their understanding of the area of a square.
- Accurately calculate the area of triangles and parallelograms and explain how they achieved their answer.
The Warlord's Kites
Achievement objectives
GM4-3: Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids.
Description of mathematics
The area of a 2-dimensional shape is expressed in square units.
Every triangle is half of a parallelogram. This relationship can be used to find the area of both shapes.
Required materials
- rulers
- tissue paper
- triangles of coloured paper of several varieties and sizes
- 1 cm grid paper
- Warlord’s Kites by Virginia Walton Pilegard
Activity: Kite squares
This is another “mathematical adventure” in the Warlord series that takes place in ancient China. This time, when the palace is attacked by an invading army, the two young apprentices devise a way to scare off the invaders using kites. The kites are constructed from very precious handmade paper, and thus the area must be measured accurately so no paper is wasted. It is a simple introduction to square units but serves as a springboard for exploring more complex relationships between shape and area.
1.
Prior to reading, explore your students’ understanding of area and seek out examples from their own lives when area needs to be calculated or considered (painting, wallpaper, sewing, wrapping presents, selecting a towel, etc.). Compare and contrast the concepts of perimeter and volume.
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: u2 |
| volume | length and width and height (box: 3-D) | units cubed: u3 |
2.
Share the book with your students. As you read the story, stress the preciousness of the paper that was handmade and how accurate measurements needed to be taken before it could be used.
3.
Discuss how the area of squares is calculated. Discuss how this can be expressed as a formula that works for every square: length x width.
4.
Handout some paper isosceles triangles and ask students to work in pairs and find a formula for working out the area of their triangle based on what they know about squares. (They should reach the conclusion that they can create a square by reflecting (doubling) the triangle and that the shorter sides of their triangle would become the sides of the square, and thus half the area of their square will be the area of their triangle.)
5.
Handout some other triangles that are not isosceles and ask students to figure out the area for each. If students get stuck, support them in discovering that a square is a parallelogram and that any triangle is half of a parallelogram. Therefore, the area of their triangle must be half the area of the parallelogram. Ask them to prove their calculations by demonstrating on grid paper.
6.
Ask the student to draw and cut out an elongated diamond kite shape from tissue paper. Ask them to calculate the area of their kite, knowing what they know about triangles and parallelograms.
- Do they recognise the 2 triangles within the kite?
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