This is an activity based on the picture book The Warlord’s Kites
- Students will be able to derive a formula for finding the area of a triangle based on their understanding of the area of a square.
- Students will be able to accurately calculate the area of triangles and parallelograms and explain how they achieved their answer.
- 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.
triangles of coloured paper of several varieties and sizes
1 cm grid paper
The Warlord’s Kites by Virginia Walton Pilegard
This activity is based on the picture book: The Warlord’s Kites
Author: Virginia Walton Pilegard
Illustrator: Nicholas Debon
Publisher: Pelican (2004)
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 the 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 to exploring more complex relationships between shape and area.
- 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
- Share the book with your students. As you read the story, stress the preciousness of paper that was handmade and how accurate measurements needed to be taken before it could be used.
- 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.
- 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.)
- Handout some other triangles that are not isosceles and ask students to figure out the area for each. If students get stuck support them to discover 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.
- Ask student 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?