This problem solving activity has a geometry focus.
Flip made a flag for her boat.
She took a red square.
She then put a white triangular piece of material over the red square.
Her working sketch is shown here.
If P and Q are the midpoints of the original square, what fraction of the square did the white flag cover?
In order to find the area of the white piece of material it is necessary to break up the square into different smaller rectangles and square and compare these to the original square. This is the main problem solving strategy here and is a common feature of finding complicated areas. The idea is used again in Bill’s Badge, Measurement, Level 5.
Flip made a flag for her boat. She took a red square. She then put a white triangular piece of material over the red square. Her working sketch is shown here.
If P and Q are the midpoints of the original square, what fraction of the square did the white flag cover?
Introduce the problem by looking at the country flags. Ask the students to make "mathematical" statements about them. Ask the students to estimate the fractional relationships between the different parts of the flags.
Bahamas | Columbia | Kuwait |
Suppose Flip’s original red square was a rectangle. Could she produce a white triangular piece that was 5/8 of the original rectangle?
Can she do this using some other shape?
In the rectangle ABRP, PB is a diagonal. Hence area of triangle APB = area of triangle PBR. Since rectangle ABPR is 1/2 of square, the area of triangle APB is 1/4 of square.
Similarly the area of triangle QBC is 1/4 square of square. Now triangle PDQ is 1/2 of area of square PXQD. This square is 1/4 of the original square. Hence triangle PDQ has area 1/8 of square.
So the white flag covers 1 - 1/4 - 1/4 - 1/8 = 1 - 5/8 = 3/8.
The same calculations show that the white piece below has area 3/8 of the rectangle. Here P, Q are midpoints of the appropriate sides.
One other possible answer is shown below. Here P and Q are again midpoints.
The possibilities are probably endless.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/flip-s-flag at 8:58pm on the 26th February 2024