2
Same fraction, different shape
Discover Mathematics P2: Term 2, Lessons 101–110
GoalSee that equal parts of the same whole can have different shapes but name the same fraction.
New words
same whole · the shapes we compare are the same sizediagonal · a line from one corner to the opposite cornershaded · coloured in
Explanation
The same whole can be cut into halves in many ways. A square can be cut straight down, straight across, or from corner to corner. Each way makes 2 equal parts, so each part is 1/2 of the square, even if the parts look different. A fraction depends on equal parts of the same whole, not on the shape of the parts. Fourths can be cut in different ways too.
Worked examples
Cut across: the top half is shaded. The whole has 2 equal parts and 1 is shaded, so 1/2.
Cut from corner to corner: one triangle is shaded. The two triangles are equal, so the shaded part is 1/2.
Fourths in a different way: a square cut into 4 equal strips with 1 shaded. This is 1/4, like the 4 small squares.
Class activity
Cut it in different ways. Fold four squares of paper. Fold the first in half down, the second across, the third corner to corner. Colour half of each. Do the halves look different? Put each half on another to see if they cover the same amount. Then fold the fourth square into fourths in a new way.
Practice
1
What fraction of the square is shaded?
1/4.
2
The square is cut from corner to corner. What fraction is shaded?
1/2.
3
Karim says a half cut across is smaller than a half cut down. Is he right?
No. Both halves of the same square are equal in size.
4
Draw a square and cut it into halves in two different ways. Colour half each time.
For example one cut straight down the middle and one from corner to corner.
5
What fraction of the square is shaded? Write it as fourths.
2/4, which is the same as 1/2.