GoalCheck whether a shape is really cut into equal parts and find the mistake when it is not.
New words
equal parts · parts that are exactly the same sizeunequal parts · parts that are not the same sizematch exactly · fit on top of each other with no gaps or extra
Explanation
To name a fraction, the parts must be equal. A shape cut into 4 parts is not cut into fourths unless all 4 parts are the same size. Having the right number of parts is not enough. To check, we can fold the shape, trace one part and lay it on another part, or count the squares in each part. Parts can look different and still be equal. A square cut from corner to corner makes 2 triangles that match exactly, so they are halves. When you find unequal parts, say what is wrong: for example, some parts are bigger than others.
Worked examples
A baker cuts a tray of basbousa as shown and says the pieces are fourths. There are 4 pieces, but the two wide pieces are twice as wide as the two narrow ones. The parts are not equal, so they are not fourths.
A square sandwich is cut from corner to corner. The two triangles fit exactly on top of each other, so they are equal. Each one is a half, even though they do not look like rectangles.
A rope 25 cm long is cut into 3 pieces of 10 cm, 10 cm and 5 cm. There are 3 pieces, but one is shorter, so they are not thirds.
Class activity
Mistake hunt. Draw three rectangles. Cut the first into 2 equal parts, the second into 3 parts where one part is clearly bigger, and the third into 4 equal parts. Show them to someone at home and ask which one has a mistake in its parts. How can you check?
Practice
1
Hana says this rectangle is cut into fourths. Is she right?
No. There are 4 parts, but two parts are wide and two are narrow, so the parts are not equal.
2
Is this rectangle cut into thirds?
Yes. There are 3 parts and each is 2 units wide, so the parts are equal.
3
A pizza is cut into 3 pieces, but one piece is very small. Can we call the pieces thirds?
No. Thirds must be equal in size.
4
Mostafa cuts a square along a diagonal into 2 triangles that match exactly. He says each is a half. Is he right?
Yes. The two parts are equal, so each one is a half.
5
A ribbon 12 cm long is cut into 3 pieces of 5 cm, 4 cm and 3 cm. Are they thirds? How long would each third be?
No, the pieces are not equal. Each third would be 12 ÷ 3 = 4 cm long.
