2
Squares made from triangles
Discover Mathematics P3: Term 1, Lessons 31–40
GoalFind how many triangles make a number of squares, and the other way round, by doubling and halving.
New words
triangle · a shape with 3 straight sidesdiagonal · a straight line from one corner of a square to the opposite cornerdouble · two times as manyhalf · one of two equal parts
Explanation
Draw a line from one corner of a square to the opposite corner. This line is called a diagonal. It cuts the square into 2 equal triangles, so one square is made of 2 triangles. If a drawing has 5 squares, the number of triangles is double: 5 × 2 = 10. For any number of squares, multiply by 2. To go the other way, divide by 2. For example, 14 triangles make 14 ÷ 2 = 7 squares. We can check by multiplying: 7 × 2 = 14.
Worked examples
Mona draws 4 squares and cuts each one along a diagonal. Each square gives 2 triangles, so 4 × 2 = 8 triangles.
Karim draws 6 squares with a diagonal in each. Repeated addition: 2 + 2 + 2 + 2 + 2 + 2 = 12. Multiplication: 6 × 2 = 12. There are 12 triangles.
Salma counts 14 triangles in a row of squares. Two triangles make one square, so 14 ÷ 2 = 7 squares. Check: 7 × 2 = 14.
Class activity
Fold and cut. Cut 6 squares of paper. Fold each one along a diagonal and cut. Count the triangles and write the multiplication. Then put 2 triangles together to make a square again, and count how many squares you can make from all your triangles.
Practice
1
How many triangles are there in the 5 squares?
5 × 2 = 10 triangles.
2
Youssef draws 9 squares and puts a diagonal in each. How many triangles are there?
9 × 2 = 18 triangles.
3
A pattern has 16 triangles. How many squares were cut to make them?
16 ÷ 2 = 8 squares.
4
Seif says 6 squares need 8 triangles, because 6 + 2 = 8. What is his mistake? What is the right answer?
He added 2 instead of multiplying by 2. Each square gives 2 triangles, so 6 × 2 = 12 triangles.
5
Marina has 12 squares of paper and cuts each along a diagonal. How many triangles does she get? How many squares could she make from 30 triangles?
12 × 2 = 24 triangles. From 30 triangles she can make 30 ÷ 2 = 15 squares.