GoalUse fact triangles to write multiplication and division facts, and find mistakes in sums.
New words
fact triangle · a triangle with a product at the top and its two factors at the bottomfact family · equations that use the same three numbersregroup · to carry or borrow when adding or subtracting
Explanation
A fact triangle has the product at the top and the two factors at the bottom. The numbers 6, 7 and 42 give four facts: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6. If one number is missing, use the other two. For the triangle with 54 at the top and 9 at the bottom, the missing factor is 54 ÷ 9 = 6. We can also find mistakes. Karim wrote 467 + 285 = 642. Check by subtracting: 642 − 285 = 357, not 467, so the sum is wrong. He forgot to add the 1s he carried. The right sum is 752, and 752 − 285 = 467.
Worked examples
Multiplication
Division
6 × 7 = 42
42 ÷ 6 = 7
7 × 6 = 42
42 ÷ 7 = 6
The fact triangle 42, 6, 7 gives the family: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6.
Find the missing number in the triangle with 54 at the top and 9 at the bottom left. The product is 54 and one factor is 9, so the other factor is 54 ÷ 9 = 6. Check: 9 × 6 = 54.
Place
Work
Write
Ones
7 + 5 = 12
2
Tens
6 + 8 + 1 = 15
5
Hundreds
4 + 2 + 1 = 7
7
Karim says 467 + 285 = 642. Check: 642 − 285 = 357, not 467. He forgot the carried 1s. Correct work: 7 + 5 = 12, 6 + 8 + 1 = 15 and 4 + 2 + 1 = 7, so 467 + 285 = 752.
Class activity
Fact triangle game. Draw six triangles. In each, write a product at the top and one factor at the bottom, and hide the other factor. Swap with a partner. Find the missing factor and say the four facts in its family. Check each answer with multiplication.
