الرياضيات (بالإنجليزية) الصف الثالث الابتدائي، الأسبوع 8: Fact families in triangles

Fact families and quadrilaterals

الأسبوع 8 · عائلات الحقائق ورباعيات الأضلاع · 3 دروس

Fact families in triangles

Discover Mathematics P3: Term 1, Lessons 21–30

GoalUse a fact triangle to write the four equations of a fact family and to find a missing factor.

New words

fact family · multiplication and division equations that use the same three numbersfact triangle · a triangle with the product at the top and the two factors at the bottommissing factor · a factor you have to find

Explanation

Three numbers can make a fact family. In a fact triangle the product goes at the top and the two factors go at the bottom. The numbers 3, 4 and 12 make four equations: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3. If one number is missing, cover it and use the family. To solve ? × 5 = 35, use the division 35 ÷ 5 = 7, so the missing factor is 7. Fact families also help with riddles. Two numbers have a product of 24 and a sum of 10. List the factor pairs of 24 and add each pair to find the one whose sum is 10.

Worked examples

The fact triangle has 30 at the top and 5 and 6 at the bottom. The family is 5 × 6 = 30, 6 × 5 = 30, 30 ÷ 5 = 6 and 30 ÷ 6 = 5.

One factor is missing: ? × 5 = 35. The triangle has 35 at the top and 5 at the bottom. Use the division 35 ÷ 5 = 7. The missing factor is 7, and we check: 7 × 5 = 35.

Pair	Product	Sum
1 and 24	24	25
2 and 12	24	14
3 and 8	24	11
4 and 6	24	10

Mystery numbers: the product is 24 and the sum is 10. The factor pairs of 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6. Only 4 and 6 have a sum of 10, so the mystery numbers are 4 and 6.

Class activity

Fact triangle cards. Make triangle cards for 2, 5, 10 and for 3, 7, 21 and for 4, 9, 36 and for 6, 8, 48. Your partner covers one corner and you say the missing number. Then say all four equations of the family.

Practice

Write the four equations of the fact family.

The two factors are 6 and 7. What number goes at the top of the triangle?

Find the missing factor: ? × 4 = 28.

Write the fact family for 2, 9 and 18.

Two numbers have a product of 12 and a sum of 7. What are they?