Egypt Primary 3 Mathematics, Week 9: Splitting an array into parts

Rectangles, squares and splitting arrays

Week 9 · Rectangles, squares and splitting arrays · 3 lessons

Splitting an array into parts

Discover Mathematics P3: Term 1, Lessons 31–40

GoalSplit an array into two smaller arrays and add the two products to find the whole product.

New words

split array · an array cut into two smaller arrayspart · one of the smaller arraystotal · the whole amount, found by adding the parts

Explanation

An array can be split into two smaller arrays. Look at an array with 4 rows and 7 columns. Draw a line between the 5th and the 6th column. The left part is 4 rows of 5, so 4 × 5 = 20. The right part is 4 rows of 2, so 4 × 2 = 8. Together 20 + 8 = 28, so 4 × 7 = 28. The total does not change when we split, so we can use easy facts, like the fives, to find a harder one.

Worked examples

A 6 by 8 array is split after the 5th column. The parts are 6 × 5 = 30 and 6 × 3 = 18. The total is 30 + 18 = 48, so 6 × 8 = 48.

A 7 by 6 array is split into two equal parts. Each part is 7 × 3 = 21. The total is 21 + 21 = 42, so 7 × 6 = 42.

We can also split the rows. An array with 5 rows of 8 is split into 2 rows and 3 rows. The parts are 2 × 8 = 16 and 3 × 8 = 24. The total is 16 + 24 = 40, so 5 × 8 = 40.

Class activity

Split the beans. Put 24 beans in an array of 3 rows of 8. Use a string to split the array in two parts. Write the two multiplications and add them. Move the string and split it in a different place. Is the total still 24?

Practice

This 3 by 9 array is split after the 5th column. Write the two multiplication facts and the total.

Split a 5 by 6 array into two equal parts and find the product.

Fill in the missing number: 8 × 5 = (8 × 3) + (8 × ?).

Hana splits a 4 by 6 array into 4 × 2 and 4 × 3. She adds 8 + 12 = 20. What is wrong?

Show two different ways to split a 6 by 4 array and write the equations.