2
Two ways to count an array
Discover Mathematics P2: Term 2, Lessons 71–80
GoalCount an array by rows or by columns and choose the easier way.
New words
repeated addition · adding the same number again and againtotal · how many in allequal groups · groups with the same number in each
Explanation
We get the same total whether we add the rows or add the columns. Choose the way that is easier. An array with 5 rows of 3 can be added by rows: 3 + 3 + 3 + 3 + 3 = 15. Or by columns: there are 3 columns of 5, and 5 + 5 + 5 = 15. Counting by fives is faster. When one number is 2, 5 or 10 it helps to count by that number. Write both sentences and check that they match. If they do not match, count again.
| Add by | Sentence | Total |
|---|---|---|
| rows | 3 + 3 + 3 + 3 + 3 | 15 |
| columns | 5 + 5 + 5 | 15 |
Worked examples
A bus has 4 rows of 2 seats. Rows: 2 + 2 + 2 + 2 = 8. Columns: 4 + 4 = 8. There are 8 seats.
5 rows of 3 flowers. Columns are easier: 5 + 5 + 5 = 15 flowers.
2 rows of 7 fish. Rows: 7 + 7 = 14 fish. Columns: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14.
Class activity
Build your own array. Use 12 buttons, beans or small stones. Arrange them in an array, then trade with a partner. Your partner writes the sentence for the rows and the sentence for the columns. Can you make a different array with the same 12 things?
Practice
1
Mina has 3 rows of 6 pencils. How many pencils? Write the sentence for the rows.
6 + 6 + 6 = 18 pencils.
2
Write the sentence for the columns of Mina's array.
3 + 3 + 3 + 3 + 3 + 3 = 18.
3
An array has 4 rows of 5. Which way is easier to add, rows or columns?
Rows: 5 + 5 + 5 + 5 = 20. Counting by fives is easy. (Columns: 4 + 4 + 4 + 4 + 4 = 20.)
4
A chocolate bar has 2 rows of 6 pieces. How many pieces?
6 + 6 = 12 pieces.
5
Nour wrote 5 + 5 + 5 for an array and 3 + 3 + 3 + 3 for the same array. Is that possible?
No. The totals are 15 and 12, so one is wrong. Count again.