Question

An array has 3 rows with 3 items in each row. How many number sentences can you write to show the total? Explain.

a) There are 9 possible number sentences.

b) There are 12 possible number sentences.

c) There are 6 possible number sentences.

d) There are 18 possible number sentences.

Answer 1

The total number of possible number sentences to show the sum of items in a 3x3 array is 6, counting both horizontal and vertical sums.

Step-by-step explanation:

The question is about an array with 3 rows and 3 items in each row. To find the total number of items, you can write number sentences that represent the sum of items in each row. Each row has 3 items, so you can write a number sentence for each row:

1. Row 1: 3 items
2. Row 2: 3 items
3. Row 3: 3 items

Since there are three rows, you can write 3 number sentences, each one adding the items of each row:

1. 3 + 3 + 3 (summing horizontally)

However, if considering column-wise addition as separate number sentences too, you can also write:

1. 3 + 3 + 3 (summing vertically)

Since the array is square (3x3), the number of number sentences for rows and for columns is the same, adding up to 6 in total, corresponding to 3 horizontal number sentences and 3 vertical number sentences. Therefore, the correct answer is:

c) There are 6 possible number sentences.