Grade 3What Multiplication Means3.OA.A.1

Arrays

Rows and columns of objects show a multiplication.

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An array is equal groups lined up in rows. Every row has the same number, like seats in a theater or eggs in a carton.

4 rows with 6 dots in each row. Each row is one equal group.

Why it works

Each row is a group, and every row is the same size. So an array with 4 rows of 6 is 4 groups of 6, which is $4 \times 6$. You can count by rows instead of by dots: 6, 12, 18, 24.

Key idea

An array with $r$ rows and $c$ in each row shows $r \times c$. Rows go across; columns go up and down.

Worked example: Count by rows

How many dots are in an array with 4 rows of 6?
  1. Each row has 6. There are 4 rows.
  2. Count by 6s, one count for each row: 6, 12, 18, 24.
  3. So $4 \times 6 = 24$.

Answer: $24$ dots

Worked example: Seats

A theater has 7 rows with 5 seats in each row. How many seats?
  1. 7 rows of 5 is $7 \times 5$.
  2. Count by 5s seven times: 5, 10, 15, 20, 25, 30, 35.

Answer: $35$ seats

Common mistake

Counting every dot one by one. It works for small arrays, but it is slow and easy to lose your place. Find the size of one row, then count by that number once for each row.
Drag the gold corner (or use the buttons) to make an array with 24 dots. Is there more than one way?

Practice

Pass with 3 right answers, the last 2 in a row. Each right answer earns 1 XP.

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Builds on

Leads to

Sources and further reading

  • Common Core State Standards for Mathematics, Grade 3, 3.OA.A.1 (interpret products, for example as arrays)
  • Common Core State Standards for Mathematics, Grade 3, 3.OA.A.3 (arrays in word problems)
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