Interpret Multiplication Using Arrays

Students learn to represent and interpret multiplication using rectangular arrays — arrangements of objects in rows and columns. They connect arrays to multiplication expressions by identifying the number of rows and the number of objects in each row as the two factors.

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Grade 3 · Understanding Multiplication · question 1 of 3

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12 rungs. A star at the top.

Cleo ties boats at 4 docks by the pond. Each dock holds 3 boats. How many boats does she tie up?

How it is taught

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An array is equal rows and equal columns.

Rows times columns is the total.

Read it: Same number in each group

You have 3 trays of apples. You could count every apple from one. Look at 3, then 6, then 9 — three on each tray.

Count the trays: 3 equal groups.
Count the apples on one tray: 3 in each group.
Say 3 for each tray: 3, 6, 9. That is 3 × 3 = 9.

Counting all 9 apples from one works, but it is slow, and you can skip an apple.

Each tray holds the same 3, so you only need to know one tray and how many trays.

Skip counting 3, 6, 9 names the running total as you pass each tray.

When each group has the same number, count the groups, not every apple.

Counting 3 trays and 9 apples and adding them to make 12.

The 3 is how many trays. The other 3 is apples on each tray. 3 groups of 3 is 9.

2 × 3 = ___ — 6. 2 trays with 3 apples in each: skip-count the trays — 3, 6.

3 × 4 = 12

An array is a neat arrangement of objects in rows and columns. Let's use one to see multiplication!

Here are our dots, lined up in a tidy rectangle.

First, we count the rows going across. One, two, three — three rows in all.

Write the number of rows: three.

Now look at one row. Each row has the same number of dots — one, two, three, four.

Times four, because each of our three rows has four dots.

Three times four equals twelve — the total number of dots in the whole array.

Three rows of four make twelve. That's how arrays turn rows and columns into multiplication!

Grade 3 · Rows and columns become multiplication

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standards

CCSS.3.OA.A.1

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each

CCSS.3.OA.A.3

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities

Grade 3

Quoted from the Common Core State Standards.

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What a star here means

A star here is the top of a twelve-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 3

This is one rung of 104 in Grade 3 mathematics, in the order they build on each other.

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