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Interpret Multiplication as Equal Groups

Students learn to interpret a multiplication expression such as 5 x 7 as representing 5 groups with 7 objects in each group. They connect the abstract equation to concrete representations using drawings, counters, and real-world contexts to build conceptual understanding of what multiplication means.

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Interpret Multiplication as Equal Groups

Grade 3 · Understanding Multiplication · question 1 of 3

0 of 12

12 rungs. A star at the top.

Which of these means 5 × 3?

How it is taught

0:00 of 3:41

Times means equal groups.

First factor: how many groups.

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.

  1. Count the trays: 3 equal groups.
  2. Count the apples on one tray: 3 in each group.
  3. 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.

3 × 5 = ___ — 15. 3 trays with 5 apples in each: skip-count the trays — 5, 10, 15.

3 × 4

Imagine three baskets, and each basket has four apples. How many apples in all?

Here is the first group — four apples.

Here is the second group — four more apples.

And the third group — four more apples.

We have three equal groups, with four in each group.

We can write this as three times four.

The first number, three, tells us how many groups we have.

The second number, four, tells us how many are in each group.

Let's count them all: four, eight, twelve.

Three times four equals twelve. Multiplication is just adding equal groups!

3 baskets · 4 apples each4443 groups · 4 in each3×4=123 = number of groups4 = how many in each groupANSWER12apples in all
Grade 3 · Three groups of four apples

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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