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Math · Grade 3 Math

Chapter 1: Multiplication and Division as Equal Groups

Multiplying by 2, 5, and 10

The three easiest tables, and why they are easy.

Lesson
6
Time
About 12 minutes
0 of 9 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Watch the idea first — 57 seconds. Then read on, and try it yourself in the next step.

The 2 times table is doubling

You already know your doubles from before. 7 × 2 is just double 7.

The 10 times table

Every answer ends in 0. 6 × 10 = 60, because it is 6 tens.

The 5 times table

Every answer ends in 5 or 0. And 5 is half of 10, so 6 × 5 is half of 60.

Step 2: Try It Yourself

Tap and try it out.

Set the columns to 2, 5, or 10 and step the rows through.

5 + 5 + 5 + 5 + 5 + 5 = 30

6 × 5 = 30

6 rows of 5 makes 30.

The same total, laid out every way it goes. What will not fit sits outside.

6 × 5 = 30. 6 and 5 are a factor pair of 30.

Pairs you have found

  • 5 × 6

Step 3: In Real Life

Counting money

A nickel is 5 cents and a dime is 10. Counting a handful of nickels is the 5 times table said out loud: 5, 10, 15, 20. Counting dimes is the 10 times table. A shopkeeper counts the cash drawer this way every evening.

Step 4: Watch an Example

One step at a time.

Watch Leo Halve a Ten

Leo is asked for 8 × 5.

  1. Step 1

    He does not count in fives all the way up.

Step 5: Your Turn

Practice makes it stick.

The Coins

Problem 1 of 2

Ana has 7 five-pence coins. How many pence is that?

pence

The Boxes

Problem 2 of 2

9 boxes each hold 10 pencils. How many pencils?

pencils

Twos, Fives, Tens

1 of 4

7 × 2 = ?

2 of 4

6 × 5 = ?

3 of 4

8 × 10 = ?

4 of 4

9 × 5 = ?

Build the Array

Build it, then check.

Build 6 rows of 5.

Set the rows and the columns.

1 = 1

1 row of 1 makes 1.

Step 6: Quick Check

Show what you know.

Question 1 of 2

7 × 5 = ?

Question 2 of 2

What do all the answers in the 10 times table end in?

What You Learned

  • The 2 times table is doubling.
  • The 10 times table always ends in 0.
  • A five is half of a ten, so halve the ten answer.
For the grown-up

This lesson is where the child recalls the 2, 5, and 10 times tables and explains the pattern in each. Multiplication is equal groups before it is a fact to recall. Three fours is three groups of four, and division is the same picture asked from the other end.

Watch for multiplication and division being learned as separate subjects. They are one relationship, and a child who sees that halves what there is to remember.

When they are stuck on a division, ask the multiplication instead: "what times 4 gives 24?" Nearly every child can answer that when they cannot answer 24 divided by 4.

Why these three come firstThe 2s are doubles, which you already knew before. The 10s just put a zero on the end. The 5s are half the 10s. All three connect to something you can already do quickly, which is why they are learned before the rest.

Why multiplying by ten adds a zero7 × 10 = 70 because seven tens is seven in the tens place with nothing in the ones. The digit has moved one column to the left and a zero holds its old place open. Saying "add a zero" is a fine shortcut as long as you know why it works — it will stop working when you meet decimals.

Fives are half of tens8 × 5 must be half of 8 × 10 = 80, so it is 40. Every answer in the 5 times table ends in 0 or 5, alternating. Two independent ways to reach the same fact makes it far more likely to stick.

Why these three are the easy ones× 10: the digits shift up a place. 7 × 10 = 70 × 5: half of the ten. 7 × 5 is half of 70, which is 35. × 2: just a double. 7 × 2 = 14 These three are quick because each one leans on something you already have.