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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 14 minutes
0 of 16 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Try it first

A crayon box holds 10 crayons. Leo has 4 boxes. How many crayons in all?

? in all10101010
crayons

Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.

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 nickels says the 5 times table 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 Ana Use a Ten to Find a Five

Ana is asked for 9 × 5.

  1. Step 1

    Ana does not count by fives. She starts with the ten.

Watch Maya Find a Five

Maya is asked for 3 × 5. She starts, and you finish.

  1. Step 1

    Maya starts with the ten, not the five. First she needs 3 × 10.

Step 5: Your Turn

Practice makes it stick.

The Nickels

Problem 1 of 12

Priya has 5 nickels. A nickel is 5 cents. How many cents is that?

cents

The Book Fair

Problem 2 of 12

Every book costs $10. Noor's class buys 9 books. How much do they pay?

dollars

Twos, Fives, Tens

Use the quick way for each table.

Problem 3 of 12

6 × 2 = ?

Problem 4 of 12

10 × 10 = ?

Problem 5 of 12

Which number is in the 5 times table?

Find the Mistake

One line on each page is a slip. Find it, then fix it.

Problem 6 of 12

Dev finds 5 × 2. One line is a slip. Which?

Dev's answer for 5 × 2

  1. 15 × 2
  2. 2double 5
  3. Answer5 × 2 = 7

Problem 7 of 12

What should Dev's answer be?

Problem 8 of 12

Maya finds 4 × 5. One line is a slip. Which?

Maya's answer for 4 × 5

  1. 14 × 5
  2. 24 × 10 = 40
  3. 3half of 40 is 30
  4. Answer4 × 5 = 30

Problem 9 of 12

What should Maya's answer be?

Which Way?

Pick the way that fits the table.

Problem 10 of 12

Sam needs 6 × 5. He knows 6 × 10 = 60. Which way finds 6 × 5?

Problem 11 of 12

Noor needs 4 × 2. Which way finds it?

Build the Tens

Build it, then check.

Problem 12 of 12

Build 5 rows of 10. Each row is a ten.

Set the rows, then how many in each row.

1 = 1

1 × 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?

Ready for more?Optional. Past the lesson, for anyone who wants it.

Stretch 1 of 2

A number is in both the 2 and 5 times tables. It is bigger than 15 and smaller than 25. What is it?

Stretch 2 of 2

Noor has 6 dimes and 2 nickels. A dime is 10 cents. How many cents in all?

10¢10¢10¢10¢10¢10¢5¢5¢
cents

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.

The slip this lesson targets is treating × 2, × 5 and × 10 as three lists to memorise. Each is a move: a two is a double, a ten is the digit with a 0 after it, a five is half of the ten. Dev's slip is adding 2 instead of doubling (5 × 2 = 7); Maya's is halving by taking 10 away (half of 40 as 30) instead of splitting 40 into two equal parts. Before any five, ask "what is the ten?"; before any two, ask "what is the double?". The last-digit check catches most slips: a ten answer ends in 0, a five answer in 5 or 0.

Why these three come first — The 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 zero — 7 × 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 tens — 8 × 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.