Math Core

Lesson 1.3 · Understanding Multiplication

Multiplication on a number line

A frog hops along a path. Every hop is exactly 3 feet long. After 4 hops, how far has it gone? A number line lets you see multiplication as equal jumps.

Equal jumps

Start at 0. Make jumps that are all the same size. Each jump is one equal group.

Here are 4 jumps of 3:

0123456789101112131415+3+3+3+3

The jumps land on 3, 6, 9 and 12. That is skip counting by threes!

So 4 jumps of 3 shows:

4×3=124 \times 3 = 12

Multiplying on a number line

To find a×ba \times b on a number line:

  1. Start at 0.
  2. Make aa jumps.
  3. Make every jump bb long.
  4. The number where you land is the product.

Reading a number line

You can also go the other way. Look at the jumps and write the multiplication.

0123456789101112+2+2+2+2+2

Count the jumps: there are 5. Each jump goes up by 2. The last jump lands on 10.

5×2=105 \times 2 = 10

Worked example: Jumps of 5

Use a number line to find 3×53 \times 5.

Start at 0. Make 3 jumps of 5.

05101520+5+5+5

The jumps land on 5, 10, 15. So 3×5=153 \times 5 = 15.

Worked example: Write the multiplication

What multiplication does this number line show?

06121824+6+6+6+6

There are 4 jumps. Each jump is 6 long, from 0 to 6, then 6 to 12, and so on. The last jump lands on 24.

The number line shows 4×6=244 \times 6 = 24.

Worked example: The hopping frog

A frog makes 6 hops. Each hop is 3 feet. How far does it go?

This is 6 jumps of 3. Skip count by threes: 3, 6, 9, 12, 15, 18.

01234567891011121314151617181920+3+3+3+3+3+3

6×3=186 \times 3 = 18. The frog goes 18 feet.

Common mistake

Count the jumps, not the tick marks or the numbers you land on. If you start at 0 and land on 3, 6 and 9, that is 3 jumps, not 4. The 0 is where you start. It is not a jump.

Tip

The size of each jump is the distance between where the jump starts and where it ends. A jump from 8 to 12 is 4 long, because 12−8=412 - 8 = 4.

Practice

Practice 1

What product does this number line show?

012345678910+2+2+2+2

Type a number.

Practice 2

How many jumps are on this number line?

0123456789101112131415+4+4+4

Type a number.

Practice 3

Which multiplication matches this number line?

0510152025+5+5+5+5
Practice 4

On a number line, you make 2 jumps of 3, starting at 0. Where do you land?

Type a number.

Practice 5

Use jumps of 7 to find 3×73 \times 7.

Type a number.

Practice 6

Each jump on this number line is the same size. How long is each jump?

051015202530+5+5+5+5+5+5

Type a number.

Practice 7

A kangaroo hops 4 meters with each hop. How far does it go in 4 hops?

Type a number.

Practice 8

Jake starts at 0 and makes jumps of 3. He lands on 18. How many jumps did he make?

Type a number.