Multiplication Patterns

In Grade 3 we are learning our multiplication tables. We found patterns in each of the tables and created posters to show them. Read on to learn more…

We wrote out each of the multiplication tables from 1 to 10. We then coloured them on hundred squares to see the patterns they made. Can you work out which multiplication table this is?

We also found patterns in each multiplication table when we looked at the number of units and when we worked out the digital roots.

We drew all the patterns on paper circles and then made them with paper plates and wool.

Unit Patterns
We looked at the number of units there were in each answer and saw that there was a repeating pattern.

Eg. What is the number of units in 4 x 3 = 12?

12 = 1 ten and 2 units.

So the number of units is 2.

x 3

0 x 3 = 3 (0 units)

1 x 3 = 3 (3 units)

2 x 3 = 6 (6 units)

3 x 3 = 9 (9 units)

4 x 3 = 12 (2 units)

5 x 3 = 15 (5 units)

6 x 3 = 18 (8 units)

7 x 3 = 21 (1 unit)

8 x 3 = 24 (4 units)

9 x 3 = 27 (7 units)

10 x 3 = 30 (0 units)

This is the pattern: 0, 3, 6, 9, 2, 5, 8, 1, 4, 7, 0.

Digital Root Patterns

A digital root is the number you get when you add up the digits of a number. If the number it comes to is a two digit number you add the digits up again until you get a one digit number.

E.g. What is the digital root of 6 x 4 = 24?

You add up the 2 and the 4 together equals 6.

So the digital root is 6.

x 4

1 x 4 = 4 (4)

2 x 4 = 8 (8)

3 x 4 = 12 (3)

4 x 4 = 16 (7)

5 x 4 = 20 (2)

6 x 4 = 24 (6)

7 x 4 = 28 (1)

8 x 4 = 32 (4)

9 x 4 = 36 (9)

10 x 4 = 40 (4)

This is the pattern: 4, 8, 3, 7, 2, 6, 1, 4, 9, 4.

When we worked out the digital roots for each answer in a multiplication table, we saw a repeating pattern.

We each made a poster to show all the patterns we found. Take a look at our slideshow for a closer look.

We noticed that some multiplication tables shared the same patterns. When two patterns were the same, we noticed that one was drawn in a clockwise direction and the other one in an anticlockwise direction.

Now we wonder what the patterns would look like for the 11, 12 and 13 times tables? Do you think they will make new patterns, or will they have patterns we have already seen?

Tomorrow in class, we will look at how we can make these patterns in another way, using a computer program called Logo and our ‘Roamer’ robot.