**Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?**

Three students were asked to draw this matchstick pattern:

Watch how Phoebe drew it.

Can you describe what Phoebe did?

How many ‘downs’ and how many inverted C’s are there?

How many matchsticks altogether?

Now picture what Phoebe would do if there had been 25 squares.

How many ‘downs’ and how many inverted C’s would there be?

How many matchsticks altogether?

If there had been 100 squares? How many matchsticks altogether?

A million and one squares? How many matchsticks?

Watch how Alice drew it.

Can you describe what Alice did?

How many ‘alongs’ and how many ‘downs’ are there?

How many matchsticks altogether?

Now picture what Alice would do if there had been 25 squares.

How many ‘alongs’ and how many ‘downs’ would there be?

How many matchsticks altogether?

If there had been 100 squares? How many matchsticks altogether?

A million and one squares? How many matchsticks?

Watch how Luke drew it.

Can you describe what Luke did?

How many squares and how many inverted C’s are there?

How many matchsticks altogether?

Now picture what Luke would do if there had been 25 squares.

How many squares and how many inverted C’s would there be?

How many matchsticks altogether?

If there had been 100 squares? How many matchsticks altogether?

A million and one squares? How many matchsticks?

**Now choose a couple of the patterns below.**

Try to picture how to make the next, and the next, and the next…

Use this to help you find the number of squares, or lines, or perimeter, or dots needed for the 25th, 100th and nth pattern.

Can you describe your reasoning?

**Growing rectangles**

- height 2 and width 25
- height 2 and width 100
- height 2 and width n

**L Shapes**

- height 25 and width 25
- height 100 and width 100
- height n and width n

**Two squares**

- 25 black dots
- 100 black dots
- n black dots

**Square of Squares**

- side length 25
- side length 100
- side length n

**Dots and More Dots**

- side length 25
- side length 100
- side length n

**Rectangle of Dots**

- side length 25
- side length 100
- side length n

Age 11 to 14