Here is a row of squares built from matchsticks. One square takes 4 sticks. Two squares side by side take 7 sticks, because the middle stick is shared. Three squares take 10.

Here are two growing patterns marked out along the number line. Each mark shows a count, and the gap between one mark and the next is the jump.

Here is a second pattern. Look at how big each gap is.

One of these grows by the same jump every time. The other grows by a jump that gets bigger. See if you can tell which is which from the gaps.

Now we work two patterns on the same number line, one after the other. One pupil comes up to mark a count while the rest of the class watches and agrees or corrects out loud. Press Reset to clear the line before the second pattern.

Then reset the line and mark a shrinking pattern: 20, 16, 12. Find how the jump changes and mark what comes next.

Now we investigate the "add 3 sticks" pattern all the way through, using the pattern record table you drew in your copy.

1. Check your first four counts are 4, 7, 10, 13.
2. Describe the rule in your own words: where it starts and how much it jumps.
3. Keep adding 3 to reach step 6. How many sticks does step 6 have? You do not have to build it.
4. Keep going in the table to step 10. Notice that each count is 3 lots of the step number, plus 1. Predict how many sticks step 10 has, and explain how the table helped you jump ahead.