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.
How many sticks will the fourth square row need? Have a guess before we build it.
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.
First, the counts from the matchstick-square pattern. The line starts at 4 and two jumps of 3 are already drawn, landing on 7 and 10: that is one, two and three squares. Say the rule, then tap +3 to add the next jump. Keep going to reach step 6 without laying out six rows of matchsticks.
Then press Reset and try a shrinking pattern: 20, 16, 12. Set the start to 20, find the jump, and jump back to land on each count. What comes next?
In your maths copy, draw the first four steps of the "add 3 sticks" square pattern — one square, then two joined, then three, then four. Beside your drawing, make a pattern record table: one column for the step number and one column for the stick count. Fill in 4, 7, 10, 13. Then write the rule you found underneath.
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