Patterns and rules: Applied

Lina has a new business – selling friendship bracelets at a craft fair! At the last two fairs, she sold out of all her bracelets. So she decides to hire some helpers. For the next five days, Lina, Maria, and Leon get together after school to make bracelets. Let’s see how each of the friends gets on.

On the first day, Monday, Maria makes eight bracelets. After that, her total increases by three every day. What pattern does Maria follow? Well, on Tuesday, she makes Monday’s total, that’s eight, plus three. Eight plus three is 11.

Wednesday’s total is 11 plus three. That’s 14. Thursday’s total is 14 plus three. 17. And Friday’s total is 17 plus 3, that’s 20.

8, 11, 14, 17, 20. Way to go, Maria – that’s a steady pace. Now Leon?... That’s a different story. On Monday, Leon is full of enthusiasm.

He gets off to a great start with 16 bracelets. On Tuesday, he begins to get a little bored of bracelet making. Other things start to distract him. Leon’s total halves on Tuesday, and each day after. What pattern does Leon follow?

Tuesday’s total is half of Monday’s. Half of 16 is eight. Wednesday’s total is half of eight. That’s four. Thursday’s total is half of four.

Two. And Friday’s total is… just one bracelet. Leon’s pattern is 16, 8, 4, 2, 1. Leon’s pattern goes down by halves, Maria’s pattern goes up by threes. How does Lina make out?

Lina’s pattern is 6, 12, 18, 24, 30. She wants to know what the rule behind her pattern is. Let’s see. How do we get from six to 12? Well we have to go up somehow.

We could… double? Double six is 12. Let’s try it for the next number. Double 12 is… 24. Hmm, that doesn’t work.

How else could we go up? We could add instead. How do we get from six to 12 by adding? We add six. And what do we get if we add six again?

12 add six is… 18! And 18 add six is 24. We’ve found the rule behind your pattern, Lina. This week, you started by making six bracelets and your total went up by six each day. But enough of the math.

Leon is on to other things…