Three shapes made of tiles stand side by side. They grow steadily - the same amount is added every time.
First count the tiles in shape 1 and then the tiles in shape 2. The difference is the growth. It goes into the first box.
But the question is not about the next shape. It is about one much further along, shape 10 for example. Drawing that would take forever.
So you calculate instead. From shape 1 to shape 10 there are nine steps. With a start of 4 and a growth of 3 that means 4 + 9 × 3 = 31.
In the hard puzzles you know the tiles and you are looking for the shape. Then you keep track of how often you have to add the growth.
Example
For parents
What does this exercise practice?
This is where continuing a pattern turns into generalising it. When a child continues a pattern, it draws the next shape; here the shape in question is so far away that drawing is no longer an option. Exactly that jump forces a rule, and the rule is the real subject of the lesson. The separate box for the growth makes it visible instead of letting it vanish inside the child's head. This is the first step toward what will later be called a term or a formula, using nothing beyond second-grade means, because the growth stays the same every time.
Common pitfalls
The most common mistake is to forget the starting number and simply multiply the shape number by the growth. With a start of 4 and a growth of 3 that gives 30 instead of 31. It helps to count out loud how many steps it is from shape 1 to the shape in question - it is always one less than the shape number. The second stumbling block is carrying on drawing. That is not wrong, but it is very laborious, and by shape 10 a miscount is almost certain. A child who already has a rule may check it against shape 3 and then calculate.
How to practice at home
Build a sequence yourselves with blocks or coins. One person lays out shape 1, shape 2 and shape 3, the other has to say how many pieces shape 10 has - without building it. Then build it and check. Whoever finds the rule faster wins.
Related: Continuing patterns, Number Sequence