Read the row
A shape pattern is a row of shapes that follows a rule. Read it from the left, saying each shape out loud: circle, square, circle, square. The same two shapes come again and again, always in the same order.
The row reads circle, square, circle, square, and the fifth place is still empty.
The repeating group
The part that repeats is called the repeating group. In this row it is circle, then square. The whole row is that group, over and over.
To find the next shape, find how far the row has got through its group. The row ends with a square, the last shape of the group, so the group is finished and starts again. The next shape is the first shape of the group: a circle.
The number under each shape is its place in the group. The fifth shape starts a new group, so it is a circle.
Longer groups
A group can have more than two shapes. Read this row: triangle, square, square, triangle. To find the group, keep reading until the first shape comes back. The triangle comes back in the fourth place, so the group is triangle, square, square.
The fourth place starts a new group with its triangle. The fifth place is the second shape of the group, which is a square.
The group is triangle, square, square. The fifth shape is the second of a new group: a square.
Two slips to avoid
Do not repeat the last shape you can see. A pattern moves on to the next shape of its group, so after a square comes whatever the group puts after that square.
Do not start the group again too soon. In triangle, square, square, one square is not the end of the group: the triangle comes back only after both squares. Read until the first shape comes back before you decide what the group is.
Worked example: A Row of Shapes That Repeats Every Three Shapes
Question Lin makes a row of shapes. The row goes circle, square, triangle, circle, square. The shapes keep going in the same way. (a) Which shape comes next? (b) Which shape is number 8 in the row?
1.Say the shapes out loud: circle, square, triangle, circle, square. Look for the place where the row starts again.
Say the shapes out loud: circle, square, triangle, circle, square. 2.After the triangle there is a circle again. The part that repeats is circle, square, triangle. It has 3 shapes.
After the triangle there is a circle again. The part that repeats is circle, square, triangle. 3.(a) Shape 4 is a circle and shape 5 is a square. A triangle comes after the square, so shape 6 is a triangle. It is the same as shape 3.
(a) A triangle comes after the square, so shape 6 is a triangle. It is the same as shape 3. 4.Carry on in the same way. Shape 7 is a circle and shape 8 is a square.
Carry on in the same way. Shape 7 is a circle and shape 8 is a square. 5.(b) Shape number 8 is a square. It is the same as shape 2 and shape 5.
(b) Shape number 8 is a square. It is the same as shape 2 and shape 5.
Answer: (a) a triangle, the same as shape 3; (b) a square, the same as shape 2
Common mistakes
- Saying that a circle comes next because the row began with a circle. The row starts again only when the part that repeats is finished, and its triangle has not come yet.
- Counting 8 more shapes from the end of the row. Shape number 8 is counted from the first circle, so only 3 more shapes are needed after shape 5.
Worked example: A Missing Shape in the Middle of a Repeating Row
Question Tom makes a row of 10 shapes. The row goes circle, square, triangle, rectangle, circle, square, a gap, rectangle, circle, square. One shape is missing at the gap. (a) Which shape is missing? (b) How many triangles are in the full row?
1.Read the row from the start: circle, square, triangle, rectangle. Then a circle comes again.
Read the row from the start: circle, square, triangle, rectangle. Then a circle comes again. 2.The part that repeats is circle, square, triangle, rectangle. It has 4 shapes.
The part that repeats is circle, square, triangle, rectangle. It has 4 shapes. 3.The gap is shape number 7. It comes after a square and before a rectangle.
The gap is shape number 7. It comes after a square and before a rectangle. 4.(a) In the part that repeats, the triangle is between the square and the rectangle. The missing shape is a triangle.
(a) In the part that repeats, the triangle is between the square and the rectangle. The missing shape is a triangle. 5.(b) Count the triangles in the full row. Shape 3 and shape 7 are triangles. There are 2 triangles.
(b) Shape 3 and shape 7 are triangles. There are 2 triangles in the full row.
Answer: (a) a triangle, the same as shape 3; (b) 2 triangles
Common mistakes
- Thinking that the part that repeats is circle, square. The third shape is a triangle and not a circle, so the part that repeats is longer. Keep reading until the first shape comes again.
- Writing 1 for part (b) because only 1 triangle can be seen. The missing shape is a triangle too, so the full row has 2 triangles.