The idea in brief. Find the repeating unit, count whole units, and read any leftover from the start of the unit shape by shape. On bead strings, the same unit can be a gap; a closed loop adds the final gap back. In the lesson. A closed loop has the same number of gaps as black beads.
Lesson video, with the working
A repeating unit
3 min 58 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
A row of 90 shapes is printed on a border strip. The shapes repeat in the same order all the way along: 4 circles, then 3 squares, then 4 circles, then 3 squares, and so on. How many squares are in the row?
Squares in all = 36 + 2 = 38
Ans: 38
Example 1
A garden border is 21.6 m long and 20 cm wide. It is paved from end to end with a pattern that repeats along its whole length: two square tiles of side 20 cm, then one rectangular tile measuring 40 cm by 20 cm. How many square tiles are used?
Square tiles = 27 × 2 = 54
Ans: 54
Example 2
A string of beads is made with 3 white beads between every 2 black beads. The string begins with a black bead and ends with a black bead, and there are 4 black beads in all. How many gaps are on the string, and how many on the same beads closed into a loop?
Gaps on a string = 4 − 1 = 3
Gaps on a loop = 4
Ans: 34
How to solve it
Find where the shapes begin again and bracket one repeating unit: 4 circles and 3 squares make 7 shapes.
Divide the total by the unit: 90 divided by 7 is 12 whole units with 6 left over, never a decimal.
Read the leftover off the start of the unit: the 6 left over are 4 circles and 2 squares.
Count what you want: 12 units of 3 squares is 36, and the leftover adds 2 more, so 38 squares.
A string of beads has 2 ends, so one fewer gap than black beads. Closed into a loop, it has as many gaps as beads.
A string has two ends, and a loop has none. Going round the loop, every black bead is followed by a gap. A closed loop has the same number of gaps as black beads.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
Question 1 of 7 · Basic · free to tryA string of beads is made from a pattern that repeats all the way along: 3…A string of beads is made from a…
A string of beads is made from a pattern that repeats all the way along: 3 white beads, then 1 black bead. The string ends with a black bead. There are 17 black beads on the string. How many beads are on the string altogether?
each unit holds one black bead, so number of units = 17
beads altogether = 17 × 4 = 68
Answer: 68
For parents
How do you solve repeating pattern questions in P6?
A repeating pattern goes round the same group of shapes, colours or beads again and again.
What your child learns here
A repeating pattern goes round the same group of shapes, colours or beads again and again. On this Primary 6 page division with a remainder does the counting, building on the number patterns of earlier years.
Find the repeating unit by marking where the pattern begins again.
Divide the total by the size of the unit to get whole units and a leftover, kept as a remainder, never a decimal.
Read the leftover from the start of the unit, item by item.
Run the pattern backwards: from the count of one colour to the number of units and the total.
Count gaps correctly: a string with two ends has one fewer gap than beads, and a closed loop has as many gaps as beads.
Does the answer make sense?
A count of one colour or shape must be smaller than the total number of items, and close to its share of one repeat: if 2 of every 4 flags are red, about half the row is red. When your child is asked for the total, it must be more than the count given.
How to practise these questions
Basic questions train finding the repeating unit, dividing the total by it, and counting one colour. Intermediate questions add reading the leftover after the whole units, item by item. Challenge questions arrange items on a closed loop or in the gaps between others, and build the unit's length from its parts first. When a repeating unit is hard to spot, read the written step-by-step solution together.
Questions parents ask
How does division with a remainder help with repeating patterns? Dividing the total by the size of the repeating unit gives the number of whole units, and the remainder tells how far into the next unit the pattern stops.
Why is the remainder not written as a decimal? The remainder counts real items left over, such as 2 beads. A decimal would describe part of a unit, which does not help to name the next item.
How is a loop of beads different from a string? A string has two ends, so it has one fewer gap than beads. A loop has no ends, so it has as many gaps as beads.
