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. Divide by one repeating unit, then read any leftover from the start of the unit.
Lesson video, with the working
A repeating unit
3 min 16 s
The film teaches 2 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?
Shapes in one unit = 4 + 3 = 7
Units = 90 ÷ 7 = 12 R 6
Shapes in 12 units = 12 × 7 = 84
Squares in 12 units = 12 × 3 = 36
Squares altogether = 36 + 2 = 38
There are 38 squares in the row.
Ans: There are 38 squares in the row.
Example 2
A string of beads has 3 white beads between every 2 black beads. It begins and ends with a black bead, and there are 4 black beads. How many gaps between black beads are on the string? The ends are then tied together to make a loop. How many gaps are on the loop?
Gaps on the string = 4 − 1 = 3
Gaps on the loop = 4
The string has 3 gaps and the loop has 4 gaps.
Ans: The string has 3 gaps and the loop has 4 gaps.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
Question 1 of 8 · Basic · free to tryA row of 48 flags is hung along a corridor. The colours repeat in the same…A row of 48 flags is hung along…
A row of 48 flags is hung along a corridor. The colours repeat in the same order all the way along: red, red, blue, yellow, red, red, blue, yellow, and so on. How many red flags are there in the row?
How do I explain positions in P4 repeating patterns to my child?
Your child uses a repeating unit to locate an item without counting the entire sequence one position at a time.
What your child learns here
Your child uses a repeating unit to locate an item without counting the entire sequence one position at a time. This is an application of the MOE Primary 4 outcome on number sequences, supported by division. The key distinction is between the size of a complete group and a position inside that group.
Identify a complete group whose order repeats across all the items shown, checking more than one repetition before using that group.
Number the positions within the repeating unit from the first item to the last, keeping the same starting point throughout the question.
Divide a target position by the number of items in one complete group and interpret the quotient as a count of complete groups.
Use a non-zero remainder to locate the item in the next group, while recognising that remainder zero points to the previous group's last item.
Count occurrences by combining the contribution from complete groups with any matching items in the unfinished group at the end.
Does the answer make sense?
If division gives remainder zero, the target position must land on the final item of a complete repeating unit. Your child can check the interpretation on the first complete group, where the last position is visible, before applying it to the more distant position.
How to practise these questions
Basic practice counts occurrences in complete repeats and recovers a whole string from the count of one kind of bead. Intermediate questions introduce an unfinished repeat and ask for items at particular letter positions. Challenge questions extend the grouping idea to complete tile repeats, strings with stated endpoints and a closed bead loop. Ask your child to identify the repeating group and any special treatment at the ends before choosing a division. A closed loop has no first or last endpoint to add separately. After the attempt, compare the group count with the total or length given, then account for each leftover item or unused part.
Questions parents ask
Why does remainder zero mean the last item? Positions begin at one, so a complete group ends at its full size. When the target position is an exact multiple of that size, all the groups are complete. There is no extra item in a new group, and the answer is the last item just counted.
Can a repeating unit contain the same item twice? Yes. The unit is defined by the whole ordered group, so one colour, shape or letter may occur in several positions. Your child should identify the position required before naming its item. When counting occurrences, include every matching position within each full group.
What can I ask if my child counts the sequence aloud? Ask where one complete group ends and the next begins. Then ask how many such groups fit before the required position. This connects the child's counting method with division and leaves only the unfinished part to inspect individually at the end.
