Unit 1 · Patterns and Sequences
Ollie's Necklace — Bead Pattern Sequence
Lesson 2 of 6
Ollie makes a necklace by repeating one step: 2 red beads then 3 blue beads. The finished necklace has 12 blue beads. How many red beads? The trick is that red and blue are added in a fixed ratio each step — so find how many steps ran, then multiply red beads per step by the number of steps.
Two-colour (or two-item) repeating pattern questions appear in the very easy to easy band of OC MR. They test ratio reasoning within a repeating cycle. The most common mistake is option A (6) — students divide 12 by 2 (the red count) instead of 12 by 3 (the blue count per step).
The examiner is testing whether students can identify the repeating unit (2 red, 3 blue), use the given total of one colour to find the number of repetitions, then apply that repetition count to find the total of the other colour. Option E (24 = 12 × 2) catches students who multiply directly without first finding the step count.
A pattern step adds fixed amounts of two different items (e.g. 2 red + 3 blue per cycle). The total of one item is given. Students must find the number of cycles and multiply by the per-cycle amount of the other item. All distractors arise from applying the wrong operation (dividing by wrong number, multiplying directly, subtracting).
Best approach: Step 1: Identify the repeating unit (2 red, 3 blue per step). Step 2: Use the known total to find the number of steps — total blue ÷ blue per step = 12 ÷ 3 = 4 steps. Step 3: Multiply red per step × number of steps = 2 × 4 = 8. Step 4: Verify both totals are consistent.
Question
Ollie makes a necklace by putting beads on a string.
He makes the necklace by repeating this step:
- Add 2 red beads and then 3 blue beads onto the string.
The finished necklace has 12 blue beads.
How many red beads does it have?
Select an answer to see the explanation.
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