Maths · Number Sequences
Frog Sequence Hop
The frog can only land on a stone that carries on the pattern. Tap the lily pads to fill both blank stones.
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Why this works
The trap here is to spot the first gap and assume every gap is the same. From 3 to 6 the gap is 3, but from 6 to 12 the gap is 6, and from 12 to 24 it is 12. When the gaps themselves keep growing, stop adding and start looking for a multiplier: 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24, so the sequence doubles and the next terms are 48 and 96. The general strategy for any sequence is to write the differences underneath first. Equal differences mean add the same number every time. Growing differences mean try multiplying, and if that fails try squares or a two-step rule such as double then add one.
Helping a child through Frog Sequence Hop
Hints, least revealing first
- Work out what happens between each pair of stones. Write the jumps down: 3 to 6, 6 to 12, 12 to 24.
- The jumps are 3, then 6, then 12. They are not the same size, so this is not an adding sequence.
- Each stone is the one before it multiplied by 2. So the next stone is 24 times 2.
When they finish it: “Both stones landed. The frog is across!”
3 11+ skills this exercise practises
Each of these has its own page, with a worked example on it.
- Continue a number sequenceInfer and apply one arithmetic sequence rule.
- Find a sequence termUse a stated or inferred linear rule to find a named term.
- Continue a letter or number sequenceInfer and apply one or two repeating symbolic rules.
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