Math // Mathematical Thinking

Spotting mathematical patterns

Notice simple patterns and structures: spot that changing order doesn't change the total, and recognise how numbers relate to each other

Ages
5 to 6
Type
Thinking skill
Builds on
2 topics
Leads to
1 topic

Quick check

Has the learner noticed that adding numbers in a different order gives the same answer — like 3 + 5 and 5 + 3 both equal 8 — and can they explain why that makes sense?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Notice that 3 + 2 gives the same answer as 2 + 3 (early commutativity)
  • Recognise that teen numbers are 'ten and some more' (e.g. 14 is 10 and 4)
  • Spot a pattern in a sequence of objects or numbers and predict what comes next

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Addition as combining or putting together twoHelpful

    Addition & Subtraction // Ages 4 to 6

    Noticing commutativity of addition exercises spotting structural patterns

  • The teen numbersHelpful

    Number Representation & Place Value // Ages 5 to 7

    Recognising teen numbers as 'ten and some more' exercises noticing structure

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Spotting mathematical patterns

Ages 5 to 6 // Thinking skill

Leads to

1 topic
  • Shape patternsRequired

    Mathematical Thinking // Ages 6 to 7

    Age 6-7 using structure deliberately builds on age 5-6 noticing simple patterns and structure

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For 5-6 year olds, 'using structure' means beginning to notice that numbers and shapes are related rather than a heap of separate facts: 3+2 totals the same as 2+3, a teen number is 'ten and some more', and a repeating sequence continues predictably. The adult's job is to arrange experiences (paired counter groups, ten-frames, rekenrek/bead strings, repeating patterns) so the child spots the regularity themselves and is invited to say what they notice, rather than being told the rule. For this age, hands-on manipulation where the invariant visibly holds, or the pattern visibly continues, is the main route; labelling tasks and prediction checks are useful scaffolds and light checks, and discussion ('what do you notice?') runs alongside throughout.

Common misconceptions

  • Treats 2+3 as a brand-new problem after solving 3+2, recounting from the start rather than seeing the order swapped
  • Over-extends 'order doesn't matter' to subtraction, expecting 5-3 to equal 3-5
  • Hears a teen number as one indivisible word ('fourteen') with no sense of the ten inside it
  • Continues a repeating pattern by copying the last item rather than reading the repeating unit

Useful representations

  • Ten-frame (a teen quantity fills one frame + spills into a second, showing 'ten and some more')
  • Paired counter groups that can be physically swapped to show 3+2 = 2+3
  • Repeating object/colour/shape sequences (AB, ABB, ABC)
  • Rekenrek / bead string grouped in fives and tens

Teaching practices

  • Show the same total two ways at once (3 counters + 2 counters, then physically swap the groups) and ask 'is it still five? how do you know?' so the child articulates the invariance rather than recounting
  • Use the ten-frame so a teen quantity self-organises into a full ten plus leftovers, making '14 is ten and four' visible rather than a memorised word
  • Build repeating patterns (red-blue-red-blue) and ask the child to predict and justify what comes next, then break a pattern deliberately and ask what's wrong
  • Prize noticing over speed: ask 'what do you notice? what stays the same? what changes?' and let the child name the pattern in their own words

Activities to try

  1. 1

    Flip-the-groups: the total that stays put

    Why it works: The whole (5) stays fixed while the parts trade places, so swapping the order of an addition cannot change the total — you don't have to recount.

    1. Drop 3 counters in one bowl and 2 in another; count the running total of 5
    2. Swap the two bowls past each other so it now reads 2+3, and watch the total counter
    3. Say out loud whether it is still 5 and how you know, in your own words
    4. Answer the adult's prompt: 'Is it still five? How do you know?' — aiming for 'same numbers, just swapped round, so I don't need to count again'
  2. 2

    The ten hiding inside a teen number

    Why it works: A teen number is 'ten and some more' — 14 is a full ten plus four — not one indivisible word to be memorised.

    1. Place a teen quantity (e.g. 14 counters) one per box into ten-frames: fill the first frame completely, then put the rest into a second frame
    2. Say how many filled the full frame and how many spilled over, e.g. 'ten and four'
    3. Point to where the ten is and where the four are when asked 'Where is the ten hiding? Where are the four?'
  3. 3

    Read the repeating unit, not the last item

    Why it works: A repeating pattern is driven by a repeating unit; predicting the next item means reading that unit, not just copying the last thing you saw.

    1. Build or look at a repeating pattern (e.g. red-blue-red-blue, or ABB, ABC) and predict what comes next, saying why
    2. Spot a deliberately broken pattern: 'Is this right? What should be there?' and explain what the repeating unit tells you
    3. Continue the pattern several more steps by reading the whole repeating unit

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