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Shape patterns

META
Mathematics›Mathematical Thinking|Ages 6—7|ID: mt_DW2D1c0fKx

Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently

Mastery Evidence

  • Use the commutative property deliberately (e.g. reorder 3 + 9 as 9 + 3 to count on from the larger number)
  • Use place-value structure to add or subtract tens (e.g. 47 + 10 = 57 because only the tens digit changes)
  • Recognise structural similarities between shapes (e.g. rectangles and squares both have 4 sides and 4 right angles)

Assessment Prompt

“When [child] notices a pattern in their maths work — like how multiplying by 10 always adds a zero — do they use that pattern to solve similar problems more quickly?”

Prerequisites3

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  • Addition in any order soft

    Deliberately applying commutativity to make addition easier exercises using structure

  • The two digits of a two-digit number soft

    Using place-value structure (tens and ones) to solve problems efficiently

    • A Ten Is Ten Ones hard

      Understanding tens and ones place value requires the concept of 10 as a bundle

      • The teen numbers hard

        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'

        • How Many in Total? hard

          Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

          • One-to-one counting hard

            Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

        • Reading and writing numbers to 20 hard

          Composing/decomposing teen numbers requires reading and writing those numerals

          • How Many in Total? hard

            Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • Writing digits 0-9 hard

            Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

    • The teen numbers hard

      General two-digit place value extends from understanding teen number composition

      • How Many in Total? hard

        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Reading and writing numbers to 20 hard

        Composing/decomposing teen numbers requires reading and writing those numerals

        • How Many in Total? hard

          Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)

          • One-to-one counting hard

            Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

        • Writing digits 0-9 hard

          Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

  • Spotting mathematical patterns hard

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

    • Addition as combining or putting together two soft

      Noticing commutativity of addition exercises spotting structural patterns

      • How Many in Total? hard

        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

    • The teen numbers soft

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

      • How Many in Total? hard

        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Reading and writing numbers to 20 hard

        Composing/decomposing teen numbers requires reading and writing those numerals

        • How Many in Total? hard

          Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)

          • One-to-one counting hard

            Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

        • Writing digits 0-9 hard

          Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)

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