← Home

Generalising Patterns

META
Mathematics›Mathematical Thinking|Ages 6—7|ID: mt_fZTn0W_iZR

Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts

Mastery Evidence

  • Use a known doubles fact to derive a near-doubles answer (e.g. 6 + 7 = 6 + 6 + 1 = 13)
  • Notice that subtracting 10 from any two-digit number always reduces the tens digit by 1
  • Describe a rule for a pattern and use it to extend or predict (e.g. 'each time we add 5, the ones digit alternates between 0 and 5')

Assessment Prompt

“When [child] is practising times tables or number patterns, do they spot a shortcut — like "if 6 × 7 = 42, then 6 × 8 must be 48" — and use known facts to work out ones they haven't memorised yet?”

Prerequisites3

Show full prerequisite tree
  • 10 More or 10 Less soft

    Mentally finding 10 more/less uses generalised repeated reasoning about place value

    • One More Each Time soft

      10 more/less generalises the concept of one more/one less to tens

      • How Many in Total? hard

        Understanding 'one more/one less' requires understanding that each number represents a quantity (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 two digits of a two-digit number hard

      Mentally finding 10 more/less requires understanding that the tens digit changes

      • 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)

  • Addition and subtraction within 20 soft

    Deriving facts within 20 from known facts (near doubles, make ten) exercises generalising from patterns

  • Finding efficient methods hard

    Age 6-7 generalising from repeated reasoning builds on age 5-6 noticing repeated patterns

    • Counting in 2s soft

      Skip counting exercises recognising repeating calculation patterns

    • One More Each Time soft

      The +1 pattern in counting is the earliest repeated reasoning

      • How Many in Total? hard

        Understanding 'one more/one less' requires understanding that each number represents a quantity (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'

Unlocks1