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Representing Numbers

REPRESENTATIONAL
Mathematics›Number Representation & Place Value|Ages 6—8|ID: mt_9L3NQqgqRd

Identify, represent, and estimate numbers using different representations including the number line

Mastery Evidence

  • Place a two-digit number on a 0–100 number line in approximately the right position
  • Estimate 'about how many' objects are in a set of 30–50 without counting
  • Represent the same number using base-ten blocks, a number line, and a drawing
  • Represent a three-digit number using base-ten blocks, a number line, or a place-value chart
  • Estimate where a number falls on a 0–1000 number line
  • Match a base-ten representation to the correct numeral

Assessment Prompt

“Can [child] show a number like 346 in different ways — as base-ten blocks, on a number line, or as a drawing — and explain what each representation shows?”

Curriculum Standards2 alignments

Ma/KS2/Y3/NPV/4The national curriculum in England
Identify and estimate numbers

identify, represent and estimate numbers using different representations

Mathematics · Key Stage 2
Maths/Y2/NPV/3The national curriculum in England
Identify and represent numbers

Identify, represent and estimate numbers using different representations, including the number line.

Mathematics · Key Stage 1

Prerequisites3

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  • The three digits of a three-digit number hard

    Representing numbers requires place-value understanding

    • A Hundred Is Ten Tens hard

      Three-digit place value requires understanding 100 as a unit

      • A Ten Is Ten Ones hard

        100 as ten tens extends understanding of 10 as ten ones

        • 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 two digits of a two-digit number hard

        Must understand two-digit place value before extending to hundreds

        • 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)

    • The two digits of a two-digit number hard

      Three-digit PV extends two-digit PV (tens and ones)

      • 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)

  • Representing numbers with objects hard

    Representing and estimating numbers on a number line builds on Y1 number representations

    • How Many in Total? hard

      Representing numbers with objects/pictures/number line requires understanding that 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'

  • The two digits of a two-digit number soft

    Estimating placement on a 0-100 number line benefits from place value understanding

    • 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)

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