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Place Value × 10 Pattern

CONCEPTUAL
Mathematics›Number Representation & Place Value|Ages 9—10|ID: mt_QqG6IdmTSE

Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)

Mastery Evidence

  • Explain that the 3 in 3,000 is ten times the 3 in 300
  • Complete: 700 ÷ 70 = __ and explain using place-value reasoning
  • State how many times greater the value of the 5 in 50,000 is than the 5 in 5,000

Assessment Prompt

“Can [child] explain that in 700, the 7 is worth 10 times more than in 70 — because moving one place to the left multiplies the value by 10?”

Prerequisites1

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  • Place value of each digit hard

    Four-digit place value is prerequisite to understanding ×10 relationship between places

    • The three digits of a three-digit number hard

      Four-digit place value extends three-digit place value

      • 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)

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