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Counting forwards and backwards (age 9+)

PROCEDURAL
Mathematics›Number Representation & Place Value|Ages 9—10|ID: mt_tAtMET4EIU

Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000

Mastery Evidence

  • Count on in 10,000s from 462,000
  • Count back in 100,000s from 800,000
  • Identify the next three terms: 375,000; 475,000; 575,000; ...

Assessment Prompt

“Can [child] count forwards and backwards in steps of 1,000 or 10,000 from any starting number — like 34,500, 44,500, 54,500 — without losing track?”

Prerequisites2

Show full prerequisite tree
  • 1000 More or Less hard

    Finding 1000 more/less is prerequisite to counting in powers of 10

    • 10 or 100 More or Less hard

      Finding 1000 more/less extends finding 10/100 more/less

      • The three digits of a three-digit number hard

        Requires three-digit place value to understand which digit changes

        • 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)

      • 10 More or 10 Less hard

        Finding 10/100 more/less within 1000 extends finding 10 more/less of two-digit numbers

        • 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)

    • Place value of each digit hard

      Requires four-digit place-value understanding

      • 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)

  • Place Value × 10 Pattern hard

    ×10 relationship understanding supports counting in powers of 10

    • 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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