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Multiplying and dividing

PROCEDURAL
Mathematics›Multiplication & Division|Ages 9—10|ID: mt_LlMl2PbaZe

Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

Mastery Evidence

  • Calculate 3.45 × 100 = 345
  • Calculate 72 ÷ 1000 = 0.072
  • Explain that multiplying by 10 shifts each digit one place to the left

Assessment Prompt

“Can [child] quickly work out '4.7 × 100' or '3,600 ÷ 1,000' — knowing that digits shift left or right in the place-value chart depending on whether they're multiplying or dividing?”

Prerequisites2

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  • Dividing by 10 and 100 hard

    Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals

    • Tenths (age 8+) hard

      Must understand hundredths to identify digit values when dividing by 10/100

      • Tenths hard

        Count in tenths is prerequisite to extending to hundredths

        • Fractions of amounts hard

          Tenths extend fraction understanding from halves, thirds, quarters

          • Finding halves and quarters (age 5+) hard

            Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

            • What Is a Half? hard

              Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away 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'

          • What Is a Half? hard

            Working with fractions extends from Y1 understanding of halves

            • Division as equal sharing hard

              Finding a half requires equal sharing into 2 groups — a division concept

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away 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'

          • Division as equal sharing soft

            Finding fractions of quantities uses equal sharing (division)

            • Subtraction as taking away or separating hard

              Division as equal sharing/grouping requires understanding subtraction as taking away/separating

              • How Many in Total? hard

                Understanding subtraction as taking away 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'

          • Fraction Notation hard

            Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

        • Counting in 2s soft

          Skip counting supports counting in tenths

    • Decimal equivalents of tenths and hundredths hard

      Must know decimal notation to express results of dividing by 10/100

      • Tenths (age 8+) hard

        Must understand hundredths before writing decimal equivalents

        • Tenths hard

          Count in tenths is prerequisite to extending to hundredths

          • Fractions of amounts hard

            Tenths extend fraction understanding from halves, thirds, quarters

            • Finding halves and quarters (age 5+) hard

              Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

              • What Is a Half? hard

                Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

                • Division as equal sharing hard

                  Finding a half requires equal sharing into 2 groups — a division concept

                  • Subtraction as taking away or separating hard

                    Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                    • How Many in Total? hard

                      Understanding subtraction as taking away 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'

            • What Is a Half? hard

              Working with fractions extends from Y1 understanding of halves

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away 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'

            • Division as equal sharing soft

              Finding fractions of quantities uses equal sharing (division)

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away 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'

            • Fraction Notation hard

              Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

          • Counting in 2s soft

            Skip counting supports counting in tenths

      • Decimal & Percent Notation hard

        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary

  • Place Value × 10 Pattern hard

    ×10 place-value relationship is prerequisite to ×÷ by 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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