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Reading and writing numbers (age 9+)

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Mathematics›Number Representation & Place Value|Ages 9—10|ID: mt_JwP9QFv6gQ

Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding

Mastery Evidence

  • Write 403,072 in words and in expanded form
  • Compare 548,301 and 543,801 using < and explain the reasoning
  • Order four six-digit numbers from smallest to largest

Assessment Prompt

“Can [child] read and write numbers into the millions — like 1,340,000 — and put a set of large numbers in order correctly?”

Prerequisites2

Show full prerequisite tree
  • Comparing Large Numbers hard

    Comparing beyond 1000 is prerequisite to comparing up to 1,000,000

    • Ordering Numbers to 1000 hard

      Comparing beyond 1000 extends comparing to 1000

      • The three digits of a three-digit number hard

        Comparing three-digit numbers requires 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)

      • Comparing and ordering numbers hard

        Comparing to 1000 extends comparing two-digit numbers

        • The two digits of a two-digit number hard

          Comparing two-digit numbers using PV requires understanding 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)

        • Two written numerals between 1 and 10 soft

          Comparing two-digit numbers extends from comparing single-digit written numerals

          • Comparing groups: more or fewer soft

            Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required

            • Counting objects to 20 soft

              Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

              • How Many in Total? hard

                Answering 'how many?' requires the cardinality principle

                • 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'

              • One-to-one counting hard

                Counting objects to answer 'how many?' requires one-to-one correspondence

    • Place value of each digit hard

      Comparing four-digit numbers requires four-digit PV

      • 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)

    • Numbers to 10,000 hard

      Ordering and comparing numbers over 1000 requires the full 10,000 representations toolkit

      • Representing Numbers hard

        Representing to 10,000 extends representing to 1000

        • 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)

      • Place value of each digit hard

        Representing four-digit numbers requires knowing their place value

        • 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

    Understanding ×10 place-value relationship supports reading/writing larger numbers

    • 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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