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Fractions on a number line

CONCEPTUAL
Mathematics›Number Representation & Place Value|Ages 11—12|ID: mt_PsylzZ9lHW

Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line

Mastery Evidence

  • Identify the value of any digit in numbers of any size including decimals
  • Place positive and negative integers, decimals, and fractions on a number line
  • Use place value to compare and order numbers across the full number system

Assessment Prompt

“Can [child] place a mix of numbers — like 3, −2, 0.5, −1.75, and ¼ — all on the same number line, in the right order?”

Curriculum Standards1 alignment

KS3.Maths.Num.1The national curriculum in England
Place Value

understand and use place value for decimals, measures and integers of any size

Mathematics · Key Stage 3

Prerequisites1

Show full prerequisite tree
  • Reading and writing numbers to 10,000,000 hard

    Extending place value to any size builds directly on Y6 reading/writing/ordering numbers to 10,000,000

    • Place Value × 10 and ÷ 10 soft

      ×10 relationship supports understanding of larger numbers

    • Reading and writing numbers (age 9+) hard

      Numbers to 10M extends Y5 numbers to 1M

      • 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)

                      • 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)

                      • 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)

                      • 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'

                  • 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)

                      • 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)

                      • 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)

                      • 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'

                  • 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)

                      • 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)

                      • 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)

                      • 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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