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Fractions on a number line (age 11+)

REPRESENTATIONAL
Mathematics›Number Representation & Place Value|Ages 11—12|ID: mt_uDJY0X0hgo

Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations

Mastery Evidence

  • Order a mixed set of positive and negative integers, decimals, and fractions
  • Use the symbols =, ≠, <, >, ≤, ≥ correctly in mathematical statements
  • Compare numbers presented in different forms such as 0.75 and 3/4

Assessment Prompt

“If [child] is given a mixed list like 2.5, −3, ¾, 0, and −0.5, can they put them in order from least to greatest using a number line if needed?”

Curriculum Standards4 alignments

6.NS.7Common Core State Standards for Mathematics
Understand Ordering and Absolute Value

Understand ordering and absolute value of rational numbers.

NS
6.NS.7aCommon Core State Standards for Mathematics
Interpret Statements of Inequality

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

NS
6.NS.7bCommon Core State Standards for Mathematics
Write and Interpret Statements of Order

Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 °C > –7 °C to express the fact that –3 °C is warmer than –7 °C.

NS
KS3.Maths.Num.2The national curriculum in England
Ordering Numbers and Symbols

order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

Mathematics · Key Stage 3

Prerequisites3

Show full prerequisite tree
  • Positive and Negative Numbers hard

    Ordering all number types (integers, decimals, fractions) on a number line extends the negative-number number-line representation

    • Measuring temperature hard

      Negative number arithmetic extends Y6 using negative numbers in context

      • Negative numbers in context hard

        Calculating intervals across zero extends Y5 negative number context

        • Negative Numbers hard

          Counting through zero is prerequisite to interpreting negative numbers in context

          • Counting Within 1,000 hard

            Counting backwards through zero extends counting backwards within 1000

            • Counting in 2s hard

              Counting to 1000 by 5s/10s/100s extends skip counting from Year 2

            • The multiples of 100 soft

              Understanding multiples of 100 supports skip counting by 100s

              • A Hundred Is Ten Tens hard

                Multiples of 100 require 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)

  • Fractions on a number line hard

    Ordering all number types requires understanding place value across the full system

    • 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)

                      • 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)

            • 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)

                      • 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)

                      • 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)

          • 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'

                  • 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

                • 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'

                  • 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)

              • 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)

                      • 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

        • 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)

                      • 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)

  • Measuring temperature hard

    Ordering with inequality symbols extends Y6 work with negative numbers in context

    • Negative numbers in context hard

      Calculating intervals across zero extends Y5 negative number context

      • Negative Numbers hard

        Counting through zero is prerequisite to interpreting negative numbers in context

        • Counting Within 1,000 hard

          Counting backwards through zero extends counting backwards within 1000

          • Counting in 2s hard

            Counting to 1000 by 5s/10s/100s extends skip counting from Year 2

          • The multiples of 100 soft

            Understanding multiples of 100 supports skip counting by 100s

            • A Hundred Is Ten Tens hard

              Multiples of 100 require 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)

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