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Positive and Negative Numbers

REPRESENTATIONAL
Mathematics›Addition & Subtraction|Ages 11—13|ID: mt_9QzSnn8m80

Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

Mastery Evidence

  • Represent positive and negative numbers on a number line and explain what zero means in context
  • Add a positive or negative number to any integer using number line reasoning
  • Subtract a positive or negative number from any integer, understanding that subtracting a negative is equivalent to adding

Assessment Prompt

“If [child] sees temperatures like −3°C and +5°C on a weather forecast, can they figure out how much warmer one day is than the other — even when the answer crosses zero?”

Curriculum Standards9 alignments

6.NS.5Common Core State Standards for Mathematics
Understand Positive and Negative Numbers

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

NS
6.NS.6Common Core State Standards for Mathematics
Understand Rational Numbers on Number Line

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

NS
6.NS.6aCommon Core State Standards for Mathematics
Recognize Opposite Signs

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

NS
7.NS.1Common Core State Standards for Mathematics
Apply and extend previous understandings of addition and subtraction to rational numbers

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

NS
7.NS.1aCommon Core State Standards for Mathematics
Describe situations in which opposite quantities combine to make 0

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

NS
7.NS.1bCommon Core State Standards for Mathematics
Understand p + q as the number located a distance |q| from p

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

NS
7.NS.1cCommon Core State Standards for Mathematics
Understand subtraction of rational numbers as adding the additive inverse

Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

NS
7.NS.1dCommon Core State Standards for Mathematics
Apply properties of operations as strategies to add and subtract rational numbers

Apply properties of operations as strategies to add and subtract rational numbers.

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

Prerequisites1

Show full prerequisite tree
  • 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)

                      • 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)

Unlocks3