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Sign Rules for Multiplication

PROCEDURAL
Mathematics›Multiplication & Division|Ages 11—13|ID: mt_rxInpOQ74w

Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient

Mastery Evidence

  • Apply the sign rules when multiplying two integers (positive × negative, negative × negative)
  • Apply the sign rules when dividing two integers
  • Solve multi-step real-world problems involving all four operations with positive and negative rational numbers

Assessment Prompt

“If [child] knows that a negative times a negative makes a positive, can they use that rule to work out calculations like '−3 × −4 = 12' — and explain why it makes sense?”

Curriculum Standards5 alignments

7.NS.2Common Core State Standards for Mathematics
Apply and extend previous understandings of multiplication and division to rational numbers

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

NS
7.NS.2aCommon Core State Standards for Mathematics
Understand that multiplication is extended from fractions to rational numbers

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

NS
7.NS.2bCommon Core State Standards for Mathematics
Understand that integers can be divided

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

NS
7.NS.2cCommon Core State Standards for Mathematics
Apply properties of operations as strategies to multiply and divide rational numbers

Apply properties of operations as strategies to multiply and divide rational numbers.

NS
KS3.Maths.Num.4The national curriculum in England
The Four Operations

use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Mathematics · Key Stage 3

Prerequisites1

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  • Positive and Negative Numbers hard

    Multiplying/dividing negatives requires adding/subtracting negatives first

    • 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)

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