Working with Negative Numbers

Comparing positive and negative numbers

Addition with negatives

Subtraction with negatives

Multiplying with negatives

Dividing with negatives

Problem Solving with Negative Numbers

Prerequisite Knowledge

• Use negative numbers in context, and calculate intervals across zero
• Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature.
• Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

Key Concepts

• A negative sign represents a change in direction on a number line.
• Using number lines can help students with negative number calculations, especially addition and subtraction.
• A thermometer is helpful when comparing negative and positive numbers.
• Students should understand multiplication and division with negatives as an extension of addition and subtraction.

Working mathematically

Develop fluency

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system.
• Substitute values in expressions, rearrange and simplify expressions, and solve equations

Reason mathematically

• Extend their understanding of the number system; make connections between number relationships

Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

Subject Content

Number

• order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative