The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

A number and its additive inverse make a zero pair.

The absolute value of a number is its distance from zero. E.g. 5 and (−5) are both 5 away from zero and so both have an absolute value of 5

Addition of positive and negative integers

Maths

Checking understanding of arithmetic procedures with integers and decimals

Securing understanding of arithmetic procedures with integers and decimals

Checking and securing understanding of negative numbers in context

Subtraction of positive and negative integers

Checking and securing understanding of written addition and subtraction strategies

Checking and securing understanding of multiplication and division

Multiplication and division where only one value is negative

Multiplication and division where two or more values are negative

Simplifying multiplication and division using multiples of 10

Multiplying with decimals

Dividing with decimals

Priority of operations with positive integers

Priority of operations with positive and negative integers and decimals

Using the associative, commutative and distributive laws together

Using your calculator efficiently

Problem solving with integers and decimals

Pupils use their understanding of place value and fluency with decimals from this unit in order to extend this understanding to fractions.  In the future unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required.

The prior unit on factors, multiples, squares and cubes helped pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used here to explore multiplying and dividing with decimals.

In this unit pupils develop their ability and efficacy with the four operations including more complicated and challenging calculations involving fractions, decimals and negative numbers. This leads into an exploration of the priority order of operations.

Arithmetic procedures with integers and decimals

Match together each number with its additive inverse.

Which integer does this set of counters represent?

Starting with the calculation with the lowest answer, sort these calculations in order of size from lowest answer to highest answer.

Starting with the lowest temperature, put these temperatures in order from coldest to warmest.

The temperature in Reykjavik is $${-5}^\circ \text{C}$$. It is $${3}^\circ \text{C}$$ warmer in Paris. What is the temperature in Paris?

Andeep has a balance of £1.50 at the school canteen. He buys a sandwich for £2.10, an apple for 25 p and some fruit juice for £1.15. What is Andeep's new balance?

A submarine is 200 metres below sea level. The submarine rises 150 metres and then dives down 300 metres. The submarine is now {{ }} metres below sea level.

Addition of positive and negative integers

Lesson outcome