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

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Priority of operations with positive 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

Addition of positive and negative integers

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 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

This image is a help guide to the priority of operations. Which set of operations must you always apply first when they are in a calculation?

How would you complete a calculation when an operation is repeated?

Without using a calculator, work out: $$4\times5  + 6\times7$$ = {{ }}

Without using a calculator, work out: $$200\;-(12\;–\;8)\times5\times3^2$$ = {{ }}

The answer to this calculation is 54. Match the triangle, star, square and arrow to the correct operation or numerical value.

Without using a calculator, work out: $$90 + \sqrt{40\times10}-12\times5$$ = {{ }}

when added to the original number, gives the sum of 0

when added to the original number, gives the sum of 1

when multiplied by the reciprocal the product is 1

when multiplied by the reciprocal the product is (-1)

Complete the statement. The additive inverse of a number is a number that, __________

Match each number with its additive inverse.

Select all the fractions that are equivalent to $${2} \over {3}$$.

Match each calculation with an equivalent commutative calculation.

Work out the missing number: $$9.8 \times 0.5 + 9.8 \times$$ {{ }} $$= 9.8$$

Work out the missing number: $$34 \times 0.8 + 34 \times$$ {{ }} $$= 68$$

Priority of operations with positive integers

Lesson outcome