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 and negative integers and decimals

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 integers

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

Using the priority of operations, work out: $$20-(-5)\times10 =$$ {{ }}

Using the priority of operations, work out: $$100+(-50)\times2=$$ {{ }}

Using the priority of operations, work out the answer to  $$(-8)+30\div2 =$$ {{ }}

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

Without using a calculator, evaluate  $$10+(-9)\div (-3)-(- 4) $$ 

Without using a calculator, evaluate $$9.4 -3.2+ \frac {12^2} {\sqrt{75+25}}$$

Which operation is last in the priority of operations?

The __________ of a number is a number that, when added to the original number, gives the sum of 0

Without using a calculator, work out: $$11\times5 - 2\times3 =$$ {{ }}

Without using a calculator, work out: $$3000\;–\;(54\;–\;4)\times2\times5^2 =$$ {{ }}

Select the calculation with an answer of 1

Work out the value of $$12 + 3 \times 10 - 8 + 1$$

Priority of operations with positive and negative integers and decimals

Lesson outcome