An integer is any positive or negative whole number or zero.

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

Problem solving with 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

Priority of operations with positive and negative integers and decimals

Using the associative, commutative and distributive laws together

Using your calculator efficiently

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

Laura has £23.21. She spends £12.45 and then spends £9.29. She then finds £2.89. Without using a calculator, work out how much money she has left. £{{ }}

Lucas has a £20 note. He needs to buy 6 packets of donuts for a party. Each packet costs £3.12. Work out how much change Lucas will have left. £{{ }}

Some children each grow a tomato plant. Alex’s plant is 28.4 cm, Jacob’s plant is 35.8 cm, Sofia’s plant is 32.4 cm and Andeep’s plant is 24.4 cm. Work out the mean height of the plants. {{ }} cm

An isosceles triangle has one angle of $$43.6^\circ$$ and another angle of $$92.8^\circ$$.  Three students work out the third angle. Who is correct?

The starting line is at 0. If you twist this combination clock anticlockwise 50, which number will the combination lock starting line be on?

A combination lock starts at 0. It is twisted 23 anticlockwise, then 78 clockwise, then 80 anticlockwise and then 13 clockwise. Which number is the combination lock now indicating? {{ }}

Match each calculation to its correct answer. Use your knowledge of identifying a reasonable answer and do not work out the calculations.

Without using a calculator, work out the answer to $$4\times8  + 6\times5 = $$ {{ }}

Match each number with its additive inverse.

Starting with the calculation with the lowest answer, sort these calculations into order of size. 

Work out the missing number:  $$33 \times 0.6 + 33 \times$$ {{ }} $$= 33$$

Work out the missing number:  $$4.5 \times 0.23 + 4.5 \times$$ {{ }} $$= 4.5$$

Problem solving with integers and decimals

Lesson outcome