Making Connections
Pupils should make rich connections across mathematical ideas to develop fluency mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.
(National Curriculum page 10)
Connections within Mathematics
Making connections to other topics within this year group
Addition and subtraction

add and subtract whole numbers with more than 4 digits including using formal written methods (columnar addition and subtraction)

add and subtract numbers mentally with increasingly large numbers

use rounding to check answers to calculations and determine in the context of a problem levels of accuracy
When working on number and place value and/or addition and subtraction there are opportunities to make connections between them for example:
Numbers with decimals are frequently seen in real life, so give the children opportunities to add and subtract these in context. For example, you could give them catalogues or take away menus and ask them to choose two or three items to buy. You could give them a budget and ask them total the prices and find out how much of their budget is left.
You could ask the children to measure the lengths of different objects around the classroom and to find their total length. They could then represent these measurements in centimetres and metres. They could then convert them into metre measurements using decimals, for example 3m 24cm would become 3.24m. You could ask them to find out what length they would need to make a longer length that you give them, such as 10m. They could do similar activities for volume and capacity and also mass.
Encourage the children to consider whether a mental calculation strategy or a written strategy would be most efficient for their additions and subtractions. They could also make estimates of the totals and differences using rounding.
Multiplication and division

multiply numbers up to 4 digits by a one or twodigit number using a formal written method including long multiplication for twodigit numbers

multiply and divide numbers mentally drawing upon known facts

divide numbers up to 4 digits by a onedigit number using the formal written method of short division and interpret remainders appropriately for the context

multiply and divide whole numbers and those involving decimals by 10 100 and 1 000
When working on number and place value and/or multiplication and division there are opportunities to make connections between them, for example:
You could make up problems for the children to solve that involve multiplication and division for example:

Harris had £38. 96. He shared his money into four equal piles. How much money was in each pile?

Naomi was making some fruit juice for a party. She decided each person would need 350ml of juice. If there were 24 people at the party, how many litres of juice does she need to make?
Give the children place value grids similar to the one below and a set of digit cards:
1000 
100 
10 
1 
. 
1/10 
1/100 







Ask them to make a three digit number, such as 569 and place it in the grid. They can then multiply the number by ten, using the zero as a place holder. They could then divide their number by 10, 100 and 1000 and describe what is happening: the number is becoming 10/100/1000 times smaller the digits are moving to the right.
Fractions (including decimals and percentages)

recognise and use thousandths and relate them to tenths hundredths and decimal equivalents

round decimals with two decimal places to the nearest whole number and to one decimal place

read write order and compare numbers with up to three decimal places

solve problems involving number up to three decimal places
When working on number and place value and/or fractions (including decimals and percentages) there are opportunities to make connections between them for example:
Using the place value grid suggested above and digit cards, ask the children to make a number that fills the grid. Discuss what each digit is worth. For example, with the number 2315.67 the 2 is in the thousands position so that tells us how many thousands it represents – so the value shown in that column is 2000 the 3 is in the hundreds position so is 300 and so on. When you discuss the 6 and 7 ensure that the children recognise that the 6 is in the tenths position so is worth 6/10 or 0.6 and the 7 is in the hundredths position so is worth 7/100 or 0.07. They could write the numbers they make in words so that they reinforce their place value. They should also model them with structured base 10 apparatus.
You could take five examples of the numbers that the children have made in their grids write them on the board and then ask the children to order them in ascending or descending order.
Ask problems involving mass, for example:

Charlie has three cats. Macy weighs 3kg 250g , Tia weighs 2kg 175g and Elvis weighs 4kg 125g. What would these masses be in kilograms only? In kilograms work out the total mass of the three cats?

Georgie was making a cake; she needed 1.6kg of flour 350g of butter and 750g of sugar. What is the total mass of these ingredients?

Samir made five jugs of juice. For each he used 2 litres of water and 245ml of cordial. How many litres of liquid did he use altogether.
Measurement

convert between different units of metric measure [for example kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]
When working on number and place value and/or measures there are opportunities to make connections between them, for example:
Give the children a list of different metric units and ask them to write them in different ways. For example:

3km 50m could also be written as 3050m or 3.05km

2m 10cm could also be written as 210cm or 2.1m

13cm 7mm could also be written as 137mm or 13.7cm

6l 75ml could also be written as 6075ml or 6.075l
Using maps the children could work out distances to different places. These are likely to have a scale in centimetres. The children could convert these to kilometres to find the actual distances.
Making connections to this topic in adjacent year groups
Year 4

count in multiples of 6 7 9 25 and 1 000

find 1 000 more or less than a given number

count backwards through zero to include negative numbers

recognise the place value of each digit in a fourdigit number (thousands hundreds tens and ones)

order and compare numbers beyond 1 000

identify represent and estimate numbers using different representations

round any number to the nearest 10 100 or 1 000

solve number and practical problems that involve all of the above and with increasingly large positive numbers

read Roman numerals to 100 (I to C) and know that over time the numeral system changed to include the concept of zero and place value
Nonstatutory guidance
Using a variety of representations including measures pupils become fluent in the order and place value of numbers beyond 1 000 including counting in 10s and 100s and maintaining fluency in other multiples through varied and frequent.
They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far.
They connect estimation and rounding numbers to the use of measuring instruments.
Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a period of time.
Year 6

read write order and compare numbers up to 10 000 000 and determine the value of each digit

round any whole number to a required degree of accuracy

use negative numbers in context and calculate intervals across zero

solve number and practical problems that involve all of the above
Nonstatutory guidance
Pupils use the whole number system including saying reading and writing numbers accurately.
Crosscurricular and real life connections
Within the science curriculum there are opportunities to work with number and place value, for example, in the introduction of the Upper Key Stage 2 Programme of Study it states that pupils should select the most appropriate ways to answer science questions using different types of scientific enquiry including observing changes over different periods of time noticing patterns grouping and classifying things carrying out comparative and fair tests and finding things out using a wide range of secondary sources of information. The children could, for example, record changes over periods of time and compare them. You could discuss the differences in the place value of periods of time and the number system. They could record, for example, heights of plants accurately using decimal notation.
Within the geography curriculum there are opportunities to connect with number and place value for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and understanding beyond the local area to include the United Kingdom and Europe North and South America. This will include the location and characteristics of a range of the world’s most significant human and physical features. Children could, for example, find and compare distances between countries or cities temperatures lengths of rivers heights of mountains. These comparisons will involve finding differences which involve a secure understanding of place value.
See, for example:
Within the history curriculum there are opportunities to work with number and place value for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should continue to develop a chronologically secure knowledge and understanding of British local and world history establishing clear narratives within and across the periods they study. The children could, when studying the Roman period, focus on their number system and find out how it developed. A Little bit of History in issue 2 of the Primary Magazine has information about this. They could also look at the development of our number system. A Little bit of History in issue 8 of the Primary Magazine has information about this.