# 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 x)*

## Connections within Mathematics

### Making connections to other topics within this year group

#### Number and place value

#### Statutory requirements that are particularly relevant:

Pupils should be taught to:

- recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- order and compare numbers beyond 1000
- identify, represent and estimate numbers using different representations
- round any number to the nearest 10, 100 or 1000
- solve number and practical problems that involve all of the above and with increasingly large positive numbers

When working on measurement and/or number and place value, there are opportunities to make connections between them, for example:

When converting between different units of measurement children need to know about the place value of digits. If converting, for example, 1.5km to metres they need to know that 1km is 1000m and that 0.5km is half of 1000m in order to give an answer of 1500m.

When solving problems involving measures or carrying out practical activities, it would be helpful to give the children opportunities to order different lengths, masses, capacities and volumes and also to round amounts to the nearest whole unit, ten, hundred etc. For example,you could ask the children to pick four cards and make a 4 digit number. They pretend their number represents grams and write them in as many different ways as they can, for example 4563 grams, 4kg 563g, 4.563kg. You could then ask them to round the grams to the nearest 10 (4560g), 100 (4600g) and 1000 (5000g). They could repeat this with metres and millilitres.

#### Addition and subtraction

#### Statutory requirements (all are relevant):

Pupils should be taught to:

- add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
- estimate and use inverse operations to check answers to a calculation
- solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

When working on measurement and/or addition and subtraction, there are opportunities to make connections between them, for example:

When carrying out activities in measurement, provide opportunities for the children to solve problems that involve these types of calculation. For example:

- Freddie had a length of string which was 1m 75cm. He cut off two pieces, one 28cm and another 75cm and gave them to a friend. How much string did he have left?
- Hattie had 2l bottle of juice. She filled three glasses with 250ml of juice in each. How much juice was left in the bottle?
- Amy had saved £575. She bought laptop for £245.50 and a printer for £125. How much of her saving did she have left?
- Mandy left home at 10:30am. She arrived at the shopping centre 40 minutes later. What time did she get to the shopping centre?
- The film started at 17:45. Bobby was 35 minutes early. At what time did he arrive at the cinema?

They should be encouraged to decide which operations and methods to use and why.

#### Multiplication and division

#### Statutory requirements that are particularly relevant:

Pupils should be taught to:

- recognise and use factor pairs and commutativity in mental calculations
- multiply two-digit and three-digit numbers by a one-digit number using formal written layout

When working on measurement and/or multiplication and division, there are opportunities to make connections between them, for example:

When converting from larger to smaller units the children should use multiplication, for example, 2km would be multiplied by 1000 to give 2000m. When converting from smaller to larger units division would be involved, for example, 200ml divided by 1000 would be 0.2l.

When looking at perimeter the children need to explore the algebraic formula of 2(a + b) where a and b are the dimensions in the same unit. This involves doubling or multiplying by two.

The notes and guidance suggests that the children study area through arrays of squares and discover for themselves that areas can be found by multiplying the number of rows by the number of columns which is the same as the length multiplied by the width.

Provide the children with opportunities to solve problems which involve multiplication and division. For example:

- Hammed wants to cover his back yard with grass. His back yard measures 12m by 10m. What area will he cover?
- Ahmed is going to sow grass seed in his garden. It is a rectangular measuring 8m by 4.5m. He needs to know the perimeter and area so he can buy the grass seed and bricks for the wall he wants to build around it. What are the perimeter and area of his garden?

#### Fractions

#### Statutory requirements that are particularly relevant:

Pupils should be taught to:

- count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
- solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
- add and subtract fractions with the same denominator
- recognise and write decimal equivalents of any number of tenths or hundredths
- recognise and write decimal equivalents to , ,
- find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
- round decimals with one decimal place to the nearest whole number
- compare numbers with the same number of decimal places up to two decimal places
- solve simple measure and money problems involving fractions and decimals to two decimal places.

When working on measurement and/or fractions there are opportunities to make connections between them, for example:

You could encourage the children to explore simple fractions of measurement such as ½, ¼ and ¾ of different numbers of centimetres, metres, kilometres, litres and kilograms. They could also do this for hours, perimeters and areas. This would reinforce the concept of finding a fraction by division.

### Making connections to this topic in adjacent year groups

#### Year 3

- measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
- measure the perimeter of simple 2-D shapes
- add and subtract amounts of money to give change, using both £ and p in practical contexts
- tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24- hour clocks
- estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight
- know the number of seconds in a minute and the number of days in each month, year and leap year
- compare durations of events, for example to calculate the time taken by particular events or tasks

#### Non Statutory Guidance

Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (e.g. 1 kg and 200g) and simple equivalents of mixed units (e.g. 5m = 500cm).

The comparison of measures should also include simple scaling by integers (e.g. a given quantity or measure is twice as long or five times as high) and this should connect to multiplication.

Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. They record £ and p separately. The decimal recording of money is introduced formally in year 4.

Pupils use both analogue and digital 12-hour clocks and record their times. In this way they become fluent in and prepared for using digital 24-hour clocks in year 4.

#### Year 5

- convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)
- understand and use equivalences between metric units and common imperial units such as inches, pounds and pints
- measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
- calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes
- estimate volume (e.g. using 1 cm3 blocks to build cubes and cuboids) and capacity (e.g. using water)
- solve problems involving converting between units of time
- use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.

#### Non Statutory Guidance

Pupils use their knowledge of place value and multiplication and division to convert between standard units.

Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm.

They calculate the area from scale drawings using given measurements.

Pupils use all four operations in problems involving time and money, including conversions (e.g. days to weeks, leaving the answer as weeks and days).

## Cross-curricular and real life connections

Learners will encounter measurement in:

Within the science curriculum there are opportunities to connect with measurement, for example, one of the requirements for *states of matter* is that the children should be taught to identify the part played by evaporation and condensation in the water cycle and associate the rate of evaporation with temperature. This could involve measuring temperatures using a thermometer and tracking the changes over, for example, a morning. The children record the temperature every 40 minutes making a note of the time in 24 hour digital format.

Within the design and technology curriculum there will be plenty of opportunities for accurate measuring, particularly of length using different units in the designing and making stages.

Within the cooking and nutrition curriculum the children should be taught to prepare and cook a variety of predominantly savoury dishes using a range of cooking techniques. As they work on these practically they will need to measure mass and volume. You could provide them with recipes and ask them to scale them up or down for different numbers of people and then to measure out the correct ingredients. If they require cooking time, the children could make up timetables to show preparation, cooking and clearing up times using 12 or 24 hour digital formats.

Within the history curriculum, see, for example:

Within the art curriculum, see for example, the work of Kandinsky

In real life, measurement is something that we frequently do without even thinking about it. You could ask the children to think about what they have done from waking up in the morning that has involved measuring. They might think of ideas to do with length (distance walking into school), mass (weight of their back pack),capacity and volume (filling their flask with juice), time (leaving home to get to school on time).