Year 1 - Addition and Subtraction
New Curriculum
- read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
- represent and use number bonds and related subtraction facts within 20
- add and subtract one-digit and two-digit numbers to 20, including zero
- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9.
Non-Statutory Guidance
Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 + 7 = 16; 16 – 7 = 9; 7 = 16 – 9). They should realise the effect of adding or subtracting zero. This establishes addition and subtraction as related operations.
Pupils combine and increase numbers, counting forwards and backwards.
They discuss and solve problems in familiar practical contexts, including using quantities. Problems should include the terms: put together, add, altogether, total, take away, distance between, difference between, more than and less than, so that pupils develop the concept of addition and subtraction and are enabled to use these operations flexibly.
Links and Resources
“Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.”
– The National Curriculum in England Framework document, September 2013, page 10
Making connections to other topics within this year group
Multiplication and division
When working on addition and subtraction and/or multiplication and division, there are opportunities to make connections between them, for example:
Multiplication must be understood both as ‘repeated addition’ and as ‘scaling’. Likewise, division is both ‘repeated subtraction’ and reduction (multiply by a scale factor of less than 1). You should model these concepts using manipulatives including bead strings and arrays. For example:
Give each child a bead string with 20 beads on it. Ask them to find 3 multiplied by 4 by moving 3 beads at a time four times giving 12. Next, ask them to divide 12 by 3 by taking away groups of 3. As they do this you could demonstrate what they are doing on a number line. It is important that the children use practical apparatus before using a number line because a number line alone is too abstract for some children.
Give the children 12 counters and ask them to set these out in three rows of four on a piece of paper or a whiteboard:
Discuss how they can make 12 by adding four three times, and, if they turn their array around they can add three four times. They could record these as addition and multiplication number sentences.
Fractions
When working on addition and subtraction and/or fractions there are opportunities to make connections between them, for example:
You could give the children opportunities to find halves and quarters of different quantities, for example 20. They could find half by dividing by two or sharing single a set of 20 objects into two piles. They could then count how many are in each half and then add them together to check that when they do they get the whole amount. They could do the same for quarters, adding two groups to find two quarters or ½ and three for ¾.
Measurement
When working on addition and subtraction and/or measurement there are opportunities to make connections between them, for example:
You could ask the children to measure different lengths in metres using metre sticks or centimetres using rulers. They could then find totals or differences of pairs of lengths. They could repeat this for measuring masses in kilograms and capacities or volumes in litres.
Making connections to this topic in adjacent year groups
Early Years Foundation Stage
- Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number.
- Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer.
Year 2
- solve problems with addition and subtraction:
- using concrete objects and pictorial representations, including those involving numbers, quantities and measures
- applying their increasing knowledge of mental and written methods
- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
- a two-digit number and ones
- a two-digit number and tens
- two two-digit numbers
- adding three one-digit numbers
- show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
Non statutory guidance
Pupils extend their understanding of the language of addition and subtraction to include sum and difference.
Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 – 3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30. They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (for example, 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition.
Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.
Cross-curricular and real life connections
Learners will encounter addition and subtraction:
Within the science curriculum there are opportunities to connect with addition and subtraction, for example, in the programmes of study the children are expected to use their local environment throughout the year to explore and answer questions about animals in their habitat. They need to be able to sort and group them. This would give opportunities for children add and subtract to find totals and differences.
Within the geography curriculum, the children are expected to identify seasonal and daily weather patterns in the United Kingdom and the location of hot and cold areas of the world in relation to the Equator and the North and South Poles. When they do this they could use subtraction to find differences in the temperatures of the different areas.
Within the history curriculum, the children are expected to explore where the people and events they study fit within a chronological framework. This could involve using subtraction or counting on to find time differences between these events. They could use addition to find, for example the number of years the people they studied lived or the lengths of reign of different Kings and Queens.
| Programme of study statements | Activities | |||
|---|---|---|---|---|
| A | B | C | D | |
| read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs | ||||
| represent and use number bonds and related subtraction facts within 20 | ||||
| add and subtract one-digit and two-digit numbers to 20, including zero | ||||
| solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? – 9 |
||||
Activity set A
It is really important that the children understand the equals sign as a sign of equivalence, that what is on one side of it has the same value as what is on the other. Many children develop the misconception that the answer to a calculation is on the right-hand side of the equals sign. To ensure that they don’t develop this misconception you could give them a set of balance scales and some interlocking cubes. They can then explore adding different numbers of cubes on each side of the balance to find out what happens. For example, if they put 5 cubes on one side and 10 on the other, the scales won’t balance. They can then find out how many they need to add to the side with 5 cubes so that they balance. They could record this in a number sentence such as, 5 + 5 = 10 or 10 = 5 + 5.
They could explore subtraction in the same way, for example, they put 20 cubes on one side and 12 on the other. They then find out how many they should take away from the 20 cubes so that the scales balance with 12 cubes on each side. Again they could record this in a number sentence such as, 20 – 8 = 12.
You could give the children missing number sentences and ask them to find the solutions using the scales, for example:
- ? + 3 = 12 (put 12 cubes on one side of the balance and 3 on the other, add cubes to the 3 until they balance)
- 8 + ? = 15 (put 15 cubes on one side of the balance and 8 on the other, add cubes to the 8 until they balance)
- 20 - ? = 13 (put 20 cubes on one side of the balance and 13 on the other, take cubes from the 20 until they balance)
- ? – 4 = 7 (put 7 cubes on one side of the balance and another amount on the other, they explore how many they need so that when they take 4 away the scales will balance)
When the children are confident at doing this, they could then use the bar model and draw the problem, for example:
| ? | 3 |
| 12 | |
| 8 | ? |
| 15 | |
| 20 | |
| ? | 13 |
| ? | |
| 4 | 7 |
Activity set B
The children need to learn number bonds or number pairs for all numbers to 20 not simply those that make 10 and 20.
You could give them counters or cubes for the number you wish to focus on and ask the children to put them into two groups. How many different groups can they make. They would need to keep track of their work by writing number sentences, for example:
Making 7
1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7, 4 + 3 = 7 and so on…
You might be interested in using ‘Number pair Love Hearts’ from the "What makes a good resource?" section of the NCETM website. The instructions and downloadable resources are available. You could adapt this for any numbers to 20.
Activity set C
Give the children calculations to solve that involve adding and subtracting numbers to 20. They should use manipulatives, such as bead strings, cubes or counters, so that their experiences are concrete. Alongside these encourage them to write the appropriate number sentences. You could also encourage them to draw number lines to show what they have done.
You could ask them to write the age they are on a piece of paper. They then try to make their age using as many different additions and subtractions as they can. Here is an example:
Activity set D
You could give the children problems such as these to solve:
- Harry had 6 marbles. His friend gave him 12 more. How many marbles does Harry have now?
They could solve these using the bar model as described for the first requirement, for example:
6 + 12
| 6 | 12 |
| ? | |
The children could place the correct number of objects in the two numbered sections of the bar and then count them all to find the missing number.
- Holly 13 biscuits. She ate 5. How many does she have left
13-5
| 13 | |
| 5 | ? |
You could ask them ‘What number am I thinking of?’ type questions, for example:
- I am thinking of a number .When I add 3, I get 8. What number am I thinking of?
- I am thinking of a number. When I take away 4, I get 7. What number am I thinking of?
You could use straws, dice and elastic bands and play a game that will introduce the children to the concept of exchange:
- Throw a dice. Collect that number of straws.
- When you have 10 make a bundle using an elastic band.
- The winner is the first player to make more than 20.
This can also be done for subtraction:
- Take two bundles of straws.
- Throw the dice. Take that number of straws away. (The children will need to ‘unbundle’ one bundle)
- The winner is the first player to lose all their straws.
