Progression through Addition FS2 – Year Six Updated October 2015
In EYFS children begin to learn about counting and numbers getting greater through song, for example, singing One Potato, Two Potatoes, Once I caught a fish alive etc. Through song children will learn that each time another object is added the number get bigger.
Year 1 Vocabulary: addition, +, add, more, plus, make, sum, total, altogether, equals, double, near double, one more, two more, ten more. Add and subtract one-digit and two-digit numbers to 20, including zero (mentally) Children should be provided with opportunities to learn and recall doubles of numbers up to 5. Children will learn that ‘double’ means adding the same number together twice.
Within EYFS children should hear and use some addition related vocabulary, for example: add, more, and, make, sum, total, altogether, double, one more, two more, ten more. Through a variety of different practical contexts children should experience combining two or more groups of objects together. For example, if a child has 3 eggs and his/her friend has 2 eggs they should be taught to count up to find out how many eggs they have altogether.
Children should also be taught mental strategies for addition of one digit and two digit numbers to 20. Read, write and interpret mathematical statements involving addition (+) and equals (=) signs. Katie has 7p in her purse and Holly has 2p in hers. How much money they have altogether?
Children should have the opportunity to apply their addition skills in both indoor and outdoor contexts. Some children will be able to demonstrate their mathematical language and calculate in role-play situations. Children learnt to read addition calculations involving numbers within 20, solve physically using cubes and counters and start to use number tracks.
Children should become familiar with the symbols ‘+’ and ‘=’. They should see symbols within number sentences and learn to use them to record their own addition calculations in a variety of different contexts.
Year 1 continued …
Year 1 continued … Children should start to use a number line or a number track to support their workings out.
I can use my finger to count on each number on a number line.
Number track 5 + 4 =
Represent and use number bonds and related subtraction facts within 20. Children in Year 1 should begin by learning their number bonds to 10 and related subtraction facts. Weekly Big Maths Beat That challenges should be planned for children to begin to learn to recall firstly the addition facts and then progressing onto the subtraction facts. It is important that they have a thorough understanding of this and be confident in identifying the subtraction facts in problem solving activities before moving on to number bonds to 20. Once they are secure they can use their knowledge to find and learn the number bonds to 20. 3 + 7 = 10 10 - 7 = 3
7+ 3 = 10 10 – 3 = 7
13 + 7 = 20 20 – 13 = 7
7 + 13 = 20 20 – 7 = 13
In Year 1 children should also be provided with opportunities to apply their knowledge of their number bonds to 10 and 20 within different contexts, e.g. money and measures. Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations and missing number problems such as 7 = - 9 Children should be introduced to the Bar Model for addition:
They should be given plenty of opportunity to investigate this model with coloured cuizinaire rods before using it for numbers. 7
2 ?
Number line 5 + 4 =
Children should solve missing number problems using practical apparatus (Cuizinaire rods, Deines, Numicon) and the Bar Model in order for them to become confident with the concept. 7+
=9
7
? 9
Year 2 Vocabulary: addition, +, add, more, plus, make, sum, total, altogether, jumps, equals, inverse, double, near double, one more, two more, ten more, one hundred more. Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 Children should continue to learn and practice number bonds to 10 and 20 and the related subtraction facts and practise these in weekly Big Maths Beat That Challenges.
Year 2 continued …
Year 2 continued …
They should use these facts to derive and use the number bonds to 100 and related subtraction facts. 13 + 7 = 10 7+ 13 = 20 30 + 70 = 100 70 + 30 = 100 20 - 7 = 13 20 – 13 = 7 100 – 30 = 70 100 – 70 = 30 In Year 2 children should also be provided with opportunities to apply their knowledge of their number bonds to 10, 20 and 100 within different contexts, e.g. money and measures.
Solve problems with addition and subtraction, using concrete, pictorial and abstract representations Harry had £32 and Luke had £7. How much money did they have altogether?
Add and subtract numbers using concrete objects, pictorial representations, and mentally, including TU+U, TU+T, TU+TU and U+U+U Children should be taught to start to use their knowledge of number bonds and doubles to support them with mental calculations. Direct time should be allocated in Mathematics lessons to develop children’s mental skills. Modelling will be required to teach children how to record their mental calculations in writing (number sentences). Children should become increasing confident with a range of vocabulary and independently record their work as number sentences as they progress through Year 2.
Early in Year 2 children should learn to use a prepared number line to add on in jumps of 1. They need to learn to start with the greatest number first and then add on the other number/s.
As children become secure within level 2 they should continue to use a prepared number line but they should learn to use larger jumps to add numbers. Some children may progress onto adding jumps of two before jumps of ten. Harry had £32 and Luke had £14. How much money did they have altogether? I can add on in jumps of 2.
Children should be encouraged to explain their mental calculation strategies and teachers should emphasise that there is more than one possible way of solving the mental calculation.
36 + 19 = I can add 20 onto 36 which I know is 56 and then I can subtract 1 back off to give me a final answer of 55.
63 + 27 = I know that 63 add 7 equals 70 because I know my number bonds to 10. I can then add on two tens to give me an answer of 90.
When children become more confident with adding multiples of 10 children should be taught to add the ones number first then the tens. Initially children should be provided with questions that do not cross the tens boundary. Lucy has 22m of ribbon and Hannah has 14m. How much do they have altogether? I can add two two-digit numbers by adding the 22m + 14m = ones first and then the tens.
Year 2 continued …
Year 2 continued …
When children are more secure with adding two two-digit numbers they should learn to add numbers that do cross the tens boundary. Children should also be adding numbers that have more than one ten. Lucy has 27m of ribbon and Hannah has 27m. How much do they have altogether?
Children should be taught and use a range of appropriate mathematical vocabulary. All adults should model a wide range of addition vocabulary and children should see and hear words and symbols around the classroom and school environment.
Harry saves his pocket money for six weeks and has £27. For his birthday he receives £66. How much money does he have altogether? I start by drawing my own number line and placing the greatest number on the left. Then I use my knowledge of my number bonds to 10 to add one the ones.
Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing problems Within Year 2 children will learn that addition is the inverse of subtraction and vice versa through a range of different activities. An increasing emphasis is placed on children recording number sentences using both numbers and symbols. Can you place the numbers 6, 15 and 19 into these number sentences?
Can you find as many addition and subtraction sentences as you can that use these numbers: 26, 18, 8, 10, 16, 34? Use the bar model to support with inverse calculations: 7
?
?
9 7
9 2
?
2
2
7 ?
Some children throughout Year 2 will feel more confident to add on jumps of ten each time rather than e.g. 20 all in one go. However children more secure would be expected to add on bigger jumps using multiples of 10. Harry saves his pocket money for six weeks and has £127. For his birthday he receives £136. How much money does he have altogether?
Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
Year 2 challenging higher attaining pupils Children secure with the number line should be able to add 30 on all in one jump.
Columnar addition should be introduced with practical apparatus, such as Deines and a calculation mat, first with calculations that do not cross the tens or hundreds boundaries. They should write the columnar addition alongside the calculation mat and fill it in as they go.
100s
10s
1s
32 + 25 _
Into Year 3 A bunch of tulips cost £1.60 and daffodils cost 55p. How much will the two bunches of flowers cost altogether?
I can change £1.60 into 160 pence.
I can combine the units and the tens to find the total.
I can then change 215pence back into £2.15 .
100s £1.60 + 55p = £2.15
Year 3
10s
1s
32 + 25 57
Vocabulary: addition, +, add, more, plus, make, sum, total, altogether, jumps, equals, inverse, double, near double, one more, two more, ten more, one hundred more, tens boundary, hundreds boundary, partition, partitioned column. Add and subtract numbers mentally including HTU+U, HTU+T and HTU+H The ability to calculate mentally becomes increasingly more important through the school. The demand on mental recall of facts and the ability to calculate quickly can be supported by a counting session within the daily Mathematics lesson. Children should be encouraged to explain their mental calculation strategies and teachers should emphasise that there is more than one possible way of solving the mental calculation.
Children should be confident with this before moving on to adding 3 digit numbers in the same way, without crossing the hundreds boundary.
100s
10s
1s
124 + 245 __ 100s
I can combine the units, tens and hundreds to find the total. Once the children are confident with setting out columnar addition they can move on to calculations which cross the tens boundary.
100s
100s
10s
10s
I can regroup 10 ones as 1 ten and move it to the tens column. I now have 5 tens and 2 ones.
Year 4 continued …
Year 3 moving into Year 4
1s
47 + 5 _
It is important that children are always aware of the best way to work out a calculation. They should be taught to decide whether they would solve mentally or need a written method. This calculation would best solved mentally but need to solve in this way in this instance in order to learn regrouping.
10s
1s 1
47 + 5 52
Solve simple measures and money problems involving fractions and decimals to 2 decimal places Children can use a similar calculation mat for problems involving money to support with columnar addition.
£1.23 + £1.1 2 £2.35
1s
If I add the 5 ones to the 7 ones I will have 12 ones. I can’t have 12 ones in the units column.
When confident with columnar addition crossing the tens and hundreds boundary children can solve money and measures problems in the same way.
•
Year 4 continued… Add and subtract whole numbers with more than 4 digits, including using formal written methods
100s
10s
1s
11
568 + 135 703
If I have 8 ½ and I wanted to make 10 what would I need to add on? • ½ plus ¾ Children should also learn to mentally add decimals e.g. • 2.6 + 0.8 • 3.7 plus 7.7 • Emphasis should be placed on children explaining their mental calculation strategies using the correct vocabulary. Children need to understand that there will be more than one possible method of mentally calculating given questions. Strategies should be explored as a class. Solve problems with numbers up to 3 decimal places £1.15
Make sure children use correct language when explaining their calculations. If I add 8 ones to 5 ones I will have 13 ones. I will need to
regroup this into 1 ten and 3 ones. I now add 6 tens to 3 tens and 1 ten which equals 10 tens. I need to regroup this into 1 hundred. I add 5 hundreds, 1 hundred and 1 hundred to give me the total of 7 hundreds. My total is 703.
Year 5 Vocabulary: increase, addition, +, add, more, plus, make, sum, total, altogether, equals, inverse, column addition, column, partition, units boundary, tenths boundary. The vocabulary ‘carry’ should not be used. Instead ‘exchange’ and ‘regroup’ should be used as previously. Add and subtract numbers mentally with increasingly large numbers When working within Year 5 and above children will still require regular daily time to practice and develop their mental skills (in this case addition). As part of a mental/oral starter, children could practice mentally adding fractions e.g. • Double 2 ½ • If I have ½ and add ½ what do I get?
£0.62
£1.47
? Although it is vital that children have opportunities to use apparatus throughout school they should become confident to solve problems without relying on the calculations mat. They may wish to use coins as a support initially before they are secure without. 1 1
£1. 15 + £0.62 £3.24
Level 5 continued …
Year 5 continued …
Interpret negative numbers in context 1368 + 2544 =
I know 8 + 4 = 12 to I need to move the 10 into the tens column.
I know that 10 + 60 + 40 = 110 so I have to move the 100 over into the hundreds column.
1202 + 45 + 367 =
Add and subtract whole numbers with up to 5 digits (including decimals
I know that 6 hundredths and 5 hundredths equals 11 hundredths.
Therefore I need to move ten hundredths into the tenths column.
Although this calculation has 3 numbers all with a different number of digits I can complete it easily as long as I remember to put each number in the correct column.
Year 5 continued …
Year 6 Vocabulary: increase, addition, +, add, more, plus, make, sum, total, altogether, equals, inverse, column addition, column, partition, units boundary, tenths boundary. The vocabulary ‘carry’ should not be used. Instead ‘exchange’ and ‘regroup’ should be used as previously.
Children should learn to add numbers with a differing amount of decimal places, for example, 12.631 add 3.29
I can put a zero in as the place holder in the thousandths column.
I know that 3 hundredths plus 9 hundredths equal 12 hundredths.
Therefore I need to move 10 hundredths into the tenths column.
Children should also move onto adding more than two decimal numbers e.g. 421.36 + 25.7 + 53.25 =
No new calculation strategies are introduced in Year 6. Time should be spend developing children’s procedural fluency and applying their knowledge into problems. Perform mental calculations, including with mixed operations and large numbers They should also be to solve simple problems involving negative numbers (for example, see below). Here is part of a number line. It is divided into equal sections.
I know that -4 + -2 equals -6. Write the letter of each section where each of these numbers And -5belong. and -1 = The number 99 has been done for you. -6.
Within Year 6 mental addition opportunities should use fractions, decimals, negative numbers and numbers with different standard units of measurement. For Example, • 3.6m plus 124 cm • Add -9 and 5 • Add three-quarters to one and half • Add 8 to minus 3 • Find the sum of -4 and 7 • ¾+?=2½