Nt1310 Unit 2 Assignment

In this essay, I will be exploring different ways on how ‘addition’ can be taught in Year 2 and how they link to the National Curriculum; looking at the best mental approaches that a child should take. I will then progress by exploring a particular calculation in extra detail, evaluating ways to teach how to solve the problem and use ‘manipulatives’ to support it.

‘Addition’ is the first operation that children learn from a young age and mastering it, is the first step toward the long-lasting appreciation of mathematics. Children in Early Years Foundation Stage (EYFS) do not need to memorise complex additions in order to become confident in dealing with basic ones. They need to practice counting such as ‘Counting On’, ‘Doubling’, learning

‘Place Value’ visually and use physical objects called ‘manipulatives’ to learn different strategies. They also repeat mathematical terminologies in their discussions, such as "one more", “two more”, “a lot”, and “altogether” (Development Matters, 2012). The National Curriculum (NC, 2013) highlights that children in Year 1, are expected to learn ‘addition’ in depth and look at various problems involving this subject such as, adding one and two digit numbers to twenty. Children recite number bonds, utilise number facts to solve problems and understand that combining or adding two numbers together increases the total number. As children progress in Year 2, they mentally solve addition using concrete objects and pictorial representations. They understand that two numbers can be added in any order (commutative law) and still have the same answers (‘15+13=28’ or ‘13+15=28)’ and develop sophisticated strategies in using inverse operations (NC, 2013).

One of the approaches, which is recommended for children to practise, is to mentally follow addition calculations (working out in their head) using various strategies, which is the focus of this essay. Tony Cotton (2013, p.109) states that, developing mental approaches are more efficient and helps children to become fluent in mental calculations. But however, performing mental addition can be challenging and confusing for some children. Therefore, introducing appropriate strategies (Counting On, Partitioning, Bridging through 10) and using drawing images or ‘mark-making’ will encourage children to ‘see’ calculations in their heads and will motivate them to use the strategy which is most suited for them (Cotton, 2013, p. 110).
Ian Thompson (2007) suggests that, visual representation plays an important role in developing mental addition. For example, a number line helps children to recognise place value and prior knowledge of the ordinal sense of numbers, helps them to move from counting in ones to counting in larger steps, such as 2, 5, 10, 100 and so on.

I will now be discussing the efficient strategies which are likely to be used when solving each of the following mental calculations.

A typical mental calculation would be ‘47 + 9’ that children are expected to solve by the end of Year 2. The effective strategy which could be used for this calculation is the compensation strategy. The process is, temporarily adding an appropriate small number, such as 1 to number 9 to make the number 10. ‘47 + 10’. The reason for this is that ‘9 + 1’ is a complement of 10 and it is much easier to add ‘10 to 47’ than it is to add ‘9 to 47’ in our head. Adding these two numbers will give a total of 57 and this can be adjusted by subtracting the extra 1 to get the answer 56.
example:
- 47 + 9 → 47 + 10
- 47 + 10 = 57
- 57 – 1 = 56.

The second mental calculation ‘36 + 5’ can be carried out using the Bridging through 10 methods.

This method requires using the next multiples of 10 as a bridge to help move on from one set of number to the next 10. The key to this is to know how much more is needed to round it to the nearest 10 or compliments to 10. So, the nearest multiples of 10 to 36 is 40 and to reach 40 (secure knowledge on place value structures, number fact and multiples of 10) we need to add 4 more. In order to get 4, we need to split the number 5 into 4 and 1 (36 + 5 → 36 + 4 + 1) and take the 4 and add to the number 36 giving a total number of 40 (multiples of 10). Finally, the remaining number 1 is added to 40, to give the total amount of

41.
Working out:
- 36 + 5 → 36 + 4 + 1
- 36 + 4 = 40
- 40 + 1 = 41
Furthermore, the Bridging through 10 strategy requires understanding the decimal structure of the number system and supports children to work out without having to use fingers.

The Commutative law (also known as reordering) and partitioning the second number would be most suited for the calculation ‘12 + 20’. The commutative law means two sets of numbers can be put in any order for example, ‘12 + 20 or 20 + 12’ and will still give the same results. This strategy also requires secure knowledge on place value.
Placing the biggest number on the left-hand side, (12 + 20 →20 + 12), will make the counting easier because it is easier to add smaller numbers to bigger ones in case we need to count on. The second step would be to partition (with an understanding of place value the child can split numbers into tens and ones) 12 into ‘10 + 2’ and make a new calculation of ‘20 + 10 + 2’. At this stage, we can use our multiples of 10 knowledge and add 20 to 10 to give a total of 30(tens). Overall we can add the number 2 (ones), to 30 to give an answer 32.
Working out:
- 12 + 20 → 20 + 12
- 20 + 12 → 20 + 12→ (10 + 2)
- 20 + 10 = 30
- 30 + 2 = 32
An empty number line can be used for visual representation, which will help children to develop knowledge of place value and sequencing.

The fourth example of a calculation which is used in Year 2 is ‘28 + 13’.

An appropriate mental method would be to partition both numbers into tens and ones and then adding them together according to their place value. This strategy requires a strong understanding of place value and encourages to split larger numbers into smaller units so they are easier to work with. First of all, I would change the calculation; 28 into ‘20 + 8’ and 13 into ‘10 + 3’. Now, I would add the tens together: ‘20 + 10 = 30’ and then add the ones together: ‘8 + 3 = 11’, which gives a calculation of ‘30 + 11’. The 11 can also be split into tens and ones (11 → 10 + 1). Once this is complete, I can add the tens (30 + 10 = 40) and then add the ones (40 + 1) to give a total of 41. The purpose of using this method is to encourage children to use the ‘jotting’ (informal) process to visualise mental mathematics and to work out larers number in their practise heads before moving onto addition written calculations in

columns;
Working out:
- 28 + 13 → 20 + 8 + 10 + 3
- 20 + 10 = 30
- 8 + 3 = 11
- 11 → 10 + 1
- 30 + 10 = 40
- 40 + 1 = 41

I will now select one of the calculations and will explain in details on how I would teach Year 2 to solve the calculation mentally.

I have chosen the ‘28 + 13’ calculation and will be using the partitioning strategy to solve it. In order for children to carry out the partitioning method effectively, children should understand and recall number facts; known facts such as number bonds to 20 or multiplication facts for 2, 5 and 10 (Teaching Children to calculate mentally, 2010). Children are also expected to use 'jotting' and mark-making to record their steps of working out and their thoughts in order to ‘facilitate the execution of the calculation’ (Ian Thompson, 2004).

I have selected partitioning because a variety of ‘manipulatives’ can be used to support learners when teaching it. The strategy also provides children different ways of visualising the mathematic problem and helps them to work out fluently in their minds. Furthermore, it supports them to become confident at recognising place value in two digit numbers before moving onto written addition such as adding numbers in columns.
The National Curriculum (2013) states, children in Year 2 are expected to use concrete objects to solve addition problems with two-digit numbers. Therefore, I am going to use Base 10 blocks (‘dienes’), to support partitioning the ‘28 + 13’ calculation. The reason for using this manipulative is because it can be used to explain place value in concrete terms. For instance, a one comes as a single cube, a ten ('long') comes in a rod (ten ones joined together) and a hundred cube (a ‘flat’) made up of ten long rods. Derek Haylock (2014, p.75 - 78) also states that, “…it provides effective concrete embodiments of the place - value principle and therefore helps us to explain the way our number system works." On top of that, it also supports children to develop counting and problem-solving skills.
I would start by recalling partitioning and writing random two-digit number calculations on the whiteboard and get children to partition those numbers into tens and ones. An example would be, ‘25 + 11 → 20 + 5 + 10 + 1’. I would then choose the number ‘28’ and show them Base Ten equipment, and explain that the ‘long’ rod (represents the tens: 10, 20, 30 etc.) and the one cube (numbers 1 to 9) can be utilised to split two digit numbers into tens and ones. I would also emphasise that counting the ones, one at a time is time-consuming, whereas using a ten rod (as we know it is made up of ten ones) makes the process time efficient.
I would first encourage children to partition the numbers into tens and ones: ‘28 + 13 → 20 + 8 + 10 + 3’. The second step, children will use the number sentence but will place the two and one ten blocks to represent the number 20 and 10 as well as place ones to represent both of the digits 8 and 3. The third step; I will ask children to add the tens together, giving a total number of 30. They will then arrange the ones alongside the tens (which makes 11) and will see that they have made a new ten without having to count in one and may replace 10 ones with a ten block. Finally, they will add them together - first adding the tens: 10, 20, 30 and 40 and then adding the remaining 1 (ones) to equal 41.

Working out:

I might also accommodate interactive resources/games such as ‘Topmarks website’ for partitioning (Topmarks, 2008) within the lesson/plenary session, to assess their mathematical knowledge on partitioning. These games support learners by familiarising them with the 'dienes' blocks which represent ones, tens, and hundreds. The advantage of using this resource is to motivate learners into enjoying mathematical calculations; builds their confidence and helps develop a positive attitude towards the subject. Similarly, Way (1999) also emphasises that interactive activities supports pupil with language barriers and develops their mathematical language.

Once children are comfortable with the place value of tens and ones, similar larger calculations such as ‘26 + 22’ can be mentally calculated using an empty number line. One of the strategies which can be manipulated is partitioning the second number into tens and ones, and then counting on.
I will ask children to draw an empty number line and ask them to put the number 26 at the beginning of the line. Next, they will partition the second number 22 into tens and ones: (22 → 20 and 2). Next, Children will add the 20 (tens) to 26, which takes it to 46 and then add the 2 (ones) to equal 48. The purpose of using an empty number line as a manipulative for partitioning is that it allows the children to put whatever numbers they like, without worrying about the scale, ensuring that the numbers are in the right order and relative to each other.

Working out:

To conclude, it is essential that children start with practical experience and use visual images, manipulatives and ‘jottings ‘to develop their mental addition and early written skills. Firm subject knowledge (place value, number facts off by ‘heart’ etc.) provides a foundation for understanding more complex mathematical concepts and supports children to carry out various addition processes (partitioning, bridging, compensating) fluently. Teaching mental addition stimulates children’s minds and allows them to develop their thinking and evaluation skills. Likewise, having concrete experiences to recall previous concepts and new ideas will enable children to carry out mathematical task confidently and use it to tackle real life situations.