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Year 2 Heddington C.E Primary School M. Dobbin 2013 1 Introduction This booklet is intended to clarify and explain some of the ways in which your child is taught to write down calculations. You may be surprised to find your child’s Mathematics book contains writing, pictures, diagrams, jottings or blank number lines and not many ‘formal calculations’. Certainly, many of the methods your child uses may be very different from those that you learned at school and this can cause confusion when you are trying to support your child at home. From the very early years at school the emphasis on mathematics learning is upon children understanding and applying the skills they have learnt rather than just learning by wrote a formal written method that they may not fully understand. Here in this booklet we have tried as simply as possible to aid you in understanding some of the strategies your children may use, in their current year group, to help you, to help your children. You’ll be amazed at how many different ways there are to attempt the same idea!. The booklet contains the approaches your children may use to support their thinking when solving addition, subtraction, multiplication and division calculations. We have also included typical mathematical vocabulary your child may be acquiring and using at this stage. This is a guide only; children will always progress at different speeds, however support from you will undoubtedly be of great benefit to them at all times. We have tried to make the strategies as clear as possible however if you are unsure of any ideas in the booklet please do not hesitate to ask your child’s class teacher Mrs. Dobbin (Numeracy leader) 2 Key Vocabulary: add, addition, more , less, sum, total , altogether, how many more, partition, hundreds, tens, units, ones, one more, ten more, how much more is.. Addition In year 2 children will add combinations of single digit and 2 digit numbers. They will be encouraged to put the larger number first and count on by the smaller number. This will often be modeled using informal jottings on a number line to give children a visual representation of what they are doing Informal jottings Using a marked number line to add This can begin with the use of a marked number line to solve simple addition problems within 20 ie: 7 + 6= 13 4 5 6 7 8 9 10 11 12 13 14 15 Then this progresses to using an empty number line to support mental calculations with 2 digit numbers. Using an empty number line supports children until they are ready to do it ‘in their heads’ Informal jottings using an empty number line Some children may initially make individual jumps of tens and units Eg: 23+25 +10 23 +10 33 +1 43 +1 44 +1 45 3 +1 46 +1 47 48 However as their confidence increases mentally, they will be able to make bigger jumps including adding multiples of ten . Eg: 23+ 25 + 20 23 +5 43 48 Answer= 48 Children will also continue to use the 100 square, as in year 1 to support their addition skills. Using a number square to add by counting on This will initially be to aid children when counting on in units. Eg: 8 + 7=15 4 48 + 36=84 Partitioning : Mental Methods with Jottings Many children will progress in year 2 to the method of partitioning numbers into their value of tens and ones, adding the parts and then recombining them to find to find the total. Eg: 13 + 26 = Partition the numbers into tens and units (or ones): 10 + 3 + 20 + 6 Add the tens together and add the units together: 10 + 20 = 30 3 + 6 = 9 Recombine the numbers to give the total: 30 + 9 = 39 5 Key Vocabulary: Subtract, minus, left, less, fewer, difference between, decrease by, partition. recombine Subtraction Children will be encouraged to think of subtraction in two ways, finding the difference and taking away. Within school children are taught both methods and will choose whichever is most appropriate or easiest for them to use according to the problem they are solving. Informal jottings, using a number line to subtract Children will again begin by using a marked number line to find answers to simple subtractions Eg: 15 –8=7 4 5 6 7 8 9 10 11 12 13 14 15 This will then progress to using a number line which may be used to count back in groups (take away) For example 23 – 8 (23 –3 –5) -5 10 11 12 13 14 15 16 17 6 -3 18 19 20 21 22 23 Informal jottings using an empty number line These methods can then be developed for use with larger numbers on an empty number line . (Some children may initially make 2 jumps of ten before being able to make a jump of 20) Informal jottings using an empty number line (by counting forwards eg; finding the difference) Children will also be taught a method of counting up from the smallest number to the largest, by finding the difference, also using the number line. Children usually find it easiest to make the first jump to the next multiple of 10. The number of jumps will vary. For some children, they will find it comfortable to initially make lots of jumps of ten . Eg: 74 – 27=47 +3 27 +10 30 +10 40 +10 50 60 +10 70 Then total the jumps 10+10+10+10+ 3+4= 47 7 +4 74 Others will need less jumps, especially as they become confident and proficient in using this method. Eg: 74-27=3+40+4=47 Using a number square to count backwards As with addition children are also encouraged to use a hundred square to aid in counting back initially in units, 15-7=8 8 Then in tens and units 74-27=47 9 Key Vocabulary: times, multiply, lots of, multiple repeated addition, array, double, groups of Multiplication Children in year 2 need to focus on learning their 2x,5x,10x tables and their related division facts. Children will be encouraged to use arrays and number lines to aid them in their understanding of what multiplication means, as well as counting on in equal steps in order to lead them into learning their multiplication tables. Multiplication using and array Eg: 2 x 5 = 2lots of 5 = 10 Using a number line to understand multiplication as repeated addition. Again the number line will be used in order to help children support mental strategies ie; 5x2 = 2+2+2+2+2 = 10 0 1 2 3 4 5 6 7 8 9 10 This may progress to jottings using repeated addition without the number line. Eg; 5 x3= 3+3+3+3+3 =15 10 Key Vocabulary: share. group, divide, remainder, half, array, repeated subtraction, divided by Division In year 2 children will investigate division as both grouping and sharing, including examples with remainders. Experiences will still include lots of practical activities and then will progress to children using pictures to aid them with their mental calculations. Division as grouping Eg; How many groups of 5 can I get from 10? (10 ÷ 5 = 2) Division as sharing Eg: 9 shared between 2 people 4 each with 1 left over 9÷2 = 4 r 1 Using a number line to divide by repeated subtraction (which could include remainders) Some children will progress to using the number line to show division as taking away groups. eg : 12 ÷ 2 =6 using the number line -2 -2 -2 -2 6jumps 0 1 2 3 4 5 6 7 11 -2 8 9 -2 10 11 12 It is also very important that children begin to see the link between multiplication and division and how they can use their knowledge of multiplication facts to help them solve division problems. Eg: 16 ÷ 4 = ? How many 4’s make 16 ? 4x4=16 so 16 ÷ 4 = 4 12 Web sites Many parents have asked about web sites they could use with their children to help them with their maths. Here are a few suggestions but this list is not exhaustive and remember all children in school have a Mathletics (mathletics.co.uk) account and this is probably the best website to use as it is particularly geared to your year group. If you cannot remember your sign in and password, ask your class teacher. www.mathszone.co.uk www.mathsisfun.com www.funschool.com www.ictgames.com www.woodlands-junior.kent.sch.uk/maths www.maths-games.org 13 Top tips Here are some other top tips that may help Talk to your child about maths Be positive about Maths!! Let your child know that everyone can learn math. Be positive about your own math abilities. Try to avoid saying "I was never good at maths" or "I never liked maths". Let your child know that you think math is important and fun. Praise your child when he or she makes an effort, and share in the excitement when he or she solves a problem or understands something for the first time. When your child is trying to solve a problem, ask what he or she is thinking. If your child seems puzzled, ask him or her to tell you what doesn't make sense. (Talking about their ideas and how they reach solutions helps children learn to reason mathematically.) Treat errors as opportunities to help your child learn something new. We all learn from mistakes. Make maths part of your child’s day: Include your child in everyday activities that involve math – making purchases, measuring ingredients, counting out plates and utensils for dinner. 14