Helping Your Child With Maths

1. Helping Your Child With Maths Redbourn Junior School 2011

2. Talk to your child about how you work things out. Ask your child to explain their thinking. CALCULATION The calculation work your child is doing at school may look very different to the kind of ‘sums’ you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking. Even when children are taught more formal written methods, they are only encouraged to use these methods for calculations they cannot solve in their heads. Discussing the efficiency and suitability of different strategies is an important part of maths lessons.

3. PRACTISING NUMBER FACTS Find out which number facts your child is learning at school. You can look on the PACT web for these. e.g. number bonds, times tables, doubles etc. Try to practise for a few minutes each day using a range of vocabulary. Have a ‘fact of the day’. Pin this fact up around the house. Practise reading it in a quiet, loud, squeaky voice. Ask your child over the day if they can recall the fact. Play ‘ping pong’ to practise number bonds with your child. You say a number. They reply with how much more is needed to make 10. You can also play this game with numbers totalling 20, 100 or 1000. Encourage your child to answer quickly, without counting or using fingers. Throw 2 dice. Ask your child to find the total of the numbers (+), the difference between them (-) or the product (x). Can they do this without counting? Use a set of playing cards (no pictures). Turn over two cards and ask your child to add or multiply the numbers. If they answer correctly, they keep the cards. How many cards can they collect in 2 minutes? Play Bingo. Each player chooses five answers (e.g. numbers to 10 to practise simple addition, multiples of 5 to practise the five times tables). Ask a question and if a player has the answer, they can cross it off. The winner is the first player to cross off all their answers. Give your child an answer. Ask them to write as many addition sentences as they can with this answer (e.g. 10 = + ). Try with multiplication or subtraction. Give your child a number fact (e.g. 5+3=8). Ask them what else they can find out from this fact (e.g. 3+5=8, 8-5=3, 8-3=5, 50+30=80, 500+300=800, 5+4=9, 15+3=18). Add to the list over the next few days. Try starting with a x fact as well.

4. W hen faced with a calculation problem, • encourage your child to ask… • Can I do this in my head? • Could I do this in my head using drawings or jottings to help me? • Do I need to use a written method? • Should I use a calculator? • Also help your child to estimate and then check the answer. Encourage them to ask… • Is the answer sensible?

5. ADDITION Children are taught to understand addition as combining two sets and counting on. Children will have started addition in KS1 by drawing pictures of the things they want to add together. They will have been encouraged to always start with the larger number first. They will then have moved to making marks or symbols to represent those objects as these are quicker to draw. They will have been encouraged to line up their drawings or marks in a logical way to make them easier to count. Some children in year 3 will still be using these strategies. At a party I eat 2 cakes And my friend eats 3. How Many cakes do we eat altogether. + + 3 + 2 = 47+25 Number Lines Children are encouraged to use number lines. Start by writing the larger number on the left of the number line. Many children prefer to begin by adding on the tens then the number bond to take the units to the next 10. Then jump in whatever jumps are comfortable for the child until you reached the total you needed to add on. +2 +10 +10 +3 47 70 57 72 67 184+39 +10 +10 +6 +3 +10 184 194 204 214 220 223 Partitioning Children will be taught to partition numbers into their separate values from Key Stage 1 but this remains a vital skill and one which they will regularly use at Key Stage 2. This simply means splitting numbers into their hundreds, tens units values etc

6. Children will begin column addition when they are confident to partition numbers. This may be at year three or at year 4. It is vital that they line up their digits using their place holders as a digit in a different place has a different value. 1 1 0 1 0 0 These three ones may look the same but due to the place they are in they have different values Extended Column Addition Initially Children will learn the extended method of column addition as this reinforces the value of each digit. It may look long but it is worth it in ensuring children securely understand what the digits actually mean. Start by adding the units digits and total these below. Then add the tens digits and total below. Then the hundreds and so on. Only when all columns have been covered do you add up your totals. Even when completing your final total we still use the expanded/partitioned method. Compact Version When the children securely understand the values of all the digits in this method they will be introduced to the compact method. This method is quicker but the children must understand that if they have more than 9 in any column they will need to “carry”. This as a 1 HOWEVER this 1 may represent 1, 10 100 etc. Units total Tens total Hundreds total Final total No carrying Carrying Here 1 ten has been carried to the next column.

7. POP! POP! POP! Subtraction Children are taught to understand subtraction as taking away (counting back) and finding the difference (counting up) Subtraction will also have been introduced at KS1. Some children will still be representing their calculations as drawings/ symbols but most children will be using concrete apparatus e.g. cubes or a number line/ hundred square in year 3. Once again children are encouraged to present their calculations clearly and logically. I had 5 balloons and 3 burst. How many do I have left? Take Away A teddy bear costs £5 and a doll costs £2. How much more does the teddy bear cost? Find the difference 84-27 I cut 27cm off 84cm of ribbon. How much do I have left? The next step is using an empty number line. Start by drawing a blank line. Place the larger number on the right hand side and then begin to take away the smaller number. The children will choose the size of jumps they move back in however they are encouraged to partition the number and jump back the tens first then the units in whatever size jumps are comfortable for them. 57 84 -2 -20 -5 57 84 -2 -2 -1 -2 -20 From year three onwards children will begin to be introduced to column subtraction. Initially this will involve no exchanging across columns. Children are again reminded to place the column headings on their sums. HTU 564 243- 321

8. 5 2 3 9- 1 5 6 7 502 - 198 (1570) 3 +2 +300 +2 3 0 (1600) 3 2 (to 200) 2 (2000) 1 4 0 0 300 (to 500) 500 502 200 198 (5239) 3 2 3 9 2 (to 502) 304 Subtraction Children are taught to understand subtraction as taking away( counting back) and finding the difference (counting up) 502 - 198 Expanded Method Once they are ready they will begin the expanded method of subtraction. It still involves use of a number line so it’s a great intermediate step. With this method however the children count up and add the pieces together to find the difference in the two amounts. We do not work in columns. Always start with the smallest column and add on whatever you need to take this to the next ten. Then the children can jump in whatever size jumps are comfortable to them until they reach their total. Finally add together the pieces to find the difference. Some children may move through this stage quickly and move onto the compact method others may prefer this method for longer. 6 7 Hundreds need to exchange with thousands. Compact Method Here the children must be sure of their digit values (e.g 7 in 70 is worth less than the 7 in 700) or they will find it difficult once exchanging begins. Children will practise this by partitioning the numbers. Children are again encouraged to put their place holders on their calculations. When a column does not have sufficient in it to complete the calculation within the column children are asked to exchange a ten/hundred/ thousand from the next column. Try not to say borrow as we don’t give anything back! Units no exchanging needed. 1 1 5 2 3 9- 1 5 6 7 4 1 Tens need to exchange with hundreds 3 6 7 2 Thousands no exchanging needed.

9. Multiplication Your child will be encouraged to learn their tables as part of their P.A.C.T. work. Tables provide a cornerstone to much mathematical understanding There is no substitute to learning tables. Knowledge of their tables will make your children feel confident to tackle many different areas of maths. 4 x3 A chew costs 4p and I buy 3. How much money do I spend? Initially at key stage 1 multiplication is taught as repeated addition. At key stage 2 we begin work on arrays. Here children draw dots or marks to show the groups in a logical way. This is a great first step as it clearly shows the relationship between the tables facts and the division facts. 4x3=12 12÷3=4 3x4=12 12÷4=3 We then go onto the grid method. We use this method first as it reinforces the true values of the digits the children are multiplying. This is a three step process which can be used right up to long multiplication if your child feels comfortable with it or can be a staging post to quicker methods. Step 1 Partition the digits in the numbers and place on the grid. Step 2 Multiply the partitioned numbers into their grid squares. Step 3 Add up the answers from the grid. 124 x 5 = X 100 20 4 5 500 10020 Step 1 Partition and put on grid. Step 2 Multiply numbers on the grid. Step 3 Add the grid answers. HTU 500 100 20+ 620 X 200 50 3 10 5 If you have to multiply by a two digit number partition this too! After this we moveonto the expanded column method. This uses the same partitioning system but is laid out in a column format. Please always start with the smallest column. HTU HTU 124 253 5 x 15 x 20 (4x5) 15 (3x5) 100 (20x5) 250 (50x5) 500 (100x5) 1000 (200x) 620 Add together 30 (3x10) 500 (50x10) 2000 (200x10) 3780 Total HTU 124 5 x 620 HTU 253 15 x 1265 2530 3795 Finally the children will do the compact method. Always start with the smallest digit first and carry any figures below. Carrying figures 21 122

12. REAL LIFE PROBLEMS • Go shopping with your child to buy two or three items. Ask them to work out the total amount spent and how much change you will get. • Buy some items with a percentage extra free. Help your child to calculate how much of the product is free. • Plan an outing during the holidays. Ask your child to think about what time you will need to set off and how much money you will need to take. • Use a TV guide. Ask your child to work out the length of their favourite programmes. Can they calculate how long they spend watching TV each day / each week? • Use a bus or train timetable. Ask your child to workout how long a journey between two places should take? Go on the journey. Do you arrive earlier or later than expected? How much earlier/later? • Help your child to scale a recipe up or down to feed the right amount of people. • Work together to plan a party or meal on a budget. These are just a few ideas to give you a starting point. Try to involve your child in as many problem solving activities as possible. The more ‘real’ a problem is, the more motivated they will be when trying to solve it.

13. SHAPES AND MEASURES • Choose a shape of the week e.g. cylinder. • Look for this shape in the environment (tins, candles etc). • Ask your child to describe the shape to you (2 circular • faces, 2 curved edges ..) • Play ‘guess my shape’. You think of a shape. Your child asks • questions to try to identify it but you can only answer ‘yes’ • or ‘no’ (e.g. Does it have more than 4 vertices /corners? Does it have • any curved sides?) • Hunt for right angles around your home. Can your child also • spot angles bigger-obtuse or smaller-acute than a right angle? • Look for symmetrical objects. Help your child to draw or • paint symmetrical pictures / patterns? • Make a model using boxes/containers of different shapes • and sizes. Ask your child to describe their model. • Practise measuring the lengths or heights of objects (in • metres or cm). Help your child to use different rulers and • tape measures correctly. Encourage them to estimate • before measuring. • Let your child help with cooking at home. Help them to • measure ingredients accurately using weighing scales or • measuring jugs. Talk about what each division on the scale • stands for. • Choose some food items out of the cupboard. Try to put • the objects in order of weight, by feel alone. Check by • looking at the amounts on the packets. • Practise telling the time with your child. Use both digital • and analogue clocks. Ask your child to be a ‘timekeeper’ • (e.g. tell me when it is half past four because then we are • going swimming). • Use a stop clock to time how long it takes to do everyday • tasks (e.g. how long does it take to get dressed?). • Encourage your child to estimate first.