Games you could play to help

Games you could play to help Dominoes playing properly, playing snap by counting the dots and much more! Card games playing Black Jack, whist, 2s Draw graphs and charts of things you see, how many different colour cars etc Play darts or go bowling and ask your child to do all the calculations during the game Keep a running record of sports match scores such as the Football League, Cricket matches etc Get them to teach you ask them to show you how to do their maths and their calculations. And if you can think of any others, then do let us know and we ll share them on the school website! Email head@trumacar.lancs.sch.uk or let the Classteacher know. How we do Mental Calculations in Year 3 Year 6 A Guide for Parents

Introduction In this booklet you will see a variety of ways of working our different calculations. This booklet is designed to explain how some of the different methods of calculating are being taught in school. The methods may look different to what you are familiar with but they will be how your child will be learning to calculate at school. The methods of calculating in this booklet follow on from some of the mental methods of calculating your child will be familiar with from Key Stage. All calculations should be written horizontally at first, until children decide for themselves which way to work them out, for example 45 + 3 = 58 and not vertically. 45 +3 Your child will be becoming more familiar with the words calculation and calculate as they are being used in school all the time. The word sum should only be used when adding numbers together. It is very important to use the correct words when talking about numbers in calculations. The numbers themselves are said using their value, and not just the digit, e.g. 53 + 4 would be 50 + 0 and 3 + 4 Long division is one step further and showing your working out. Let s use the same question 4. 4 5 7 2 This is to be used only when the children are totally confident with short division. What s the Hunk? It s the biggest Chunk? So if we take 92 6 =? We know 60 is 0 x 6 which leaves us 32. So 32 6 = 5 with 2 left over. So 92 6 = 5 r2 5 2 2 2 0 2. 0 2. 0 What s the Hunk Method? 0

Short division is used when dividing larger numbers. 5 72 Ask how many 5 s are in 7, which is with remainder 2. So we write above the 7 and the remainder next to the next digit in the original question: 5 7 2 2 We then say how many 5 s are in 22? Answer, 4 with remainder 2 and write: 4 r 2 5 7 2 2 If we are working into decimals, we would carry on by writing a decimal point and zero on the end of the original question, like this and putting the remainder in as we did before: 4 5 7 2 2. 2 0 And then putting a decimal point in our answer and asking how many 5 s are in 20 answer 4 so: So, 45 + 3 = A method of adding is to separate the numbers into parts, add the parts and then recombine to find the total. This is called Partitioning. Partition the numbers into tens and ones (units) 45 is 40 + 5 and 3 is 0 + 3 Add the tens together 40 + 0 = 50 Add the ones (units) together 5 + 3 = 8 Recombine the numbers to give the total 50 + 8 = 58 Addition 4. 4 5 7 2 2. 2 0

Division This knowledge of partitioning can then be used in a vertical calculation where the largest part of the number is added first and the smallest part of the number is added last. 45 +3 50 adding the tens first 8 adding the ones (units) last 58 totalling the numbers 345 + 23 400 adding the hundreds first 60 adding the tens next 8 adding the ones (units) last 468 totalling the numbers Early division begins with sharing in practical activities. Children need to recognise that 5 3 = Can mean 5 shared between 3 or How many lots of 3 are there in 5? We can use the number line to find out how many threes there are in fifteen by counting forwards or backwards in threes. So 5 3 = 5 Again try and think of real life sharing such as sharing sweets, toys, dominoes, cards, lego bricks etc

Column Multiplication We can also do Multiplication like this 4 3 2 6 x 2 5 8 (because 43 x 6 =) 8 6 0 (because 43 x 20 =) 8 (added together) We must remember the value of each number when we are using this method. For example if we are looking at 425 x 63 then we would have three steps, 425 x 3; 425 x 60 and 425 x 00 then add them together, like this: 4 2 5 6 3 x 2 7 5 (because 425 x 3 =) 2 5 5 3 0 0 (because 425 x 60=) 4 2 5 0 0 (because 425 x 00 =) 6 9 2 7 5 (added together) Again, try and think of real life problems to try this method out such as: My room is 23 cm by 256 cm and I need to find out how much carpet I need to cover it, work out the area by multiplying 23 by 256. The same method can be used to add the smallest part of the number first and the largest part last. 45 +3 8 adding the ones first 50 adding the tens lest 58 totalling the numbers 345 + 23 8 adding the ones first 60 adding the tens next 400 adding the hundreds last 468 totalling the numbers Of course your child could then check their answer using a calculator, but please only use this for checking when practising this sort of calculation as it is very important that they can do it without a calculator as well!

Once they have succeeded in using this method, they can then progress to a faster and more compact method. 625 Add the ones, five add eight is + 48 thirteen. So we write ten under 3 the tens column and 3 in the ones column. The size of the grid increases as the size of the numbers increase, For example 72 x 38 = Partition both numbers and put in the grid like this X 70 2 30 8 625 Add the tens, twenty add forty is + 48 sixty, plus the ten underneath is 73 seventy. So we put 7 tens in the tens column. 625 Now add the hundreds, 6 hundreds + 48 add 0 hundreds is 6 hundreds so we 673 write 6 hundreds in the hundreds column. If you look closely you will see we encourage the children to always put carrying figures underneath the answer line. 625 + 48 673 Then 70 x 30 is 200; 2 x 30 is 60 so we can complete the top line of the grid X 70 2 30 200 60 8 Then the next line of the grid, 70 x 8 and 2 x 8 X 70 2 30 200 60 8 560 6 Total each row, 200 + 60 = 260 560 + 6 = 576 and then add them together, 260 + 576 = 2736

The Grid Method Numbers are partitioned when using the grid method to multiply. 32 x 3 = X 30 2 3 We partition 32 into 30 and 2 and put the multiplying number into the grid on the left hand side. Now we multiply the tens column first and write the answer in the grid X 30 2 3 90 And then multiply the ones column and write that answer in the grid X 30 2 3 90 6 Finally we total the numbers so 90 + 6 is 96 32 x 3 = 96 This compact method can also be used with larger numbers: 587 Add the ones, seven add + 475 five is twelve. So we put 2 ten under the tens column and the 2 in the ones column 587 Add the tens, eighty add + 475 seventy is 50 then add the ten 62 underneath is 60. So we write under the hundreds column and 60 in the tens column. 587 Then add the hundreds, 5 + 475 hundreds add 4 hundreds is 062 9 hundreds plus the hundred underneath is thousand. So we write thousand in the thousands column and 0 in the hundreds column. Now we can check our answer on a calculator to see if we got it right and then try some more! It s a good idea to try and link any calculations to things that are real, for example, I have 69 blue lego bricks and 74 yellow lego bricks, how many lego bricks do I have altogether? At home I have 5 Enid Blyton books and 39 Beast Quest books, how many bokos have I got altogether?

Subtraction An empty number line can be used to subtract (take away) two numbers, e.g. 22-7 Start by marking 22 on the number line. It is easier for children to work around the multiples of 0 and 00 when calculating, so encourage your child to count back to the nearest multiple of 0, which in this example is 20. How many have you subtracted (counted back)? 2 How many more have you still got to count back? 5 so, Multiplication can also be done as repeated addition. For example, 0 x 3 = 30 0 + 0 + 0 = 30 Children use partitioning when multiplying larger numbers, 32 x 3 = is the same as 30 x 3 add 2 x 3 We know 3 x 3 is 9 so 30 x 3 is 90 So we have 90 add 6 = 96 A way of explaining multiplication (and division) to children is use an array or picture like this: Find 3 x 4 Draw an array, We can see 3 rows of 4 circles, or 4 columns of 3 circles so 3+3+3+3 = 2 (3 x 4) or 4+4+4 = 2 (4 x 3) Check how many you have counted back...7, so 22-7 is 5 and we write, 22 7 = 5

Multiplication Early multiplication skills begin in Reception with counting in different steps eg in twos, in fives, in tens. Learning and recalling multiplication tables begins in Year 2. Children in Year 2 are encouraged to count in 2s, 5s and 0s and also to start counting in 2s and 4s. A strategy to help children to learn multiplication tables facts from counting is to say or show the child a multiplication fact such as: 6 x 2 = Ask your child to put up 6 fingers and count across the 6 fingers in twos, 2, 4, 6, 8, 0, 2 So 6 lots of 2 is 2. You could also do 7 x 0 = by asking your child to put 7 fingers up and count in 0s, 0, 20, 30, 40, 50, 60, 70 So 7 lots of 0 is 70. It is important for children to know that 0 x 7 will give the same answer as 7 x 0 (we call this commutative). Please make sure that when you practise multiplication tables, you sound the whole phrase out for example, times 2 is 2, 2 times 2 is 4, 3 times 2 is 6 etc, The number line can also be used to subtract by counting up from the smaller number to the larger. 22-7= Start by marking zero and the two numbers on the number line. We want to take 7 away from 22, so we first of all cross out the line up to 7. How many do we have left? Count up from 7 to the next multiple of 0, which is 20. Then count up from 20 to 22. So the answer is 5. This method is often used when finding the difference between two numbers, but it can be used for any subtraction calculation.

This expanded method then leads to a more compact version This method can also be used with larger numbers. A Year 4 example might be: 784 35 = This can be started by marking zero and the two numbers on the number line and complete as before: Or children can simply mark the two numbers on the number line and count up to find the answer. (Please remember that number lines do not need to have equal spaces when used to work calculations out). And then total the amount we added on starting with the largest number, 600 + 80 + 60 + 5 + 4 = 749 so 754 286 = Partition first 700 50 4 7 5 4-200 80 6-2 8 6 40 4 4 700 50 4 7 5 4 exchange ten -200 80 6-2 8 6 600 40 4 6 4 700 50 4 7 5 4 exchange -200 80 6-2 8 6 hundred So... 600 40 4 6 4 700 50 4 7 5 4 exchange -200 80 6-2 8 6 hundred 400 60 8 4 6 8 784 35 = 749

This method of counting up can also be recorded vertically: This method can be used to subtract numbers with different numbers of digits: 347 89 = Partition each number: 300 40 7-80 9 30 7 300 40 7 exchange ten for 0 ones - 80 9 so 7 9 = 8 then 8 200 30 7 300 40 7 now exchange hundred for - 80 9 0 tens and subtract 80 from 50 8 30 200 30 7 300 40 7 Finally subtract 0 hundreds - 80 9 from 200 and get 200 50 8 784-35 5 count up from 35 to 40 60 count up from 40 to 00 600 count up from 00 to 700 80 count up from 700 to 780 4 count up from 78 to 784 749 Find the total as before by adding the Largest numbers first. And then check on a calculator! Can you think of any real life problems where we can use subtraction? I had 37 wine gums and I gave 79 to my friends, how many wine gums did I have left? We are travelling to York. It is 82 miles away and we have travelled 66 miles. How much further do we have to go? I am 88 cm tall, my son is 35 cm tall. How much bigger am I? Recombine the numbers to give the answer, 347 89 = 258

Decomposition Another method used to subtract (take away) is a method called decomposition. This method partitions (splits) each number and takes each part of one number away from the other number, e.g. 784 35 = First of all partition both numbers into hundreds, tens and ones (units) like this 784 700 80 4-35 - 30 5 Starting with the ones take away 5 from 4. There isn't enough so we need to exchange one ten for ten ones. The tens column becomes ten less and the ones column becomes ten more: 70 4 700 80 4-30 5 We can now take 5 away from 4: 70 4 700 80 4-30 5 9 Move to the tens column, can we take thirty from seventy? Yes, so 70 4 700 80 4-30 5 40 9 Move to the hundreds column, can we take no hundreds from seven hundreds? Yes 70 4 700 80 4-30 5 700 40 9 Now recombine the number back together again and we get the answer 749, so 784 35 = 749 Check again with a calculator OR you can easily check by adding your answer to the number you took away in the first place, so: 749 + 35 784, the number we started with!