Cumwhinton Calculation Methods 2014.pdf
Cumwhinton School Calculation Methods
Mathematics will be at the core of your child’s schooling from the moment they start to the moment they leave. They will be involved in drawing, measuring, handling data and lots of other practical activities that will help your child to understand and enjoy the subject. This booklet offers guidance to the methods used to help our pupils with calculations. The methods that we use in school may or may not be familiar to you. Children are often confused when they ask parents for help at home and they try to teach the methods that they themselves were taught. Knowing how the methods in this booklet work will help you to help your children. All staff in school work from this document so that we can ensure the consistency of our approach and can make sure that the children move onto the next step when they are ready.
Why do children need to do written calculations? To To To To
represent work that has been done practically. support, record and explain mental calculation keep track of steps in a longer task work out calculations that are too difficult to do mentally
What can parents do to help?
Count with their child Play number games Involve children when taking measurements or weighing items Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc. Give children opportunities to use money to shop, check change etc. Talking about the mathematics in football e.g. ‘How many points does your favourite team need to catch the next team in the league?’ When helping their children calculate use the method that they have been taught
Key vocabulary Addition Add Addition Plus And Count on More Sum Total Altogether Increase
Subtraction Subtraction Subtract Take Away Minus Less Fewer Difference
Multiplication Lots of Groups of Times Multiply Multiplication Jumps Multiple Numberline Product Twice Three times Array Row Column Double Repeated addition
Division Lots of Groups of Share Group Jumps Numberline Equal Halve Divide Division Divided by Remainder Factor Decimal Decimal place Divisible
Addition Stage 1 Counting sets of objects Stage 2 Combining two sets of objects into one group and counting practically. Stage 3 Number bonds to 5 and 10 using songs, diagrams, pictures, objects and washing lines etc.
Stage 4 Counting on using a number line with numbers.
Stage 5 Steps in addition can be recorded on a number line. The steps often bridge through a multiple of 10. 7 + 8 = 15
Stage 6 Add two 2 digit numbers (TU and TU) 37 + 28 = 65
Stage 7 Adding several numbers. Look for number bonds to 10 or 20 to help.
Stage 8 Partition 2 digit numbers into tens and ones before adding.
Stage 9 Write the numbers in columns - Always begin adding from the furthest number to the right. - Make sure the columns line up according to the place value – tens in one column, units in the other. To begin with the children will not carry at all.
Stage 10 This then becomes the shorter method where numbers get carried to the next column.
Stage 11 Moving to adding several amounts using column addition.
Stage 12 Use column addition to add decimals. The decimal point always remains in the same place and the digits are aligned according to their place value either side of the decimal point.
Subtraction Stage 1 Counting back from a given number and using songs and rhymes to subtract one.
Stage 2 Practically get a group of objects together and take some away.
Stage 3 Count back on a number line with numbers already written on it.
Stage 4 Using a number line - work out the answer by counting back - find the difference by counting on
Stage 5 Partitioned numbers are written under one another. This is how we start to introduce the column subtraction method.
Stage 6 Column subtraction methods - Always begin subtracting from the furthest number to the right. - Make sure the columns line up according to the place value – tens in one column, units in the other. - The largest number should go on the top. To begin with the children will not carry at all.
Stage 7 The children will begin to ‘borrow ten from next door’.
You cannot do 6 subtract 8 so you borrow ten from next door (4). The 4 becomes a 3 then the ten is carried to make 6 turn into 16. Stage 8 Borrowing from a 0 You cannot do 7 – 8 or take away from 0. Therefore you need to borrow from the 30. If you subtract 1 from 30 you get 29. Place the 1 ten with the 7 so you get 17. You can now do 17 – 8.
Stage 9 Subtract decimals using column subtraction.
Multiplication Stage 1 Counting in multiples other than one – twos, tens, fives.
Stage 2 Doubling numbers
Stage 3 Repeated addition
2+2=4 5 + 5 = 10
Stage 4 Arrays show multiplication in a pictorial form.
Stage 5 The grid method is introduced by multiplying a 2 digit number by a 1 digit number (TU x U)
Stage 6 When multiplying larger numbers the grids can be expanded.
Stage 7 Short multiplication for TU x U or HTU x U
Stage 8 Long multiplication can be used when calculations become more complex/
10 x 24 = 240 6 x 24 = 144 Add 240 and 144 = 384
Division Stage 1 Halving numbers
Stage 2 Sharing into sets or groups
Stage 3 Use knowledge of multiplication facts to solve division questions.
2x4=8 so 8 ÷4 = 2 and 8 ÷ 2 = 4
Stage 4 Share objects with remainders
Stage 5 Children can also use number lines to find answers using repeated subtraction.
Stage 6 Children will develop their use of repeated subtraction to be able to subtract multiples of the divisor. Initially this should be multiples that the children are familiar with – 10, 5, 2
Stage 7 Chunking can be used to divide larger numbers.
We start with 72 and create the first chunk by calculating 10 x 3 = 30. So 72 – 30 = 42 We can then take another chunk of 10 x 3 = 30 which leaves us with 12. Next we take a chunk of 2 x 3 =6 which leaves us with 6. Finally our last chunk is 2 x 3 = 6. We then add the chunks of 10, 10, 2 and 2 together to give us 24. So 72 ÷ 3 = 24 Stage 8 The bus stop method is used to divide larger numbers.
432 ÷ 5 = How many 5s are there in 4? This cannot be done. Therefore we move across and look at both digits as 43. How many 5s are there in 43? The answer is 8. The remainder of 3 is then placed above the 2 to make 32. How many 5s are there in 32? The answer is 6 leaving 2 as a remainder. 432 ÷ 5 = 86 r 2 Stage 9 Long division
How many 15s are there in 4? This cannot be done. How many 15s are there in 43? The answer is 2 which is placed above the bus stop. 2 x 15 = 30 which is placed directly below the bus stop. Then 43 – 30 = 13 - this is the remainder The 2 drops down alongside the 13. Now, how many 15s are in 132? The answer is 8. So 8 goes above the bus stop. 8 x 15 = 120 This goes underneath the 132. 132 – 120 = 12 - this is the remainder Bring down the 0 because 15 does not go into 12. This gives us 120. Put the decimal point in place. How many 15s in 120? The answer is 8. 432 ÷ 15 = 28.8
Mathematics will be at the core of your child’s schooling from the moment they start to the moment they leave. They will be involved in drawing, measuring, handling data and lots of other practical activities that will help your child to understand and enjoy the subject. This booklet offers guidance to the methods used to help our pupils with calculations. The methods that we use in school may or may not be familiar to you. Children are often confused when they ask parents for help at home and they try to teach the methods that they themselves were taught. Knowing how the methods in this booklet work will help you to help your children. All staff in school work from this document so that we can ensure the consistency of our approach and can make sure that the children move onto the next step when they are ready.
Why do children need to do written calculations? To To To To
represent work that has been done practically. support, record and explain mental calculation keep track of steps in a longer task work out calculations that are too difficult to do mentally
What can parents do to help?
Count with their child Play number games Involve children when taking measurements or weighing items Take note of numbers in real life e.g. telephone numbers, bus numbers, lottery numbers etc. Give children opportunities to use money to shop, check change etc. Talking about the mathematics in football e.g. ‘How many points does your favourite team need to catch the next team in the league?’ When helping their children calculate use the method that they have been taught
Key vocabulary Addition Add Addition Plus And Count on More Sum Total Altogether Increase
Subtraction Subtraction Subtract Take Away Minus Less Fewer Difference
Multiplication Lots of Groups of Times Multiply Multiplication Jumps Multiple Numberline Product Twice Three times Array Row Column Double Repeated addition
Division Lots of Groups of Share Group Jumps Numberline Equal Halve Divide Division Divided by Remainder Factor Decimal Decimal place Divisible
Addition Stage 1 Counting sets of objects Stage 2 Combining two sets of objects into one group and counting practically. Stage 3 Number bonds to 5 and 10 using songs, diagrams, pictures, objects and washing lines etc.
Stage 4 Counting on using a number line with numbers.
Stage 5 Steps in addition can be recorded on a number line. The steps often bridge through a multiple of 10. 7 + 8 = 15
Stage 6 Add two 2 digit numbers (TU and TU) 37 + 28 = 65
Stage 7 Adding several numbers. Look for number bonds to 10 or 20 to help.
Stage 8 Partition 2 digit numbers into tens and ones before adding.
Stage 9 Write the numbers in columns - Always begin adding from the furthest number to the right. - Make sure the columns line up according to the place value – tens in one column, units in the other. To begin with the children will not carry at all.
Stage 10 This then becomes the shorter method where numbers get carried to the next column.
Stage 11 Moving to adding several amounts using column addition.
Stage 12 Use column addition to add decimals. The decimal point always remains in the same place and the digits are aligned according to their place value either side of the decimal point.
Subtraction Stage 1 Counting back from a given number and using songs and rhymes to subtract one.
Stage 2 Practically get a group of objects together and take some away.
Stage 3 Count back on a number line with numbers already written on it.
Stage 4 Using a number line - work out the answer by counting back - find the difference by counting on
Stage 5 Partitioned numbers are written under one another. This is how we start to introduce the column subtraction method.
Stage 6 Column subtraction methods - Always begin subtracting from the furthest number to the right. - Make sure the columns line up according to the place value – tens in one column, units in the other. - The largest number should go on the top. To begin with the children will not carry at all.
Stage 7 The children will begin to ‘borrow ten from next door’.
You cannot do 6 subtract 8 so you borrow ten from next door (4). The 4 becomes a 3 then the ten is carried to make 6 turn into 16. Stage 8 Borrowing from a 0 You cannot do 7 – 8 or take away from 0. Therefore you need to borrow from the 30. If you subtract 1 from 30 you get 29. Place the 1 ten with the 7 so you get 17. You can now do 17 – 8.
Stage 9 Subtract decimals using column subtraction.
Multiplication Stage 1 Counting in multiples other than one – twos, tens, fives.
Stage 2 Doubling numbers
Stage 3 Repeated addition
2+2=4 5 + 5 = 10
Stage 4 Arrays show multiplication in a pictorial form.
Stage 5 The grid method is introduced by multiplying a 2 digit number by a 1 digit number (TU x U)
Stage 6 When multiplying larger numbers the grids can be expanded.
Stage 7 Short multiplication for TU x U or HTU x U
Stage 8 Long multiplication can be used when calculations become more complex/
10 x 24 = 240 6 x 24 = 144 Add 240 and 144 = 384
Division Stage 1 Halving numbers
Stage 2 Sharing into sets or groups
Stage 3 Use knowledge of multiplication facts to solve division questions.
2x4=8 so 8 ÷4 = 2 and 8 ÷ 2 = 4
Stage 4 Share objects with remainders
Stage 5 Children can also use number lines to find answers using repeated subtraction.
Stage 6 Children will develop their use of repeated subtraction to be able to subtract multiples of the divisor. Initially this should be multiples that the children are familiar with – 10, 5, 2
Stage 7 Chunking can be used to divide larger numbers.
We start with 72 and create the first chunk by calculating 10 x 3 = 30. So 72 – 30 = 42 We can then take another chunk of 10 x 3 = 30 which leaves us with 12. Next we take a chunk of 2 x 3 =6 which leaves us with 6. Finally our last chunk is 2 x 3 = 6. We then add the chunks of 10, 10, 2 and 2 together to give us 24. So 72 ÷ 3 = 24 Stage 8 The bus stop method is used to divide larger numbers.
432 ÷ 5 = How many 5s are there in 4? This cannot be done. Therefore we move across and look at both digits as 43. How many 5s are there in 43? The answer is 8. The remainder of 3 is then placed above the 2 to make 32. How many 5s are there in 32? The answer is 6 leaving 2 as a remainder. 432 ÷ 5 = 86 r 2 Stage 9 Long division
How many 15s are there in 4? This cannot be done. How many 15s are there in 43? The answer is 2 which is placed above the bus stop. 2 x 15 = 30 which is placed directly below the bus stop. Then 43 – 30 = 13 - this is the remainder The 2 drops down alongside the 13. Now, how many 15s are in 132? The answer is 8. So 8 goes above the bus stop. 8 x 15 = 120 This goes underneath the 132. 132 – 120 = 12 - this is the remainder Bring down the 0 because 15 does not go into 12. This gives us 120. Put the decimal point in place. How many 15s in 120? The answer is 8. 432 ÷ 15 = 28.8
