Rickleton Primary School Calculation Policy - + Addition Subtraction Select an operation to become a maths wizard! ÷ x Multiplication Division Quit *Only click when prompted to ensure all steps are seen. Home Guide to Written Calculations

Rickleton Primary School Select a stage! Pre-Written Methods Addition - Stage 1 Addition - Stage 2 Addition - Stage 3 Addition - Stage 4 Zap a stage! Rachel I have looked at all four operations and have noted some errors. Subtraction stage 3 shows multiplication stage1. Multiplication stage 3 has a long pause unless you click without being prompted. Division stage 1 continues without clicking next. Division stage 2 needs pace looking at. Division stage 3 shows stage 1. Multiplication continues through each stage without returning to the menu. I hope this is useful. If there is anything you need me to do just shout. Sally Home Guide to Written Calculations

Select a stage! Subtraction - Stage 1 Subtraction - Stage 2 Pre-Written Methods Subtraction - Stage 1 Subtraction - Stage 2 Subtraction - Stage 3 Subtraction - Stage 4 Zap a stage!

Select a stage! Multiplication - Stage 1 Multiplication - Stage 2 Pre-Written Methods Multiplication - Stage 1 Multiplication - Stage 2 Multiplication - Stage 3 Multiplication - Stage 4 Zap a stage!

Select a stage! Division - Stage 1 Division - Stage 2 Pre-Written Methods Division - Stage 1 Division - Stage 2 Division - Stage 3 Division - Stage 4 Zap a stage!

+ Addition ~ Watch and Learn! + Rickleton Primary School Stage 1 ~ 1 22 + 33 = Begin by drawing a number line starting with the biggest number ______________________________ 33 Next Home Guide to Written Calculations

+ Addition ~ Watch and Learn! + Stage 1 ~ 2 Add 2 tens first T 22 + 33 = +10 +10 ______________________________ 33 43 53 Next

+ Addition ~ Watch and Learn! + Stage 1 ~ 3 Then add 2 units U 22 + 33 = +10 +10 +1 +1 ______________________________ 33 43 So 22 + 33 is 55 55 53 54 55 Select a stage.

+ Addition ~ Watch and Learn! + Stage 2 ~ 1 Start by partitioning the tens and the units. TU TU 36 + 43 = 30 + 40 6 + 3 Next

+ Addition ~ Watch and Learn! + Stage 2 ~ 2 Add the tens together and then the units. 36 + 43 = 30 + 40 = 70 6 + 3 = 9 70 + 9 = 79 Select a stage. So 36 + 43 is 79

+ Addition ~ Watch and Learn! + Stage 3 ~ 1 Write the numbers so that the Tens and the Units are in line. T U 47 + 76 = 47 + 76 Next

+ Addition ~ Watch and Learn! + Stage 3 ~ 2 Start by adding the the units. 7 + 6 = U 47 + 76 = 47 + 76 13 Next

+ Addition ~ Watch and Learn! + Stage 3 ~ 3 Then add the tens. 40 + 70 = T 47 + 76 = 47 + 76 13 110 Next

+ Addition ~ Watch and Learn! + Stage 3 ~ 4 47 + 76 = 47 + 76 Now add these together 110 + 13 = 13 + 110 123 Select a stage. So 47 + 76 is 123 HTU + HTU

+ Addition ~ Watch and Learn! + HTU + HTU 247 + 176 = Set out as before. Add the units and tens as before and record. The extra step, add the hundreds together 200 + 100 = 300 Then add the numbers. 247 + 176 13 + 110 300 Select a stage. 423 So 247 + 176 is 423

+ Addition ~ Watch and Learn! + Stage 4 ~ 1 47 + 76 = Write the numbers so that the Tens and the Units are in line. T U 47 + 76 Next

+ Addition ~ Watch and Learn! + Stage 4 ~ 2 Now add the units 7 + 6 = 13 U 47 + 36 = 7 + 6 = 13 47 + 36 Exchange 10 units for 1 ten. This goes under in the tens column 3 units go in the units column 3 3 units go in the units column 1 Next

+ Addition ~ Watch and Learn! + Stage 4 ~ 3 47 + 36 = Now add the tens 40 + 30 = 70 T 47 + 36 You need to put the ten digit in the tens column 8 3 Remember there is one ten here to add too. 7 tens + 1 ten = 8 tens 1 Select a stage. So 47 + 36 is 83 See HTU + HTU

+ Addition ~ Watch and Learn! + HTU + HTU 147 + 186 = Carry any units over 9, any tens over 90. Remember to add the carry! 7 + 6 = 13 carry the ten 40 + 80 + 10 = 130 carry the hundred 100 + 100 + 100 = 300 147 + 186 3 3 3 1 1 Select a stage. So 147 + 186 is 333

- Subtraction ~ Watch and Learn! - Stage 1 ~ 1 Then take away in jumps of 1. 3 units equal 3 jumps. Take away in steps of 10 first as this is easier. 23 = 2 tens. 47 - 23 = 24 24 25 26 27 37 47 ______________________________ -1 -1 -1 -10 -10 Place the largest number at the end of the line. Select a stage. So 47 – 23 = 24 See HTU-HTU

- Subtraction ~ Watch and Learn! - HTU-HTU Then take away the tens. Then the units. Take away in steps of 100 first as this is easier. 123 = 100. 347 - 123 = 224 224 227 247 347 ______________________________ -20 -3 -100 Place the largest number at the end of the line. Select a stage. So 347 – 123 = 224

- Subtraction ~ Watch and Learn! - Stage 2 ~ 1 taking away by counting up Write the numbers so that the Tens and the Units are in line. T U 74 - 35 = Start at 35 add 5 to make 40. Then add suitable numbers to reach 74. 74 - 35 +5 (40) +30 (70) +4 (74) Add the numbers together. Select a stage. 39 So 74 - 35 is 39

- Subtraction ~ Watch and Learn! - Stage 3 ~ 1 563 - 241 = Partition 563 into hundreds, tens and units. 500 + 60 + 3 - 200 + 40 + 1 Repeat with 241 Next

- Subtraction ~ Watch and Learn! - Stage 3 ~ 2 563 - 241 = H T U Start with the units 3 – 1 = 2 500 + 60 + 3 - 200 + 40 + 1 Next, subtract the hundreds 500 – 200 = 300 - 200 + 40 + 1 300 20 2 Next, subtract the tens 60 – 40 = 20 Next

- Subtraction ~ Watch and Learn! - Stage 3 ~ 3 563 - 241 = 500 + 60 + 3 Add the answers together 300 + 20 + 2 = 322 - 200 + 40 + 1 - 200 + 40 + 2 300 20 2 = 322 Select a stage. So 563 - 241 = 322

- Subtraction ~ Watch and Learn! - Stage 4 ~ 1 Decomposition 137 - 85 = H T U Write the numbers so that they are in place value position. 137 - 85 Next

- Subtraction ~ Watch and Learn! - Stage 4 ~ 2 Subtract the units first. 7 – 5 = And write under the units. 1 137 - 85 = 1 3 7 - 8 5 The tens can’t be subtracted as 30 – 80 = - 50 Borrow 1 hundred from the hundred column. The tens column now has 130 in it and the hundred has 0. 2 Next Cross out the hundred and leave a 0 above. The 100 is put in the tens as a 1.

- Subtraction ~ Watch and Learn! - Stage 4 ~ 3 1 137 - 85 = 1 3 7 - 8 5 There are 0 hundreds to subtract. 5 2 Now solve 130 – 80 and write the answer. Select a stage. So 137 - 85 = 52

x Multiplication ~ Watch and Learn! x Stage 1 ~ 1 Partition the 14 into 2 parts, tens and units. 14 x 5 = = 10 x 5 = 4 x 5 Next

x Multiplication ~ Watch and Learn! x Stage 1 ~ 2 14 x 5 = Now add 50 + 20 and write the answer. 10 x 5 = 50 4 x 5 = 20 So 14 x 5 = 70 Select a stage.

x Multiplication ~ Watch and Learn! x Stage 2 ~ 1 Partition 16 into 1 ten and 6 units 10 6 16 x 4 = 4 Draw a box two across and one down because you are multiplying a 2 digit number by a 1 digit number. Next

x Multiplication ~ Watch and Learn! x Stage 2 ~ 2 16 x 4 = x The answer to 4 x 6 goes here. 10 6 4 40 24 The answer to 10 x 4 goes here. Now add these answers together. 40 + 24 = Select a stage. So 16 x 4 = 64 See TU x TU See HTU x U

x Multiplication ~ Watch and Learn! x TU x TU ~ 1 Partition 27 into 2 tens and 7 units 56 x 27 = 20 7 Partition 56 into 5 tens and 6 units 50 6 Next

x Multiplication ~ Watch and Learn! x TU x TU ~ 2 56 x 27 = The answer to 50 x 7 goes here. x 20 7 The answer to 50 x 20 goes here. 1000 50 350 The answer to 6 x 20 goes here. 120 42 6 The answer to 6 x 7 goes here Next

x Multiplication ~ Watch and Learn! x TU x TU ~ 3 56 x 27 = 1000 350 x 120 42 20 7 50 Add these four numbers together. 1000 + 350 + 120 + 42 = Children can use the addition methods to help them add. 6 Select a stage. So 56 x 27 = 1512 See HTU x U

x Multiplication ~ Watch and Learn! x HTU x U ~ 1 Partition 126 into 1 hundred, 2 tens and 6 units 126 x 4 = 100 20 6 4 Next

x Multiplication ~ Watch and Learn! x HTU x U ~ 2 Partition 126 into 100, 20 and 6 126 x 4 = The answer to 6 x 4 goes here. 100 20 6 400 80 24 4 The answer to 4 x 100 goes here. The answer to 20 x 4 goes here Next

x Multiplication ~ Watch and Learn! x HTU x U ~ 3 126 x 4 = 100 20 6 400 80 24 4 Add 400 + 80 + 24 Select a stage. So 126 x 4 = 504 See TU x TU

x Multiplication ~ Watch and Learn! x Stage 3 ~ 1 Set the sum out like this so that the numbers are in the correct columns. T U 38 x 7 = 38 x 7 Next

x Multiplication ~ Watch and Learn! x Stage 3 ~ 2 38 x 7 = Multiply the units by 7 7 x 8 = 56 38 x 7 56 Multiply the tens by 7 7 x 30 = 210 Next 210

x Multiplication ~ Watch and Learn! x Stage 3 ~ 3 38 x 7 = 38 x 7 56 210 Now add these two answers together. 56 + 210. 266 Select a stage. So 38 x 7 = 266 See TU x TU

x Multiplication ~ Watch and Learn! x TU x TU ~ 1 Set the sum out like this so that the numbers are in the correct columns. T U 15 x 24 = 15 x 24 Next

x Multiplication ~ Watch and Learn! x TU x TU ~ 2 15 x 24 = Multiply by the units 4 x 5 = 20 and 4 x 10 = 40 15 X 24 20 Next 40

x Multiplication ~ Watch and Learn! x TU x TU ~ 3 15 x 24 = 15 X 24 20 40 Next Multiply by tens 20 x 5 = 100 and 20 x 10 = 200 100 200

x Multiplication ~ Watch and Learn! x TU x TU ~ 4 15 15 x 24 = X 24 20 40 Now add these numbers together. 100 200 Select a stage. 360 So 15 x 24 = 360

x Multiplication ~ Watch and Learn! x Stage 4 ~ 1 T U 38 x 7 = 38 x 7 Set the sum out like this so that the numbers are in the correct columns. Next

x Multiplication ~ Watch and Learn! x Stage 4 ~ 2 38 x 7 = 38 x 7 6 5 Now multiply 7 x 8 = 56 and write the units and carry the tens underneath. Next

x Multiplication ~ Watch and Learn! x Stage 4 ~ 3 38 x 7 = 38 x 7 6 6 2 5 Now multiply 7 x 30= 210 and add the 5 tens to the 10 and write this and carry the hundreds underneath. Next

x Multiplication ~ Watch and Learn! x Stage 4 ~ 4 38 x 7 = 38 x 7 2 6 6 2 5 Now put the hundreds into the answer Select a stage. So 38 x 7 = 266 See TUxTU

x Multiplication ~ Watch and Learn! x Set out as shown. TU x TU – Magic 0 First multiply 7 x 8 = 56. Carry the 5 tens and record the 6. Then 7 x 3 = 21 plus the 5 = 26 (record) 38 x 27 = 38 x 27 Nb. Each number is considered as a unit in this calculation to make it easier. eg. 30 is 3 and 20 is 2. 2 6 6 Next place the magic 0 into the units column. Now 2 x 8 = 16 Carry the 1 and record the 6. Now 2 x 3 = 6 and add to the 1 carry 5 7 6 1 Next

x Multiplication ~ Watch and Learn! x TU x TU – Magic 0 Finally add 266 and 760. 38 x 27 = 38 x 27 Nb. Each number is considered as a unit in this calculation to make it easier. eg. 30 is 3 and 20 is 2. 2 6 6 5 7 6 1 1 2 6 Select a stage. 1 1 So 38 x 27 = 1026

÷ Division ~ Watch and Learn! ÷ Stage 1 ~ 1 Repeated subtraction How many 6s make 30? Well I know that 2 x 6 = 12 Write the number to divide at the end of a number line. 24 ÷ 3 = 3 6 9 12 15 18 21 24 -3 -3 -3 -3 -3 -3 -3 -3 Now count the number of jumps. 8 jumps Jump back in 3’s (the divider) until no more can be taken. Select a stage. So 24 ÷ 3 = 8

÷ Division ~ Watch and Learn! ÷ Stage 2 ~ 1 - chunking Two ways to set out 63 ÷ 3 = or 3 63 Next

÷ Division ~ Watch and Learn! ÷ Stage 2 ~ 2 Children will look for chunks. First take chunks (multiples) of 10,then 5 and then single units until you have the divided number - 63 63 ÷ 3 = 21 21 3 63 30 + 30 + 3 = 63 so we have taken all chunks possible. 30 (3 x 10) 30 (3 x 10) Add the chunks. 10 + 10 + 1 = 21 3 (3 x 1) Select a stage. So 63 ÷ 3 = 21

÷ Division ~ Watch and Learn! ÷ Children will look for chunks. Try to use multiples of 10, 20, 30 etc to remove the largest possible multiple of 6. Stage 3 ~ 1 – Long division 33 Record the chunk in brackets and put the answer underneath the original number. Subtract the chunk from the divided number. Then look for more chunks. 6 198 - 180 (6 x 30) 18 Once all chunks have been taken and 0 or a remainder is left, show the answer at the top by adding the chunks. 30 + 3 = 33 - 18 (6 x 3) Next So 198 ÷ 6 = 33

÷ Division ~ Watch and Learn! ÷ Stage 3 ~ 2 With remainders HTU ÷ TU Children will look for chunks. Try to use multiples of 10, 20, 30 etc to remove the largest possible multiple of 24. 23 r 8 Record the chunk in brackets and put the answer underneath the original number. Subtract the chunk from the divided number. Then look for more chunks. 24 560 - 480 (24 x 20) 80 Once all chunks have been taken and 0 or a remainder is left, show the answer at the top by adding the chunks. There is not enough to make another 24 so there is a remainder of 8. 20 + 3 = 23 r 8 - 72 (24 x 3) 8 Select a stage. So 560 ÷ 24 = 23 r 8

÷ Division ~ Watch and Learn! ÷ Stage 4 ~ 1 short division Regard each digit on its own. Work from left to right. 2 7 81 ÷ 3 = 3 8 1 2 Mental Working How many 3’s are in 8? 2 with 2 remaining. Record the 2 above the line. Then carry the remaining 2 over. Record the 2 next to the one making 21. Next How many 3’s in 21 = 7. Record above the 21. So 81 ÷ 3 = 27

÷ Division ~ Watch and Learn! ÷ Stage 4 ~ With remainders 1 8 r 8 224 ÷ 12 = 2 10 Regard each digit on its own. Work from left to right. 12 2 2 4 Mental Working How many 12’s are in 2? 0 with 2 remaining. Record the 0 above the line. Then carry the remaining 2 over. Record the 2 next to the two making 22. How many 12’s in 22 = 1 – Record above the 22. Next Carry the 10 and record how many 12’s in 104. Record the 8 and remember the 8 remaining. So 224 ÷ 12 = 18 r8

÷ Division ~ Watch and Learn! ÷ Stage 4 ~ With decimals 6 2 . 5 250 ÷ 4 = 2 1 . 0 2 4 2 5 0 Mental Working How many 4’s are in 2? 0 with 2 remaining. Record the 0 above the line. Then carry the remaining 2 over making 25. How many 4’s in 25 = 6 with 1 remainder. Record above the 25. Carry the 1 and record how many 4’s in 10 = 2 with 2 remaining. Select a stage. Now add a decimal point and carry the 2 making 20. How many 4’s in 20 = 5. Record above Only record to a maximum of 2 decimal places. So 250 ÷ 4 = 62.5