Column addition and subtraction LO To calculate accurately

Column addition and subtraction LO: To calculate accurately using column and partition methods. Year 4

Warm up activity 1 Th + H Example T U 6 3 9 4 2 5 5 5 8 9 8 47 Just by looking at it. Does it look correct? The Units and the Thousands are correct 9 1 The person has forgotten to carry over the ten to the hundreds column

Warm up activity 2 Th 6 H 7 Example T 2 U 4 Just by looking at it. Does it look correct? The digit in the hundreds column is correct + 2 98 1 5 2 5 7 5 The Units and the Tens Column are correct 9 The person has forgotten to carry over the hundred to the thousands

Warm up activity 3 Th H 6/ 5 1 1 - Example T U 1 5/ 4 4 2 5 2 3 4 6 2 5 Just by looking at it. Does it look correct? The Units and the Tens Column are correct because he has borrowed across 9 The person has borrowed from the Thousands column but forgot to take 1000 away leaving 6 instead of turning it to 5 The person has borrowed the ten and has changed the 5 digit to a 4

Now we shall move onto partitioning a number to help us solve this additional sum: Just like the column method we can use and split up the digits in their Hundreds, tens and Units 643 + 25 = 668 600 40 3 20 5 600 + 60 + 8

Now we shall move onto partitioning a number to help us solve this subtraction sum: Just like the column method we can use and split up the digits in their Hundreds, tens and Units 622 667 - 45 = 600 60 7 40 5 600 - 2

Which is the better method to use? Column or partitioning method? Why? 439 + 27 = 651 – 35 =

I think it would be easier to do column method for both as I need to carry over and borrow. 439 + 27 = 651 – 35 =

In the second sum I notice that in the tens columns the digits 5 and 3 do not add up to 10 or beyond and in the units or ones column, the digits 1 and 5 do not add up to or beyond 10 either. I need to use the column method for both. 450 + 27 = 651 – 35 = In the first sum I notice the tens columns, the digits are 5 and 2, they do not add up to 10 or beyond and in the units or ones column, the digits 0 and 7 do not add up to or beyond 10 either.

Fluency of thought – thinking about place value and using it quickly!! You notice that it is addition of 3 tens 567 + 30 = You then move to the tens column and make a mental note of the digit – 6 which represents 6 tens As you can see the digit has increased by 3 making the number go up by 10’s 597 6+3 =9

Fluency of thought – thinking about place value and using it quickly!! You notice that it is subtraction of 3 tens 567 - 30 = You then move to the tens column and make a mental note of the digit – 6 which represents 6 tens As you can see the digit has decreased by 3 making the number go down by 10’s 537 6 -3 =3

Complete these addition and subtract questions by choosing the efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 4 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 347 + 20 = 213 + 35 = 432 + 39 = 532 + 23 = 654 + 72 = 789 + 64 = 551 + 35 = Subtraction a) b) c) d) e) f) g) 345 - 13 = 224 - 53 = 342 – 27 = 190 – 83 = 459 – 44 = 657 – 34 = 834 – 62 =

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 4 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 347 + 20 = 213 + 35 = 432 + 39 = 532 + 23 = 654 + 72 = 789 + 64 = 551 + 35 = Subtraction 367 248 471 555 726 853 586 a) b) c) d) e) f) g) 345 - 13 = 224 - 53 = 342 – 27 = 190 – 83 = 459 – 44 = 657 – 34 = 834 – 32 = 332 171 315 107 415 623 802 ANSWERS

Which is the better method to use? Column or partitioning method? Why? 439 + 127 = 651 – 135 =

In the second sum, the digits 1 in the larger number is smaller than 5 so we have to borrow from the tens column. I need to use the column method for both. 439 + 127 = 651 – 35 = In the first sum I notice the tens columns, the digits are 3 and 2, they do not add up to 10 or beyond and in the units or ones column, the digits 9 and 7 add beyond.

Fluency of thought – thinking about place value and using it quickly!! You notice that it is addition of 5 tens As you can see the digits have increased by making the number go up by 10’s and it changes the hundreds column with an extra 1 making the 8 to a 9 867 + 150 = You then move to the tens column and make a mental note of the digit 917 COLUMN METHOD I THINK! 6 + 5 = 11

Fluency of thought – thinking about place value and using it quickly!! You notice that it is subtraction of 2 tens As you can see the digits has decreased by making the number go down but in the ones column remains the same value 457 - 220 = You then move to the tens column and make a mental note of the digit 5 237 PARTITION I THINK! 5 -2 =3 4 -2 =2

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 4 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 347 + 120 = 213 + 235 = 432 + 239 = 532 + 323 = 654 + 272 = 789 + 464 = 551 + 235 = Subtraction a) b) c) d) e) f) g) 345 - 113 = 224 - 153 = 342 – 227 = 190 – 183 = 459 – 244 = 657 – 334 = 834 – 462 =

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 4 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 347 + 120 = 213 + 235 = 432 + 239 = 532 + 323 = 654 + 272 = 789 + 464 = 551 + 235 = Subtraction a) b) c) d) e) 1253 f) 786 g) 467 448 671 855 926 345 - 113 = 224 - 153 = 342 – 227 = 190 – 183 = 459 – 244 = 657 – 334 = 834 – 462 = 232 71 115 7 235 323 372 ANSWERS

I think it would be easier to do column method for both as I need to carry over and borrow. 2, 450 + 127 = 1, 652 – 238 =

In the second sum, the digits 2 in the larger number is smaller than 8 so we have to borrow from the tens column. I need to use partition method for the first sum and I need to use the column method for the second. 2, 450 + 127 = 1, 652 – 238 = In the first sum I notice the hundreds column, the digits are 4 and 1, they do not add up to 10 and beyond; the tens columns, the digits are 5 and 2, they do not add up to 10 or beyond and in the units or ones column, the digits 0 and 7 add beyond.

Fluency of thought – thinking about place value and using it quickly!! You notice that it is additional of 2 hundred Also you will notice that it is an addition of 2 tens 2, 567 + 220 = 3, 787 As you can see the digit has increased by 2 making the number go up by 200 You then move to the third digit and find the digit 5 in the hundreds column You then move to the second digit and find the digit 6 in the hundreds column

Fluency of thought – thinking about place value and using it quickly!! You notice that it is subtraction of 3 hundred Also you will notice that it is a subtraction of 3 tens 2, 967 - 330 = 2, 637 You then move to the third number and find the digit in the hundreds column which is 9 As you can see the digit has decreased by 3 making the number go down by 30 As you can see the digit has decreased by 3 or three hundred making the digit reduces to 6 or six hundred You then move to the second number and find the digit in the hundreds column which is 6

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 2 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 1347 + 120 = 1213 + 235 = 2432 + 239 = 2532 + 623 = 2654 + 872 = 1789 + 964 = 3551 + 235 = Subtraction a) b) c) d) e) f) g) 2345 - 113 = 2224 - 153 = 4342 – 627 = 4190 – 483 = 5459 – 244 = 3457 – 534 = 3834 – 462 =

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 2 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 1347 + 120 = 1213 + 235 = 2432 + 239 = 2532 + 623 = 2654 + 872 = 1789 + 964 = 3551 + 235 = Subtraction 1467 1448 2671 3155 3526 2753 3786 a) b) c) d) e) f) g) 2345 - 113 = 2224 - 153 = 4342 – 627 = 4190 – 483 = 5459 – 244 = 3457 – 534 = 3834 – 462 = 2232 2071 3715 3707 5215 2923 3372 ANSWERS

Which is the better method to use? Column or partitioning method? Why? 2439 + 2227 = 4651 – 2155 =

In the second sum I notice that the first number each digit 655 in their place value is larger than 231. In the first sum I notice the hundreds column, the digits are 4 and 1, they do not add up to 10 and beyond; the tens columns, the digits are 3 and 2, they do not add up to 10 or beyond and in the units or ones column, the digits 9 and 7 add beyond 10. So I need to use partition method for both these sums. 2439 + 2127 = 4655 – 2231 =

Fluency of thought – thinking about place value and using it quickly!! You notice that it is additional of 1 thousand Also you will notice that it is an addition of 2 hundreds 2, 567 + 1200 = 3, 767 You then move to the first number and find the digit in the thousand column – digit is 2 As you can see the digit has increased by 2 making the number go up by 200 As you can see the digit has increased by 1 making the number go up by 1000 You then move to the second number and find the digit in the hundreds column – digit is 5

Fluency of thought – thinking about place value and using it quickly!! You notice that it is additional of 1 thousand Also you will notice that it is a subtraction of 3 hundreds 5, 567 - 1300 = 4, 267 You then move to the first number and find the digit in the thousand column – digit is 5 As you can see the digit has decreased by 3 making the number go down by 300 As you can see the digit has decreased by 1 making the number go down by 1000 You then move to the second number and find the digit in the hundreds column – digit is 5

Fluency of thought – thinking about place value and using it quickly!! You notice that it is addition of 1 thousand Also you will notice that it is an addition of 5 hundreds You then move to the third number and notice the tens unit 4, 213 + 1530 = 5, 743 So the digit 4 will move up one digit In the units or ones column 3 + 0 = 3 As you can see the digit is 3 You then move to the second digit and find the digit in the hundreds column As you can see the digit has increased by 2 making the number go up by 200 Now the digit is 4 as it has increased by ten As you can see the digit has increased by 1 making the number go up by 1000

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 2 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 1347 + 1120 = 1213 + 1235 = 2432 + 1239 = 2532 + 2623 = 2654 + 2872 = 1789 + 2964 = 3551 + 3235 = Subtraction a) b) c) d) e) f) g) 2345 - 1113 = 2224 - 1153 = 4342 – 22627 = 4599 – 2483 = 5459 – 2244 = 3457 – 2534 = 3834 – 3462 =

Complete these addition and subtract questions by choosing the most efficient method to use. PARTITION OR COLUMN METHOD (YOU CAN USE COLUMN FOR ALL BUT PARTITION JUST FOR 2 IN EACH SECTION ) Addition a) b) c) d) e) f) g) 1347 + 1120 = 1213 + 1235 = 2432 + 1239 = 2532 + 2623 = 2654 + 2872 = 1789 + 2964 = 3551 + 3235 = Subtraction 2467 2448 3671 5155 5526 4753 6786 a) b) c) d) e) f) g) 2345 - 1113 = 1232 2224 - 1153 = 1071 4342 – 2267 = 2075 4599 – 2483 = 1707 5459 – 2244 = 3215 3457 – 2534 = 923 3834 – 3462 = 372 ANSWERS

The next slides are some problem solving using partition and/or column methods.

Why? What did you do to calculate this? How would this look using place value counters? How would this look using column method?

Daniel has asked his dad to check his answer He has used the column method for the following calculation. 345 + 392 = Is Daniel correct? Explain your answer. + 345 392 637

Arian has been using the Partition method to calculate four digit numbers. Fill in the missing digits in his working out? 1233 + 2321 + 3342 = _____+ 200+ 30 + 3 2000 + ___+ 20 + ___ 3000 + 300+ __ + 2 6000 + ______+ 6

Amy and Ruth are twins and are very good at maths. They both make a calculation of the same sum, but for some reason they come up with two different answers. Is anyone right? Explain your answer. 2427 – 1249 - Amy 2427 1249 0028 Ruth 1227 1249 0028 - 1227 1249 0978

What is the missing four digit numbers for the following addition column sums? ? 6 8 + ? 3 9 ? 9 4 ? 5 9 1 + ? 5 7 ? 3 6 1 ? 6 2 1 ? 4 0 ? + 2 5 3 ? 8 ? 3 8 1 8 ? 1

ANSWERS Jack has forgotten that each column is interconnected together. Jack is wrong because if two digits together such as 3 and 9 taken from 1340 + 1920 as the hundreds add up beyond 1000 then the thousand column the digits change. 300 + 900 = 1200

ANSWERS 2 3 4 Suri answer is wrong because she has added an extra ten 3 4 5 8 -7 =1 1 5 8 9 1 5 7 9 1 + Corrected answer in red 1 2 3 4 5 4 6 8 4 1 5 7 9 + Eleanor answer is completely wrong because she has added an extra ten, forgot to add on 5 in the units or ones column, added an extra 100 and added an extra three thousands

Daniel has asked his dad to check his answer He has used the column method for the following calculation. 345 + 392 = Is Daniel correct? Explain your answer. You can see that Daniel has completed the first column correctly Now Daniel is right to write 3 in the answer section but he has forgotten to carry over into the hundred and thus the 6 should have been 7 - the answer must be 737 4 ANSWER 345 + 392 7637 1 NO

ANSWER 1730

Arian has been using the Partition method to calculate four digit numbers. Fill in the missing digits in his working out? 1233 + 2321 + 3342 =6, 896 1000+ 200+ 30 + 3 2000 + 300+ 20 + 1 3000 + 300+ 40 + 2 6000 + 800+ 90+ 6 ANSWERS

and Ruth is are twins and are very good at maths. 1. Amy answer completely wrong because she They both make a calculation of the sum, but needed to borrow a ten from the tenssame column for some reason they column) come updigit with different turning the 2 (tens to two 1 (tens) answers. Is making anyonethe right? Explain 8 your answer column), unit answer (which she. got right). 17 -9 = 8 2. This then leaves only 10 so we have to borrow Ruth copied out the from the hundreds (digit 4 turns into 3) column to first number wrong turn the 1 into 11 in the hundreds column 1227 3. Now we can calculate 11 -4 = 7 1249 4. So, 300 – 200 = 100 so she should have written 0028 1 not 0 5. Then she needed to calculate 2 -1 to write the digit 1 2427 – 1249 2427 1249 The answer should have been 1, 178 0028 ANSWERS 2227 1249 0978

What is the missing four digit numbers for the following addition column sums? 2 6 8 + 5 3 9 5 9 4 4 5 9 1 + 2 5 7 2 3 6 1 5 6 2 1 6 4 0 3 + 2 5 3 5 8 4 3 8 1 8 3 1 ANSWERS

Maths Challenge Competition Who would like to make up a maths problem for your classmates? All entries will be used in a special addition Power. Point and winners will receive a Certificate. Using the same type of questions you have been working on (slides 36 -42) you must provide the maths problem/s and the/their solution. Send your maths problem/solution with your name and class to. DJones@thrapston. net