Calculations Policy. A shared document between parents and teachers.

Transcription

1 Calculations Policy A shared document between parents and teachers. R. Fairgrieve November

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3 Introduction This calculations policy takes into account the changes in the curriculum since September It is intended to be used as a document between teachers and parents, to support the teaching of formal written methods in addition, subtraction, multiplication and division. It is set out in year group expectations with the expectation that most pupils will achieve this at broadly the same pace. However, as teachers and parents we know that this is not always the case and children s understanding and readiness will be taken into account. Parents, we hope you find this document useful. If there are any questions you want to ask, please don t hesitate to contact your child s teacher or myself. In class, teachers use Steps to Success. Essentially, for Maths, these are the processes (the steps) which need to be completed to complete the task successfully. At Kirk Sandall Junior School, we expect high standards of presentation across all subjects. The importance of setting work out neatly in Maths is of the uppermost importance. For this reason, we use squared paper and insist on placing one digit per box. Where a decimal is needed, it should be placed in its own square and column. Mr Fairgrieve Maths Subject Leader. 3

4 Year 3 What the national curriculum says: Add numbers up to three digits, using formal written methods Steps to success: 1. Add together the numbers in the ones column. 2. Add together the numbers in the tens column 3. Add together the numbers in the hundreds column. It is important for the children to remember the place value of each of the numbers: adding the ones together is 5+4. adding the tens together represents adding adding the hundreds together represents adding

5 Children who are confident with this method can progress onto carrying Steps to success: 1. Add together the numbers in the ones column. If the answer is above 10, carry the ten, placing a 1 below the line in the tens column. 2. Add together the numbers in the tens column and the number carried previously. Cross out the carrying once added so that you know you have added it. 3. Again, carrying below the line if necessary. 4. Add together the numbers in the hundreds column and any that have been carried. Again, cross out any carried numbers to remind yourself that it has been added. 5

6 Year 4 What the national curriculum says: Add numbers up to four digits, using formal written methods. T , Year 5 What the national curriculum says: Add together more than four digits, using formal written methods. 10Th T , Use the steps to success shown on the previous page. 6

7 Children who are confident with these methods, will then progress to adding decimals, using the same principles as shown earlier. The decimal point has a box of its own. T O. T H T = Tenths H = Hundredths Year 6 What the national curriculum says: Solve problems involving addition. This should encompass all over the methods above, and should include: Adding more than two numbers together, Adding together more than two numbers of different sized digits, Adding together more than two decimals, Adding together decimals and whole numbers. Examples 10Th T ,

8 When adding decimal numbers together, it is essential that all the digits are place in the correct columns. 10Th T. T H

9 Year 3 What the national curriculum says: Subtract numbers up to 3 digits, using formal written methods Steps to success: 1. The largest number must always be on the top. 2. Starting with the ones column, subtract the bottom digit from the top digit. 3. Moving to the tens column, subtract the bottom digit from the top digit. 4. And finally, in the hundreds column, subtract the bottom digit from the top digit. 9

10 Children who are confident with this method can progress on to taking Steps to success: 1. Subtract 8 from 5 (or 5 8). As this is not possible, we need to take 10 from the tens column by placing a 1 next to the 5. This number is now 15. ( = 15). 2. Subtract 8 from 15 = 7. Place this number in the ones column. 3. Subtract 6 from 2 (or 2-6. Remember that this is actually 60 from 20 or 20-60). We can t do this, so we need to take from the hundreds column. 4. Now, we can subtract 6 from 12 (again, remembering that this actually represents 60 from 120). Place the answer in the hundreds column. 5. Now subtract 2 from 8, (remembering this is representing 200 from 800). Place the answer in the hundreds column. Year 4 What the national curriculum says: Subtract numbers up to 4 digits, using formal written methods. Examples T

11 Years 5 & 6 What the national curriculum says: Subtract numbers more than 4 digits, including decimals, using formal written methods. Examples T. t h Tougher examples T Note: In the above example, you cannot take 8 from 2. So, like before you need to take 10 from the tens column. However, because this has no value, you then have to go to the hundreds column and take from there so that the tens column has value. Now you can take from the 10 column for the ones. 11

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13 Year 3 What the national curriculum says: Begin to multiply a 2 digit number by a 1 digit number, using formal written methods. In multiplication, children complete an intermediate stage before progressing to a shortened version of multiplication, in order for them to understand the why it is being done in this way. Intermediate stage: 3 2 x 4 8 (4 x 2) (4 x 30) Steps to success: 1. Multiply the bottom one by the top one, placing the full answer below the line. 2. Now multiply the bottom one by the full value of the tens (in this case 4 x 30), placing the answer under the previous answer. 3. Add the two together for the final answer. 13

14 Short multiplication: 3 2 x Steps to success: 1. Multiply the bottom one by the top one (in this example 4 x 2). 2. Place the answer in the ones column. 3. Multiply the bottom one but the tens (3 x 4. However, remember this actually represents 4 times 30). 4. Place the numbers in the correct columns. Children who are confident with this method can progress on to carrying x Steps to success: 1. Multiply the bottom one by the top one (in this example, 3 x 8 = 24). 14

15 2. As the answer is above 10, place the one in the ones column (the 2) and carry the 2 (20) above the tens number. (Note: This is different from addition and subtraction where we carry below the line). 3. Multiply the bottom one but the tens (in this example, 3 x 2. However, remember this actually represents 3 times 20). 4. Add the 2 which you carried before, crossing it out when counted. 5. Place the numbers in the correct columns. Year 4 What the national curriculum says: multiply a 3 digit number by a 1 digit number, using formal written methods. Note: Some children in year 4 may need to go back to the intermediate stage before progressing to 3 digits multiplied by 1. T x T x

16 Year 5 What the national curriculum says: Multiply 4 digits by one digit. Multiply 2 digits by 2 digits Begin to multiply 4 digits by 2 digits, all with formal written methods. Intermediate stage: Children in year 5 revisit in the intermediate stage to understand the methodology. T 2 2 x (3 x 2) 6 0 (3 x 20) 4 0 (20 x 2) (20 x 20) Steps to success: 1. Multiply the bottom one by the top one (3 x 2 in this example), placing the full answer below the line. 2. Multiply the bottom one by the top ten, placing the full answer below the previous answer. 3. Multiply the bottom ten by the top one (20 x 2 in this example), placing the full answer under the previous answer. 4. Multiply the bottom ten by the top ten (20 x 20 in this example), placing the full answer under the previous answer. 5. Add all the answers together for the final answer. (Note: because we are adding the answers together here, we go back to carrying below the line). 16

17 Short Multiplication: T 2 2 x (3 x 22) (20 x 22) Steps to success: 1. Multiply the bottom one by the top one (3 x 2 in this example). 2. Multiply the bottom one by the top ten (3 x 2 in this example). 3. Place a 0 (a place holder) in the ones column on the 2 nd line. 4. Multiply the bottom ten by the top one. 5. Multiply the bottom ten by the top ten. 6. Add both answers together. 17

18 Children who are confident with this method can progress on to carrying. T x (5 x 56) (30 x 56) Steps to success 1. Multiply the bottom one by the top one carry above the tens number. 2. Multiply the bottom one by the top ten and add anything which has been carried over. (Cross any carrying out once it has been added to avoid any confusion later) 3. Place a 0 (a place holder) in the ones column on the 2 nd line. 4. Multiply the bottom ten by the top one if anything needs to be carried, do so above the tens number. 5. Multiply the bottom ten by the top ten adding any that have been carried over. 6. Add both answers together. 18

19 T x (6 x 234) (30 x 234) th T x (7 x 3343) (40 x 3343) 1 5 7, Year 6 What the national curriculum says: Have a firm understanding of multiplying 4 digits by 2 digits, using formal written methods (see above). 19

20 Years 4 & 5 What the national curriculum says: Divide numbers up to 4 digits by one digit using a formal written method. Bus Stop method Steps to success: 1. Draw the bus stop (black lines) 2. Place the number you re dividing by on the left of the bus stop. 3. Place the number you re dividing on the inside of the bus stop. 4. How many times does the number you re dividing by go into the first digit? Write it above the line? 5. How many times does it go into the second digit? Write it above the line. 6. How many times does it go into the third digit? Write it above the line. 7. Finally, how many times does it go into the fourth digit? Write it above the line. 20

21 Division involving carrying and remainders:* r Steps to success: 1. Draw the bus stop (black lines) 2. Place the number you re dividing by on the left of the bus stop. 3. Place the number you re dividing on the inside of the bus stop. 4. How many times does the number you re dividing by go into the first digit? Write it above the line. If there is a remainder, place the value of the remainder next to the next number. The remainder and the next number make the next number to be divided by (17 in the example above). 5. How many times does it go into the second digit? Write it above the line. 6. Repeat the same process with remainders if necessary. 7. If there is a remainder left at the end of the calculation then it should be written as a tiny r with the number next to it (as above). 21

22 Year 6 What the national curriculum says: Divide numbers up to 4 digits by a 2 digit number using a formal written method. Bus Stop method:* r Children may find it useful to write the the multiples of 12 at the side of the calculation to help them. *The two examples show the top of the bus stop between two lines on the squared paper. When children draw it in their books it should be completed like the diagram below: 22