Year 5/6: Addition May 2013

Transcription

1 Year 5/6: Addition May 2013 Method for addition: Column method Please note: start with examples that don t involve carrying and move on when appropriate For children who find addition challenging continue to make connections with the number line method = Make sure to line up the digits to illustrate place value, i.e. tens under tens and units under units. Write 368 under the number sentence Write 493 below 368. Make sure the 3 is under the 8 and the 9 tens is under the 6 tens etc. Draw 2 horizontal lines below 493 Write the plus sign to the left of 493 Start adding the units from the right 8 add 3 is 11. That is 1 ten and 1 unit Write 1 below the 3 and write a 1 for the ten above the 6 in the tens column carry the 1 Now add the tens. 6 tens plus 9 tens plus the carried 1 ten equal 16 tens Write 6 tens below 9 tens and carry the 1 above the 3 Cross out 1 as and when it has been added Now add the hundreds. 3 hundreds plus 4 hundreds plus the carried1 hundred equal 8 hundreds 368 plus 493 equals 861 Write 861 as the answer in the horizontal number sentence Adding decimal numbers =

2 Write 4.7 under the number sentence Write 2.6 below 47. Make sure the 6 tenth is under the 7 tenth and the 2 unit is under the 4 unit Draw 2 horizontal lines below 2.6 Write the plus sign to the left of 2.6 Start adding the tenth from the right. 7 tenth add 6 tenth is 13 tenth or 1.3, or one unit and three tenths. Write 3 below the 6 and write 1 above the 4 in the unit column Now add the units. 4 plus 2 plus 1 equal 7 Write 7 below 2 drop down the decimal point once the calculation has been checked and is complete Cross out 1 as and when it has been added 4.7 plus 2.6 is equal to 7.3 Write 7.3 as the answer in the horizontal number sentence Mental calculating: Check answers: In all addition calculations reflect on the calculation method and pose questions to the pupils: Can/did anyone work this out in their head? What part did you work out in your head? Did you get the same answer when you did it in your head? Jot, to help keep your mental calculations in order. How did you calculate this problem? Did you need a written method for this problem? Estimate what the answer might be before calculating Reflect on the answer getting larger when adding i.e. does this always happen? why? how? Use the inverse related number sentence to check

3 Year 5/6: Subtraction Method of subtraction: Column method For the children who are struggling to subtract they may continue to use the number line method. (see Y3 method of subtraction) Start by subtracting numbers which do not require borrowing; once consolidated, teach borrowing: = Write 47 under the number sentence Write 28 below 47. Make sure the 8 is under the 6 and the 1 ten is under the 7 tens Draw 2 horizontal lines below 18 Write the subtraction sign to the left of 18 Start subtracting the units from the right what is 6 take away/subtract 8 Cannot do it. Borrow 1 ten from the 7 tens to make the 6 units 16 units Cross out the 7 tens and replace it with 6 tens (see illustration) Now subtract 8 units from 16 units which leaves 8 units Write the 8 units underneath the 8 Now subtract the tens:6 tens subtract 1 tenequals 5 tens Write 5tens below 1 ten 76subtract 18 equals 58 Write 58 as the answer in the horizontal number sentence For decimals follow the same method and drop the decimal directly down into the parallel answer lines after calculating.

4 Mental calculating: In all subtraction calculations reflect on the calculation method and pose questions to the pupils: Can/did anyone work this out in their head? What part did you work out in your head? Did you get the same answer when you did it in your head? Jot, to help keep your mental calculations in order. How did you calculate this problem? Did you need a written method for this problem? Check answers: Estimate what the answer might be before calculating Reflect on the answer getting smaller when subtracting i.e. does this always happen? why? how? Use the inverse related number sentence to check

5 Year 5/6: Multiplication Method for multiplication: Column Method 2 digit number X 1 digit number: Teach the column method without carrying initially to consolidate process. Once pupils are confident introduce carrying. 43 x 3 = x Set out the calculation as above making sure the digits are placed correctly below one another according to place value Write the times sign to the left of the bottom digit Start by multiplying the units: what is 3 multiplied by 4? Write the 2 units in the units column and carry the 1 ten into the tens column above the 4 tens Now multiply the tens by 4: What is 4 multiplied by 4 (40) 16 tens plus the 1 ten is 17 tens? Write the 7 tens in the tens column and the 1 hundred in the hundreds column Write 172 as the answer in the horizontal number sentence. NB: When pupils are ready, practice 3 digit numbers multiplied by one digit number For multiplying decimals, pupils count the decimal places altogether then apply the decimal point to the answer with the same total amount of decimal places x thetwo numbers multiplying have 1 decimal place altogether therefore bring in the 1 decimal place to the answer discussion must be had around ten times smaller/greater as appropriate i.e. we have made 4.3 ten times greater to multiply (by ignoring the decimal point) so we must make the answer ten times smaller x.4 1.7_2 the numbers have 2 x1 decimal places altogether therefore bring in the 2 decimal places to the answer 2 digit number X 2 digit number:

6 43 x 58 = x Set out the calculation as above making sure the digits are placed correctly below one another according to place value Write the times sign to the left of the bottom digit Start by multiplying the units: what is 8 multiplied by 3? 24 Write the 4 in the units column and carry the 2 tens into the tens column above the 4 tens Now multiply the unit by the tens: What is 8 multiplied by 4(make pupils clear this is 40 not 4)? 32 (320) plus the 2 tens is 34 (340). Once the carried digit is used cross it out. Write the 4 tens in the tens column and the 3 hundreds in the hundreds column Write a zero (place holder) in the units column to show that you are now multiplying a ten. What is 5 (50) multiplied by 3? 15 (150). Place the 5 tens in the tens column and carry the 1 in the hundreds column. What is 5 (50) multiplied by 4 (40)? 20 (20 hundreds or 2000). Add the 1 (100) carried to make 21 (2100) and put the 1 in the hundreds column and the 2 in the thousands column. Add down as in a normal column addition. For multiplying using decimals leave the decimal places until the calculating is completed and checked then pupils count the decimal places altogether then apply the decimal point to the answer with the same total amount of decimal places x In order to place the decimal point correctly in the answer pupils must add up the decimal places (d.p.) altogether in the numbers being multiplied. 2 d.p + 1d.p. = 3 d.p. The answer must have 3 d.p.

7 Mental calculating: Check answers: In all multiplication calculations reflect on the calculation method and pose questions to the pupils: Can/did anyone work this out in their head? What part did you work out in your head? Did you get the same answer when you did it in your head? Jot, to help keep your mental calculations in order. How did you calculate this problem? Did you need a written method for this problem? Estimate what the answer might be before calculating Reflect on the answer getting larger when multiplying i.e. does this always happen? why? how? Use the inverse related number sentence to check

8 Year 5/6: Division Method for division: Short division 58 4 = 14 r 2 / r2 4 ) Pupils set out the short division calculation as above Start by saying: how many groups/lots/4s are there in 5 (50)? There is 1 (10) lot/s of 4 in 5 (50) with 1 (10) left over. Write the 1 lot of 4 above the 5. Add the 1 ten to 8 units to make 18 units. How many 4s are there in 18? 4. Write the 4 above the 18. Remainder 2 The answer 14 r2 should e written in the number sentence For a decimal remainder _1_ ) carry the 2 remainderbelow placing it next to the 8 units. Place a decimal point above (in the answer) to show the place value of the 2 is a tenth. 4 cannot go into 2 tenths: add a 0 to make it 20 hundredths. How many 4s in 20? 5. Place the 5 above the 20. The answer 14.5 should be written in the number sentence For two digit divisors use a chunking number line (see year 4) or long division = 31 r9 31r9 43 is the divisor 43) is the dividend How many 43s are there in 1? None. 13? None.134? 3. Put the three above the 4. Multiply 43 by 3 to make 1290 and take it away from the original dividend as shown.

9 How many 43s in 52? 1. Place the 1 above the 2 and multiply 43 by 1. Put the answer underneath the 52 and subtract is 9, which becomes the remainder. The easiest way to remember how to divide with decimals is to remember that 150 is the same as With decimal remainders: pupils round to the nearest 1 or 2 d.p = ) and so on How many 43s are there in 1? None. 13? None. 134? 3. Put the three above the 4. Multiply 43 by 3 to make 1290 and take it away from the original dividend as shown. How many 43s in 52? 1. Place the 1 above the 2 and multiply 43 by 1. Put the answer underneath the 52 and subtract is cannot go into 9 so place a decimal point after the answer31 and add a 0 to 9 to make 90. How many 43s in 90? 2. Place the two behind the decimal point and multiply 43 by 2. Place the answer underneath the 90 and subtract, which leaves 4. How many 43s are there in 4? 0. How many 43s are there in 40? 0. Put the 0 next to the 2 in the answer and add a 0 to 40 to make 400. How many 43s are in 400? multiplied by 9 is 387. Place this underneath the 400 and subtract to make 13. This process can be infinite so the pupils must be asked to answer rounded to 1 or 2 decimal places.

10 Mental calculating: Check answers: In all division calculations reflect on the calculation method and pose questions to the pupils: Can/did anyone work this out in their head? What part did you work out in your head? Did you get the same answer when you did it in your head? Jot, to help keep your mental calculations in order. How did you calculate this problem? Did you need a written method for this problem? Estimate what the answer might be before calculating Reflect on the answer getting smaller when dividing i.e. does this always happen? why? how? Use the inverse related number sentence to check 14.5 x 4