Addition Using Pencil & Paper Methods Mathematics Addition Using Pencil & Paper Methods

The aim of this powerpoint is to teach you pencil & paper methods for adding large numbers and decimal numbers. EITHER Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along) OR At the end of the powerpoint, printout the notes called Calc4a

Pencil & Paper – Whole Numbers For small numbers, you should be able to add these in your head or jot down things to help (such as match up complements to 10 etc.) For larger numbers you will need to use ‘pencil & paper’ methods which involving writing the numbers in columns (one on top of the other). When you write them in columns MAKE SURE that the correct column values of each number all match up – i.e. all the units values should be in one straight column. It might help to write Th H T U etc. out and then write the numbers below these column value headings.

Carrying… Starting from the smallest column on the RIGHT, add the column of digits up and write the answer below the column between the answer lines. However, if the total comes to more than 10… …write the units digit beneath the column you have just added up (between the answer lines) and the tens digit beneath the answer line of the NEXT column of digits. Now move to the left and repeat, adding up each column of digits including any carried over values written below the answer line.

Mental check using rounded numbers for 37 and 42: Example 1 Lets do: 37 + 42 Step 2: add the units column first  Step 3: add the tens column next  Step 1: write them in column form  37 + 42 37 + 42 37 + 42 7 9 There were no carries for this example. Mental check using rounded numbers for 37 and 42: 40 + 40 = 80 which is close to 79!

Example 2 Lets do: 326 + 418 H T U 3 2 6 + 4 1 8 3 2 6 + 4 1 8 3 2 6 + 4 1 8 3 2 6 + 4 1 8 Step 3: add the tens column next  Step 1: write them in column form  Step 2: add the units column first  Step 4: now add the hundreds column  7 4 4 There was a carry for this example but there could be more than just one and also more than two numbers to add up! 1 Mental Check using rounded numbers for 326 and 418: 300 + 400 = 700 which is in same size bracket as 744!

Example 3 – Last one!!! Lets do: 8027 + 659 + 1028 Th H T U First write them in column form  8 0 2 7 6 5 9 + 1 0 2 8 ________ Next add each column (RIGHT to left). Try to work this out on paper before clicking to move on to the next slide. Remember to mentally check that your answer makes sense using ‘rounded’ values!

Example 3 – Answer Th H T U 8 0 2 7 6 5 9 + 1 0 2 8 9 7 1 4 2 6 5 9 + 1 0 2 8 2 Check by adding rounded numbers for 8027, 659 and 1028 in your head: 8000 + 700 + 1000 = 9700 The answer should be about 9700 and it is, it’s 9714! 9 7 1 4 1

Practice Showing your workings, in your books work out the answers to the following calculations. At the end of each one show what mental calculation you used to check your answer! 1) 51 + 47 =   2) 26 + 67 = 3) 58 + 75 = 4) 214 + 37 = 5) 26 + 359 = 6) 408 + 247 =   7) 683 + 247 = 8) 2651 + 4908 = 9) 3792 + 6804 = 10) 82 + 2836 + 751 =

Answers 1) 51 + 47 = 98 (Check: 50 + 50 = 100) 2) 26 + 67 = 93 1) 51 + 47 = 98 (Check: 50 + 50 = 100)   2) 26 + 67 = 93 (Check: 30 + 70 = 100) 3) 58 + 75 = 133 (Check: 60 + 80 = 140) 4) 214 + 37 = 251 (Check: 210 + 40 = 250) 5) 26 + 359 = 385 (Check: 30 + 360 = 390) 6) 408 + 247 = 655 (Check: 400 + 200 = 600)   7) 683 + 247 = 930 (Check: 700 + 200 = 900) 8) 2651 + 4908 = 7559 (Check: 3000 + 5000 = 8000) 9) 3792 + 6804 = 10596 (Check: 4000 + 7000 = 11000) 10) 82 + 2836 + 751 = 3669 (Check: 100 + 2800 + 800 = 3700)

What next? If you haven’t made any notes or copied any examples, questions and answers out so far, print out the notes called Calc4a. Read through them and make sure you answer any questions on adding integers or whole numbers. Work through the MyMaths lesson (and then the online homework) called Adding in Columns found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/addingColumns&taskID=1020 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/addingColumnsOH&taskID=1020 Save and complete the worksheet called IntA-S1.xlsx Now continue with the rest of this powerpoint…

Pencil & Paper – Decimals The pencil & paper methods for adding decimal numbers is the same as for adding whole numbers but you must be especially careful when writing the numbers in columns. MAKE SURE that the correct column values of each number all match up – i.e. all the units values should be in one straight column, the decimal points should be lined up and so on… Remember that whole numbers can have a decimal point written immediately after them. You may also like to line them up on the right hand side by adding extra zeros on the end (AFTER the decimal point).

Example Check your answer seems sensible using rounded values in a mental calculation… 10 + 30 + 8 = 48 Lets do: 13.56 + 25 + 7.8 First write them in column form  1 3 . 5 6 (Line up the columns carefully) + 2 5 (Inserting decimals and extra zeros helps) 7 . 8 Now add columns from right to left… …adding any ‘carries’ on to the next column. . 0 0 4 6 . 3 6 1 1

Practice Showing your workings, in your books work out the answers to the following calculations. At the end of each one show what mental calculation you used to check your answer! 1) 3.8 + 24.7 =   2) 0.026 + 3.67 = 3) 5.809 + 7.05 = 4) 2.1854 + 37.3 + 18 = 5) 12.608 + 35.0992 =

Answers 1) 3.8 + 24.7 = 28.5 (Check: 4 + 20 = 24)   2) 0.026 + 3.67 = 3.696 (Check: 0.03 + 4 = 4.03) 3) 5.809 + 7.05 = 12.859 (Check: 6 + 7 = 13) 4) 2.1854 + 37.3 + 18 = 57.4854 (Check: 2 + 40 + 20 = 62) 5) 12.608 + 35.0992 = 47.7072 (Check: 10 + 40 = 50)

What next? If you haven’t made any notes or copied any examples, questions and answers out during the second half of this presentation, print out the notes called Calc4a. Read through them and make sure you finish answering all the questions. Work through the MyMaths lesson (and then the online homework) called Adding Decimals in Columns Intro at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=decimals/decimalStartAdd&taskID=1381 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=decimals/decimalStartAddOH&taskID=1381 Save and complete the worksheet called DecA-NS1.xlsx Now move on to the Calc4b-PP-S powerpoint