1. MATHEMATICS Mental Subtraction

2. The aim of this powerpoint is to teach you techniques for subtracting numbers mentally. 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 Calc3b

3. Step 1: Complements to 10 Learn the complements to 10 These are the pairs of numbers which add up to 10 1 + 9or9 + 1 2 + 8or8 + 2 3 + 7or7 + 3 4 + 6or6 + 4 5 + 5 Using ‘numicon’ can help you learn quicker and visualise things in your head later on

4. Using Complements to 10 Addition and subtraction are inverse operations If you know 1 + 9 = 10 then you also know… 10 – 1 = 9and10 – 9 = 1 If you know 2 + 8 = 10 then you also know… 10 – 2 = 8and10 – 8 = 2 Using ‘numicon’ place the 10 block down and then put the block of the number you are subtracting on top. How much of the 10 block remains uncovered?

5. Step 2: Complements to 100 Learn the ‘tens’ complements to 100 These are the pairs of tens values which add up to 100 10 + 90or90 + 10 20 + 80or80 + 20 30 + 70or70 + 30 40 + 60or60 + 40 50 + 50 Don’t forget if you know the addition fact, you automatically know the linked subtraction facts too!

6. Step 3: Mental Subtraction Using a visual aid such as ‘numicon’ or number lines can help with mental subtraction. There are a number of different methods you could use for mental subtraction. The following slides demonstrate a range of techniques. Use the one(s) which you find the easiest!

7. Mental Subtraction – Method 1 Start from the first number then subtract each part of the second number separately (in either order) E.g.41 – 15 From 41, take off the 10 and then the 5 of the 15 OR From 41, take off the 5 and then the 10 of the 15… -5-10 26 31 41 41 – 10  31 – 5  26

8. Applying Complements You can apply your knowledge of complements to your method E.g. 41 – 15 To get from 41 to 40 you take off 1 leaving you another 4 units to take off and 4 from a tens value will give a value ending in 6 and then there is just one more 10 to take off -10 -4 -1 2636 40 41 In written form only… 41 – 1  40 – 4  36 – 10 = 26

9. Mental Subtraction – Method 2 Find an equivalent calculation by adding or subtracting the same amount to/from both numbers to simplify the amount being subtracted (i.e. the second number) but make sure that the difference/distance between them stays the same! E.g.41 – 15 Add 5 on to 15 (to get it to the round number of 20) Add 5 on to 41 (taking it up to 46) 46 – 20 may be easier to process = 26

10. Mental Subtraction – Compensation This method works particularly well when subtracting something ending in 9. 9 is the same as 10 – 1 so instead of subtracting 9, take off 10 then add 1 back on at the end! E.g.78 – 29 (think of 29 as linked to 30 – 1) Take 30 off the 78 (which is too many off) then add on 1 78 – 30  48 then + 1  49

11. Mental Subtraction – Compensation The same method can be used for subtracting anything ending in an 8. Simply subtract the nearest tens amount (which will be 2 too many taken off) and add 2 back on at the end. (You could do this for 7’s and 3’s etc.) E.g.85 – 18 (think of 18 as linked to 20 – 2) Take 20 off the 85 (which is too many off) then add on 2 85 – 20  65 then + 2  67

12. What next? (Page 1 of 2) If you haven’t made any notes or copied any examples out during this presentation, print out the notes called Calc3b. Read through them and make sure you answer any questions. Work through the MyMaths lesson (and then the online homework) called Mixed Sums 10s and 100s found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=AddSubtract/addSilver2&taskID=1343 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=AddSubtract/addSilver2OH&taskID=1343 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=AddSubtract/addSilver2&taskID=1343 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=AddSubtract/addSilver2OH&taskID=1343 Work through the MyMaths lesson (and then the online homework) called Subtract Single Digits found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/subtractingSingleDigits&taskID=1224 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/subtractingSingleDigitsOH&taskID=1224 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/subtractingSingleDigits&taskID=1224 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/subtractingSingleDigitsOH&taskID=1224 Continued on the next slide…

13. What next? (Page 2 of 2) Work through the MyMaths lesson (and then the online homework) called Subtraction Lines found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/subtractionLines&taskID=1055 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/subtractionLinesOH&taskID=1055 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/subtractionLines&taskID=1055 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/subtractionLinesOH&taskID=1055 Save and complete the worksheet called: EquivS-S1.xlsx Now move on to the Calc4a-PP-A powerpoint