1. MATHEMATICS Division – Mental Methods

2. The aim of this powerpoint is to teach you further techniques for dividing 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) and work through the MyMaths lessons listed. OR At the end of the powerpoint, printout the notes called Calc7b

3. Halving Start with the biggest value column and move to the right. Halve each digit but be careful, if any answer has a remainder of 1, put it in front of the next digit to be halved. E.g.268 ÷ 2  halve 2 (hundreds)  1 halve 6 (tens)  3 halve 8 (units)  4= 134 E.g.496 ÷ 2  halve 4 (hundreds)  2 halve 9 (tens)  4 + remainder/carry 1 halve 1 6 (units)  8= 248

4. Practice Halving Work through pages 6 to 8 of the MyMaths lesson called Doubling and Halving found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/doubles&taskID=1023 Complete the MyMaths online homework called Doubling and Halving found at: http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/doublesOH&taskID=1023 If you want some more practice, use the halving mix ‘n’ match cards or the doubling double-sided cards – you can find these documents to save, print out and cut up on the VLE website.

5. Dividing by 4 or by 8 If you are good at halving then… Dividing by 4 is halving TWICE E.g.596 ÷ 4 596 halved  298 halved = 149 Dividing by 8 is halving THRICE (i.e. three times) E.g.1000 ÷ 8 1000 halved  500 halved  250 halved = 125 Save and complete the worksheets called 4Times.xlsx and 8Times.xlsx

6. Dividing by 10 – Whole Numbers This trick ONLY works for whole numbers ending in zeros! Knock a zero off the end of the number you are dividing by 10. E.g.80 ÷ 10 = 8 E.g.5200 ÷ 10 = 520 E.g. 7040 ÷ 10 = 704

7. Dividing by 100 – Whole Numbers This trick ONLY works for whole numbers ending in zeros! Knock two zeros off the end of the number you are multiplying by 100. E.g.800 ÷ 100 = 8 E.g.52000 ÷ 100 = 520 E.g. 70400 ÷ 100 = 704

8. Dividing any number by 10, 100… When we are dividing by 10, we are decreasing every part of the number tenfold which moves each digit one column to the right (to see this in whole numbers you have to knock a zero off the units column!) When we are dividing by 100, we are decreasing every part of the number a hundredfold which moves each digit two columns to the right (which is seen in whole numbers by knocking two zeros off the tens and units columns!). When we are dividing by any power of 10 (e.g. 1000, 10000, 100000 and so on), however many zeros comes after the 1 tells you by how many columns the digits in the original value will move to the right.

9. Effect on Integers & Decimals The effect of moving digits in whole numbers to the right means that the columns on the left become empty and we may also have to write a point and move into the decimal columns. E.g.73000 ÷ 1000 = With decimals the digits simply move to the right (or the decimal point looks like it moves to the left!). E.g.47.6 ÷ 100 = TTh Th H T U 7 3 0 0 0 (original value) 7 3 0 0( ÷ 10) 7 3 0( ÷ 100) 7 3( ÷ 1000) 3 zeros after the 1 so move digits 3 columns to the right 73 H T U. t th h th 4 7. 6 (original value) 4. 7 6( ÷ 10) 0. 4 7 6( ÷ 100) 2 zeros after the 1 so move digits 2 columns to the right 0.476

10. Practice Dividing by 10 and 100 Work through the MyMaths lesson (and then the online homework) called Multiplying by 10 found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiplyby10Part1&taskID=1368 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiplyby10Part1OH&taskID=1368 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiplyby10Part1&taskID=1368 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiplyby10Part1OH&taskID=1368 Work through pages 6 to 9 of the MyMaths lesson (and then the online homework) called Dividing by 10 and 100: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/divideBy10&taskID=1392 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/divideBy10OH&taskID=1392 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/divideBy10&taskID=1392 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/divideBy10OH&taskID=1392 Save and complete the ByTen-S0b.xlsx worksheet.

11. Dividing by 20 This trick ONLY works for whole numbers ending in zeros! Knock a zero off the end of the number then halve it. E.g.160 ÷ 20  16  halved  8 E.g.1040 ÷ 20  104  halved  52 E.g. 14080 ÷ 20  1408  halved  704

12. Dividing by 5 or 50 To divide by 5… Divide the value by 10 first (by knocking a zero off the end) then double that answer OR double the value then knock a zero off the end. E.g.210 ÷ 5  21 doubled = 42 E.g.1600 ÷ 5  160 doubled= 320 To divide by 50… Divide the value by 100 first (by knocking two zeros off the end) then double that answer OR double the value then knock off two zeros. E.g.2400 ÷ 50  24 doubled = 48 E.g.37000 ÷ 50  370 doubled= 740

13. Practice Dividing by 20, 5 or 50 To practice, you could use the ‘Multiples of 5’ double- sided cards and/or the ‘Multiples of 50’ double-sided cards. Save and complete the worksheet called 5and20D.xlsx

14. Equivalent Calculations Equivalent division calculations can be found by multiplying or dividing BOTH values by the same amount. However, you should only do this if it is going to make the equivalent calculation easier to do! I find it easier to divide by 2 or 10 or 100 so… E.g. 1600 ÷ 25E.g.104 ÷ 4 6400 ÷ 100 = 64 52 ÷ 2 = 26 Save and complete the EquivD1.xlsx worksheet × 4 x 4 ÷ 2 ÷ 2

15. What next? If you haven’t made any notes or copied any examples, questions and answers out during this presentation, print out the notes called Calc7b. Read through them and make sure you answer any questions. Please ensure you have worked through all the MyMaths lessons and online homeworks identified throughout this powerpoint and for further practice use the additional resources (such as mix and match cards etc.) also listed. Please ensure you have saved and completed all the worksheets listed (and emailed them to the VLE teacher). Now move on to the Calc6a-ShortM powerpoint