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MATHEMATICS Short Multiplication

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The aim of this powerpoint is to teach you pencil & paper methods for multiplying large numbers by a single digit. 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 Calc6a

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Traditional Method Write the largest value on the top and the single digit on the bottom; Working from right to left, multiply each of the digits in the top number by the bottom digit; If any product comes to more than 10, carry the tens value into the next column and add it on to the next product.

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Example 9 × 384 Step 1: Write 384 on top Write 9 underneath it Line up numbers in the correct column values, i.e. from right to left 3 8 4 × 9

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Example 9 × 384 3 8 4 × 9 Step 2: From right to left multiply each top digit (4 then 8 then 3) by the 9 3 6

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Example 9 × 384 3 8 4 × 9 7 3 6 5 Step 3: Remember to add any ‘carry’ values on to the next product

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Example 9 × 384 3 8 4 × 9 7 3 6 5 Step 4: Remember to check your answer is sensible by doing a rounded calculation in your head 9 x 400 = 3600 3 4

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Grid / Area Method Draw a rectangle and split it into as many columns as there are digits in the larger number; Partition the larger number separating its hundreds, tens, units etc. and write each above each column of the split rectangle; Write the single digit on the left hand side of the rectangle; Multiply each component part by the single digit and put the answer in to each part of the rectangle; Add all the values inside the grid to find your answer.

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2 Examples of same question 69 × 7 (Split 69 into 60 + 9) × 60 9 742063= 483 69 × 7 (Split 69 into 70 – 1) × 70 – 1 7490 – 7 = 483 Mental check: The actual answer will be slightly less than 70 × 7 = 490

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Gelosia Method Draw a grid which is 1 row by the number of columns equal to the number of digits in the biggest number. Draw UPHILL diagonal lines (bottom left to top right) in every square of the grid. Write the largest number across the top (1 digit above each column) and the smallest number down the right hand side. Multiply each pair of digits together putting the tens value in the right half and the units value in the left half of each square of the grid Once the grid is completely filled in, add down the diagonals to get the final answer (see example on next slide).

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Example 9 × 384 38 4 9 × 2 7 7 2 6 3 4 83 9

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Example 9 × 384 38 4 9 × 2 7 7 2 6 3 6 3 4 5 1 Mental Check: The actual answer will be less than 10 x 384 = 3840

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Practice Showing all your workings in your books (using whichever method you prefer), work out the answers to the following calculations, and after each, show what mental calculation you used to check your answer! 1)26 × 8 = 2)35 × 7 = 3)4 × 81 = 4)6 × 94 = 5)237 × 9 = When you have worked out your answers, move on to the next slide and mark your work.

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Answers 1)26 × 8 = 208 (Check: It will be less than 30 x 8 = 240) 2)35 × 7 = 245 (Check: It will be between 30 x 7 = 210 and 40 x 7 = 280) 3)4 × 81 = 324 (Check : It will be more than 4 x 80 = 320) 4)6 × 94 = 564 (Check : It will be more than 6 x 90 = 540) 5)237 × 9 = 2133 (Check : It will be less than 237 x 10 = 2370) 2 6 x 8 2 0 8 4 x 30 5 7 210 35 210 + 35 = 245 8 1 x 4 3 2 4 3 9 4 x 5 4 2 4 6 __________ 5 6 4 2 3 7 x 9 2 1 3 3 2 3 6

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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 Calc6a. Read through them and make sure you answer any questions. Work through the MyMaths lesson (and then the online homework) called Multiply Single Digit found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiply1&taskID=1024 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiply1OH&taskID=1024 http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiply1&taskID=1024 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiply1OH&taskID=1024 Save and complete the worksheet called ShortM-S1.xlsx Now move on to the Calc6b-LongM powerpoint

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