EDUC4105

If we read pages 10 to 19 of a book are we reading 9 pages? Well the answer is no! We are reading 10 pages. People commonly do the sum 19-10 and conclude that 9 pages have been read. What about if you are asked to read pages 1 to 9 of a book? I think most would realise straight away that they were about to read 9 pages but 9 – 1 = 8 not 9. So why does subtraction give us the wrong answer?

The answer lies in whether the first digit is included in the sum. For instance if we have the set of numbers 1,2,3,4,5,6 and we take away two of the numbers lets say 5 and 6. We end up with the set of numbers 1,2,3,4 thus we have 4 numbers left over, 6 – 2 = 4. So the subtraction method works. However if we start counting from the number 2 and end at the number 6 we get 2,3,4,5,6. Notice that we have 5 numbers not 6 – 2 = 4 numbers. This is because we included the number 2 in our count. We needed to add 1 to our final solution.

This sort of thing causes problems all the time with students. The following are situations relating to the subtraction problem:

• Reading pages of a book.

• When trying to draw fractions like 3/8 using a bar they commonly draw 8 lines in the bar rather than 7. Thus they end up with the fraction 3/9.

• If you need to build a fence 1000 metres long and you need to have a fence post every 10 metres how many fence posts do you need?

Students need to see the potential for mistakes in using subtraction. They need to think about whether there is an extra digit that needs to be included in the solution.

This entry was posted on Wednesday, April 2nd, 2008 at 1:57 am and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.