When I started volunteering in my local primary school in 2002, one thing I missed almost immediately was a set of scientific calculators. Over the years, I have taken note of times when such calculators were on some sort of offer in local shops – and have bought a few at a time for the school. What follows are a few reasons why I find them so useful in educating primary students.
The first example is about something I started in the secondary school where I spent most of my teaching career. It was a small school and each year we held a parents’ evening where each department could talk to the potential Year 7 parents and students about what the department could offer. Some departments, of course, produced wonderful displays of their work. What I chose to do, as Head of Maths, was to put out a couple of non-scientific and a couple of scientific calculators and a note which said in large print
What is 1 + 2 × 3 ?
When parents and students sat down and asked about the note, I handed the student a scientific calculator and the parents a non-scientific calculator. Before allowing them to use the calculators, I asked them for the answer to the question. Naturally, the usual answer was 9. When I asked them to check the answer on their calculators what happened, of course, was that the parents got the answer 9 – and the student got the answer 7!
This then prompted a discussion about why the answers were different. I told them that the non-scientific calculators simply worked left to right, so that once the calculator “saw” 1+2, it wrote3 for the sum even before it multiplied by the 3. The scientific calculator had no problem with 2-stage operations so it waited until the question was completed before working out in proper mathematical order – which is, basically, work out × and ÷ before + and -.
Therefore when I am working with a whole class in the primary school, I have at times given each pair of students one scientific and one non-scientific calculator. I will then ask them to try to work out things like 1+2×3 or 10-6÷2 before using their calculator to check. Because each pair of students gets a different answer on their calculator, it provokes a discussion before the correct answer 7 in each of the examples is agreed upon.
A second example came up just last week while working with groups of 5 or 6 students from Years 5 and 6 when the topic to be covered was the connection between fractions, decimals and percentages. I had prepared a sheet of “odd one out” questions, where each question contained a fraction, a decimal and a percentage but one did not have the same value as the other two – and the students had to decide in each question which was the odd one out.
I followed this by collecting the students together so that they could clearly see the screen on my scientific calculator. I told them that the calculator gave answers as fractions and asked, for example, what would the calculator say if I put in 0.8 and pressed the = sign? Some said 8/10 which I said was not wrong – but the calculator would simplify it and we agreed on the answer 4/5. When I pressed =, that’s what came up. Then I put in the fraction 4/16. Some said 2/8 and we then had a conversation about the fact that the calculator would find ALL the common factors between top and bottom - so that we came up with ¼ - which is what I confirmed by pressing =.
So now we had tried a fraction and a decimal, so the next stage what to put in 76% and discuss what the calculator would say when I pressed =? They were happy to describe 76% as 76 out of a hundred but, of course, became suspicious that it would not give 76/100 as the answer! We did agree, even before I pressed =, that it would give 19/25. I then pointed out that there was a button to press which converted the answer to a decimal and it was easy to agree that that answer would be 0.76.
After a few such examples, with their understanding – and, more significantly, their interest – gaining with each answer, I thought it was time to throw in a slightly different example. I put 8÷9 into the calculator – easy enough, it simply came to 8/9. But, I asked, what would the decimal button give? I clicked on the button that converts to a decimal, and asked them to look closely and see what they found. What they saw was a little dot over the 8 (which I don’t know how to get on my computer !!). I explained that it meant 0.8 recurring and, interestingly, if you pressed the decimal sign again, it gave 0.8888888889. This naturally prompted a discussion as to why the 9 was on the end. We then had a discussion about recurring decimals and also about rounding, so the calculator had allowed me to help strengthen their understanding of the connection between fractions, decimals and percentages while also bringing up recurring decimals and rounding... and STILL retaining their total interest.
One other conversation I had with students recently was about the Lottery. Since I’ve never played the Lottery, I asked some students how many numbers there were these days to choose from, knowing it had gone up from 49? One student told me 56 – I’ve just checked and I gather it’s actually 59. In the lesson, I showed the students how the scientific calculator could tell me how many ways there were of picking 6 numbers from 56. The answer was just under 32½ million. Now that I know the actual number is 59, I’ve just found that the real number of different possible answers is just over 45 million.