Roughly speaking...the importance of estimation
Post date: Aug 14, 2014 10:13:04 AM
I’m sure you can all identify with this scenario…
There’s a calculation on a book, board etc., and you ask your class to estimate the answer. Instead of estimating, most children will try to calculate the answer and give you the exact answer. Others, realising that giving the exact answer will reveal that they did in fact calculate it, will adjust their calculation slightly, to make it look like they estimated and were amazingly close to the actual answer!
Either way, they’re missing the whole point… estimating is supposed to be a quick response, an approximate or a “ball-park” figure as the Americans would say, that gives you an idea of how the answer should look, and allows you to check the reasonableness of your answer at the end.
In the Mathematics Teacher Guidelines, on pages 32 & 33, the following Estimation Strategies are listed and explained:
· Front-end strategy
· Clustering strategy
· Rounding strategy
· Special numbers strategy
And while I agree with many of the statements from this section of the Teacher Guidelines, again I feel that it too is missing the main point…estimation needs to be a quick activity; it shouldn't take as long to do as the actual calculation itself. And I don’t feel that has been emphasised strongly enough in those pages, or in maths textbooks.
So now I’ll explain what are my TOP Estimation Strategies.
Reasonableness of answer:
What would be a reasonable answer? And after the calculation, does the answer look reasonable?
This involves looking at an answer in the same way that we’d often write down a word to see if its spelling looks correct.
When I ask teachers at courses if they regularly estimate the answers to their own calculations, most respond that they don’t. However, when asked have they ever experienced the scenario where they’ve used a calculator to tot something up, but the final answer looks too big or small, convincing them they hit a wrong button somewhere along the way, almost all will nod in agreement. It’s that instinctive number sense, that helps us as adults to identify large discrepancies between our result and what we instinctively expected as a result. And this is a skill that we need to teach.
We need to encourage the children to look at the size of the numbers involved, i.e. the number of digits, and to use their understanding to predict what size the answer should be. According to the Teacher Guidleines, “they can be encouraged to develop their own ways of deciding when an answer is reasonable”. I would do this by getting them to look at calculations already done and corrected, to identify any patterns, e.g. if we add a 2-digit number to a 2-digit number, how many digits should be in the answer? What if we multiply a 2-digit number by a 2-digit number etc? Their understanding of the rules that govern odd and even numbers can also be used here e.g. if you’ve added 2 even numbers then the answer should also be even and if it’s not, well then, you know it needs to be redone.
Ball Park Estimate:
As the Americans would say, give me a ball park estimate. For this I tend to use the front-end strategy, which looks at the front of the calculation e.g. the tens, hundreds, thousands, etc to give an approximate or rough answer. You could also use rounding to get a ball park estimate, but, while it does give a more accurate estimate than front-end estimation, it is usually much slower for children and it's therefore less likely they will use it when left to their own devices. I would recommend looking at this Learnzillion lesson below that teaches about using front-end estimation to test the reasonableness of answers.
Developing good number sense is key to being able to estimate. I really like this Estimate game, and often use it as a quick oral and mental starter in class, for that purpose. A similar site for this is Estimation 180; what I especially like about this site is how it is also focused on measures, and not just number, and that you can't calculate the answers, you have to estimate, but you can use what you learn in one example to help frame your estimate for subsequent examples. A perfect example of using what you know, to help solve what you don't know.
Another way to promote the development of children’s estimations skills is to present them with possible solutions to a problem and they pick the most reasonable one, like this activity from IXL. com (it's a subscription site, but you can do 20 free questions every day, which is how I use it). I usually would do something like this, again, a as part of a quick oral and mental starter and get the children in pairs to record the most suitable estimate on their mini whiteboards. Just don’t leave the problem up on the board too long, or they’ll be calculating the answer, rather than an estimate! (hint: I show them the problem, and then hide it using the controls on the projector remote)
Remember: to be efficient, estimation must be quick and fast – otherwise it doesn't serve its purpose
For further ideas check out my Estimation board on Pinterest