Below is a video of a lesson I have done for the last few years that is in relation to area. Students are required to determine both the number of post it notes that will fit on the board and the time it will take to complete the task.
In getting students to complete the task I first deprive them of the measurements I start with a set of estimation exercises. First they use the video of the first 20 as shown above as a way to estimate the time and the number for the whole board. They are then shown an image of 100 post-its on the board (shown above) and are asked to adjust their estimate and give reason for what change they made and why. This process is repeated with 200 and 300.
What was interesting about the process of this activity this year is the strong desire of the students for the measurements initially. The just wanted to apply a formula they knew to the problem, they placed absolutely no value on the process of estimating both the number of post its and the time, they did not see it as a valid way to approach the problem.
However in reality estimation is an incredibly important skill for students to become comfortable as we use it all the time, in fact we use it a lot more than we use an exact calculation. In an article I read a few years ago (I can't remember the source of the article now) it stated that of all the maths we doing in our lives 80% of it is estimation, only 20% requires an exact calculation. If this is the case then the estimates I was getting them to do is arguably a more important process than getting them to calculate the exact numbers. However I also feel that little emphasis is place on estimation within mathematics classes, our desire as teachers often is to apply the formula and to deal with exactness of the solution, we don want to look at the messy and imprecise nature of an estimate.
Students also seem to have a fundamental level of misunderstanding of how to estimate. In some of the diagnostic testing we do this misunderstanding of estimation also becomes evident. When asked how they would estimate the value of 18 x 79 the most common response is to calculate 18 x 79 and then give the answer. Other common answers have students performing the calculation and then rounding. The number of students who calculate 20 x 80 instead as a good estimate is very small but is the most appropriate way to approach the task. It makes me think that estimation needs to be a much larger section of my program than it currently is and I know that one very good source of questions requiring estimation is Estimation 180. It is a great website that potentially has tho ability to provide students with 1 estimation question for each lessonn of the year as a warm- activity.I am also thinking more about how I can get students to estimate before they calculate more often over the course of their year.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.