Asking the students to work on a real-life scale can be useful in helping them to see division in the world around them. The next activity continues to ask the students to explore the division algorithm and to use symbolic mathematical language, but this time they will be working on a bigger scale.
Thinking about a real situation and preparing an answer to a problem they have identified will help the students further develop their powers of visualisation and give visual meaning to symbolic mathematics.
In this activity students will create a tiling plan for a particular part of their school, for example an area of the playground.
When taking students to work in the school grounds (Figure 2), you should always make sure your students are aware of safety hazards they might encounter, such as moving vehicles or building works, and prepare for changes in the weather.
Divide the class into groups of two or three students. Ask each group to do the following:
Once they are done, every group comes back to the classroom to report.
On the blackboard, make a table as shown in Table 1 with as many rows as there are groups.
L | l | q | r | B | l | q | r | |
---|---|---|---|---|---|---|---|---|
Group 1 | ||||||||
Group 2 | ||||||||
Group 3 | ||||||||
Group 4 | ||||||||
Group 5 | ||||||||
Group … |
The activity
Ask the groups to fill in their row in the table on the blackboard with their findings from Part 1 of this activity. Discuss the following with the class:
Now this was an extremely interesting activity for the students to take part in. I had to, of course, get tape measures for them to take the measurements. They all had a great time making a plan of the different areas they could measure and they enjoyed discussing where tiles would be a very good idea.
Some of the groups were talking about trying to measure some difficult-shaped areas, so I advised them to keep it simple. They went out quickly once their plans were made because I told them they had just ten minutes to get their measurements and be back in the classroom! I stood outside the classroom with my watch reminding them to be quick about what they had to do.
When they were all back in the classroom they had to decide whether to use big or little tiles; some of them thought that big tiles would be best but then did not like the division sums that they had set themselves so went for smaller ones. After about another five minutes they all had their answers ready to go into the table which I had drawn on the blackboard.
The discussion about whether any of them got r = 0 was interesting and there was a lot of talk about how and when they could get that. It also led to the talk about multiplicands and the divisibility of numbers and when we could say a number can be completely divided by another. We also had a talk about how remainders can be any number left when we remove a certain multiple of the divisor and why we try to remove the maximum numbers of times of the divisor. This included thinking about how the remainder could not be more than the divisor.
I think by the end of this activity I can say that most of my students were able to understand the division algorithm and would know why they were doing what they were doing when using it.
![]() Pause for thought
|
OpenLearn - Using real-life contexts: the formal division algorithm Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.