My first formal lesson with year 7 and the LO is to be able to calculate the perimeter and area of a rectangle.

What I like about this LO is that chances are, all of my class are going to be able to do this. It means that I get to think of a different way to introduce practising this skill.

Can they be equal by nrich is an excellent activity to do for this.

The first part of the problem is below:

After going through one basic example of how to find the area and perimeter of a rectangle and how I wanted them to set the work out, I introduced them to this problem.

As I was walking around the room it was really interesting to see what rectangles the students were trying and the conversations they were having. . Some students without prompting soon realised that the width needed to be 2.5 for this problem to produce a rectangle with an area of 25 and a perimeter of 25. Some of my other students said they thought they were becoming close with a width of 2 and a width of 3 but then wasn’t quite sure what to do. Some of my students asked if it was possible to use a decimal for a width to which I simply replied ‘Is a decimal a number?’ and ‘did the question specifically state that you needed to use an integer?’. When these students were confident that they could use a decimal they were soon on their way. This is my first reason for thinking this task is brilliant. Quite a few of my students when conducting investigations often stick to integers and have a hard time with using other types of numbers such as fraction, decimals or as they get to KS4 surds etc. I think students need to realise that there is a whole range of numbers out there not just integers and start to realise that fractions, decimals, surds etc are all just numbers. A classic example is when students solve equations and tell me that they got a fraction for an answer and is this OK? To which my reply simple is, is a fraction a number? After a moment of thought they normally go, well yes. I want my students from early on to realise that these things are numbers and to feel comfortable working with them.


Once the first part of this problem was completed, students moved onto the second part of this problem which is below:

Once again students got to work trying out different rectangles and trying to find the answers. At the end of the allocated time for the task I asked the students to share their findings. One answer given was a 6 by 3 rectangle which all of my students accepted and said yes they agreed this was indeed an answer. Another one of my students gave the answer a 4 by 4 square. This however caused many comments to be made around the class ‘You can’t use that, that is a square’, ‘the question specifically states a rectangle, that answer surely can’t be allowed’. Here comes the second reason why this activity has great value. Once the comments had been made I challenged one of the students: ‘What is the definition of a rectangle?’ It has 4 sides. So I continued to press on, is that the only defining feature of a rectangle? We soon got to that a rectangle has 4 sides, 4 right angles, 2 sets of parallel sides that are the same length. From there I drew a square on the board and showed that a square is in fact a special type of rectangle therefore the answer was indeed valid. This is a brilliant way to challenge the misconception that so many year 7s posses.

Overall, I think this is an excellent activity to undertake in lesson. It’s a great way to introduce problem solving into lesson and to take an area of maths that a lot of students can already do and make them think about it in a different way and encourage team work. It also encourages students to realise that unless a question stipulates that an integer must be used then they can use an array of numbers and hopefully build their confidence with these numbers. Finally, it stimulates good conversation about the properties of squares and rectangles and challenges that common misconception that year 7s can posses, that a square is not a rectangle. I do truly believe that this activity has a lot of value and I certainly encourage teachers to use this activity.

I would encourage teachers to visit the nrich website when planning lessons and look through the excellent resources that are on that website:

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