I saw a task where students had to play a game against a partner. They rolled two dice and multiplied the numbers together, they could then draw a rectangle on the grid with a perimeter equal to the product of these two numbers.
I decided to create a task loosely based on this idea but I decided I wanted to look at areas instead. I then realised my task wasn’t really about area but about factors. Students need to also consider which numbers have only one or two solutions. If students look at the first two areas in the list they should note that 14 has factors; 1, 2, 7, 14 but a 1 by 14 rectangle isn’t possible in this grid so it needs to 2 by 7. Likewise 3 by 9 is the only possibility here. Once they have drawn in 3 by 9 on the grid it leaves a thin rectangle with a width of 1 so 1 by 6 is the only rectangle that fits here (or a 1 by 1)
I have had the pleasure of using the ICCAMS lessons and in particular Boat Hire
It looks at comparing two different boat hire companies and every time i have used it with a class I have learnt something new. Students never fail to surprise me with their ideas.
I decided with my low attaining year 10 class that i would pose the following question (I left my ICCAMS hand book at home!)
Abbey boats charges an initial fee of £10 and £1 per hour for using their boats
Barking Barges charges an initial fee of £5 and £2 per hour for using their boats
Miss Konstantine wants to hire a boat, which should she use?
I gave students time to ask questions and make sense of the question i had posed.
Here are there initial thoughts:
I found the last students work quite interesting. He had used a rather nice way of recording the information for 1-5 hours. He was also able to determine which boat company to use for 1-4 hours and that both companies were the same price for 5 hours.
We used his work to move forward with the question and we discussed some of the other comments students raised at this point in the lesson.
We moved on to plotting the two boat hire companies and students naturally started to question. I asked for the class to share any questions they had about the graphs and if anyone wanted to, they could comment on what they noticed or thought.
Below are some of the comments and questions students had at this stage
I made the following problem to be used with my year 9. The boxed value was an error and they had to correct it. It also gave students a chance to discuss misconceptions.
I tried to include one where students used the Scale factor for length as 2 and the SF for area as 2
One where students correctly worked out SF for volume but then the length was halved not doubled,
Another question I included had the SF for area being used on a volume
then a question with SF for volume being used instead of area.
I then started to consider some more challenging questions that combined several ideas involving similar shapes, Scales factors and proportion.
I was looking to review the mocks with year 11 and decided instead of working through each paper, I’d work through by related topics.
I noticed Ss in my class had trouble with finding of amounts when you ended up with parts. They also didn’t notice things in diagrams like 3.5 shades out of 7 is a half or 3.5 out of 14 is a quarter. They didn’t seem comfortable with decimals in fractions
I hope students are able to find the fractions shaded in the images below
I have seen function machines throughout my teaching career but I have mostly dismissed them as a way of displaying a question and I didn’t really appreciate how they could be useful. It wasn’t until I came across the ICCAMS question below that I began to see how they could be useful in the classroom. I have used the question below with a variety of abilities and I always love hearing how the students respond to the question. Usually the lower attaining classes would say that both outputs would be the same and then try values to see this isn’t true. With higher attaining students there was a mix of students who thought it might be the same but felt it should be different and those who thought they weren’t equal but would try values and confirm that they weren’t.
What I liked most about the question was the absence of formal algebra but also that it gave students an opportunity to look at order of operations and how multiply and addition affected values when used sequentially. I also liked how students could reverse the machine and think about inverse operations.
Another thing I liked about the function machines was it gave students the opportunity to notice connection between expressions so I thought about a few of my own questions. In the first pair of machines, I hope that students will notice the outputs are equal and start to think about why this is the case. I like an image that I saw in the ICCAMS project handbook. I have used it as a model to create a similar image for the first set of function machines.
A little puzzle that doesn’t have a unique solution. Students in my year 9 class enjoyed solving it
I enjoyed seeing some responses from class on a perimeter question. There was a shape and its perimeter was given and then students had to find the perimeter of a larger shape made up of the smaller shape.
Students spent time finding the length and width of the smaller shape and then using it to find the larger shape. It wasn’t badly answered, students managed to understand how they would go about answering it and this method worked but the perimeter was 15cm so one of the lengths was 2.5cm. None of the students looked at the edges of the larger shape and saw how they related to the smaller shape. Perimeter
Students in year 11 were struggling with a Perimeter question and I started making up some other questions for them to try. They found each one challenging and had to reason to why certain lengths were equal and how to find the missing lengths.