Twenty-one gas cylinders are to be loaded onto three lorries.
Seven cylinders are full, seven are half-full and seven are empty.
A full cylinder weighs 50kg and an empty cylinder weighs 20kg.
How should they be loaded onto the lorries so that each lorry is carrying the same weight?
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I will give this problem to my grade 7 and 9 learners. In grade 7 I’ll give the problem together with a chart showing the three empty trucks, 50 kg full cylinders, half cylinders and empty cylinders in groups of 7. Then guide them while working on the problem, whereas in grade 9 I’ll give this problem as an investigation task expecting them to show all the calculations as well as represent the information diagramatically.This will help me in the Cass marks expected for grade 9 learners.
That’s good planning. Other teachers will be interested to know how these lessons work out so your reflections here after your lessons will be valuable.
There are different ways to think about this problem so different groups of learners may come up with different methods. Teachers should be careful not to steer learners to solve problems the way the teacher solved it.
The method you suggest is fine. Another method is to think of 7 full cylinders and 7 half-full cylinders, making 10 and a half altogether, and then to think of ways of distributing 10 and a half between three trucks.
Toni its true that we musn’t expect learners to solve problems in our own way because learners have their own way of seeing things,of reasoning as well as of understanding, and that they are not empty vessels. I’ve discovered this from their responses in this problem, they came with different solutions,I didn’t even think of some of their responses, they surprised me.
I grouped my grade 6learners in 4s.One grp loaded as follows, 3x50kg, 1x25kg, and 2x20kg onto each truck. There is 1empty cylinder left. The other groups loaded as follows: 2x50kg, 2x25kg, and 2x20kg and 1x50kg, 1x25kg , 1x20kg is left unloaded. Is it possible that all the cylinders are loaded?
Yes, all cylinders must be loaded Thabs. I think you are having a problem with this because you have assumed that the half empty cylinder weighs 25kg. This can not be true. The full one weighs 50kg but the empty one still weighs 20kg so you must first work out how much the actual gas weighs. It is only this which can be halved as you still need the complete cylinder to contain the gas. Hope this helps. Do have another go at the problem now.
thabs please note that half cylinder weighs 20kg +half of 30 which gives you 35kg.
so it is possible . on monday i gave the problem to my grade 8 learner and they could load all the trucks with different cylinders but same total. i got 4 different solutions.
I have tried this one. They struggled with the weight of half full cylinder, the was one learner who said “If the half filled cyllinder should be 35kg then we must have 245kg per truck” after that the whole class manage to get solution.
I can give this to my grade 6 learners as they already know about mass.I like it because it is so challenging to learners as they have to use different basic operations.They can come with different ways of solving this.I thank aimssec to make me part of this course as there is a lot that I have gained.Thank you again.
I think I will give this problem to my grade10 learners as they have never been exposed to such mathematical thinking and problem solving before. Even though its meant for grades 6 and 7 as I read from other teacher’s comments but just for them to see the application of maths in real life situations.
p.s I love this interaction with other educators!
This is a very interesting and exciting lesson for my learners. I will give them time to think of different ways to divide these cylinders between the trucks equally and share their ideas with the rest of the class so that all the learners are able to see the variety of methods. They can also use small bottles or containers so that they can do this practically, I think that would help a lot with my grade 6 learners.
This lesson is very interesting to grade six learners.At first they thought that half cylinders weigh 25kg which is half of 50kg then they got answers wrong until I told them the easy way of loading whereaby they added 7full cylinders and 7half full cylinders to make 10 and a half then they divided this load amongst three lorries and they got the correct answer.I think this exercise is making learners to think wisely
is amazing,i gave this problem to grades 10 and 11,they took a lot to solve it,finally I said is a homework,they have to go and think about it,still they came back frustrated not getting it,woo at last one and only one learner from grade 11 did it,though she was not sure and afraid to come in front and show others,the learner draws lorries,put gas one by one,empty,full and half,redo and redo till she said now is balanced,she said she took almost three days to come up with it,everyday she tried it in a different way,did it till she got solution.This shows some learners give up quickly if they can’t the solution while others they said i will work on it till i got it,after discussion is only then learners manage to see and understand it,not sure if the question was challenging or learners are lazy in thinking.
Well done. By encouraging the learners, and not giving them too much help, you taught them that they must think for themselves. One learner had the perseverance to keep working until she found a solution. Perhaps she has inspired the other learners to keep working until they succeed next time. I don’t think your learners are ‘lazy in thinking’ but just not sufficiently accustomed yet to problem solving.