Area: "Here is a plan of our bathroom; on the drawing, 2cm equals 1m."

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LiseyDot05

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Hi again, everyone. Me back looking for help with a maths homework problem. ?
The bath area measures 2.5cm by 4.9cm. We have measured both sides numerous times, with various rulers & that one particular side is still coming up at 4.9cm.
My son is looking for a wee bit of guidance through this one if possible, please.
 

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LiseyDot05 said:
Hi again, everyone. Me back looking for help with a maths homework problem. ?
The bath area measures 2.5cm by 4.9cm. We have measured both sides numerous times, with various rulers & that one particular side is still coming up at 4.9cm.
My son is looking for a wee bit of guidance through this one if possible, please.
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I'm not sure why you are so concerned about the 4.9 cm measurement; I can see a couple different issues you might be seeing, but they show up later in the process. There is nothing wrong in those numbers themselves.

Please show us whatever work you have done after accepting your measurements. What are the actual dimensions of the bath? How did you calculate the number of tiles for the whole floor? And so on.

I have to say, this problem merits much more of an answer than a few blanks; some words explaining how you plan to place tiles will be needed in order to justify your answers. But we'll get there after you answer my questions above.
 
Ok, so for Question 10. His reasoning is:

4m × 3m = 12cm²
0.4cm x 0.5cm = 0.2cm²
12 ÷ 0.2 = 60 so he thinks 60 tiles would be needed.
 
LiseyDot05 said:
Ok, so for Question 10. His reasoning is:

4m × 3m = 12cm²
0.4cm x 0.5cm = 0.2cm²
12 ÷ 0.2 = 60 so he thinks 60 tiles would be needed.
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You meant 12 m2, right?

And 0.4 m * 0.5 m = 0.2 m2?

If so, then, yes, it will take 60 tiles; good work.

But in real life you'd need to consider how they will fit on the floor. I don't know whether they want you to do that (the fact that they ask for the area last suggests they may), but I would. Do you see in which direction you have to lay each tile to make it work? (This is one of the issues I was wondering about.)

Now, tell me about the bath. You may want to answer 12 first, as you answered 13 before 10, but that's up to you.
 
I did mean m², sorry! ? This heat is getting to me! ?
This is a 9 year old's homework so I don't think the teacher is looking for how they will fit. I'll be back with the others. Thank you for your help.
 
I have had my son have a look at it & he has no idea where to start. I'm not sure either, if I'm honest.
 
LiseyDot05 said:
I have had my son have a look at it & he has no idea where to start. I'm not sure either, if I'm honest.
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The first thing to do is to determine the actual dimensions of the bath, from your measured dimensions on the drawing.

I would assume that is what they are currently teaching him, so he should have some information about it. Since there are several different ways they might say this, it would be best if you could show a worked example he was given. I don't know what method they would teach at this level; most of the sites I find are for older students.

But the basic idea is that if 2 cm on the drawing represents 1 m in reality, and 2.5 cm on the drawing represents some unknown length in reality, they are proportional. One way to handle this is to see how many meters are represented by 1 cm, and then multiply.
 
We'll take this in baby steps so he can learn & follow as we go.

He thinks:
2.5cm is equal to 1.25m
4.9cm is equal to 2.45m
 
LiseyDot05 said:
We'll take this in baby steps so he can learn & follow as we go.

He thinks:
2.5cm is equal to 1.25m
4.9cm is equal to 2.45m
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Excellent. I wouldn't mind seeing how he thought about that, in order to get a better picture of what he knows, and help him better as we go along.

Now, does he want to answer 11 or 12 first? He can try either.

The hard part is going to be how to handle decimal answers and rounding. I'll really need to see any examples that were given that are anything like this.
 
No examples have been given. Up to this point he's been taught about area and finding the area of something within but it's always been whole numbers . This is the first time we've been met by this problem and decimal numbers.
 
LiseyDot05 said:
No examples have been given. Up to this point he's been taught about area and finding the area of something within but it's always been whole numbers . This is the first time we've been met by this problem and decimal numbers.
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If he were to work in cm (instead of metres) then that would be "whole numbers" (but would he know how to convert between cm2 & m2 if that were required?) ?
(1 m = 100 cm but 1 m2 = 10,000 cm2)
 
LiseyDot05 said:
No examples have been given. Up to this point he's been taught about area and finding the area of something within but it's always been whole numbers . This is the first time we've been met by this problem and decimal numbers.
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I'm not sure what to suggest. He can go ahead and do the calculations as decimals, and just think about how to round the answer (assuming he's learned about decimals and rounding in the first place).

Or, he might consider reversing the process, and drawing tiles of the appropriate size on the picture, and just count. (How big will each tile be when you draw it?)

But I tried straightening out your image and measuring it, with the idea of being able to draw on it, and it seems to be a little distorted:

1685642872871.png​

The actual dimensions of the whole thing should be 6 by 8 cm. If not, then it isn't really a scale drawing, and you can't really measure to find the size of the bath. It's possible that's the main difficulty here. It looks to me as if the bath is just about exactly 1/3 the width of the room, which would make it 2 cm on the drawing, and 1 m in the room. That would make the problem far more suitable to what he has learned.

So, find out whether this was printed correctly!
 
Folks, I think we've cracked it?I hope you can understand from his working out.
 

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LiseyDot05 said:
Folks, I think we've cracked it?I hope you can understand from his working out.
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Yes, you have the correct answer.

It looks like what you did was to ignore the (false) claim that 2 cm represent 1 m, and focus on proportions. Since the bath is 1/2 as high and 1/3 as wide as the room, it takes up 1/6 of the area, something I had confirmed visually by making 6 copies of the bath to fill the room:

1685646544537.png​

In effect, you found the actual scale to be 2.5 cm = 1 m horizontally, and 2.45 cm = 1 m in the vertical direction. That means I was right that it wasn't truly to scale, in addition to stating the wrong scale.

This should be reported as a bad problem, since it caused you such unnecessary trouble when you tried to solve it using the claimed facts.
 
It just seemed like the easiest 'solve' for us when we looked at it & maybe more age appropriate in this instance. It was the scale that was throwing me off completely. Thank you so much for all of your help (& patience!)
 
LiseyDot05 said:
It just seemed like the easiest 'solve' for us when we looked at it & maybe more age appropriate in this instance. It was the scale that was throwing me off completely. Thank you so much for all of your help (& patience!)
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Yes, you had to ignore the scale in order to solve it. That's what's wrong with the problem; good for you for solving it anyway.
 
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