Stumped by DDs YR 5 maths homework!

[trebleclef101]

Helping DD (9) with her maths homework. She is in year 5. I'm stumped by the last question (c)!

I understood it to mean draw 2 more shapes that each have the same area as perimeter (but not specifically 16cm). Then failed to come up with any simple shapes that fit the requirements.

The grid was made up of 1cm squares.

Have we misunderstood the question? Feel like I'm missing something obvious!

They don’t have to be rectangles/ squares I don’t think, which makes it easier. Could be L shapes or T shapes for example. Get her to experiment drawing some out.

What do you/she not understand? The simplist way to answer 1 and 2 would be with a square and a rectangle the correct sizes and for 3 draw 2 different size rectangles which meet the requirements.

I don’t think it’s you, I think it’s the way the question is worded! It says THIS property but which??

I'd read it the same as you but the only other shape I can think of that would fit the bill is a 3 x 6 rectangle.

Yes if the property is the same area as the perimeter you would be looking at two more squares eg 5cm x 5cm or 6x6 etc

The area and perimeter of these squares are not the same.

5x5 has area 25 but perimeter 20.
6x6 has area 36 but perimeter 24.

These don't have the same area and perimeter though.

5 x 5 - Area = 25 and perimeter = 20

6 x 6 - Area = 36 and perimeter = 24

It's hard to follow; does it mean draw two more shapes with the same area as perimeter?

I thought the same but still struggled to come up with any shapes that fit the requirements 😂

Oh a rectangle of 0.5 x 2 would work!p

ignofe me. No it wouldn’t.

Thank you! Yes, 6 x 3 would fit the bill

She just needs to have a go at drawing some and counting the area and perimeter. I’ve done this activity with y5 classes and there definitely are some.

Wouldn't 0.5 x 2 have an area of 1 but a perimeter of 5?

Sorry, just seen the responses suggesting that have been edited 😊

@trebleclef101 perhaps you could get away with doing a 3 x 6 and a 6 x 3 and calling them different.

From my old days teaching primary I think this is the case of the person making the worksheet in a rush thinking it sounded like a good challenge without realising how few shapes meet this criteria.

In fact I bet they had 5 x 5 and 6 x 6 etc in mind and will only realise when it gets handed back in that it is wrong.

This link suggests the only whole number solutions are 3x6 and 4x4 (go to the student solutions tab)

nrich.maths.org/problems/can-they-be-equal-poster

I think it means draw two shapes where the area is the same number as the perimeter. Its a badly worded question though. And it gives the impression that 16cm and 16 cm squared are the same thing!

That's what we've gone with, one 3 x 6 and one 6 x 3. She's had other questions where rotated shapes have been accepted as different. Thanks again!

What about a rhombus?

Yes, sorry, not quite sure what I was thinking there 🤦‍♀️😂

It's easy if you go irregular. Fix the perimeter first, then adjust the area to match (random example attached - I didn't have any squared paper, hence why my "squares" are a bit squished!)

Ps this trick won't work for 16 though, because any rectangle with a perimeter of 16 will have an area less than 16 (square maximises area)

I think a circle with 2cm radius would work

1. perimeter 18
   Triangle of 666 (6+6+6)
   Rectangle of 3*6 (3+3+6+6)

2. area if 36

square 66
Rectangle 312

I did try this but started with too small a shape where the area was already smaller than the perimeter. Should have gone super size!

Love this one, that would really impress her teacher 😂