year 5 maths homework help

[Clive]

Can anyone help me explain this to my son (he is thai) as I simply don't get it
The question is:
A rectangle has a squared area of 10cm squared. The dimensions are not given. If you double 2 of the sides what is the area?
I know the answer is 40cm squared but I just don't get the calculation as I thought that if you double the 2 sides of the rectangle then you double the area giving 20cm squared and not 40 cm squared.
Thank you

[stubuzz]

WxH

probably 2.5 x 4 = 10cm2

[SlyAnimal]

Use pictures to explain it to him

Also I can understand why your son is confused, as the question isn't really phrased very well if the answer is 40cm.

As doubling 2x sides, on a 2.5cm x 4cm rectangle would mean either the 2.5cm or the 4cm was doubled (since each dimension represents 2x sides).

Doubling the length of all 4 sides would however produce the 40cm.

Pictures can help to show this, or explaining that

4cm x 2.5cm = 10cm2

(2 x 4cm) x (2 x 2.5cm) = (2x2) x 10cm2

8cm x 5cm = 2 squared x 10cm2

8cm x 5cm = 4 x 10cm2

8cm x 5cm = 40cm2

As once you expand the equation it becomes easier to understand. You could either include the answer part of the equation, or not, and give him multiple examples of how it works when the rectangle is of different dimensions.

But if you can show him a picture, that'll likely help him a lot by being able to visualize the problem and thus understand it better.

Edit: probably using 2cm x 5cm for the dimensions is probably better for the first example you give him. He'll need multiple examples though to see the relation between doubling the 2x factors on the left resulting in multiplying by 2 squared on the right.

[Tywais]

WH = 10

2Wx2H = 4WH

therefore

WH = 10

4WH = X

cross multiply (some teachers don't except that method though)

X = 40

[Mrjlh]

This might help: http://www.wikihow.com/Calculate-the-Area-of-a-Rectangle

P.S: Any combination that equals 10 CM Squared works.....

A = L X W 10Cm squared equals 5(L) X 2(W) = 10.....Double the sides 2 X 2 = 4 AND 2 X 5 = 10.... 4 X 10 = 40 CM Squared.

Edited September 11, 2014 by Mrjlh

[Clive]

Thanks for your answers....doubling all four sides I get but I don't see how doubling only 2 sides can give 40cm2 from an original 10cm2 rectangle.
I can only see 20cm2 by doubling 2 sides

[Gulfsailor]

Can anyone help me explain this to my son (he is thai) as I simply don't get it

The question is:

A rectangle has a squared area of 10cm squared. The dimensions are not given. If you double 2 of the sides what is the area?

I know the answer is 40cm squared but I just don't get the calculation as I thought that if you double the 2 sides of the rectangle then you double the area giving 20cm squared and not 40 cm squared.

Thank you

The question is bit dubious. A rectangle has 4 sides, so if one is pedantic and assumes that if only 2 sides were to be doubled it should be two opposing sides, otherwise it wouldn't be a rectangle anymore. If that's the case you are right that the surface area would double. But I think the question is meant to be understood as if two connecting sides get doubled, and it stays a rectangle, meaning all four sides would double, thus 2x2=4 x larger surface area.

[Mrjlh]

Make sure you are not confusing a rectangle with a square. In either case you only multiply "two" sides to get the Area. Four sides has nothing to do with the problem.

Edited September 11, 2014 by Mrjlh

[CWMcMurray]

Double just 2 sides or all 4 sides? If doubling just 2 sides, then area doubles, but if doubling all 4 sides, will quadruple ..,

If 1 x 10= 10..,, 2x 10= 20... 1x20=20... 2x20=40

Or if 2.5x4=10... 5x4=20... 2.5x8=20 ... 5x8=40

[CWMcMurray]

Think its clear that there is an error in the question... As should be doubling all 4 sides... Or doubling both the length and width or similar wording...

[Mrjlh]

Double just 2 sides or all 4 sides? If doubling just 2 sides, then area doubles, but if doubling all 4 sides, will quadruple ..,

If 1 x 10= 10..,, 2x 10= 20... 1x20=20... 2x20=40

Or if 2.5x4=10... 5x4=20... 2.5x8=20 ... 5x8=40

What is this creative math? A rectangle has 4 sides of which two sides (lengths) and two sides(widths) are equal and opposite to each other. If you double one side (Length or width) you automatically double it's mate. Anything else is not a rectangle by pure definition of a rectangle. The question is worded correctly.

If either the width or length become equal then it becomes a Square.

rec·tan·gle

ˈrekˌtaNGgəl/

noun

noun: rectangle; plural noun: rectangles

1. a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Edited September 11, 2014 by Mrjlh

[CWMcMurray]

Yes has four sides.. So if you double only 2 sides of the rectangle ... by the definition of a rectangle ... Means that the other 2 sides remain the same size

[Mrjlh]

You are reading into the question more than what is being asked. If you only double two sides (L & W) you no longer have a rectangle do you? Buy level 5 they should know the definition of a rectangle and geometry the pertains to it.

[culicine]

The question is ambiguous. Is this a translation from Thai to english, or is a Thai/non-native speaker teaching this? Just curious.

It depends on which of the two sides are doubled. If it's the two opposite sides, then the answer is 20cm2. If it is the length and width, then it is 40 cm2.

1) xy= 10. The length of y is doubled giving 2xy. If xy=10, then 2xy must be 20.

2) xy=10. Length x and y are both doubled, giving 2x2y = 4xy. If xy = 10, then 4xy must be 40.

This is about the easiest way to explain it. Use diagrams to help. I teach m3/m4 and I use the area of similar shapes to teach part 2. That formula is a little too advanced for p5 though.

Hope that helps.

Edited September 11, 2014 by culicine

[Mrjlh]

I'm one of the few here that admits when he's wrong. I concede to your reasoning. Too focused on one thought.

[CWMcMurray]

You are reading into the question more than what is being asked. If you only double two sides (L & W) you no longer have a rectangle do you? Buy level 5 they should know the definition of a rectangle and geometry the pertains to it.

Yes agree... So if only 2 sides double it can not be the length and width that double... Otherwise the resulting shape would no longer be a rectangle

Can only be width and width or length and length... In order for both the length and width to double, would need to

State that all 4 sides double

[wayned]

If the answer is 40cm squared then it is not stated correctly.or is meant to be confusing. It should read "double both of the sides" The only way that it could remain a triangle and the Answer be 40cm squared you would have to double both of the sides. length and width.

If you only doubled 2 of the sides, for it to remain a rectangle you would have to either double both of the long sides or both of the short sides. In that case the area would be 20cm squared, not 40.

[culicine]

Double just 2 sides or all 4 sides? If doubling just 2 sides, then area doubles, but if doubling all 4 sides, will quadruple ..,

If 1 x 10= 10..,, 2x 10= 20... 1x20=20... 2x20=40

Or if 2.5x4=10... 5x4=20... 2.5x8=20 ... 5x8=40

What is this creative math? A rectangle has 4 sides of which two sides (lengths) and two sides(widths) are equal and opposite to each other. If you double one side (Length or width) you automatically double it's mate. Anything else is not a rectangle by pure definition of a rectangle. The question is worded correctly.

If either the width or length become equal then it becomes a Square.

rec·tan·gle

ˈrekˌtaNGgəl/

noun

noun: rectangle; plural noun: rectangles

1. a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

By definition, a square is also a rectangle, but a special kind of rectangle, where the sides are equal length. A square is also a quadrilateral, a parallelogram, and a trapezium. But primary kids don't learn this as it leads to confusion. They just learn squares have equal sides and rectangles don't.

[brianp0803]

Maybe clearer if they said double the length and width but I would assume it remains a rectangle.

If length(L) times width(W) is 10 sq meters.

Double the length only then the new length is 2L

(2L) W= 2 (LW) =20 sq meters

Double length (2L) and double width (2D)

(2L)(2W)=4 (LW)=4 (10)=40 sq meters.

[brianp0803]

If 3 dimensions and double width ( 2w). Double length (2L) and double height (2H)

The new volume is (2L)(2W)(2H)=8LWH.

So 8 times original volume.

Dimensions don't matter.

Only care it was doubled

[Metanoia]

I have to say the question is poorly worded.

It would be more appropiate for the level if it said "all dimensions are doubled".

Saying two sides are doubled leaves much ambiguity.