Solve this family (lighthearted) argument

[23Squared]

Son has homework that is causing some lighthearted arguing. (year 9)

The question is thus:

Mary says that there is only one way to draw a square with an area of 23cm squared. Do you agree? Explain.

Son says: No, because the rectangle can be DRAWN in a different orientation. (portrait or landscape) It can be DRAWN starting on the top line or starting from one of the sides.

Mother says: ok but that is not what they are looking for, they are asking for the proof - so one pair of sides should add to an odd number, other pair of sides should add to an even number, 19 + 5, 21 + 2, 17 + 6 etc.

Father says: They should have worded it that way then!

Disclaimer: one or more mother and son members may be on the spectrum

How many different ways can you pull 3 balls from a bag containing 1 yellow, 1 red and 1 blue balls?

They don't care if you are pulling them out standing on one leg, or using a grabbing tool or whatever. They want to know how many combinations there are (6).

Teen - I know that you can with different pens, but to him, thats a straw man argument cos he didn't mention pens!

I was trying to explain that wasn't the answer and showed him the proof and said it wasn't what they are looking for, but he is having none of it and says they need to ask the right question then!

can you FEEL my frustration

So he could do 2 things.

1. Answer the question as it is intended (ie correctly from a maths point of view)
2. Write a comment that the wording was ambiguous because

Then he can show he can do the maths properly whilst simultaneously feeling he has got his point across.

(They won't want to use loads of extra words ruling out all the non-meanings of the question as it just makes it more complicated for everyone else and disadvantages those with poor literacy.)

If you buy something for 40p using a £5 note, how much change do you get?

Correct answer: £4.60

Incorrect answer: well it depends, you could be given 4 coins (£2,x2, 50p and 10p) or you could be given 460x1p.

He's going to love English language - describe what the author was feeling (DD2 "How am I meant to know?", Ans - look at the words they used, does it sound like they were happy or scared or what)

Good luck (and if you haven't found it there is a y10 support thread on Secondary Education)

I don't want to hijack, but you'll understand me:
DS (AS) - German lit - he got - in a written test - a quote from Lessing and the question to answer was: Can you - given what you just read - pity the character?
His written answer: NO.
Luckily his teacher has a sense of humour.

This is the son talking here btw:
your post at 19:21
the question IS about how the lines are drawn, thats why it says "there is only one way to draw the rectangle"

Prok Sounds like Educating Rita's 'Do it on the radio' answer.

By 'get with the programme' I meant your DS can spend the next 2 years arguing why the GCSE questions are rubbish or everyone agrees they are rubbish, and he then plays a game to see how good he can get at working out what they actually want and doing that. Looking at past papers and mark schemes is helpful for that.

your post at 19:39 Fair enough!

OP's DS. Yes you are right, the question can be interpreted differently. But that won't help you get marks in your GCSEs.

😂😂😂😂😂😂

You have a few years of this to go, you'll be slightly crazy by the end of year 11

Rectangle dimensions :
1x23
2x11.5
3x7.666
4x5.75
5x4.6
6x3.833
Etc

I have my laptop back! I might email this to his maths teacher and the deputy SENCO who looks after him. and provide them with alcohol

@RandomMess I know!!!

He argues like this about many things. Mostly, it is amusing!

Good on your son for thinking outside the box (Or rectangle). He will be the entrepreneur that breaks the rules and makes things better!

Fortunately the answer is the same both ways. There are numerous different dimensions a rectangle can have and still have that area. AND there are numerous different ways you can draw any of those differently dimensioned rectangles. Factoring on both, then, Mary couldn't be more wrong - there are probably infinite numbers of ways to draw the rectangle.

I am on your side, Son!!!! But if you want to score top marks in exams set by people who are a bit woolly brained, you need to work out what they THINK they are asking, answer that, and then add your more clever answer afterwards! 😁

This reminds me of the story of the student who was told to write a review of a film she’d seen recently with a 500 word limit. She wrote a review of Fight Club. In this one sentence: The first rule of fight club is that you don’t talk about fight club.
Apparently the teacher had a sense of humour and gave her an A.

Son needs to give his original answer (landscape/portrait) but extrapolate to say a rectangle of 23 square cm could be 1x23cm or 23x1cm (or any other multiples that equal 23)

Mary is wrong as the number of ways to draw the rectangle is infinte based on the chosen side lengths, orientation, location, starting position, writing implement, writing medium, pen shape, pen colour, line width etc.

If your question is limited to only the shape, and using whole numbers, then it would be limited to 23 x 1 or 1 x 23, so Mary is still wrong.

TheAlternative If it was limited to whole numbers then Mary would be right as in maths 1x23 is the same as 23x1. The drawn shapes would be congruent.