Angles - what is the smaller angle?

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LiseyDot05

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Afternoon everyone. Looking for a wee bit of confirmation that O is on the right track. He divided 360° by 8 and got 45° for each section.
He's hesitating over questions 31, 32, 33, 34 & 35.
Ignoring his current answers, because he has since realised his mistake, is he on the right track with the following?

31. 90°
32. 45°
33. 45°
34. 135°
35. 135°

20230613_154957.jpg
 
LiseyDot05 said:
Afternoon everyone. Looking for a wee bit of confirmation that O is on the right track. He divided 360° by 8 and got 45° for each section.
He's hesitating over questions 31, 32, 33, 34 & 35.
Ignoring his current answers, because he has since realised his mistake, is he on the right track with the following?

31. 90°
32. 45°
33. 45°
34. 135°
35. 135°

View attachment 35988
Click to expand...
You've corrected #31 from 45 to 90; how about #28? My guess is that he was misinterpreting "the smaller angle between"; have you discussed that?
 
LiseyDot05 said:
His thinking is that it is 90° and the larger angle would be 270°. Should he instead be thinking 45° for the smaller slice of that 90°?
Click to expand...
Hmm, re-reading the problem I now agree that the answer is 90.
 
LiseyDot05 said:
Afternoon everyone. Looking for a wee bit of confirmation that O is on the right track. He divided 360° by 8 and got 45° for each section.
He's hesitating over questions 31, 32, 33, 34 & 35.
Ignoring his current answers, because he has since realised his mistake, is he on the right track with the following?

31. 90°
32. 45°
33. 45°
34. 135°
35. 135°
Click to expand...
Hi @LiseyDot05,

(I presume "O" is your son's initial. ?)

How this exercise should be interpreted depends to an extent on exactly what was being taught just prior to it being given out.

I suspect it may have been this: if you choose any two lines on the compass, say, N & NE, then there are two angles between those lines: one measured in a clockwise direction (45°) and a second measured in an anti-clockwise direction (315°). It is important, therefore, to distinguish which of these two angles is 'of interest' in any discourse.

Given the language used throughout these questions where only comparative terms (larger/smaller) are used (which means that only two things are being compared), I would interpret this as meaning that the student is being asked to consider the angles between any two given lines in the clockwise direction versus that in the anti-clockwise direction.

O appears to have misinterpreted(?) that in Q.28 (and 31) when he decided that the answer(s) was 45°. If the question had said: "What is the size of the smallest angle between N and E?" then one might, indeed, argue that 45° was the correct answer because there are three angle shown in between N and E (90°, 45° and 45°) although, strictly speaking, the angle between N & E should only be considered as that from N to E (ignoring anything else in between).

It might be a worthwhile exercise to explain (or remind?) O about the difference between the use of comparative adjectives (smaller/larger) and superlative adjectives (smallest/largest); that the comparative is used where only two things are being compared and the superlative where more than two things are being compared. Unfortunately this distinction is frequently misused in everyday speech by many but Mathematics is a language and, therefore, strict definitions of terms apply.

This interpretation of the exercise is, in my opinion, reinforced by the absence of any mention of smaller or larger in questions 29 & 30 where it doesn't matter which direction (clockwise or anti-clockwise) you measure the angles, the result is the same (180°)

If you show O my modifications to your picture, below (and, perhaps, discuss with him comparative vs superlative adjectives too?), he should have no difficulty in getting/confirming all the correct answers.

Comparitive Angles.jpg​

I trust it is clear how I have used different colours to associate the questions with the corresponding angles in the diagram and have used thicker lines to indicate which of the two angles each question asks for the measure of? (You may have to 'magnify' the diagram up to see arrowheads clearly.)
(If anything is unclear, please just ask. ?)

Hope that helps. ?
 
The Highlander said:
Hi @LiseyDot05,

(I presume "O" is your son's initial. ?)

How this exercise should be interpreted depends to an extent on exactly what was being taught just prior to it being given out.

I suspect it may have been this: if you choose any two lines on the compass, say, N & NE, then there are two angles between those lines: one measured in a clockwise direction (45°) and a second measured in an anti-clockwise direction (315°). It is important, therefore, to distinguish which of these two angles is 'of interest' in any discourse.

Given the language used throughout these questions where only comparative terms (larger/smaller) are used (which means that only two things are being compared), I would interpret this as meaning that the student is being asked to consider the angles between any two given lines in the clockwise direction versus that in the anti-clockwise direction.

O appears to have misinterpreted(?) that in Q.28 (and 31) when he decided that the answer(s) was 45°. If the question had said: "What is the size of the smallest angle between N and E?" then one might, indeed, argue that 45° was the correct answer because there are three angle shown in between N and E (90°, 45° and 45°) although, strictly speaking, the angle between N & E should only be considered as that from N to E (ignoring anything else in between).

It might be a worthwhile exercise to explain (or remind?) O about the difference between the use of comparative adjectives (smaller/larger) and superlative adjectives (smallest/largest); that the comparative is used where only two things are being compared and the superlative where more than two things are being compared. Unfortunately this distinction is frequently misused in everyday speech by many but Mathematics is a language and, therefore, strict definitions of terms apply.

This interpretation of the exercise is, in my opinion, reinforced by the absence of any mention of smaller or larger in questions 29 & 30 where it doesn't matter which direction (clockwise or anti-clockwise) you measure the angles, the result is the same (180°)

If you show O my modifications to your picture, below (and, perhaps, discuss with him comparative vs superlative adjectives too?), he should have no difficulty in getting/confirming all the correct answers.


I trust it is clear how I have used different colours to associate the questions with the corresponding angles in the diagram and have used thicker lines to indicate which of the two angles each question asks for the measure of? (You may have to 'magnify' the diagram up to see arrowheads clearly.)
(If anything is unclear, please just ask. ?)

Hope that helps. ?
Click to expand...

O is my wee lad's initial, yes. ?

The problem with a lot of these questions that I pick your brains about is that they haven't been taught. These are practise test papers and the children meet problems they haven't met before. I don't necessarily agree with her way of doing things (teaching it after the fact to those that need it) but I'm sure she has her reasons.

Thank you very much for the diagram and mine of info', it's appreciated. ? By the end of looking at the problem he realised what was meant by smaller/larger angle but the diagram has definitely helped to cement that.

Thanks to you all again. I know these aren't the problems I see regularly on here but it's so handy to have people help us along the way. I can figure out most of his problems but sometimes I find it difficult to explain them which is where this site is so important for us.
 
LiseyDot05 said:
O is my wee lad's initial, yes. ?

The problem with a lot of these questions that I pick your brains about is that they haven't been taught. These are practise test papers and the children meet problems they haven't met before. I don't necessarily agree with her way of doing things (teaching it after the fact to those that need it) but I'm sure she has her reasons.

Thank you very much for the diagram and mine of info', it's appreciated. ? By the end of looking at the problem he realised what was meant by smaller/larger angle but the diagram has definitely helped to cement that.

Thanks to you all again. I know these aren't the problems I see regularly on here but it's so handy to have people help us along the way. I can figure out most of his problems but sometimes I find it difficult to explain them which is where this site is so important for us.
Click to expand...
You're very welcome.

It's just as important to help young minds to (properly) acquire the 'basics' of Mathematics as it is to assist those who encounter difficulties at more advanced stages & topics (so that they can reach those heights too!) ?.
 
The Highlander said:
You're very welcome.

It's just as important to help young minds to (properly) acquire the 'basics' of Mathematics as it is to assist those who encounter difficulties at more advanced stages & topics (so that they can reach those heights too!) ?.
Click to expand...
I love that, thank you!
 
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