Geometric Puzzle
Thirty equally spaced points on the circumference of a circle are labelled in order with the numbers 1 to 30.
Which number is diametrically opposite to 7?
(From the UK Association of Teachers of Mathematics book, Eight Days A Week)
My thoughts:
7 and it's opposite number form half of a circle.
30/2=15
So there are 7's opposite number is 15 (including it self) numbers away from 7.
7+15=22
Therefore, 22 is the the number diametrically opposite to 7.
• What process did you use to work on and solve this puzzle?
First I started form a small number which are 4 equally spaced points on the circumference. the number diametrically opposite to 1 is 3, which is 1+4/2. From that I found a pattern that a number and it's opposite number form half of a circle, and the opposite number = number + number of points/2.
• Could you create other extended puzzles related to this one -- some possible, some impossible? (Is there any value to giving your students impossible puzzles?)
It is possible to create other extended puzzles related to this one such as using another shape instead of circle. Weather there is any value to giving students impossible puzzles depends on the mathematics ability of my students. For the students who is already struggling with mathematics, I would like to build on success and avoid giving them impossible puzzle which could attack their confidence on studying mathematics. But I might give impossible puzzles to students who is capable and is looking for more challenging questions. I think I might give impossible puzzles carefully, for example, give them a hint that this might be impossible to solve. Without doing this, this might cause negative effects such as the destruction of trust,
•What makes a puzzle truly geometric, rather than simply logical?
I think a geometric puzzle involves shape and space. A logical puzzle can be solve by deductive reasoning.
Which number is diametrically opposite to 7?
(From the UK Association of Teachers of Mathematics book, Eight Days A Week)
My thoughts:
7 and it's opposite number form half of a circle.
30/2=15
So there are 7's opposite number is 15 (including it self) numbers away from 7.
7+15=22
Therefore, 22 is the the number diametrically opposite to 7.
• What process did you use to work on and solve this puzzle?
First I started form a small number which are 4 equally spaced points on the circumference. the number diametrically opposite to 1 is 3, which is 1+4/2. From that I found a pattern that a number and it's opposite number form half of a circle, and the opposite number = number + number of points/2.
• Could you create other extended puzzles related to this one -- some possible, some impossible? (Is there any value to giving your students impossible puzzles?)
It is possible to create other extended puzzles related to this one such as using another shape instead of circle. Weather there is any value to giving students impossible puzzles depends on the mathematics ability of my students. For the students who is already struggling with mathematics, I would like to build on success and avoid giving them impossible puzzle which could attack their confidence on studying mathematics. But I might give impossible puzzles to students who is capable and is looking for more challenging questions. I think I might give impossible puzzles carefully, for example, give them a hint that this might be impossible to solve. Without doing this, this might cause negative effects such as the destruction of trust,
•What makes a puzzle truly geometric, rather than simply logical?
I think a geometric puzzle involves shape and space. A logical puzzle can be solve by deductive reasoning.
Good work.
ReplyDelete