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mathschallenge.net- Irrationality Of E 17/10/2010 01:00
Prove that e is irrational.
Problem ID: 377 (17 Oct 2010) / Difficulty: 4 star - Rectangle Construction 17/10/2010 01:00
Find the connection between the constructed length and the original rectangle.
Problem ID: 376 (17 Oct 2010) / Difficulty: 2 star - Inscribed Circle In Isosceles Triangle 16/08/2010 01:00
Find the radius of the circle inscribed inside the isosceles triangle.
Problem ID: 375 (16 Aug 2010) / Difficulty: 2 star - Multiplying Magic Square 16/08/2010 01:00
Show how the values 1, 2, 4, 8, 16, 32, 64, 128, and 256 can be placed in a 3x3 square grid so that the product of each row, column, and diagonal gives the same value.
Problem ID: 374 (16 Aug 2010) / Difficulty: 3 star - Polynomial Roots 07/08/2010 01:00
Prove that the roots of the polynomial, xn + cn-1xn-1 + ... + c2x2 + c1x + c0 = 0, are irrational or integer.
Problem ID: 373 (07 Aug 2010) / Difficulty: 3 star - Hops And Slides But Never Square 07/08/2010 01:00
Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square.
Problem ID: 372 (07 Aug 2010) / Difficulty: 3 star - Irrationality Of Pi 24/12/2009
Prove that π is irrational.
Problem ID: 371 (24 Dec 2009) / Difficulty: 4 star - Square And Round Plugs 24/12/2009
Which fits better... a round plug in a square hole or a square plug in a round hole?
Problem ID: 370 (24 Dec 2009) / Difficulty: 2 star - Algebraic Cosine 30/11/2009
Prove that cos(x) is algebraic if x is a rational multiple of Pi.
Problem ID: 369 (30 Nov 2009) / Difficulty: 4 star - Inscribed Square 30/11/2009
Find the side length of the square inscribed inside the right angled triangle.
Problem ID: 368 (30 Nov 2009) / Difficulty: 2 star - Infinite Circles 15/11/2009
What fraction of the large red circle do the infinite set of smaller circles represent?
Problem ID: 367 (15 Nov 2009) / Difficulty: 4 star
- Stage 1::[problem*] How do you see it ? Here are some short problems for you to try. Talk to your friends about how you work them out.
- Stage 1::[Featured Solution] Odd times Even Not that many solutions but some good justifications offered here.
- Stage 1::[Article] From objects and images to mathematical ideas This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.
- Stage 1::[problem] Models in mind This article looks at how models support mathematical thinking about numbers and the number system
- Stage 2::[problem*] Let's divide Up! Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
- Stage 2::[problem*] How do you see it ? Here are some short problems for you to try. Talk to your friends about how you work them out.
- Stage 2::[Featured Solution] Square subtraction This challenge produced some thoughtful ideas and reasons that would lead to a proof - very good for primary school children!
- Stage 2::[Article] From objects and images to mathematical ideas This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.
- Stage 2::[problem] Models in mind This article looks at how models support mathematical thinking about numbers and the number system
- Stage 3::[problem*] What numbers can we make? Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
- Stage 3::[problem**] Always a multiple? Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
- Stage 3::[problem**] Take Three From Five Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
- Stage 3::[problem**] What numbers can we make now? Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
- Stage 3::[Featured Solution] Magic Letters We received lots of insightful comments to this problem.
- Stage 3::[Article] From objects and images to mathematical ideas This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.
- Stage 3::[Game] Cubic Net This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
- Stage 3::[Game] Diamond Collector Collect as many diamonds as you can by drawing three straight lines.
- Stage 3::[problem] Models in mind This article looks at how models support mathematical thinking about numbers and the number system
- Stage 4::[problem*] Factorising with Multilink Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
- Stage 4::[problem*] Pair Products Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
- Stage 4::[problem**] Take Three From Five Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
- Stage 4::[problem**] What numbers can we make now? Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
- Stage 4::[Article] From objects and images to mathematical ideas This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.
- Stage 4::[Game] Cubic Net This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
- Stage 5::[problem**] Maths Shop Window Make a functional window display which will both satisfy the manager and make sense to the shoppers
- Stage 5::[Featured Solution] Particularly general There were three nice solutions to this advanced problem concerning generic examples. Perhaps younger students might like to try to work through one of them, whereas older students might like to compare them.
- Stage 5::[Article] From objects and images to mathematical ideas This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.
- Stage 5::[Game] Cubic Net This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!