Resources tagged with Mathematical reasoning & proof similar to Speeding Boats:
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Ratio. Cubes & cuboids. Games. Real world. Speed and acceleration. Working systematically. Visualising. Nets. Mathematical reasoning & proof. Regular polygons and circles.There are 172 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
Concrete Wheel
Age 11 to 14 Challenge Level:
A huge wheel is rolling past your window. What do you see?
Triangle Inequality
Age 11 to 14 Challenge Level:
ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.
Convex Polygons
Age 11 to 14 Challenge Level:
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Clocked
Age 11 to 14 Challenge Level:
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
How Many Dice?
Age 11 to 14 Challenge Level:
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Konigsberg Plus
Age 11 to 14 Challenge Level:
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Sticky Numbers
Age 11 to 14 Challenge Level:
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Disappearing Square
Age 11 to 14 Challenge Level:
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
Flight of the Flibbins
Age 11 to 14 Challenge Level:
Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
Volume of a Pyramid and a Cone
Age 11 to 14
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
9 Weights
Age 11 to 14 Challenge Level:
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Online
Age 7 to 14 Challenge Level:
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Tourism
Age 11 to 14 Challenge Level:
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Königsberg
Age 11 to 14 Challenge Level:
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
Pattern of Islands
Age 11 to 14 Challenge Level:
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Yih or Luk Tsut K'i or Three Men's Morris
Age 11 to 18 Challenge Level:
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
Air Nets
Age 7 to 18 Challenge Level:
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Not Necessarily in That Order
Age 11 to 14 Challenge Level:
Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?
Proofs with Pictures
Age 14 to 18
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Calendar Capers
Age 11 to 14 Challenge Level:
Choose any three by three square of dates on a calendar page...
Children at Large
Age 11 to 14 Challenge Level:
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Rhombus in Rectangle
Age 14 to 16 Challenge Level:
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
One O Five
Age 11 to 14 Challenge Level:
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Coins on a Plate
Age 11 to 14 Challenge Level:
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
Go Forth and Generalise
Age 11 to 14
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
A Chordingly
Age 11 to 14 Challenge Level:
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
Picture Story
Age 11 to 16 Challenge Level:
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Pent
Age 14 to 18 Challenge Level:
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Rolling Coins
Age 14 to 16 Challenge Level:
A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .
Seven Squares - Group-worthy Task
Age 11 to 14 Challenge Level:
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Paradoxes
Age 7 to 14
A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Aba
Age 11 to 14 Challenge Level:
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
Tis Unique
Age 11 to 14 Challenge Level:
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
Always the Same
Age 11 to 14 Challenge Level:
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
Winning Team
Age 11 to 14 Challenge Level:
Nine cross country runners compete in a team competition in which there are three matches. If you were a judge how would you decide who would win?
Tri-colour
Age 11 to 14 Challenge Level:
Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?
Three Frogs
Age 14 to 16 Challenge Level:
Three frogs started jumping randomly over any adjacent frog. Is it possible for them to finish up in the same order they started?
Logic
Age 7 to 14
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
What Numbers Can We Make?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Greetings
Age 11 to 14 Challenge Level:
From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How. . . .
Sprouts Explained
Age 7 to 18
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .
Mindreader
Age 11 to 14 Challenge Level:
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Encircling
Age 14 to 16 Challenge Level:
An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?
NRICH is part of the family of activities in the Millennium Mathematics Project.