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Resources tagged with Mathematical reasoning & proof similar to Counting Counters:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof Top-heavy Pyramids

Age 11 to 14 Challenge Level:

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200. Age 5 to 11 Challenge Level:

Who said that adding couldn't be fun? Eleven

Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct. 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? Calendar Capers

Age 11 to 14 Challenge Level:

Choose any three by three square of dates on a calendar page... Age 7 to 11 Challenge Level:

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . . 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. 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. 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? 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. Cows and Sheep

Age 7 to 11 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field. Pyramids

Age 11 to 14 Challenge Level:

What are the missing numbers in the pyramids? Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know? 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? Square Subtraction

Age 7 to 11 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it? Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true? 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? Ratty

Age 11 to 14 Challenge Level:

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? Concrete Wheel

Age 11 to 14 Challenge Level:

A huge wheel is rolling past your window. What do you see? Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate? 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? 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. 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... 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? Online

Age 7 to 11 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. Take One Example

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure. 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. 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. Making Pathways

Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs? 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. Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed? Tower of Hanoi

Age 11 to 14 Challenge Level:

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice. 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? Marbles

Age 11 to 14 Challenge Level:

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades? What Do You Need?

Age 7 to 11 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number? 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. . . . More Marbles

Age 11 to 14 Challenge Level:

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour? 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. . . . More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... 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. 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. 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. Chocolate Maths

Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . . Three Neighbours

Age 7 to 11 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice? Con Tricks

Age 11 to 14

Here are some examples of 'cons', and see if you can figure out where the trick is. 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. 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? 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? 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.