# Resources tagged with: Mathematical reasoning & proof

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### There are 96 results

Broad Topics > Thinking Mathematically > Mathematical reasoning & proof

### Tower of Hanoi

##### Age 11 to 14Challenge Level

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

### Chocolate Maths

##### Age 11 to 14Challenge 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. . . .

### More Number Pyramids

##### Age 11 to 14Challenge Level

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

### 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.

### Seven Squares - Group-worthy Task

##### Age 11 to 14Challenge 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?

### Always, Sometimes or Never?

##### Age 5 to 11Challenge Level

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

### Clocked

##### Age 11 to 14Challenge 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?

### One O Five

##### Age 11 to 14Challenge 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. . . .

### The Triangle Game

##### Age 11 to 16Challenge Level

Can you discover whether this is a fair game?

### The Genie in the Jar

##### Age 11 to 14Challenge Level

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

### More Mathematical Mysteries

##### Age 11 to 14Challenge Level

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

### Sticky Numbers

##### Age 11 to 14Challenge Level

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

### Elevenses

##### Age 11 to 14Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

##### Age 5 to 11Challenge Level

Who said that adding couldn't be fun?

### Convex Polygons

##### Age 11 to 14Challenge Level

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

### Guess What?

##### Age 7 to 11Challenge Level

Can you find out which 3D shape your partner has chosen before they work out your shape?

### Eleven

##### Age 11 to 14Challenge Level

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

### Calendar Capers

##### Age 11 to 14Challenge Level

Choose any three by three square of dates on a calendar page...

### Disappearing Square

##### Age 11 to 14Challenge 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. . . .

### Concrete Wheel

##### Age 11 to 14Challenge Level

A huge wheel is rolling past your window. What do you see?

### Tourism

##### Age 11 to 14Challenge 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.

### Konigsberg Plus

##### Age 11 to 14Challenge 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.

### Online

##### Age 7 to 11Challenge 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.

### Largest Product

##### Age 11 to 14Challenge Level

Which set of numbers that add to 10 have the largest product?

### 1 Step 2 Step

##### Age 11 to 14Challenge Level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

### KÃ¶nigsberg

##### Age 11 to 14Challenge 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?

### Aba

##### Age 11 to 14Challenge 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.

### Less Is More

##### Age 5 to 11Challenge Level

Use your knowledge of place value to try to win this game. How will you maximise your score?

### More Marbles

##### Age 11 to 14Challenge 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?

### Marbles

##### Age 11 to 14Challenge 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?

### Gabriel's Problem

##### Age 11 to 14Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

##### Age 11 to 14Challenge 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. . . .

### 9 Weights

##### Age 11 to 14Challenge 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?

### How Many Dice?

##### Age 11 to 14Challenge 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. . . .

### Dicing with Numbers

##### Age 11 to 14Challenge Level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

### 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.

### Flight of the Flibbins

##### Age 11 to 14Challenge 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. . . .

### Square Subtraction

##### Age 7 to 11Challenge 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?

### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Reasoning: the Journey from Novice to Expert (article)

##### Age 5 to 11

This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.

### Same Length

##### Age 11 to 16Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

### Reasoning: Identifying Opportunities (article)

##### Age 5 to 11

In this article for primary teachers we consider in depth when we might reason which helps us understand what reasoning 'looks like'.

### 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. . . .

### Advent Calendar 2011 - Secondary

##### Age 11 to 18Challenge Level

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

### Always, Sometimes or Never? Number

##### Age 7 to 11Challenge Level

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

##### Age 11 to 16Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Unit Fractions

##### Age 11 to 14Challenge Level

Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.

### Children at Large

##### Age 11 to 14Challenge Level

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

### Top-heavy Pyramids

##### Age 11 to 14Challenge Level

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.