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Resources tagged with Mathematical reasoning & proof similar to James's Code Challenge:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof 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. 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? 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. Con Tricks

Age 11 to 14

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

Age 11 to 14 Challenge Level:

We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can. . . . More Mathematical Mysteries

Age 11 to 14 Challenge 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. . . . The Genie in the Jar

Age 11 to 14 Challenge 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. . . . 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. . . . 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. 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? Cycle It

Age 11 to 14 Challenge Level:

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total. Breaking the Equation ' Empirical Argument = Proof '

Age 7 to 18

This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning. 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. Master Minding

Age 11 to 14 Challenge Level:

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions? Advent Calendar 2011 - Secondary

Age 11 to 18 Challenge Level:

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

Age 11 to 16 Challenge Level:

When is it impossible to make number sandwiches? Unit Fractions

Age 11 to 14 Challenge 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. 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? 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? 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? Impossible Sandwiches

Age 11 to 18

In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot. 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. . . . 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. 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. Cross-country Race

Age 11 to 14 Challenge Level:

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places? 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. 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. 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. 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. 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. More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... 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. 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. . . . 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, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? 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? What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

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

Age 11 to 16 Challenge Level:

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

Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs? 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? Age 11 to 16 Challenge Level:

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