Resources tagged with: Mathematical reasoning & proof

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Broad Topics > Thinking Mathematically > Mathematical reasoning & proof

Add 3 Dice

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. . . .

Dicey Addition

Age 5 to 11
Challenge Level

Who said that adding couldn't be fun?

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.

Less Is More

Age 5 to 11
Challenge Level

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

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?

True or False?

Age 7 to 11
Challenge Level

Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?

Dicing with Numbers

Age 11 to 14
Challenge 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?

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?

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.

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?

Interactive Balance

Age 5 to 11
Challenge Level

In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!

Making Pathways

Age 7 to 11
Challenge Level

Can you find different ways of creating paths using these paving slabs?

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. . . .

Eleven

Age 11 to 14
Challenge Level

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

Adding All Nine

Age 11 to 14
Challenge Level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

Largest Product

Age 11 to 14
Challenge Level

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

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.

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. . . .

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. . . .

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.

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'.

The Triangle Game

Age 11 to 16
Challenge Level

Can you discover whether this is a fair game?

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.

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?

Gabriel's Problem

Age 11 to 14
Challenge Level

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

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. . . .

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?

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?

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? Number

Age 7 to 11
Challenge Level

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

Sweetie Box

Age 5 to 11
Challenge Level

Max and Bryony both have a box of sweets. What do you know about the number of sweets they each have?

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...

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. . . .

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?

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?

Elevenses

Age 11 to 14
Challenge 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?

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. . . .

More Number Pyramids

Age 11 to 14
Challenge Level

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

Guess What?

Age 7 to 11
Challenge Level

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

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.

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.

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.

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?

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.

Calendar Capers

Age 11 to 14
Challenge Level

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

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. . . .

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. . . .

Even So

Age 11 to 14
Challenge Level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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?

1 Step 2 Step

Age 11 to 14
Challenge 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?