Search by Topic

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 58 results

Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Calculating with fractions

problem icon

Ratios and Dilutions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

problem icon

Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

problem icon

The Greedy Algorithm

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

problem icon

Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

problem icon

More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

It would be nice to have a strategy for disentangling any tangled ropes...

problem icon

Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:1

Take a look at the video and try to find a sequence of moves that will take you back to zero.

problem icon

A Chance to Win?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

problem icon

Fractions Jigsaw

Stage: 3 Challenge Level: Challenge Level:1

A jigsaw where pieces only go together if the fractions are equivalent.

problem icon

Harmonic Triangle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you see how to build a harmonic triangle? Can you work out the next two rows?

problem icon

Andy's Marbles

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

problem icon

Orange Drink

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

problem icon

Ben's Game

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

problem icon

Fair Feast

Stage: 2 Challenge Level: Challenge Level:1

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

problem icon

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

problem icon

Egyptian Fractions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

problem icon

Shopping Basket

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

problem icon

Fractions in a Box

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

problem icon

Forgot the Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

problem icon

Fair Shares?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

problem icon

There's a Limit

Stage: 4 and 5 Challenge Level: Challenge Level:1

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

problem icon

Snake Coils

Stage: 2 Challenge Level: Challenge Level:1

This challenge asks you to imagine a snake coiling on itself.

problem icon

Tray Bake

Stage: 3 Challenge Level: Challenge Level:1

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

problem icon

Jumping

Stage: 2 Challenge Level: Challenge Level:1

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

problem icon

Diminishing Returns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

problem icon

Reductant Ratios

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What does the empirical formula of this mixture of iron oxides tell you about its consituents?

problem icon

Countdown Fractions

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a chance to play a fractions version of the classic Countdown Game.

problem icon

Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

problem icon

Turning Tangles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Look carefully at the video of a tangle and explain what's happening.

problem icon

All Tangled Up

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you tangle yourself up and reach any fraction?

problem icon

Balance of Halves

Stage: 2 Challenge Level: Challenge Level:1

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

problem icon

Making Longer, Making Shorter

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

problem icon

Introduction to Fractions

Stage: 1 and 2 Challenge Level: Challenge Level:1

The resources in this trail aim to enrich the experiences of children who are just being introduced to fractions.

problem icon

Magic Matrix

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

problem icon

Once Upon a Time

Stage: 2 Challenge Level: Challenge Level:1

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

problem icon

The Harmonic Triangle and Pascal's Triangle

Stage: 5

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

problem icon

Fractions Made Faster

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!

problem icon

Fracmax

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

problem icon

And So on - and on -and On

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the value of this function involving algebraic fractions for x=2000?

problem icon

Hello Again

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

problem icon

Smaller and Smaller

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

problem icon

Hands Together

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

problem icon

Fun Time

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

On Saturday, Asha and Kishan's grandad took them to a Theme Park. Use the information to work out how long were they in the theme park.

problem icon

In the Money

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

problem icon

Red Balloons, Blue Balloons

Stage: 2 Challenge Level: Challenge Level:1

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

problem icon

Pies

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

problem icon

Mathematical Swimmer

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

problem icon

Archimedes and Numerical Roots

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

problem icon

Blue and White

Stage: 3 Challenge Level: Challenge Level:1

In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

problem icon

Unit Fractions

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem icon

One or Both

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?