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Invent a scoring system for a 'guess the weight' competition.

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Is there a temperature at which Celsius and Fahrenheit readings are the same?

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Which countries have the most naturally athletic populations?

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To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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Use your skill and judgement to match the sets of random data.

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Can you deduce which Olympic athletics events are represented by the graphs?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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How would you design the tiering of seats in a stadium so that all spectators have a good view?

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Have you ever wondered what it would be like to race against Usain Bolt?

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Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?

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Get some practice using big and small numbers in chemistry.

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Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the. . . .

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In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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Can you work out which processes are represented by the graphs?

Challenge Level

Formulate and investigate a simple mathematical model for the design of a table mat.

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Where should runners start the 200m race so that they have all run the same distance by the finish?

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In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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Simple models which help us to investigate how epidemics grow and die out.

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Which dilutions can you make using only 10ml pipettes?

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What shape would fit your pens and pencils best? How can you make it?

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What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

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Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Challenge Level

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Challenge Level

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Challenge Level

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Challenge Level

Explore the relationship between resistance and temperature

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Analyse these beautiful biological images and attempt to rank them in size order.

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An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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These Olympic quantities have been jumbled up! Can you put them back together again?

Challenge Level

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Challenge Level

When you change the units, do the numbers get bigger or smaller?

Challenge Level

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Challenge Level

Which units would you choose best to fit these situations?