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

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

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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?

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

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

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

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The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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

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

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

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

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

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

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

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.

Challenge Level

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

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.

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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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Which dilutions can you make using only 10ml pipettes?

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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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Get some practice using big and small numbers in chemistry.

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

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

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Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

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

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Which units would you choose best to fit these situations?

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How would you go about estimating populations of dolphins?