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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 draw the height-time chart as this complicated vessel fills with water?

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

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Make your own pinhole camera for safe observation of the sun, and find out how it works.

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

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

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

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

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Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

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

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

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

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

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

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

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

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

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

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

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Explore the relationship between resistance and temperature

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

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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?

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Starting with two basic vector steps, which destinations can you reach on a vector walk?

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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?

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Which countries have the most naturally athletic populations?

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How would you go about estimating populations of dolphins?

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Work out the numerical values for these physical quantities.