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Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.

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What shape and size of drinks mat is best for flipping and catching?

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

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Examine these estimates. Do they sound about right?

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

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

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

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

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Which units would you choose best to fit these situations?

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Is it really greener to go on the bus, or to buy local?

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

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Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

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

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Get some practice using big and small numbers in chemistry.

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Which dilutions can you make using only 10ml pipettes?

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Use trigonometry to determine whether solar eclipses on earth can be perfect.

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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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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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How would you go about estimating populations of dolphins?

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Explore the relationship between resistance and temperature

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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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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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Work out the numerical values for these physical quantities.

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

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

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

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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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Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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

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10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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This problem explores the biology behind Rudolph's glowing red nose.