
Reasoning, convincing and proving
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problemI want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
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Doodles
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections? -
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Be reasonable
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression. -
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Fixing it
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS? -
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Building with solid shapes
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
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Chain of changes
In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it?
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A city of towers
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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Colouring triangles
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
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Let's investigate triangles
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?