Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Differences
A chance to win?
Pair products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Warmsnug double glazing
Where is the dot?
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
A little light thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Standard index form matching
Quad in quad
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Plus minus
Of all the areas
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Fair shares?
What's possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Attractive tablecloths
Tiny nines
Pick's theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Triangle in a triangle
Can you work out the fraction of the original triangle that is covered by the inner triangle?
Perpendicular lines
Nicely similar
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Filling the gaps