Year 11 Visualising and representing

problem

Vector journeys

Age

14 to 18

Challenge level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

problem

Factorising with multilink

Age

14 to 16

Challenge level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

problem

Double trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...

problem

Salinon

Age

14 to 16

Challenge level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

problem

Spotting the loophole

Age

14 to 16

Challenge level

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

problem

Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

problem

Square number surprises

Age

14 to 16

Challenge level

There are unexpected discoveries to be made about square numbers...

problem

Picture story

Age

14 to 16

Challenge level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

problem

Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?

problem

Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

problem

Doesn't add up

Age

14 to 16

Challenge level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

problem

Triangles and petals

Age

14 to 16

Challenge level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

problem

The spider and the fly

Age

14 to 16

Challenge level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

problem

A question of scale

Age

14 to 16

Challenge level

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?

problem

Immersion

Age

14 to 16

Challenge level

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

problem

Partly painted cube

Age

14 to 16

Challenge level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?