Year 11 Exploring and noticing

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

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

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

Two ladders are propped up against facing walls. At what height do the ladders cross?

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?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value. Can you find that x, y pair?

Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

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?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

What is special about the difference between squares of numbers adjacent to multiples of three?

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

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Can you find the area of a parallelogram defined by two vectors?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

If a sum invested gains 10% each year how long before it has doubled its value?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

What is the same and what is different about these circle questions? What connections can you make?

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?

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

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?