Year 10 Exploring and noticing

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Can you find the values at the vertices when you know the values on the edges?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

How can we make sense of national and global statistics involving very large numbers?

Match the cumulative frequency curves with their corresponding box plots.

Can you match these calculations in Standard Index Form with their answers?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

What do you notice about these families of recurring decimals?

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.

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

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?

Can you match up these equivalent algebraic expressions?

Which numbers can we write as a sum of square numbers?

Can you work out which spinners were used to generate the frequency charts?

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?