A sequence of activities in this guide takes you from familiar ideas about lines, then emphasises the ‘across’ and ‘up’ aspect of gradient to explain why the product of gradients of perpendicular lines is -1, then uses Pythagoras Theorem to produce the equations of circles and recaps on properties of perpendicular lines […]
Explain your findings about the four lines in this diagram and their gradients.
Match each sketch graph from column A below with a description and a fact about gradients from the other two columns.
When would you be turning the steering wheel to the right?
When would you be turning the steering wheel […]
Now join the blue dots, C and D, with a straight line.
At what angle do the two lines cross?
Investigate the number of squares “along” and “down” from A to B compared with the number […]
The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .
What is the weight of a single sheet of paper?
What is the weight of the envelope?
If w is the weight of the letter (including the envelope) and s is […]
A point whose x- and y-coordinates are both whole numbers is called a lattice point.
How many lattice points are there in the first quadrant (where both x and y coordinates are positive) that lie on the line 3x + 4y = 59?
Find these points. How many different methods can you think of to […]
7, 10, 13, 16, 19, …
15, 18, 21, 24, 27, …
1, -2, -5, -8, -11, …
What do you notice?
The first two sequences come from a multiplication table shifted up. Which […]
(i) Write down the coordinates (0; c) of the point of intersection of the line with the y-axis (the y intercept).
(ii) Choose two points on the line . […]
Look for squares of different sizes and also tilted squares
Start with a 3 by 3 grid of nine dots. Can you find six squares?
Then go on to the 4 by 4 grid of sixteen dots.
What can you say […]