The lattice points are where the lines intersect. How many interior lattice points do your lines go through?
Draw more grids. Before you draw the diagonals, can you predict how many lattice points they will go through? How do you know?
A point whose […]
(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 . […]
When would you be turning the steering wheel to the right?
When would you be turning the steering wheel […]
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 […]
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.
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 […]
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 […]