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 […]
Starting with real experiences like guessing the numbers on two cards from clues such as “the numbers add up to 20 and one number is three times the other number” learners progess to illustrating the clues by drawing straight line graphs, writing down simultaneous equations and learning formal algebraic methods to solve […]
How is this trick done?
Can you make the trick more impressive?
You can change the x 6 and + 5 to other operations and numbers […]
This problem is adapted from the NRICH task Graphical Triangle with permission […]
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 […]
If three of the four expressions: 2x – 3 and x + 8 and 2x + 3 and 30 – x are equal, find their value and which expression is the odd one out.
In some countries temperature is measured in degrees Celsius (originally called degrees Centigrade) and in other countries it is measured in degrees Fahrenheit.
Draw a graph […]
(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 . […]