Symbolic notation is the order of the day
, 2, 3, pound;, =". How can these be brought into an activity in a useful and fun way?
One way I like to see the use of these symbols is in the game 'Guess my number". For those unfamiliar with this game, the teacher or pupil thinks of a number which can be an integer, decimal, or fraction and tells the class which numbers it lies between. The class is allowed to ask questions that have a "Yes" or "No" response. Their responses are recorded on the board until the correct number is found. Some questions that might be asked are: Is it an integer? Is it a positive number? Is it greater thanI? Is it an even number? Is it a multiple ofI ? and so on.
This activity should show the number line with the area to be considered, accompanied by the correct inequality notation - that way the pupils will then be absorbing the maths notation as part of the activity.
Here's an example. In this case the teacher has thought of a decimal (34.6). I have included a copy of only three of the diagrams that illustrate the type of diagram that should be displayed on the board. (For more examples, see the "Guess my number" game at www.mathagonyaunt.co.uk created by David Warmsley which does display the inequality.) "I am thinking of a number. The number I am thinking of lies between 10 and 50, so what number am I thinking of?"
* is it an even number? No
* is it a whole number? No
* is it greater than 30? Yes
* is it greater than 40? No
* is it greater than 35? No
* is it less than 32? No
* is it greater than 34? Yes
* is it greater than 34.5? Yes
* is it less than 34.7? Yes
* has it got three digits? Yes
* is it 34.6? Yes, well done!
If your department has developed software to support your maths lessons and would like to share it, please send it in to us.
I have returned to teaching after a 10-year break.
I seem to remember that there is a method for drawing an accurate tangent to a parabola which is not just "by eye". Do you know the method I mean?
Yes, I do. The following are the instructions. I have colour-coded each step on the diagram and provided a parabola with a minimum value and one for a maximum parabola.
* Mark the point 'P' (x,y) at which you wish to find the slope of the tangent, this is usually given in or can be deduced from the question.
* First draw the axis of symmetry of the parabola (red line).
* The line of symmetry passes through the lowest (min)highest (max) point on the parabola ('M'). Draw a line that passes through 'M' and is horizontal, ie parallel to the x-axis (blue).
* From 'P' draw a vertical line parallel to the y-axis (coloured green) which meets the horizontal through 'M' at the point 'Q' * Work out the midpoint of MQ and mark with an 'X', so MX = XQ * Now you can draw the tangent to the parabola that passes through the point 'P' on the curve by drawing a line that passes through 'P' and through 'X' (coloured orange).
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX