Resources for Teaching Mathematics: 14-16 by Colin Foster

By Colin Foster

This source comprises 70 whole lesson plans with complementary worksheets for the scholars, particularly designed for GCSE point maths.

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12 = 4 = 2). 1 a is always irrational, provided a ≠ 0 (which it cannot be, since a is irrational), because if it were 2 3 1 m a n rational then it could be expressed as = , where m and n are integers with n ≠ 0, and inverting n m 1 a both sides of this would give a = , so a would be rational, which is a contradiction. So cannot be rational if a is irrational. This is another ‘proof by contradiction’ argument, similar to the one above. , ( 3 ) = 3). 2 31 Homework (5 min) Find out why Greek mathematicians were so worried about irrational numbers.

Think about how to convince everyone that your answer is better than the calculator’s. 111 111 111 1112 – 111 111 111 1102 111 111 111 1122 – 111 111 111 1102 222 222 222 222 × 111 111 111 112 – 222 222 222 223 × 111 111 111 111 222 222 222 2222 444 444 444 444 222 222 222 2222 – 111 111 111 1112 111 111 111 111 Find other calculations that match the structures of these ones. Make up your own calculator-unfriendly calculations. Make sure that you have a way of doing them! © Colin Foster 2010 Resources for Teaching Mathematics 14–16 25 7 Being Human Introduction Very often in mathematics problems all the necessary information is carefully provided, with no extraneous details.

To make it easier Learners who struggle with bearings could be encouraged to visualize ‘North’ as being towards the TEACH ER SH EET Resources for Teaching Mathematics: 14–16 front of the classroom (whether that is actually the case or not) and then position themselves at certain specified bearings from other learners. Helpful teacher feedback can address misconceptions quickly. 20 Clock Bearings TA SK SH EE T 12 1 North 11 10 2 9 3 8 4 7 5 6 Work out or measure the bearing from each number to every other number.

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