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Thinking Mathematically

Thinking Mathematically. Some big ideas … for the rest of your course. Ian Mcdonald ianmcdonald@hotmail.com. What is Mathematics?. Activity : Write your answer to this question in a sentence. Activity : Write six words to describe what you feel about mathematics. Some Answers.

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Thinking Mathematically

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  1. Thinking Mathematically Some big ideas … for the rest of your course Ian Mcdonald ianmcdonald@hotmail.com

  2. What is Mathematics? Activity: Write your answer to this question in a sentence. Activity: Write six words to describe what you feel about mathematics.

  3. Some Answers ... Boring – learning your tables Beautiful – have a look Difficult – decimal long division! Satisfying – when you get the answer! Pointless – see difficult Rewarding – see satisfying but also could help get a job.

  4. Symbols & Meaning What do these symbols mean?    Activity: Use these symbols to write a story see if people can read the story. Here are more symbols to use:  .

  5. More Symbols ... What do these symbols mean... + - x / Activity: Write any meanings you know for the above symbols. Invent one of your own.

  6. Symbols, a Big Message Before you do anything with symbols make sure you understand their meaning, but ….. Warning - symbols that look the same can mean something completely different ! Activity: Think of some examples. Warning - Symbols that look different can mean the same thing! Activity: Think of some examples of this.

  7. Symbols & Position Where a symbol is can change what it means ... What’s the meaning of this symbol 2 and this 22 and this 222222222222222 Activity: Here is the number 21 write an explanation of what the symbols 2 and 1 mean. Can you think of other examples of position changing meaning in maths or anywhere else?

  8. More on Position What does this mean 2 + 3 Is it the same as 3 + 2 What about 3 x 2 and 2 x 3 What about 3 / 2 and 2 / 3 What about 3 - 2 and 2 - 3 Activity: Try and explain why things go wrong with / and -.

  9. Words in Mathematics As well symbols we use words. The big message also applies to words … Before you do anything with words make sure you understand them. Activity: Give some meanings of these words inside and outside mathematics: Odd, point, prime, plane.

  10. Rules There is always someone telling us what to do - for example .. • If it’s cold then wrap up warm • If you are carrying scissors then don’t run • If you watch too much television then you will get square eyes • If it’s a triangle then it has three sides Activity: Can you see a pattern to these rules. How would you describe it? Write few of your favourite rules using this pattern.

  11. Buy 2 get one free .. More on Rules Rules tell us what to expect from the world .. and they are great because sometimes you can ... Buy .. 1. If it’s raining then you get wet 2. If you get wet then you get a cold And get … if it’s raining the you get a cold. Activity: Invent some more special offers.

  12. Problem Solving Here’s one for you … A rectangle sits in a circle with one corner at the centre of the circle and one corner at the circumference. The rectangle has a diagonal length of 2 cm. What is the radius of the circle? Activity: Some people find this problem hard some people find it easy. Write down why you think this is.

  13. Bad teaching I can’t be bothered – its boring I’m just thick There’s always something good on telly I haven’t got a pen I just don’t know where to start Why stops us solving problems? These are some of the reasons people give …

  14. Things to Help you Problem Solve • Get motivated – you have to want to solve the problem • Discuss the problem with others: e.g. teacher, parent, students, online support. • Adopt a methodical approach to problem solving. • Don’t give up – problem solving takes time

  15. Problem Solving Methods -1 Brainstorming – write down everything you know about the things mentioned in the problem. Activity: Write down everything you know about squares. Try and come up with at least 10 things!

  16. Problem Solving Methods -2 Connections – look for connections between the things mentioned in the problem or the facts that your brainstorm has produced. Activity: Try and think of something that connects a square and a circle. What about a square and a rectangle?

  17. Summary • Symbols - enable us to write difficult things simply. We must get used to using them. • Meaning – Understand what the symbols mean – this can change with the position of the symbols • Words – if you are doing a problem make sure you understand all the words - don’t try and solve it until you do. • Problem Solving – Be methodical and don’t give up.

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