Real+life+examples

This page is contains details about real life examples of algebra:

=Currency conversion= If you want to work out how many euros you will get for your holiday spending money, you might think about the conversion rate: euros = pounds x conversion rate or, to avoid confusion with longs words: E = P x R If you were being really smart, you would realise that there is a commission taken by some places, so the formula is: E = P x R - C

=Days of the week= If you are asked how many days there are in a week, you would find the answer easy - there are 7. How about the number of days in two weeks? Again, the answer is fairly straightforward - there are 14. What happens when you are asked how many days there are in three weeks, or four or five? If you know the formula you could work this out. 1 week is 1 × 7 days = 7 2 weeks is 2 × 7 days = 14 3 weeks is 3 × 7 days = 21 4 weeks is 4 × 7 days = 28 So, the formula to work out the number of days is: number of days = number of weeks × 7

=The coffee shop= This is wonderfully exemplified using the Teachers TV video, but could be done without quite so much 'moving around'. The scenario is someone is just opening a coffee shop and needs to know how many chairs to buy so that every customer has a seat. It takes (for example) 30 seconds to buy a cup of coffee and 3 minutes (ok - so the numbers are unrealistic!) to drink it. Assuming that there is a steady queue of people waiting to buy coffee, how many chairs are needed? The expression is simply time to drink / time to buy or D / B This can be demonstrated with queues of students (as in the video), which is a powerful way of reinforcing the learning, and begs further questions about 'what happens if..' eg
 * buy more chairs
 * reduce queuing time (use more tills)

Jess found some cool videos on Teachers TV:
 * 1) [|Algebra video (fruit and veg)] This has a number of key points: a **magic trick** to engage, a **practical demonstration** of how algebra (actually apples and oranges!) can be used to prove a theory //for any number (//rather than just for one number), and a demonstration of how algebra can be used to **solve real problems**
 * 2) [|Juggling] This shows juggling being used to transition between number patterns and algebra, simply to represent an 'unknown number'. The technique was quite simple - start by develpoing number patterns to represent different juggling patterns, and then asking the pupils to suggest a pattern for the beanbags in a box. Students try guessing the number of beanbags (which is needed in order to propose a suitable a pattern), but then the teacher says "no more guesses allowed. What do we normally do in maths to represent an known number?". Bingo!

Let's not forget the //kitchen scales// thing for introducing equations! [|Interactive Kitchen Scales activity to show balancing and solving values for X.]