Say a man cycles 5km on a slope and knows (from his altimeter watch) that he has climbed 250m vertically. Gradient can also be calculated using Pythagoras' Theorem. I think it's important that students understand the connection between a 100% gradient and a 45 degree angle. The table below shows gradients and their equivalent angles of elevation. Trigonometry can then be used to calculate the rise and run in order to find the gradient. Picture a slope as a right-angled triangle - we can use a clinometer to measure the angle of elevation and perhaps a trundle wheel to measure the length of the hypotenuse. In real life it is normally impossible to measure the rise and run of a slope so we use trigonometry to calculate these lengths. This article says that anything over 16% is considered very challenging for cyclists of all abilities. Looks like hard work! As a matter of interest, this rather technical article attempts to calculate the steepest gradient that one can cycle up. Give your students a sense of 'steepness' by showing this short video of someone cycling up a road with 38% gradient. Incidentally, 25,000 balls of chocolate are rolled down this 350m-long street in an annual charity Cadbury Jaffa Race. But we usually prefer to state gradient ratios in the form 1:n, so in this case the gradient is 1 in 2.86. We could write this as the ratio 35:100, simplified to 7:20. So how can we interpret this gradient? It means we go up 35 units for every 100 units we go across. There are some impressively steep roads in San Francisco but New Zealand boasts the 'world's steepest road' according to the Guiness Book of Records - Baldwin Street in Dunedin has a gradient of 35%.
Normal Distribution: short contextual exercises Should We Send Out a Certificate? and Do You Fit In This Car?.Describing Data Sets with Outliers and Identifying Outliers are about outliers and skewness in data (see my related post on teaching skewness). Data: These activities on Haircut Costs and Speed Trap focus on comparing box plots.I also like this short Titanic activity on independence. Probability: the card activity Describing Events is an excellent introduction to probability and the activity Venn Diagrams and the Addition Rule is good too.Discrete Random Variables: a short activity Sounds Really Good! (sort of) which features a real-life use of expectation.Includes calculating a correlation coefficient, interpreting a regression equation and considering causality and outliers. Correlation and Regression: a lovely activity on coffee shops and crime.Illustrative Mathematics has some fantastic ideas for teaching S1. I've focused on A level because that's where I think it's hardest to find interesting teaching ideas. I haven't had a chance to look at all these websites yet, but here's some of my top resource recommendations from the websites I've looked at so far. Ooh, new websites! Heaven for a resourceaholic. William Emeny recently posted a link to 'Mathematics 101: Leading Sites for Math Teachers' on his blog.
So it's helpful when someone does the searching, filtering and classifying for us. And they're right - there's so many resources to choose from, no-one has the time to look at them all. It became a bit of an obsession! Unfortunately my colleagues found it all rather overwhelming. I started spending a lot of time looking for resources online and sharing these resources with colleagues. I work in a grammar school where pupils respond quite well to didactic teaching styles and textbooks exercises - arguably there's nothing wrong with this approach, but the lovely Trigonometry Pile Up worksheet reminded me that the internet is full of engaging resources and exciting teaching ideas. It all started when I saw a PGCE student photocopying this Trigonometry Pile Up activity from. Yes, I confess, I'm utterly addicted to searching the internet for maths teaching resources.