![]() ![]() Note that this is a American resource so uses the terms slope and grade instead of gradient. A wide range of exercises in this pack.My worksheet on real-life gradients on TES.For example you could use home-made clinometers and trigonometry to calculate the gradients of slopes in and around school, like staircases and ramps. These real-life applications of mathematics can easily be made into practical class activities. Now use 'rise over run' to calculate the gradient - in this case we get 5%. ![]() Use Pythagoras to calculate the base (4994m). Again, picture a right-angled triangle - the hypotenuse is 5000m and the height is 250m. 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. ![]()
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