What is a formula? A formula is a special type of equation that links two or more physical variables. w l P = 2(l + w) P represents the perimeter of a rectangle l stands for the length of the rectangle w symbolizes the rectangle’s width. Teacher notes Remind pupils that the letter symbols in formulae are called variables because their value can vary. Unlike equations where the unknown can be any real number, the variables in formulae are often limited to values determined by the context. For example, if the variable in a formula represents a length it can only take positive values. If it represents a number of objects then it can only take whole number values. We can use this formula to work out the perimeter of any rectangle given its length and width. We do this by substituting known values into the formula.

Speed, distance and time If a car travels 2 km in 1 min 40 secs, at what speed is the car travelling? S = d t Use the formula: Write the distance and the time using the correct units before substituting them into the formula. 2 kilometres = 2000 metres 1 min and 40 secs = 100 seconds Now substitute these numerical values into the formula. Teacher notes Ask pupils how we could have found the average speed of the car in km/h rather than m/s. This will be important in helping the students correctly answer the average speed questions in the next slide. S = 2000 100 Write the units in as the final step in the calculation. = 20 m/s

Adding numbers to formulae Teacher notes This activity introduces students to a variety of different formulae and gives them a brief description of what the formulae are used to calculate. Students should be encouraged to use the pen tool to show their working to calculate the correct answer. They can then press on the notelet to reveal the correct answer. Each time the reset button is pushed on this activity, a new set of conditions will be generated. This gives the activity an open-endedness that ensures it can be used several times.

Van hire

Van hire I need a van for 5 days and I will be doing 1000 miles. Which company will be cheaper? What’s the maximum mileage I can do in one day in a Green Getters van before I spend £75? Teacher notes The gentleman needs a van for 5 days during which time he will travel 1000 miles. This will cost him (£50 × 5) + (£0.20 × 1000) = £450 with Yellow Cheapies and (£25 × 5) + (£0.40 × 1000) = £525 with Green Getters. It will be cheaper for him to hire a van from Yellow Cheapies. The lady has £75 to spend in one day with Green Getters. The hire of the van is £25, so she will have £75 – £25 = £50 to spend on mileage. This will allow her to travel £50 ÷ £0.40 = 125 miles in one day. For the last question, if we have the formulae equalling each other, we can work out when d and m will give the same cost for both firms. 50d + 0.2m = 25d + 0.4m 50d – 25d = 0.4m – 0.2m 25d = 0.2m 125d = m When d = 1 and m = 125, the cost is the same for both firms. The same is true when d = 2 and m = 250. Can you find values for d and m where the cost is the same for both firms? How did you work this out?