Forming Proportional Relationships Demonstration This resource provides animated

Forming Proportional Relationships – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

In 1 day, 1 person can hand print 20 t-shirts. How many T-shirts can 2 people hand print in 1 day? 40 VOLCODE Can you form an equation to show the calculation? T-shirts printed = 20 × Number of people T-shirts printed ∝ Number of people In 1 day, 1 person can paint 2 walls. How many walls can 5 people paint in 1 day? 10 Can you form an equation to show the calculation? Walls painted = 2 × Number of people Walls painted ∝ Number of people

Proportional Relationships In 1 day, 1 person can print 20 t-shirts. VOLCODE T-shirts printed ∝ Number of people Proportional Equation When one variable increases or decreases , the other variable increases or decreases too. The variables are in direct proportion. 1 2 3 4 5 20 40 60 80 100

In 1 day, 1 person can make 5 hats. In 1 day, 1 person can make 8 shorts. In 1 hour, 2 people can make 20 cupcakes. 1 2 3 4 5 5 10 15 20 25 1 2 3 4 8 8 16 24 32 64 1 2 4 8 16 10 20 40 80 160 1 2 4 8 20 0. 5 1 2 4 8

Proportional Relationships It takes 1 person 16 hours to build a wall. How long will it take 2 people to build the same wall? 8 Hours ∝ Number of people When one variable increases the other decreases. The variables are inversely proportional. 1 2 4 8 16 16 8 4 2 1

In 32 hours, 1 person can construct a fence. 16 hours 8 hours How long does it take… … 2 people to construct the same fence? … 4 people to construct the same fence? In 24 hours, 1 person can plant a field of flowers. How long does it take… … 4 people to plant a field of flowers? 6 hours … 12 people to plant a field of flowers? 2 hours In 40 hours, 2 people can harvest a field. How long does it take… … 8 people to harvest a field? 10 hours … 10 people to harvest a field? 8 hours

A company gives a group of 5 employees a project doing data analysis. Their manager estimates the project will be finished in 40 work hours. If 1 employee is taken away from the team how long will the project take? If 3 employees are added to the team how long will the project take? We can use man-hours to calculate the total time needed to complete the task. 5 employees × 40 hours = 200 total man-hours 200 man-hours ÷ 4 employees = 50 hours 200 man-hours ÷ 8 employees = 25 hours Hours to complete Workers

Man-hours Hours to complete Workers 1) 4 students can finish a group project in 10 hours. 8 hours How long would it take 5 students to complete the project? 2) 8 construction workers can dig a ditch in 6 hours. How long would it take 3 workers to dig the ditch? 16 hours 3) 6 accountants can file the finances for a large company after 40 hours. 10 hours How much quicker would 8 accountants be? 4) 4 mechanics can rebuild a car in 5 hours. How much longer would it take 3 mechanics to rebuild the car? 1 hour 40 minutes 5) 12 workers can build a kilometre of road in 8 hours. 40 hours How long would it take 6 workers to construct 2. 5 kilometres of road?

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk