Working with rates and fractions

1. Discuss the idea of fuel consumption 
   What makes a difference to the fuel consumption of a vehicle?
   Students might bring up issues such as the size of the engine, the load on the car, urban and rural travel, and the way the car is driven.
   Explain that fuel consumption for a vehicle is often given in litres per hundred kilometres travelled. For example, 4.5L/100 means that the vehicle uses 4.5 litres of petrol to travel 100 kilometres.
    
2. Use the context to pose this rate problem:
   A vehicle has an average fuel consumption of 4.5 Litres per 100 kilometres.
   How far does it travel on 1.8 litres of petrol?
   Ask students to create a rate table for the problem then solve it. Make calculators freely available.
    
   
   Look for students to use either within or between strategies as shown below:
   • Within                                                                                    
     
      
   • Between
     
      
3. Change the problem so the amount of fuel is the missing value.
   A vehicle has an average fuel consumption of 4.5 Litres per 100 kilometres.
   How many litres of petrol does it consume to travel 160 kilometres?
   Let students solve the problem using whatever strategy they choose. Possible strategies include:
    
   
   
    
4. Pose further relevant problems with varied, given consumption rates and target measures to encourage students to generalise the strategies that work. Problems should include finding the consumption rate per 100km. Ensure students create a rate table for each problem. Consider grouping students to encourage peer scaffolding and extension.
   You might also introduce relevant te reo Māori kupu, such as pāpātanga (rate), whakawehe (divide, division), and whakarea (multiply, multiplication). 
   Examples might be:

• Carla’s car uses 15.3 litres of petrol to travel 375 kilometres. What is the average fuel consumption of her car  in litres per 100 kilometres?
  
   
• Paea’s truck uses 33 litres of diesel per 100 kilometres when fully loaded. How many litres of diesel should Paea expect her truck to use on a 640-kilometre trip?
  
   
• Jaden’s scooter has a tank that holds 3.7 litres of fuel. It uses 1.5 litres per 100km. How many kilometres will Jaden’s scooter travel on a full tank.
  Note that 66.6 is the unit rate of kilometres per litre.
  
   

Next steps 

1. Ask students to create their own rate problems for classmates to solve.
    
2. Broaden the problems to include other types of rates, such as value for money (in dollars per litres or 100 grams), water flow (in litres per minute, and population density (in people per square kilometre). You might plan these with reference to relevant learning from other curriculum areas, or to issues that are important to your community.
    
3. Pose problems in which two different rates are compared. For example:
   • Mike’s car travels 47km on 4 litres of petrol.
     Allan’s car travels 68km on 7 litres of petrol.
     Which car has the lowest fuel consumption?
   • Tui Island has an area of 12 km² and there are 28 people living on it.
     Weka Island has an area of 26 km² and there are 61 people living on it.
     Which island has the highest population density?