Finding unit rates

1. Use the cards of capsicums made from the Copymaster and toy $1 coins to pose this problem, or pose another, similar problem that makes use of a more relevant context.
   To buy six capsicums costs $18.00. What is the price of one capsicum?
   Set up a material model of the context that shows the 6 capsicums evenly spread out above a line of 18 coins, also evenly spread out. The capsicums should be placed approximately in alignment with the middle coin in every group of 3 coins. 
   
    
2. Let students attempt solving problem individually or in pairs. 
   Aks students to share and justify their use of different strategies. Look for them to justify their thinking with reference to division and the material model. For example, students might use ‘sharing’ division (partitive) as the $18 is shared equally among the six capsicums. Other students may use a form of one-by-one dealing or trial and error in conjunction with skip counting. For example, counting “two, four, six, eight, ten, twelve” and finding that each capsicum cost more than $2, and therefore estimating that they cost $3 each.
   As students share their strategies, have them record written and diagrammatic expressions.
    
3. Use the calculator to confirm the answer to the problem. 
   What operation can I put into the calculator to find out the cost of one capsicum?
   Look for students to associate equal sharing with division (i.e. 18 ÷ 6 = $3 per capsicum).
    
4. Model with the materials how the result of equal sharing is anticipated by division.
   
    
5. Draw a rate table of the problem to connect it to the previous lesson on unit rates.
   Discuss the meaning of the wording “three dollars per capsicum.” Generalise that “per” means "for every". In this case, this means you pay $3 for every capsicum.
    
    
6. Use the cards created from the copymaster and toy $1 coins to introduce the following problems, or similar problems involving money and more relevant contexts. Allow calculators if students need to use them to make and/or check calculations. Consider grouping students to encourage peer scaffolding and extension. Look for students to apply division and justify the operation by referring to equal sharing. 
   Consider introducing relevant te reo Māori kupu, such as pāpātanga (rate) and whakawehe (divide, division).
   For each problem, students should draw a rate table, including the operational arrows.

• You pay $20 for five taros. If each taro is the same price, what is the price of one taro?
  
   
• You pay $14 for four mangoes. If each mango is the same price, what is the price of one mango?
  
   
• You pay $22 for eight coconuts. If each coconut is the same price, what is the price of one coconut?
  
   

Next steps 

1. Ask students to create their own unit rate problems, modelled off the problems shown above. Let them use the cards from the copymaster and toy $1 coins to create and model the problems and solutions.
    
2. Broaden the contexts for “find the unit rate” problems to include other measurement attributes. Examples might be:
   • You scoot 650 metres in 10 minutes. How many metres do you scoot per minute?
   • There are 36 tennis balls in 12 packets. How many tennis balls are in each packet?
   • In the field there are 16 sheep and four goats. How many sheep are there for every goat?
   • The barber does 32 haircuts in eight hours. How many haircuts does she do per hour?
   • You get 10 litres of sparkling water out of four bottles. How much sparkling water does 4 bottles hold?