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Still more lollies

Student Activity: 

On Monday, Sam, Sonny and Sylvia share lollies that they've been given.
Sonny has been given twice as many lollies as Sam, and Sylvia has three times as many lollies as Sam plus two lollies.

They are given the same number of lollies each day up to (and including) Friday.
Altogether, they are given 70 lollies.

How many lollies did Sam get on Monday?

Achievement Objectives:

Achievement Objective: NA4-7: Form and solve simple linear equations.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
Solve problems that involve simple linear relationships
Write simple linear expressions
Devise and use problem-solving strategies to explore situations mathematically
Description of mathematics: 

In this problem students are encouraged to to apply algebraic reasoning to find a solution. As they use a letter to represent an unknown amount, they are able to see how other unknowns can be expressed relative to the first unknown, how an equation can be constructed and a solution found.

This is one of six problems: Lollies! (Level 1), More Lollies (Level 1), Sharing Lollies (Level 2), Lollies, Lollies, Lollies (Level 3) and Still More Lollies (Level 4), which become more algebraic in their focus at each level.

Activity: 

Problem

On Monday, Sam, Sonny and Sylvia share lollies that they've been given. Sonny has been given twice as many lollies as Sam, and Sylvia has three times as many lollies as Sam plus two lollies.

They are given the same number of lollies each day up to (and including) Friday. Altogether, they are given 70 lollies. How many lollies did Sam get on Monday?

Teaching Sequence

  1. Pose the problem to the class.
  2. Ask some simple questions to get the students thinking about the problem.
    If Sam has ten lollies on Monday, how many have Sonny and Sylvia got on?
    If Sonny has ten lollies how many do Sylvia and Sam have?

    Ask the students to suggest equations they can use to express their answers.
  3. Encourage students to use letters to express amount: For example:
    Sam s
    Sonny 2s
    Sylvia 3s + 2
  4. Have students work on the problem using equations in their written record of the solution.
  5. As the students work ask:
    What number operation have you selected? Why?
    Tell me what this equation tells us.
  6. Share solutions to the problem discussing the different approaches used.

Extension to the problem

Have students to make up similar problems for others to solve.

Solution

If Sam gets s lollies, Sonny gets 2s and Sylvia gets 3s + 2. On any one day they all get s + 2s + (3s + 2) = 6s + 2.

Over 5 days they get 5(6s + 2) = 30s + 10. This is 70. So the equation is 30s + 10 = 70. Taking 10 from both sides gives 30s = 60. Divide both sides by 30 to find s = 2. Sam got 2 lollies on Monday.

Alternatively, 70 lollies in five days is 70/5 = 14 in one day. Solve 6s + 2 = 14. So 6s = 12 and s = 2.

AttachmentSize
StillMoreLollies.pdf103.91 KB
HeRareAno.pdf206.84 KB