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.
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?
Have students to make up similar problems for others to solve.
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.
Printed from https://nzmaths.co.nz/resource/still-more-lollies at 4:54pm on the 20th January 2021