A Math Problem That Will Get Third Graders Thinking

In this Teaching Children Mathematics article, Ed Enns (Waterloo Region School District, Canada) suggests the following problem-solving challenge and invites teachers to try it with third or fourth graders and e-mail him with solutions, student work, and feedback. 

Students work in pairs or triads supplied with a large piece of paper to record solutions, pens or markers, and (optionally) calculators. Here’s the problem (given to students after some introductory discussion of allowances):

• You are going to receive an allowance for the next twelve weeks. You must choose how you would like to be paid. These are your choices:

• You get $2 for the first week, but you get $0.25 more every week after that.
• You get $0.01 for the first week, but the amount doubles every week after that.

How much would you get paid if you picked the first approach?

How much would you get paid if you picked the second? 

Which choice would give you more money?

After reviewing the problem with the class, Enns suggests having students make a prediction of which choice bring in more money and take a straw poll to see what students think. As groups work on the problem, the teacher circulates to observe problem-solving strategies and perhaps take digital photos of their work. “Try not to tell students how to do the math,” he says, “but use questions to provoke their thinking,” such as:

• What is the rule for how much money you will receive?
• How much money do you get the first week?
• How could you keep track of how much money you receive each week?
• Is that amount in cents or dollars?
• How much money would you have altogether after 12 weeks?
• Students who finish early might be challenged to try a third payment option: Flip a coin each week to determine the amount of allowance – if the coin lands on heads, you get $6, if it lands on tails, you get no allowance. Could this end up being more lucrative than the other two approaches?

When students have finished, have groups present their solutions and strategies and compare and contrast them in terms of accuracy and efficiency. 

“Which Is the Better Deal?” edited by Ed Enns in Teaching Children Mathematics, February 2015 (Vol. 21, #6, p. 328-330), www.nctm.org; Enns can be reached at ed_enns@wrdsb.on.ca.

From the Marshall Memo #575