I was inspired recently by Jocelyn Procopio's new site Storied Math. She posts a video or a picture and asks students to submit a question and solution that goes with the image. I really like the invitation to students to get in on the action of creating real world problems and contexts that are interesting to them. Thinking about a question that I could suggest made me think of a question about tree planting from the Grade 10 Math Finance textbook. When I did this question in class, my students questioned the numbers given in the problem. We decided to research at bit more using the internet to find a tree planting company and find out how they pay their tree planters. The process reminded me of Dan Meyer's Makeover Monday blog posts from a couple of summers ago where he invited teachers to reconstruct a problem from a textbook. Below is a problem ripe for a makeover.
How could we make this question better... lets start by removing all of the information and instead give the students a video of a young person planting trees and ask students what they notice and wonder.
Some questions that I had while watching this video were... How many trees can he plant in a hour/day? How much does that bag weigh when it is full of tree saplings? How much money does he get paid for each tree he plants? How many hours a day does he work? How many of those tree saplings survive and grow? Lots of interesting questions could be asked here. Like "How much of my daily income will be spent on massage therapy for my aching back?" This is a physically demanding job!
Selecting a Question to Explore
The next step is settling on an interesting question to explore and pose a solution. Once students have formulated a question, we can start to figure out what information we will need in order to answer the question. Not only does the textbook problem tell you what question to answer, it gives you exactly the information you need to solve that particular problem. There is no place for the students to think or be curious. They just take the numbers from the text and do some mathematical operations on them and hope they get the correct answer.
Let's decide to answer the same question that the textbook asked... "What would the tree planter's gross pay be for 6 weeks of work?" Now we have to figure out what information we need in order to answer this question.
Digging up the Facts
Solving the Problem
So what will the tree planter make in six weeks of work? The answer to the textbook question would be 3500 trees/wk * 6 wks * $0.17/tree = $3570 gross pay. This is not a whole lot better than working at a fast food restaurant earning minimum wage. 40 hrs/wk * 6 wks * $10.60 hr = $2544 (minimum wage in Nova Scotia as of April 1, 2015 is $10.60 per hour). Consider the cost of travel required to get to BC as well as the special equipment you might have to invest in (shovel, boots, tree bag, camping gear) and the tree planting job listed in the textbook doesn't sound so great. Not to mention days of backbreaking labour in hot and difficult conditions.
Lets say that our planter can plant 2000 trees per day for 5 days per week and earn $0.14 per tree. This would give us a gross pay of $8400 for 6 weeks. This seems a bit more enticing for a student to go out west to plant trees instead of working for minimum wage.
Instead of gross pay, you could have students figure out net pay. What will his deduction be for CPP, income tax, EI, etc? How much will have actually have in his bank account at the end of the six weeks? What are some high-paying summer jobs that are available to young people in Nova Scotia?
There is an article in the October 2015 NCTM publication Mathematics Teaching in Middle School titled Social Justice and Proportional Reasoning. The author, Ksenija Simi-Muller, has a great table at the end of the article listing strategies and advice for modifying textbook tasks to become real-world problems. One of her strategies is, "Require students to create a written argument based on the information given in the textbook problem. This is one of the most effective ways to engage students with real-world problems." I really like this suggestion to get student to critically think about the questions being posed and not just plugging numbers into equations.