Turning Textbook Questions into Problem-Based Learning Activities

Over the last few years I’ve done my best to create a student-centred Math class using a mix of Dan Meyer’s 3 Act Math strategy, Peter Liljedahl’s Thinking Classroom framework and some other routines like Notice & Wonder mixed in, all in a Pear Deck interactive slideshow.

This week I wanted a problem-based activity on volume so I turned to my version of a textbook; Khan Academy practice sets. I picked a problem that my students will see during their independent practice problems on the Khan Academy website and fleshed it out to create a student-centred activity out of it. Thought I’d share the process with you to show that you can take (sometimes boring) problems right out of a textbook & create a student-centred thinking task for your class.

Here’s the original problem from Khan Academy:Screenshot 2017-10-24 at 8.28.49 AM

So my first task was to find an actual image of a tent and use Google Drawings to add the dimensions as well as the volume to the image:Tent

So this is what I show students to start. I do not tell them yet that I want them to find the height. I have a series of questions we run through every time that I build in a Pear Deck slideshow (where students will be able to answer on their phone & I can display their answers on the board). But you can just ask the questions orally if you like.

Here are the questions/steps:

  1. What do you know / notice?
    They should tell me facts that they know.
    Eg. The tent is the shape of a triangular prism. It has a volume of 70 ft^3.
  2. What do you wonder?
    What questions come to mind?
    Eg. What is the height of the tent? How much canvas is need to make the tent?
  3. Now I tell them the question I want them to explore … for this tent the question was “Can you stand up straight in this tent without hitting your head?”
  4. Estimate:
    – too high
    – too low
    – best estimate
  5. What do you need to
    – measure
    – google
    – calculate
    in order to solve this problem? (plan)
    Whenever possible I bring a hands-on object in that they can physically measure. This time I gave them the measurements of the tent.
  6. Then I send each visibly random group of 3 to their chalkboard or whiteboard section to solve the problem. During this time I’m walking around managing what Peter Liljedahl calls FLOW by giving hints (usually in the form of a question) to those that are stuck and extensions to those that are done the original question (for this tent, how much canvas is needed?). Sometimes this involves calling all groups over to one spot & I do some direct teaching if they need to learn something new or review something to move on.
  7. When all the groups have solved the problem, students return to their seats and I debrief / consolidate the activity by “narrating a story” as Liljedahl says of the student work. I found the “5 practices” article really helpful in learning how to do this.
  8. At this point I reveal the correct answer (needed more if they are taking their own measurements to see how close their answer is to the real answer; for example how tall the lamppost outside actually is after we solve for its height using shadows & similar triangles).
  9. We go back & see who’s best estimate was closest to the actual answer. We celebrate the closest estimate.
  10. Which of the overall expectations from our course did we use today? (reflection)
    This is where the learning goal of the task comes out – at the END. If I say this up front, then it takes away all the student thinking about what math they can use as a tool to solve the problem.
  11. I encourage them to take a photo of any group’s board they wish to save in their notes.
  12. Finally, usually the following day, they do some individual practice using some of the problem sets on Khan Academy.

Hopefully that all makes sense and shows a bit about how you can take a typical textbook or worksheet type word problem & turn it into a more student-centred learning task. If you want to see examples of this type of lesson with student work, have a look at my collection of lessons I have blogged about.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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