Day 2: How to Think of a Plan
Welcome to 5 Days of Exemplars, our deep dive into using rich performance tasks to build students’ problem-solving skills. For Day 1, we explored how to get students off on the right foot at the outset of a task. Now we’ll consider what you can do to support them in finding strategies as they step up as the sense-makers, engaged with the task at hand.
Students enjoy thinking for themselves—they need your support, but not too much! So how do you offer just the right guidance and ask just enough questions without inadvertently “stealing” their opportunity to solve the problem on their own and the thrill of discovery that will keep them engaged through a challenge?
One option: set students to work collaboratively. Try a structured framework like a Think-Pair-Share protocol.
After you have unpacked the task and read for understanding using the Three Reads Protocol, invite your students to spend a minute of private think time defining for themselves how they might solve this problem. Next, ask them to turn to a table partner or put them in small virtual chat rooms to share their plan/strategies for how they want to attempt to solve their problem. Finally, bring the class back together for a whole group conversation.
Ask for student volunteers to explain the strategy that their partner shared and the mathematical reason for why it was selected. This encourages students to listen carefully to each other during the small group sharing time. As students share, the teacher should collect student’s names and strategies on a shared platform such as a whiteboard or Google slide. Make this collection of ideas available to all students as they work on solving the task.
As students work to solve the problem, they often encounter roadblocks or dead ends. The shared strategies provide alternative ideas and pathways to try. Students often utilize another student’s strategy to make mathematical connections.
During this exercise, encourage students not to write things down or to begin working on the problem! An important goal during this process is to help students develop a habit of slowing down to think of possible strategies before they begin racing to complete the task.
Another option for providing the appropriate amount of support: draw on their prior experience with problem-solving strategies. Encourage them to use common problem-solving approaches: tools, skills, and frameworks that they may have used before. This grounds them and reminds them of what they already know how to do, giving them an accessible entry into what they may not know yet.
Some strategies to suggest:
- Use concrete or digital manipulatives
- Color counters, base ten blocks, cubes, tiles, Cuisenaire rods, fraction circles, fraction tiles, geoboards, connecting cubes, pattern blocks, rekenreks, snap cubes, and tangrams all provide a safe entry into a complex task.
- Create a diagram or visual representation
- Drawing or creating images to represent and define the quantities helps students grasp their relationships in the task.
- Organize the data
- Tasks often contain lots of disorganized information that can be better understood when placed into charts, tables, number lines, graphs, and so on.
- Look for patterns
- Recognition of patterns becomes the first step in making generalizations and rules, which can help solve the problem.
- Make connections with previous problems
- Accessing prior knowledge can help students recognize how previous work can become a pathway towards solving a new problem.
- Start with simpler numbers
- Solving similar problems with easier numbers allows students to approach the task without seeing computation as a roadblock.
- Guess and check
- Entry into a task can sometimes begin simply by applying reasonable estimations and reflections on the outcomes.
- Act it out
- Getting up from the table and physically engaging in the story helps bring the problem to life, increasing and solidifying students’ understanding.
- Work backward
- Students often feel they know the correct answer, so have them start there—and have them show their thinking as they work backward towards the beginning.
- Read the task again
- Sometimes, just intentionally unpacking a task again while asking a student to think about some of the above options can give them a workable entry.
You might prompt students in this direction by asking, “What manipulatives or visual tools does the class think might help them solve the task?” This thinking continues the process of asking students to reflect and engage in the task before they attempt to put pencil to paper. It also offers them opportunities to use a second strategy to solve the task, look for patterns, and other observations in their solution.
All of these ideas are part of the Yellow section of Exemplars Problem Solving Process - Think of Your Plan—and all of them will empower your students to develop potential strategies. With them, you won’t throw your students into the “deep end of the pool” without a plan and proper preparation. But you also won’t go so far that you accidentally steal the magic that happens when they discover solutions for themselves.
Now that you know how to help your students make a plan, we’ll discuss how to support them while they’re solving the problem for Day 3. To try these approaches in your classroom starting today, sign up for a free trial of the Exemplars Library. You can also request a quote or speak to us about your needs—or support your teachers’ skills through Exemplars professional development.