Today's topic is problem solving! We will be sharing some things we already do and some new things we are looking forward to trying.
Allowing students to independently problem solve as individuals, with a partner, or in small groups is essential. Creating the problems is something I find myself doing on a daily basis. I do not plan ahead a week in advance---I am continually considering my students' current understanding of concepts, the skills they have learned, how they are progressing in guided math groups, and the standards.
Three different problems may be provided for students on a given day. For example, we may be working with adding on with the start unknown. Some students are able to work with greater numbers (three-digit) while others are adding 2 digit numbers. The problems may be identical with differing numbers. There may also be a group of students having difficulty writing an equation to match a start unknown addition word problem. Those students may continue working with a result unknown problem in the independent setting and further work will be done with guidance in a small guided math group with start unknown problems. I simply number the bags that house problems so students know exactly which problem they will be solving.
Some problems include a checklist to help guide students, while others may not---this depends on the needs of students.
A checklist example:
- Carefully read the problem.
- Label what is known (K) and unknown (U).
- Write an equation to match the problem situation.
- Solve the problem using a strategy of choice.
- Write your answer in a sentence with words.
Whatever problem students are given, one thing remains constant---students must decide what strategy they will use to solve. The strategy (pathway) is just as important as the solution. The discussion that students are allowed to have with one another gives them the opportunity to see multiple pathways for solving the same problem as well.
Problems do not always have one solution, and students don't always solve the problems they are given. Here are two examples:
- 25 trick-or-treaters went into the haunted house. Some were brave enough to go upstairs, and the rest stayed downstairs. How many went upstairs? How many stayed downstairs?
- 16 students went into the library. Two students sat on each beanbag. How many beanbags were used? What strategy would you use to solve this problem? Be prepared to tell why you would use this strategy.
No matter how well problems are planned, there are times when students get stuck. Pam from Pam's Place came up with a wonderful idea to help instill perseverance in her students---Need a Hand? Click here to read more about Pam's fabulous idea!
Below are pictures of the hands that students will be able to use during independent work time while I am meeting with small guided math groups.
Suggestions on hands include:
- Use tools to model.
- Reread the problem.
- Try a different strategy.
- Label what is known (K) and unknown (U).
- Picture the problem situation in your mind.
- Look back to your journal for a similar problem.
- Problem solve any words you do not understand.
- Draw a picture.
- Ask yourself what you have learned that can help you.
- Look for a pattern.
- Act out the problem silently or with a partner.
- Talk about the problem with a classmate.
- More will be added as the year progresses...
Something else I would like to try this year is group problem solving with roles. This idea was shared in Dr. Nicki Newton's book Guided Math in Action (Chapter 8). While students work collaboratively to solve the problem, each has a special role.
She suggest the following four roles:
- Reader--reads the problem and translates for the group
- Illustrator--draws a model to show the group's thinking about the problem
- Number Cruncher--writes an equation to show the numbers in the problem
- Checker--Solves the problem in a different way to check the original solution
We will spend needed time understanding expectations and practicing before students are expected to work independently.
Finally, I would like to recommend a couple of great resources for problem solving---one I have had for years, and a new one. Check them out!
- Introduction to Problem Solving: Strategies for the Elementary Math Classroom by Susan O'Connell (Now available in K-2 and 3-5 editions)
- Problem Solving with Math Models by Dr. Nicki Newton (available for grades K-5)
I have also worked with students using model drawing (Singapore Math) as a fifth grade teacher for many years. Here is a resource I recommend!
- Step-by-Step Model Drawing by Char Forsten
A few years ago I discovered these cards from Edupress. I purchased them at our local school supply store for about $10 a piece. Inside are 40 cards (front and back).
Please excuse the bad iPhone picture...I looked and looked for the grade 2 cards on websites but could only find the Addition and Subtraction cards for grades 2-3. I could only find the problem solving cards starting at grade 3. You can find those here.
What I like about these cards is that they can be done in small groups, or as a workstation. I have used them as both. One year, I had a "Brain Blaster of the Week". I would display the card and the students would try to problem solve what was on the card for that week. I had a bucket for them to put their work in. They could just use a slip of paper to show how they problem solved. That was a requirement. I wouldn't just take answers written on a slip, a strategy had to be shown. I would then draw a few papers from the bucket. If they were right, or close, using a strategy matched the problem, we would discuss it as a class. I would then give a fuzzy (part of our classroom management system). Some of the kids were baffled that someone could be rewarded for getting an answer wrong. I like to reinforce the idea that mathematicians are not always right, and need to practice, practice, practice!
I then would go through the rest of the bucket when the kids where gone, and I would assess who is on track and who needs more guidance. This was addressed duirng small guided math group times. We would break down the problem and discuss strategies that could be used to solve the problem. These cards are a great assessment tool, too!
We would love to hear your problem solving ideas and how you use them with your students! Feel free to link up or share in a comment! Click here for details about linking up...
AND---If you haven't already, visit a fabulous blog hop--Math Books That Will Change Your Teaching! You can enter to win some HIGHLY RECOMMENDED math resources!!
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