Wednesday, January 21, 2015

Using Math Practice #1 - Make Sense of Problems and Persevere in Solving Them

Math Practice #1 is, as Rena Sabey puts it..."Math Sweat."  The title of the practice really says everything about it.  Students are able to approach rigorous problems in a logical systematic way to help them sustain and reach a conclusion.

If a student is proficient in Math Practice #1 they can:

  • Explain the meaning of the problem.
  • Find entry points to the problem.
  • Plan a solution.
  • Compare this situation to other similar problems they may have solved in the past.
  • Keep track of their progress towards the solution.
  • Determine if their method was the most effective.
This poster was made a few years back by teachers in the district.  It sums it up pretty well.

Houghton Mifflin Harcourt put out this guide to prompting students towards MP #1 in 2012.  It helps to facilitate questioning without giving the answer away.
  • What is the problem asking?

    • How will you use that information?
    • What other information do you need?
    • Why did you choose that operation?
    • What is another way to solve that problem?
    • What did you do first? Why?
    • What can you do if you don’t know how to solve a problem?
    • Have you solved a problem similar to this one?
    • When did you realize your first method would not work for this problem?
    • How do you know your answer makes sense?

    In the blog replies below, feel free to share how you are using MP #3 so we can all grow and learn together.


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    2. In first grade, our students are currently counting with groups of 10 and leftovers. They have the opportunity to use a variety of manipulatives. When given a group of materials, the children have the opportunity to count and express their answers in a variety of ways. After they answer, they are challenged to think of another way to group and count the objects. They are prompted to explain their thinking.
      The Evergreen Team - Amanda, Amy, Becky, & Kami

    3. At Hatley, grades 3-5 have implemented a "Problem of the Week." These problems are focusing on developing perseverance in math, as well as meeting our SLO for our building. The problems this month have been logic grid problems, and students were encouraged to talk to other students and parents to share their thinking, reasoning, and solutions. At the end of each week, we share the problem in class and discuss their thinking, the steps they took, and their perseverance in trying to find an answer.

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    5. At Mountain Bay in Grade 4, we have been working in a workshop model to teaching math this year. Using this model for teaching, we are able to incorporate MP #1 on a daily basis. During Mathematical thinking, students are working in groups solving problems together. During this time, they are expected to have meaningful math conversation with their peers and make a plan and then carry out their plan. These groups are heterogeneous small groups focused on working collaboratively to solve the problem. We have a designated time within our math workshop that students can share with the rest of their peers. We have the math practices laminated and ready for each group. The math practice cards are available to them while they are working through problems.
      Mountain Bay grade 4: Sue, Jen, Kirsten, Noreen, and Mara

    6. At Hatley, grades K -2 implemented a "Problem of the Week" as well. These problems developed deeper thinking and perseverance in math. These practices are areas of focus for our PPGs and SLOs in our building. Students were encouraged to talk to other students, siblings and parents to share their thinking, reasoning, and solutions. At the end of each week, we share the problem and discus students' thinking and their perseverance in trying to find solutions.

      One of the problems was titled "Snow Many Equivalents". Students represented equivalents for three numbers of their choice. Students could represent the numbers with counters, on ten frames, tape diagrams, with tally marks, using equations etc. The possibilities were unlimited. As a building, we repeated the activity with the numbers 5,10,and 15. The charts started in Kindergarten and were passed to each grade to add their thinking. The final charts are posted in order for students to see the progression of mathematical thinking and the quantity of equivalents represented.
      Hatley K-2
      Beth, Nancy, Amy

    7. We’ve introduced and modeled the Math Practice #1 chart. During our lessons we continually refer back to it to encourage our students to think about the before and after steps of solving problems, not just diving into the work. After watching the videos, we each presented a lesson from the Inside Mathematics website to our students. This was a great way to model how the answer may not be right in front of them, and they would have to struggle a bit-which was a good thing. The Problem Solving lessons in each topic of Envisions have Read and Understand, Plan, Solve, Look Back and Check to remind them of Math Practice #1.

    8. Rothschild Elementary-Grade 3

      We started our lesson by introducing a light bulb and discussing Thomas Edison's quote "Try, try, try again" and what that means. We connected the idea of perseverance and that it means to keep trying. To reinforce we connected "Attitudes of Excellence" to our perseverance and discuss Math Practice 1. We read the book "Stuck" by Oliver Jeffers to wrap up our day of "Try, try, try again". The following day we did the lesson of "Table for 22" and had the kids work in small groups to plan out how they were going to solve the area and perimeter problems. Then they worked with in the large group setting to solve for the largest and smallest area/perimeter for the table. When they were finished, they had to explain their thinking and support their ideas with facts from the experience. Vocabulary was reinforced. At the end, we debriefed as a large group and co-created an anchor chart listing the steps for Math Practice one which included what to do before, during and after solving an unknown problem.

    9. Riverside-1st Grade

      We are using #1 practice in Topic 8 to show a 2-digit number and manipulate the number to show different ways to make tens and ones.

      Student used concrete objects like connecting cubes, ten sticks, and ones cubes to explain their thinking. They also had to explain their methods and thinking using a chart, and shared with a partner.

    10. Riverside-Kindergarten uses math practice #1 on daily basis across the currciulum be encouraging persistance, math talk, and having the children explain their thinking to their friends. Students are asked to prove their answers, explain their thinking, and find alternative solutions while using vocabulary from past and present math topics.

    11. Weston 1st Grade:
      Students are encouraged to recheck their work by using manipulatives, number charts, etc. to explain their reasoning and understanding. Students have a variety of manipulatives to choose from and may pick the manipulative that fits their needs. Students are also welcomed to collaborate with their peers and discuss possible answers. We will be trying to incorporate more DOK Level 3 by asking students to explain why select answers make sense in the margins of their lessons.

    12. We have been using a math practice one poster as a visual guide for our students to solve mathematical problems. Students were introduced to the problems solving procedures set by these posters. We model and use the terminology so this language becomes a part of their every day math conversations. Students are expected to use these steps and terminology while working through math problems. This is a process and we seeing growth in the "before" and "during" phases of problem solving. Students are moving towards proficiency in checking their answers for reasonableness.
      The posters can be found at:

    13. Objective: TSW be able to persevere when presented with a problem. They will make a plan, carry it out and evaluate its success.

      Define the word “persevere”.
      Read a story problem with the whole class.
      Students will discuss orally the story problem and ask these questions:
      What words don’t I know?
      What is the problem asking me to do?
      What information am I given?
      Is there any missing information?
      Is there any extra information?
      Restate the problem in your own words.
      Students will work independently to solve the problem
      Once they have completed their work, they will share it with their partner and justify their answer/work. If students disagree, they will have to listen to each others reasoning and rework the problem as needed.

      We will start the above process with kids verbally justifying their answer.
      We will transition to students explaining their solution in writing on a form with 3 boxes to walk students through the process.
      Finally, students will type their explanation to a problem in a google form to prepare them for the Badger Test.

    14. 4th and 5th grade teachers at Riverside have been using a lot of questioning techniques to promote perseverance and deeper thinking in their math lessons like: What did you want to add? What's another way to show your answer? What else could you do? What do you think?
      Other ideas used to promote deeper thinking / perseverance:
      -Problem of the week
      -Partner / small group work
      -Students create word problems to fit lessons
      -Ask the expert panel where students are the "experts" to promote more peer discussion
      -Asking students to find the common error during lessons
      Riverside Grade 4 and 5 Teachers

    15. Rothschild K

      Student Objective-I can use math words to talk about my math thinking.

      -Math Vocabulary to describe your problem solving
      -using math strategies to solve a number story

      Our students played the game "How Many Are Hiding." We introduced an anchor chart with the procedures on how to play the game. As we taught the game we provided students with examples of math language to use when describing their problem solving. This language was put on sentence strips for students to refer back to during the game. Modeling was done by both students and teachers on how to describe their math problem solving. Students were taught how to keep each other accountable for their math thinking. When introducing the game different math problem solving strategies (fingers, tens frame, draw a picture) were modeled and discussed. Students were able to determine which strategy they felt most effective.

    16. Rothschild First Grade
      How do you see this practice being used in the classroom?
      I see this practice being used in the classroom by having small group discussions on the various strategies that can be used to solve the same problem. Students learn best from each other. It is powerful to have students effectively communicating their thought process. The teacher serves as a coach rather than a facilitator of the lesson. The students have the power of learning. I can see this being effective in the classroom by making answer key available to the students to help them self-monitor if they have the correct answer. It would be important to teach various strategies of what to do if the answer is incorrect.

      I see this practice being used all day, every day in the classroom. In math specifically, I see kids having a visual tool kit and a strategy sheet. They will continue using key words to first figure out what the problem is asking them to do and then make up a plan of how they are going to solve this. I agree, that students learn best from each other and that more conversations about problem-solving pathways have to occur. Students need to know that the “thinking” is more important than the “answer”. Students also have to have the skills to really listen and process what their peers are sharing when discussing how they persevere in solving problems and the pathways they used to arrive at their answer.

      Where have you used aspects of this in your classroom? How can you enhance those pieces to make the practice richer?

      First and foremost, students have to believe in themselves and their abilities, which are life-long strategies that are practiced a lot more than just during math time. I think we work on confidence-building throughout the day so that students believe in their ability to solve problems on their own without always needing teacher intervention. I could do better job helping students to make the connection of why we work on confidence building and feeling good about our abilities with how that helps us persevere in solving math problems.

    17. First Grade Rothschild
      Each time we come to a problem that looks hard, we work on just silently reciting the mantra “I think I can, I think I can”. We talk about the fact that the moment you tell yourself you can’t do something, you won’t be able to do it, so we stress the importance of not letting yourself build those huge brick walls in your mind that stop your thinking from happening. I could work on making this more visual for students and help them really picture what happens in their brains when you tell yourself you can’t do something vs. when you tell yourself you can.

      Kids have a toolbox of strategies in their heads, but it might be neat for them again to have that as more of a visual and actually have a visual toolbox with different strategies that they are thinking “which strategies work best for me” and/or “which strategy is best to use in order to solve this problem”. It’s important for students to also be aware of the different pathways and processes that are happening in kids minds. It would be neat to make this more visual as well and as kids are sharing how they came up with an answer, they can create a simple visual illustration of what their brain was thinking.

      Metacognition is crucial for growth and helping kids to be aware of their thinking will help to make them more independent in their problem-solving.

      We would like to create a charts for our classrooms as a guide for the students. The chart would be a list of strategies they could use if they have the wrong answer. We will continue to work on this as a PLC.