Math.Practice.MP1

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP1:  Make sense of problems and persevere in solving them.

    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

Persistence in Problem Solving
Lesson Objective: Increase student confidence using multiple problem solving strategies
Grade 3 / Math / Word Problems
Math.Practice.MP1

Thought starters

  1. How does the graphic organizer help scaffold problem solving for students?
  2. Why does Ms. Saul choose to have students work alone without help?
  3. How do "Heads Together Butts Up" and "Student-led Solutions" contribute to the class culture around problem solving?
85 Comments

Lovie Harris

The video I selected was Persistence in Problem Solving

This video related to micro-credential with ways to allow students to explain how they came up with an answer to a math problem. They had to show three ways and by showing three ways they could see if all three ways allowed them to get the same answer which would boost their confidence in problem solving or show if a mistake was made.

I teach Kindergarteners so trying to get them to explain at first would be difficult.  They could show how to count numbers using manipulatives as well as grouping to show how many groups you can get out of a given number.(e.g. 8 would be two groups of 4 or 4 groups of 2) My concerns would be monitoring during group activity to make sure everyone in the group is participating and not just relying on one person to do the work.

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Awesome idea!!!

 

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This is an awesome idea. It might take time to implement in Middle School.
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Good idea, putting it to practice will take some time.
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It is great how these students are working, but is it realistic to have the students solve the same problem three different ways? It may be different in elementary school, but in middle school, there are so many standards to teach I am happy if the students can solve the problem using one method.
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Transcripts

  • Classroom Close Up: 3rd Grade Math: Persistence in Problem Solving with
    Jennifer Saul

    [01:00:07;10]
    Jennifer: "Is it OK to make mistakes?

    All:

    Classroom Close Up: 3rd Grade Math: Persistence in Problem Solving with
    Jennifer Saul

    [01:00:07;10]
    Jennifer: "Is it OK to make mistakes?

    All: "YES!"

    Jennifer: "So, you just fix them and learn from them. Mistakes are easy to fix."

    Establishing a strong classroom culture is essential. You have to normalize error. They have to know that it's OK to try, and try, and try again. We want them to wrestle with a problem, and to stay with it. So, we came up with Find Three Ways.

    Hopefully, this activity helps them take ownership for their own learning.

    "OK I need some more help."

    So, at the beginning, I present them with a problem, and really appeal to their sense of empathy.

    "I need your help figuring out for four hungry teachers, is my $20.00 enough to buy four burritos and, if it is enough, do I have any left over to maybe get sodas? You're going to try to find three different ways to solve the problem."

    Once the problem's been recorded on the board, they are sent back to their seats, with their record sheet. One side has areas where they can do work, and ideas for strategies to use. And, the backside's purposefully left blank. So, they have a lot of freedom.

    "Remember our initial tackling and wrestling with this problem is independent work."

    They have four minutes to wrestle with the problem independently, and to try to solve it as many ways as they can think of.

    "What did you do? Oh, from your table?"

    If they can solve it three ways, and arrive at the same answer three times, that would help with their confidence level. They can assure themselves and don't have to wait for the teacher to come around, and say "Yep, you got it."

    "OK...discuss with your table."

    And then, we do what's called "Heads Together, Butts Up!" We want their heads together, showing each other what they were successful with, maybe others who need support, or didn't know where to go with it, can get an idea.

    Sara: "How did you get this answer? I got it by adding this."

    Lisette: "I got it by adding four and four, and adding twelve and twelve."

    Sara: "OK."

    Jennifer: They're allowed to copy each other's notes as long as they're having the discussion about why something was done in a particular way. It's a chance for them to practice using the language, and have discourse over what they're doing.

    During that whole time, I try to rotate around the room, offer support. And, so I'll have in my mind, who I would like coming up to the front of the class, and sharing their work.

    "Show me learning positions please."

    They turn to the front of the room, and three students are called up, and I use my document camera and they can show and explain their work.

    Carlos: "Then I added the ones, 1,2,3,4."

    Establan: "Then I multiplied the four and the four, equals 16."

    Sara: "First, I made a table. In the first two boxes, I put the teachers and amount."

    Jennifer: Having a student-led solution enhances our culture of learning as a class. It's not me dictating how they should get to a particular result. It allows them to choose their own path, but it also opens up doors for consulting with each other, and collaboration, which are life skills that everybody needs.

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Jen Saul
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