CCSS.Math.Practice.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.
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.
Implementing in the classroom:
Before teaching our students' how to solve the problem we first need to teach them how to make a plan of action. Every problem a student approaches they should be taking two steps before picking up their pencil or tool to solve.
Step 1: What is this problem asking me?
Students need to have a solid understanding of the problem before they are able to solve. They need to know the facts of the problem, what is already known, and what they are trying to find out. If you are working in a whole group, small group or partnerships all students can turn to a partner to tell them what the understand about the problem. Any misconceptions about what the problem is asking can be clarified within partnership and whole group share. Students can also clarify what is being asked of them with a student partner. |
Step 2: What is my plan to solve it?
Students need to have a plan in mind before starting the solving process. Students once again can turn to a partner to discuss different options of plans to solve a problem. Before assessing a student on new material students should have many opportunities to discuss plans and solution strategies with one another. |
Classroom Connection
Click on the image above to view the lesson example.
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Liz O'Neill works with her first grade students engaging them in composing and decomposing numbers within twenty. She begins with two warm-up activities engaging students in working with numbers less than 20. Using sentence frames, students shared with their partner what number they saw and how they saw it. A variety of ways were discussed as a whole group after everyone had a chance to share with their partner. Students then played the game "How Many are Hiding?" Student pairs were given a bag with 10 cubes, a paper plate, and the "How Many Are Hiding Recording Sheet". The partner game gives students practice in composing and decomposing numbers within ten. In addition, sentence frames were posted on the board so students could produce academic language using structured student talk and convince their partners with oral justification.
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