Starter Set for Math Curriculum or Year Plan for
Problem Solving

Concepts or Big Ideas Outcomes Activity Sequence Evaluation
Problems are solved with a heuristic, a repertoire of strategies, metacognition or reflection, and persistence.
  • Recognizes a problem in different contexts.
  • Uses a heuristic when confronted with mathematical problems related to their lives. Begins solving problems and follows through solving them with a heuristic.
  • Use metacognition or reflection during the process.
How many pockets are there in the indoor clothes of students in class?  
A series of generalized steps (heuristic) is helpful to know when solving problems. Following a heuristic is helpful to think about what you know or have done and what you need to find out or do when solving problems.
  • Identify steps of heuristic (a generalized pattern/strategy) to solve problems.
  • Identify steps to include: 1. Understand the problem, 2. Select and try a strategy, 3. Examine the solution, and 4. Verify the solution.
  • Describe ways to aid in understanding the problem as identify the words in a problem that describe mathematical relationships, operations and numerical values.
  • Accurately explain the problem in their own words.
  • Identify information needed to solve the problem.
  • Identify unneeded information in a problem.
  • Select a strategy to solve the problem.
  • Try a different strategy when one appears to be at an impasse.
  • Solve problems.
  • Solve problems in different ways to gain confidence in the solutions.
  • Reflect on what was learned and how it might be used in other contexts. the process and the accuracy of the solution.
  • Share the process, strategies used (successful and unsuccessful), attitudes, and solutions.
How many pockets are there in the indoor clothes of students in class?




Provided a story problem and have students high-light the necessary information and cross out extraneous information. 		 
Problems can be solved with different strategies.

Strategies for solving problems include:
  • Use of manipulatives to represent objects and actions in the problem.
  • Work a simpler problem.
  • Trial and error, guess and check.
  • Work backwards
  • Use smaller numbers
  • Use systematic steps.
  • Look for, recognize and describe patterns: quantity, AB/AB, ABBA/ABBA, size, area, volume, rotation, shading, shape, position, subtraction, addition, reflection, multiplication, analogy, and recursive
  • Break a problem into two related problems and solve the original problem in two steps: one for each problem.
  • Act out the problem. Physically or mentally.
  • Use a pictures, graphical representation - model, drawing picture or diagram
  • Problems can be solved with models and equations.
  • Categorize information to find relationships and patterns that will assist reasoning and proof.
  • Organize data to look for patterns sequence, chart, table, making a graph, Venn diagrams, and dichotomous key.
  • Process of elimination or process of identification
  • Write an open sentence
  • Use algebraic reasoning
  • Use logical reasoning: matrices, deductive, inductive, truth tables
  • Brainstorming
  • Use equivalent numbers 3/5, 6/10, 60/100, .6, 60%
  • Apply and adapt a variety of appropriate strategies to solve problems.
 How many pockets are there in the indoor clothes of students in class? High - Students understand there are different strategies for solving problems, \ usually come up with their own strategies to solve problems, articulate their strategies, and try to understand other students' strategies.

 

Low - Students expect others to tell them what to do.
Reflection or metacognition helps solve problems.
  • Monitor and reflect on the process of mathematical problem solving and regulate their actions.
  • Have the habit and ability to monitor and regulate their thinking processes at each stage of the problem - solving process
  • Use self talk, group discussion, to talk through a problem and problem solving process to reflect on all the decisions that are possible to better insure an accurate solution.
 How many pockets are there in the indoor clothes of students in class?  
The more problems I solve (persistence) the easier it is to solve problems and use mathematics. Build new mathematical knowledge through problem solving; How many pockets are there in the indoor clothes of students in class?
 

 

Dr. Robert Sweetland's notes