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The Problem With Problem Solving

By Jessica Smith
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"How do mathematicians communicate their ideas to each other and to the public? If math is just numbers and symbols, how can we talk about math?"
 Overview


  Understandings & Objectives


 Content


 At A Glance




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Core Understandings
  • There are many strategies that can be applied to word problems in math.
  • Persistence, flexibility, and teamwork are life skills that are necessary for problem solving.
  • Writers have to consider the audience perspective when preparing a presentation or lesson.
Learning Objectives
  • Students will collaborate with peers to reach consensus on a problem solving strategy.
  • Students will apply a variety of problem solving strategies.
  • Students will modify their problem solving approach based on feedback from peers or teachers.
  • Students will demonstrate understanding of their strategy in a written explanation.
  • Students will evaluate the effectiveness of their strategy through discussion.
California Content Standards
English and Language Arts
Grade Five
Writing
ELA.5.1.0. Writing Strategies
Research and Technology
ELA.5.1.4. Create simple documents by using electronic media and employing organizational features (e.g., passwords, entry and pull-down menus, word searches, the thesaurus, spell checks).
Evaluation and Revision
ELA.5.1.6. Edit and revise manuscripts to improve the meaning and focus of writing by adding, deleting, consolidating, clarifying, and rearranging words and sentences.
Listening and Speaking
ELA.5.1.0. Listening and Speaking Strategies
Organization and Delivery of Oral Communication
ELA.5.1.4. Select a focus, organizational structure, and point of view for an oral presentation.
ELA.5.1.5. Clarify and support spoken ideas with evidence and examples.
ELA.5.1.6. Engage the audience with appropriate verbal cues, facial expressions, and gestures.
ELA.5.2.0. Speaking Applications (Genres and Their Characteristics)
ELA.5.2.2. Deliver informative presentations about an important idea, issue, or event by the following means:
a. Frame questions to direct the investigation.
b. Establish a controlling idea or topic.
c. Develop the topic with simple facts, details, examples, and explanations.
Mathematics
Grade Five
Mathematical Reasoning
MA.5.1.0. Students make decisions about how to approach problems:
MA.5.1.1. Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
MA.5.1.2. Determine when and how to break a problem into simpler parts.
MA.5.2.0. Students use strategies, skills, and concepts in finding solutions:
MA.5.2.1. Use estimation to verify the reasonableness of calculated results.
MA.5.2.2. Apply strategies and results from simpler problems to more complex problems.
MA.5.2.3. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
MA.5.2.4. Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
MA.5.2.6. Make precise calculations and check the validity of the results from the context of the problem.
MA.5.3.0. Students move beyond a particular problem by generalizing to other situations:
MA.5.3.1. Evaluate the reasonableness of the solution in the context of the original situation.
MA.5.3.2. Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
MA.5.3.3. Develop generalizations of the results obtained and apply them in other circumstances.