Problem Solving

These are real-world problems that students investigate as a team. The students must examine alternative approaches, select a strategy and use mathematical reasoning to formulate a solution. They are also required to communicate their findings with words, diagrams, charts and tables. They must be evaluated on a scale which recognizes the above problem solution attributes.

It's not just the answer that is important, it's how you communicate your result and justify it.

These problems directly address the National Council of Teachers of Mathematics Problem Solving Standards.

These problems have been organized for you, the coach, by difficulty, with the easiest problems listed first. The first 5 problems are developmental and train the student to approach the problem and to investigate possible solutions, while not being extremely difficult. Such problems allow the coach/teacher to concentrate on the other aspects of problem solution that students typically find difficult:

  • communicating their thinking (writing down stuff in complete sentences),
  • working in teams with each other!
  • examining more than 1 strategy, (once they get an answer they think they're through!) and
  • checking their results.

The first problem, the peanut problem, is especially good to start students with because:

  • It is easy
  • It can be approached using 5 different strategies!
  • Lets the students concentrate on the parts of problem solving they are new to: (communicating, working in teams and checking their results)
So, if your students are new to problem solving (and writing down their thinking while they solve the problem), start with this one.

Problem
Statement
Team
Response Sheet
Scoring
Guide
Example
Team Response
Applicable
Math Concepts
Easy Problems
Peanut
Problem
- Response sheet Rubric Team responses:
- Guess-and-check
- Use an equation
- make a picture
- make a table
- guess-and-check
- use an equation
- working backwards
Cactus
Problem
- Response sheet Rubric Excellent response - least common multiple
Farmer Problem
- Response sheet Rubric Excellent response - make a table
Spinner
Problem
- Response sheet
- Diagram sheet
Rubric - Excellent response
- Diagrams
- make a picture
- probability
- make a table
Garden Problem
- Response sheet
- Diagram sheets
Rubric - Excellent response
- Diagrams
- make a picture
- areas of plane figures
Moderate Problems
Cactus
Problem
(Version 2)
- Response sheet Rubric Excellent response - make a table
- least common multiple
Fences
Problem
- Response sheet
- Diagram sheets
Rubric - Excellent response
- Diagrams
- areas of plane figures
- area of triangles
- pythagorean theorem
Great Escape
Problem
- Response sheet Rubric Team Responses:
- work backwards
- write an equation
- guess-and-check
- make a picture
- use fractions
- make a picture
- guess-and-check
- working backwards
- use an equation
- fractions
Circle
Problem
- Response sheet Rubric Excellent response - make a table and
    notice a pattern
- find an equation
    given data points
Mango
Problem
- Response sheet Rubric Team responses:
- work backwards
- write an equation
- guess-and-check
- use fractions
- make a picture
- make a picture
- working backwards
- writing an equation
- guess-and-check
- fractions
The Amazon
Problem
- Response sheet
- Blank table
Rubric   Excellent response - make a table
- analyzing data
- interpreting, understanding and extending a table
- percentages
Birdhouse
Problem
- Response sheet
- Boards
Rubric
Excellent response
- Board #1
- Board #2
- 3-D structure
      visualization
- areas of plane figures
The Castle Kit
Problem
- Response sheet

Worksheets:
-Top View
-Side View
Rubric
Excellent response

- Layer top views
- Layer side view
- 3-D geometry
- scale factors
- make a table
Birdhouse
Problem
(Version 2)
- Response sheet
- Boards
Rubric
Excellent response
- Board #1
- Board #2
- 3-D structure
      visualization
- pythagorean theorem
- areas of plane figures
Monkey Diet
Problem
- Response sheet Rubric Excellent response - understand a table
- guess-and-check
Cell Phone
Problem
- Response sheet
- Graph paper
Rubric Excellent response - graphing 2 equations
- Solving 2 equations
- make a table
- inequalities
Bingo Tournament
Problem
- Response sheet Rubric Excellent response - understand a table
- constructing an equation
- make a table
Farmer
Problem
(Version 2)
- Response sheet
Rubric Excellent response - understand a table
Tiles Game
Problem
- Response sheet
- Tiles combinations table
Rubric Excellent response - permutations
- combinations
Challenging Problems
Furniture
Problem
- Response sheet
- Graph paper
Rubric Excellent response - inequalities
- solve 2 equations
- graph 2 equations
Monkey Diet
Problem
(Version 2)
- Response sheet Rubric Excellent response - understand a table
- convert percentages
- inequalities
- guess-and-check
Tiles Game
Problem
(Version 2)
- Response sheet
- Tiles combinations table
Rubric Excellent response - permutations
- combinations