Hands-on math!

Problem Solving

These problems, sometimes called significant or written problems, are typical of the Session I Washington State Math Olympiad problems. Many of them come from that competition. The student must use mathematical reasoning to formulate solutions, examine alternatives and select a strategy. They are also required to communicate their findings with words, diagrams, charts and tables. These problems do not have fixed "black-and-white" answers. They must be evaluated on a scale which recognizes the above problem solution attributes.
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 6 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 5th and 6th graders 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!
So, if your students are new to problem solving (and writing down their thinking while they solve the problem), start with this one.

Problem Difficulty Problem Statement Team Response Sheet Scoring Guide
Easy Problems
1 Peanut Problem Easy Problem
2 Cactus Problem
(Version 1)
Easy Problem
3 Farmer Problem
Easy Problem
4 Spinner Problem Easy Problem
5 Circle Problem Easy Problem
6 Fences Problem Easy Problem
7 Garden Problem Easy Problem
Moderate Problems
7 Farmer Problem (Version 2) Moderate Problem
8 Cell Phone Problem Moderate Problem
9 Cactus Problem (Version 2) Moderate Problem
10 Tiles Game Problem (Version 1) Moderate Problem
11 Mango Problem Moderate Problem
12 Great Escape Problem Moderate to Difficult Problem
13 Monkey Diet Problem
(Version 1)
Moderate to difficult Problem
Difficult Problems
14 Furniture Problem Difficult Problem
15 Monkey Diet Problem
(Version 2)
Difficult Problem
16 Tiles Game Problem
(Version 2)
Difficult Problem
17 Phone Tree Problem
(Version 1)
Difficult Problem
18 Phone Tree Problem
(Version 2)
Difficult Problem
19 Tiles Game Problem
(Version 3)
Very Difficult Problem
20 Tiles Game Problem
(Version 4)
Very Difficult Problem
21 Greenhouse Problem Very Difficult! Problem