Problem Solving
A Math World Topic
Here are unique real-life projects that involving problem solving with a math component. They were developed and field tested by Wood Enrichment Services and used in the classroom for at least ten years. The problems can be adapted to any level but were originally designed for advanced fifth and sixth grade students.
Magic Squares
Odd Number Magic Squares
Put the first number in the sequence in the upper center of the grid. Move diagonally up and to the right. Place the second number in the square. If the number is off the grid, look at its position on the grid above or to the right of the current grid. Place the number in the same position on the current grid. In the example to the left, 2 is in the lower right position of the grid above it so it is placed in the lower right position. If the position has a number already in it, go back to the last number and put the number directly below it. It will always fit. Keep going with these directions until all the squares are used. The square is finished. All the rows and columns all add up to the same number. This works with any linear sequence where all the numbers are an equal distance apart.
Continental Math
Continental Math is a problem solving competition where students take six monthly problem solving quizzes. Each quiz has six problems that need to be completed in thirty minutes. At the end of the year, those with the most correct will receive a medal. This problem has various levels but each level is for advanced students.
The Bus Problem
This is a long-time famous problem developed by Wood Services for fifth grade advanced math classes. Students analyze school bus schedules making the most efficient route with the least mileage when picking up all the students. At the end, they need to present their plan as though they were making the proposal to a school board. It can be done individually, or in groups.
The township map of Wood School District is shown here. In the school, all of the children take one of three busses. Each bus starts at the bus garage and ends at the school. The map shows the number of students boarding at each stop. Make a proposal of the three bus routes including the number of students and the total mileage of each bus by using the scale of miles. Students are evaluated by the amount of total mileage used and the accuracy of the plan according to the criteria. In addition describe how many bus stops are in the whole district, how many square miles are in the district and the largest number of students getting on at any one stop.
Logic Elimination Problems
Criteria grids can be used to solve all kinds of problems. The example below shows the types of problems found on the website linked here
Mark, Joe and Sal lived in three different locations with all different occupations. Can you use these clues to find out what occupations they had and where they live? Their occupations were a retired electrician, a retired teacher, and a restaurant owner. They live at Arash Circle, Brethren Church Road and Sweetwater Blvd.
1) Mark graduated from West Chester Teacher’s College.
2) Sal lives in the same Florida neighborhood as Mark.
3) The retired electrician lives in Pennsylvania.
4) Sweetwater Blvd.is less than one mile away from Arash Circle
5) The person who lives in Arash Circle is retired.
The Land Puzzle
A farmer had four children. The children were very jealous of each other. The children were named Sally, Raymond, Al, and Petunia. The farmer was going to retire and wanted to give each child a share of his land having the same size and shape. The farm’s land was shaped like the figure at the right. How should he divide the farm evenly among his children?
