Posted by David Wetzel
Problem solving in math helps student develop a better understanding of mathematical concepts.
This is true when making connects between math concepts and everyday objects that students look at everyday.
One thing students look at everyday is the clock, which can be used to make connections Geometry.
Geometry Math Problem
When looking a students sees that it is 3:15 PM.
What is the angle between the minute and hour hands? (It is not 0 degrees)
Geometry Problem
Answer:
7.5 degrees
Every minute on the clock represents 6 degrees (360 degrees/60 minutes)
Every hour, the hour hand moves from one number to the next (in this case, it is moving from 3 to 4) which represents 30 degrees.
Since it is exactly 1/4 past the hour, the hour hand is 1/4 of the way into its 30-degree trip or 1/4 or 30 degrees….which is 7.5 degrees.
Additional Math Problems
2 Problem Solving Activities in Math
7 Math Problem Solving Exercises
Comments:
Filed Under: Math
Posted by David Wetzel
Math Around the Clock Activity
Problem solving in math is the best way for students to demonstrate their understanding of math concepts. Being able to develop a strategy for solving math problems is critical for truly understanding math beyond rote memorization of procedures and worksheets.
“It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps… Every new discovery in mathematics, results from an attempt to solve some problem.” Howard Eves - Mathematician (1911 - 2004).
Providing students a problem solving situation as a lesson culmination activity allows students to internalize their learning and depending of the problem solving activity students may be able to visualize and artistically internalize a math concept.
Problem Solving Activity - Math Around the Clock
Students are tasked to develop an “8’s” clock similar to the “9’s Clock” pictured.
All clock numbers must be the product, addend, remainder, or dividend of a math problem that all uses the number.
Students must follow PEMDAS, along with having the ability to use any mathematics function.
Additional Math Problem Solving Resources
Math Function Generator Game
Math and Problem Solving Skills
Comments:
Filed Under: Math
Posted by David Wetzel
Problem Solving Strategies
The foundations of topology are often not part of high school math curricula, and thus for many it sounds strange and intimidating.
However, there are some readily graspable ideas at the base of topology that are interesting, fun, and highly applicable to all sorts of situations.
One of these areas is the topology of networks, first developed by Leonhard Euler in 1735. His work in this field was inspired by the following problem.
Seven Bridges Problem
In Konigsberg, Germany, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts.
Seven bridges were built so that the people of the city could get from one part to another.
The people wondered whether or not someone could walk around the city in a way that would involve crossing each bridge exactly once.
The following is drawing of the seven bridges in Konigsburg, Germany:
Sketch the above map of the city on a sheet of paper and try to ‘plan your journey’ with a pencil in such a way that you trace over each bridge once and only once and you complete the ‘plan’ with one continuous pencil stroke.
The problem now becomes one of drawing this picture without retracing any line and without picking your pencil up off the paper.
Leonhard Euler
A Swiss mathematician (1707 -1783) who made enormous contributions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory.
Problem Solving Resources
Math Problem of the Week
Math Problem Solving Game
Comments:
Filed Under: Math
