PROBLEM SOLVING in Math What you need to know

OVERVIEW: Define “Problem” Where do I start… How can I solve problems… Trying strategies –Patterns –Tables –Etc… Exercises References

DEFINE PROBLEM… Is it a problem, or an exercise, or a task? Exercise = practicing something you have done before. –For example: 387 X 469 = ? –For example: 12 / 3 = ? Task = doing something based on instructions given to you.

DEFINE PROBLEM… Problem = –You have a starting point and a goal –It involves math –You must WANT a solution –You have to get over some kind of block between you and the solution

What do I start with? To solve the problem you need: –A DESIRE to solve it –Feel it is WITHIN your ability –BELIEVE that you CAN So basically, you have to WANT to solve it and have the confidence that you CAN.

HOW? Start with knowing the basic strategies: –Look for patterns –Use tables –Try ALL possibilities (systematically) –Act it out –Make a model –Guess and check –Work backwards

HOW? More… –Make a drawing or graph –Rewrite it in your own words –Identify ALL the information you have –Write it into a sentence –Make subgoals –Solve a simpler, or similar, problem –Change your point of view –Look for hidden assumptions (facts)

Try: Patterns Using patterns means SEARCHING for a pattern when we do something. –Example: –What triangle dot number has 10 dots on a side? dots/side: Groups of 3: 1 2 3

Try: Patterns What other pattern is there? Try this: Circle all the dots on one side. Circle all the ‘uncircled’ dots on the next side. Circle all the ‘uncircled’ dots on the last side. Count the dots in each circle… do you see a pattern?

Try: Patterns Try other problems included on the worksheet:

Try: Patterns Try working it out here:

Try: Patterns Try working it out here:

References: Ohio State Board of Education. ( ). Problem Solving – A Basic Mathematics Goal: Becoming a better problem solver. Ohio State Board of Education. ( ). Problem Solving – A Basic Mathematics Goal: A Resource for Problem Solving.