<p>Polya’s 4 Steps to Problem Solving</p><p>1. Understanding the Problem:  Try to make a sketch to illustrate the problem. Label the information given.  Make a list of the given facts. Are they all pertinent to the problem?  Determine if the information you are given is sufficient to solve the problem. </p><p>2. Devise a plan to solve the problem  Have you seen the problem or a similar problem before?  Are the procedures you used to solve the similar problem applicable to the new problem?  Can you express the problem in terms of an algebraic equation?  Look for patterns or relationships in the problem that may help in solving it.  Can you express the problem more simply?  Will listing the information in a table help?  Can you substitute smaller or simpler numbers to make the problem more understandable?  Can you make an educated guess at the solution?  Sometimes if you know an approximate solution, you can work backwards and eventually determine the correct procedure to solve the problem.</p><p>3. Carry out and monitor your plan  Use the plan you devised in step 2 to solve the problem.  Check frequently to see whether it is productive or is going down a dead-end street. If unproductive, revisit Step 2.</p><p>4. Look back at your work and check your results  Ask yourself, “Does the answer make sense?” and “Is the answer reasonable?”  If the answer is not reasonable, recheck your method for solving the problem and your calculations.  Can you check the solution using the original statement?  Is there an alternative method to arrive at the same conclusion?  Can the results of this problem be used to solve other problems? When given a total amount, we can use a single variable to represent two unknowns. For example, if I have $20 and a buy something. If you do not know how much I spent, there would be two unknowns, how much I spent and how much I have left. </p><p>What if I spent $6, what would I have left? What if I spent $12, what would I have left?</p><p>You have a total of $20. If s represents the amount you spent, then 20 – s represents the amount you have.</p><p>A coin bank contains 27 coins in dimes and quarters. The coins have a total value of $4.95. Find the number of dimes and quarters in the bank. What are you being asked to find ? ______</p><p>Number Value Total dimes quarters total</p><p>Solve Coin Word Problems </p><p>Read the entire word problem, FIRST. Identify what you are going to be solving for and which variables to use. Try to write what you read, except for when there is a statement like AS MANY AS or THERE ARE __ MORE __ THAN ___. If these types of phases are used, do a balancing act!!</p><p>Almost all of these word problems need to be solved by writing two equations with two unknowns. The first equation could involve just the variables and the total #. The second equation will contain the value.</p><p>Set up a system of equations and solve it.</p><p>A bank teller cashed a check for $200 using twenty-dollar bills and ten-dollar bills. In all, twelve bills were handed to the customer. Find the number of twenty-dollar bills and the number of ten-dollar bills.</p><p>Let _____ represent the number of $20 bills</p><p>Let ____ represent the number of $10 bills</p><p>The value of the $20 bills is ______</p><p>The value of the $10 bills is ______In Mrs. Hert’s wallet there are 20 bills, some are One-Dollar bills and the rest are Five-Dollar bills. If they total $52, how many One-Dollar bills are there?</p><p>Let _____ represent the number of $1 bills</p><p>Let ____ represent the number of $5 bills</p><p>The value of the $1 bills is ______</p><p>The value of the $5 bills is ______Skeleton: x + y = total amount (value)x + (value) y = total value Note: $1.00 = 100 cents </p><p>Set up a system of equations and solve it. A coin purse contains 18 coins in dimes and nickels. The coins have a total value of $1.15. Find the number of dimes and nickels in the coin purse.</p><p>Let _____ represent the ______</p><p>Let ____ represent the ______</p><p>The value of the dimes is ______, in cents.</p><p>The value of the nickels is ______, in cents. The total value of the dimes and quarters in a bank is $2.30. There are two more dimes than quarters. Find the number of quarters in the bank.</p><p>Let _____ represent the ______</p><p>Let ____ represent the ______</p><p>The value of the dimes is ______, in cents.</p><p>The value of the quarters is ______, in cents. Investment word problems.</p><p>1st item 2nd item total Amount x + y = total Value %(x) + %(y) = interest</p><p>Eliana has invested $48,000, part at 6% and the rest in a high risk investment at 10%. How much did she invest at each rate to receive $4000 in interest after one year?</p><p>Let _____ represent the ______</p><p>Let ____ represent the ______Staples recently charged $17.99 per box of Pilot Precise rollerball pens and $7.49 per box for Bic Matic Grip mechanical pencils. If MSJC purchased 120 boxes for a total of $1234.80, how many boxes of each type did they purchase?</p><p>Let _____ represent the ______</p><p>Let ____ represent the ______</p><p>Amount:</p><p>Amount w/Value:</p>