Let’s Get to Know Each Other! How many distinct handshakes are there in our group?

Your Task  Determine the number of distinct handshakes there are in our group.  Individually meet/greet and shake hands with as many people as you can in 2 minutes.  When you shake their hands, tell them your name and where you teach.  Work with a partner to devise a plan for determining the number of distinct handshakes there are in our group.  Test your plan using chart paper.

Debrief  Compare/contrast methods on charts  In your group, write on white-board as many different problem solving strategies as you can for which you see evidence.  Food for thought:  Are all problem solving strategies appropriate for any problem?

Problem Solving Definitions  Problem solving is what you do when you don’t know what to do! The key word is “stuck”.  Problem-solving is a process where an individual uses previously acquired knowledge, skills, and understanding to satisfy the demands of an unfamiliar situation.

Problem Solving Definitions  A mathematical problem may be described as problem-solving if its solution requires creativity, insight, original thinking, or imagination.  In problem-solving the initial reaction is, “I don’t know what to do”.

Make A List An organized list is useful to show all possible solutions. How many different outfits can you make if you have two shirts and four pairs of pants? Red shirt, blue pantsRed shirt, khaki pants Yellow shirt, blue pantsYellow shirt, khaki pants Red shirt, green pantsRed shirt, black pants Yellow shirt, green pantsYellow shirt, black pants

Guess and Check Guess at a problem’s answer and check it. Keep trying until you are correct. The sum of two numbers is 27, their product is 180.What are the two numbers? Guess: = * 14 = * 14 = 182 Guess: = * 15 = * 15 = 180YES!

Draw a Picture or Diagram Use a picture or diagram to solve the problem What are the possible combinations for families with two children? BG BGBG

Find a Pattern Use a pattern to get from one numeral to the next Lisa is drawing a pyramid. She puts one block in the top row, two in the second, four in the third, eight in the fourth. If she continues this pattern, how many blocks will be in the tenth row?

Work Backwards Use inverse operations to solve problems. Trish went to the mall and spent $23.50 on a new shirt, $6.75 on lunch, and $31.25 on an new skirt. She had $16.50 left when she got home. How much money did she bring with her to the mall? $ = $77.25 $23.50 on Shirt$6.75 on Lunch $31.50 on Skirt $16.50 Left

Make a Table, Chart, or Graph Tables, charts, and graphs help organize data. There are 100 fifth graders in the school. One fifth of them like pizza, one half like spaghetti, one fifth like cheeseburgers, one tenth like tacos. How many students like each type of food?

Act It Out Act a problem out or use manipulatives. Four students sit at each lunch table. Sue is left-handed and doesn’t want to bump elbows with anyone, but she likes to sit next to her best friend Kate. Kate is to the left of Nancy. Allison likes to be on the end. Where do each of the girls sit during lunch?

Brainstorm Create a new way to look at a problem. How do 6 ¼ and 9 ¾ make 4 x 4? $ $9.75 = $ x 4 = 16 4 x 4 = 16

Use Logic Use prior knowledge to solve problems. A number is composite, and a multiple of 6. The first digit is prime, but not 2. The number is less than 50 but greater than 20. What is the number? 1.Composite numbers have factors other than one and themselves. 2.Prime numbers have only one and themselves as factors. 3.Multiples of 6 >20, 20, < 50: 24, 30, 36, 42, 48

Simplify Make the numbers simpler to solve the problem. The yard is 2,400cm long and 1,700cm wide. How many meters of fencing is needed to surround the yard? 10cm = 1dm 10dm = 1m 100cm = 1 m P = (L x 2) + (W x 2) 2,400cm = 24m 1,700cm = 17m P = (24 x 2) + (17 x 2) = 82 meters of fencing

Problem-Solving Strategies Simple ways to solve even the most complex problems:  Make a List  Guess and Check  Draw a Picture or Diagram  Find a Pattern  Act It Out  Work Backward  Make a Table, Chart, or Graph  Simplify  Use Logic  Brainstorm MODEL DRAWING