Discovering and Applying Mathematical Strategies Problem Solving Discovering and Applying Mathematical Strategies August 11 - 15

Why do Problem Solving? Apply math you have learned Exercise your brain Practice Critical Thinking Gain confidence for Performance Tasks Prepare you for a future career

This Week’s Schedule: Monday Thursday Tuesday Friday Wednesday Introduce RICE Eliminate Possibilities Strategy Draw a Diagram Strategy Crossing the Rivers with Dogs Problem Pool Problem Farmer Problem Who is Lying? Problem Tuesday Friday Work Backwards Strategy Logical Reasoning Strategy Pigeon Problem Sally and the Peanuts Dad’s Wallet The Climbing Worm Problem Wednesday Find a Pattern Strategy Beach Ball Problem Handshaking Problem

Your “Guide Book”- RICE You will be expected to use the RICE method to solve each problem this week. This is a tool that you can use on ANY problem you encounter in math class. R – Read/ Restate (underline) I – Illustration (table, drawing, graph) C – Calculate/ Computation (arithmetic) E – Explanation (sentences!) Don’t forget the Answer 

What Class Looks Like: 5 minutes- Work Alone 10 minutes- Work as a group 5 minutes – Create Your Display 5 minutes- Gallery Walk 10 minutes- Class Discussion

Working Alone Your time to think through the problem without distractions (silence) Do not use your neighbor’s work (you will see it in 5 minutes anyway) Do your best to actually come up with an answer Be prepared to share your findings with your group members

“I CAN’T” is NOT ACCEPTABLE You are capable of solving each problem…you have the math skills needed. The expectation is that you work on the problem for the entire 5 minutes or until you have a solution that you can prove correct. You won’t be stuck because you will use RICE to help you!

Working As a Group Creating Your Display Every person shares their work while group members listen TOGETHER, decide ONE solution and ONE method to get that solution (you may have to go with “majority rules”) Creating Your Display On larger paper Write out all of your work using the RICE method Use the Strategy of the Day! Circle your answer Be as neat as possible, others will look at your work

Gallery Walk Group work will be taped to the walls Everyone will be out of their seats visiting the posters of the other groups On your paper, you will note differences in how groups solved problems methods you thought of but didn’t show up on your paper any new ideas that you think are interesting

Class Discussion We will reveal the correct answer to the problem (if necessary) Volunteers will share their observations from the Gallery Walk Groups can ask questions of one another (What made you think that way?) Groups can defend their ideas

Draw a Diagram Pool Problem Curly used a shovel to dig his own swimming pool. He figured he needed a pool because digging it was hard work and he could use it to cool off after working on it all day. He also planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the deck?

Draw a Diagram Farmer Problem Farmer Ben has only ducks and cows. He can’t remember how many of each he has, but he doesn’t need to remember because he knows he has 22 animals and that 22 is also his age. He also knows that the animals have a total of 56 legs, because 56 is also his father’s age. Assuming that each animal has all legs intact and no more, how many of each animal does Farmer Ben have?

Work Backwards Pigeon Problem Bad Bargle sneaked into Homer’s pigeon loft one day. He took half of the pigeons. He decided that it wasn’t enough, so he took 1 more and left. Later, Homer opening the door of the loft to exercise his prized possessions. Half of the remaining flock flew out, leaving six inside the pen. How many pigeons did Homer have before Bad Bargle did his dirty deed?

Work Backwards Dad’s Wallet Dad was paid on Wednesday. On Thursday morning, my brother borrowed half of Dad’s money to open a checking account because he was always short of money. On Friday, I needed some money for a date, so I borrowed half of what remained. Sis came along next and borrowed half of the remaining money. Dad then went to gas up the care and used half of the rest of his money, and he wondered where it all went so fast. He had only $5 left. How much money did he start with in his wallet?

Find a Pattern Beach Ball Problem Kazuko has a beach ball. It is colored with six vertical stripes, in order: white, orange, yellow, blue, red, and green. She spins the beach ball on the surface of the water in her swimming pool, and she notices that the colors whirl by very fast. If the first color to go by is white and the ball spins around so that 500 colors go by, what is the 500th color?

Find a Pattern Locker Problem In a middle school, there is a row of 100 closed lockers numbered 1 to 100. A student goes through the row and opens every locker. A second student goes through the row and for every second locker if it is closed, she opens it and if it is open, she closes it. A third student does the same thing for every third locker, a fourth for every fourth locker and so on, all the way to the 100th person. The goal of the problem is to determine which lockers will be open at the end of the process.

Eliminate Possibilities Crossing the River with Dogs Five family members and their five dogs (each family member owned one of the dogs) were hiking when they encountered a river to cross. They rented a boat that could hold three living things: people or dogs. Unfortunately, the dogs were temperamental. Each was comfortable only with its owner and could not be near another person, not even momentarily, unless its owner was present. Dogs could be with other dogs, however. The crossing would have been impossible except that Lisa’s dog had attended a first-rate obedience school and know how to operate the boat. No other dogs were that well educated. How was the crossing arranged, and how many trips did it take?

Eliminate Possibilities Who is Lying? Jim tells lies on Fridays, Saturdays, and Sundays. He tells the truth on all other days. Freda tells lies on Tuesdays, Wednesdays, and Thursdays. She tells the truth on all other days. If they both say, “Yesterday I lied,” then what day is it today?

How many peanuts had been in Sally’s sack? Logical Reasoning Sally and the Peanuts On the way home from school, Sally likes to eat peanuts. One day, just as she was reaching into her sack, a hideous, laughing creature jumped into her path, identified itself as a pig-eyes, and grabbed her sack. It stole half her peanuts plus two more. A bit shaken, Sally continued toward home. Before she had a chance to eat even one peanut, another horrid creature jumped into her path and also stole half of her peanuts plus two more. Upset, she continue on. (What else could she do?) But, before she had a chance to eat even one peanut, another one of these tricksters jumped out and did the very same thing – took half of her peanuts plus two more. Now there were only two peanuts in Sally’s sack. She was so upset that she sat down and began to sob. The three little pig-eyes reappeared, feeling some sense of remorse, and told her they would return all of her peanuts to her if she told them how many she had altogether when she started. How many peanuts had been in Sally’s sack?

Logical Reasoning The Climbing Worm A worm is at the bottom of a 12-foot wall. Every day the worm crawls up 3 feet, but at night slips down 2 feet. How many days does it take the worm to get to the top of the wall?