Lesson 1.1.5 Concept: Making Sense of a Logic Problem Vocabulary: conjecture - a statement that appears tp be true. It is an educated guess or hypothesis.

justify – to give reasons why an answer makes sense justify – to give reasons why an answer makes sense. Reasons can be the observation of a pattern, an algebraic validation, (x + 2 = 5, x = 3) or some other logical method like a diagram, graph or chart.

An important skill that you will develop throughout this course is making sense of a problem or situation.  You will be asked to think and talk through challenging problems until they make sense to you.  You will know that an idea makes sense when you understand it so well that you can explain it to others and answer their questions about it.  In this lesson, you will make sense of a challenging logic problem and work with your team to explain your ideas.

1-33. TRAIL MIX Rowena and Polly were making trail mix.  Rowena had 4 cups of raisins, and Polly had 4 cups of peanuts.  Polly poured exactly one cup of her peanuts into Rowena’s raisins and stirred them up, as shown in the diagram at right.  Then Rowena poured exactly one cup of her new peanut-and-raisin mix back into Polly’s peanuts.  Did Rowena get more of Polly’s peanuts, or did Polly get more of Rowena’s raisins? Your task: First decide by yourself what you think the answer to this question is.  Then share your ideas with your team. Together make a guess (also called a conjecture) about which girl got more of the other’s snack item. Explain your conjecture with words, numbers and symbols, diagrams, models, or anything else you think will convince another student.

1-34. Rowena and Polly still cannot agree about who has more of the other’s item.  Rowena is still sure that Polly got more of her raisins, and Polly is sure that Rowena got more of her peanuts.  In order to make sense of what happened, they decided to try a simpler experiment. Rowena got a cup of 10 red beans, and Polly got a cup of 10 white beans.  Polly gave 3 white beans to Rowena, and Rowena stirred them into her red ones.  Then she closed her eyes and chose 3 beans from her mixture at random to give back to Polly.  The girls then examined each cup. Try their experiment a few times with a partner.  What happens each time?  Work with your team to find a way to explain why your results make sense. Would you have gotten similar results if you had exchanged 5 beans?  6 beans?  20 beans?  Be ready to explain your thinking. With your team, consider whether your ideas about Rowena’s raisins and Polly’s peanuts have changed.  If so, write and explain your new conjecture.  If not, explain why you still agree with your original conjecture.  Be sure to include anything you think will be convincing as you write down your ideas.  Be prepared to share your ideas with the class. 

1-35. LEARNING LOG   In this course, you will often be asked to reflect about your learning in a Learning Log.  Writing about your understanding will help you pull together ideas, develop new ways to describe mathematical ideas, and recognize gaps in your understanding.  Your teacher will tell you where your Learning Log entries should go.  For your first entry, you will consider the process by which you worked with your team and your class to make sense of “Trail Mix” (problem 1‑33).  Write a reflection in your Learning Log that addresses the following questions:  What did people say or what questions did they ask that helped you to make sense of this problem? What did you say or what questions did you ask that helped you to make sense of this problem? What would you advise another student to do to make sense of this problem? Title this entry “Making Sense of a Challenging Problem” and label it with today’s date.

Tonight’s homework is… Review & Preview, page , problems #1-19 to #1-23. Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 1.1.3) Show all work and justify your answers for full credit.

Daily Closure: Return Group folder to the math box. Return your individual Concept Notebook to the math section of your binder. Return the group supply box to the cart after making sure all supplies have been stored in the box and the lid is secured. Record Review/Preview in student planner.