Lesson Plan Guide

TE 407 – Fall 2007 1/14 08.27.07

Teacher Name: Sheila Frederixon Class and Grade Taught: 10th Grade Geometry Lesson Date: 10/6 Lesson Logistics and Setting Unit Topic: Introduction to Proof - Previous Lesson Topic: Different types of Reasoning - Current Lesson Topic: Truth Tables - Next Lesson Topic: Deductive Reasoning (Intro to proving)

Lesson Objectives: (The learner will know/understand/be able to …)

Use basic terms of logic “and”/”or”

Set up a truth table

Use negation in a truth table - Standards Addressed:

L3.2.1 Know and use the terms of basic logic. L3.2.2 Use the connectives “not,” “and,” “or,” and “if..., then,” in mathematical and everyday settings. Know the truth table of each connective and how to logically negate statements involving these connectives.

- How will I know students have met the objectives?

They are able to correctly set up and solve the truth table in exercise three.

Materials Needed:

Lesson Plan Guide

TE 407 – Fall 2007 2/14 08.27.07

Task One (Truth Tables Worksheet) Introductory Routines (announcements, homework review, etc.)

Cover homework from the night before

Announcements o o o o o o o

Warm Up Activity (while I take attendance) o Discuss previous day’s homework assignment

Analyze the idea of studying and passing the test

What are different possible cases? o Study-pass o Don’t study-pass o Study-don’t pass o Don’t study-don’t pass

Write each statement in p, q notation.

Determine if the argument is valid or not for each case.

Schedule:

Announcements/Attendance 5mins

Warm up activity 7mins

PowerPoint mini instruction 7mins

Students move to groups 1min

Students work on Task 2.4 25min

Students Present Tables 15min

Lesson Plan Guide

TE 407 – Fall 2007 3/14 08.27.07

Residue:

The ability to think through word problems and apply the mathematics back to the story

Demonstrate they can explain what the p,q notation means with in a truth table. Documenting Evidence:

I will video tape the entire class period, with the focus of the camera between the first row of groups and the Promethean Board. This will allow me the insight of being able to observe the class and determine if the presenters understood what they were staying or just being led by their classmates.

I will collect samples of student work. This work will show if the individual student has achieved the residue through their ability to accurately explain their work as well as complete the truth table and explain what each box means.

After the lesson, I will interview individual students after school (if they volunteer it will be extra credit). We will discuss what happened in class, why I chose what I did. How they felt about it and what they felt like they learned. It will be similar format to the interviewing students one activity in TE 407. However, they will not repeat the task, it will mostly be a debriefing so I can find out what the students were actually thinking during the task.

Lesson Activities (Attach any handouts you will use)

Lesson

Students are working … (details about how students are configured, what work they are doing and how they are recording their work)

Anticipated Student Thinking/Questions

Teacher Moves

Launch Students will be sitting in rows as the classroom is normally set up. Students will come in and take a seat. After I go through announcements, they will have warm up problems to work on (as listed above). We will go through the warm up problems together before we launch into the task.

Lesson Plan Guide

TE 407 – Fall 2007 4/14 08.27.07

We determined the different cases are study-pass, study-don’t pass, don’t study-pass, don’t study-don’t pass. (no)

1. P: study hard, q: pass the test. if you study hard then you will pass

2. P: study hard, q: don’t pass the test. if you study hard then you won’t pass

3. P: don’t study hard, q: pass the test. if you don’t study hard then you will pass

4. P: don’t study hard, q: don’t pass the test. if you don’t study hard then you won’t pass

Alright as we finish up the warm up problems who can tell me something you and your pair talked about? Good job, did anyone come up with a different case? Alright, so if we all agree on these cases, who can come up and put each problem in p, q notation for me?

Lesson Plan Guide

TE 407 – Fall 2007 5/14 08.27.07

1, 3,4 make sense Study Hard Pass the test

Thank you good job putting together your statements. Together, let’s determine which statements are valid and which ones aren’t? I am getting a lot of blank stares, which statement makes sense and which doesn’t? Good. So today we are going to talk about a way to organize these ideas. You use something called a truth table. Here is a truth table of the work we just did. See how we organized it into a table to make it easier to read. Now who wants to have to write out these statements every time? What nobody? There is another way to represent these ideas. We pick a something for p every p. So in this case what do we want p to be? Ok. And what about q? Alright so now what you do is look at our previous statements, and based on p being study hard we have two times where that is what we wrote so it is true, and two times where we wrote the opposite so those are false. Then

Lesson Plan Guide

TE 407 – Fall 2007 6/14 08.27.07

That false implies true is true.

we do the same thing with q. For p implies q we think back to our “is this a valid argument debate”. We put true for valid arguments and false for invalid arguments. What do we notice that is interesting about this table? I know that one really trips me up too. In cases like this it is important to think about what each thing means. When you do that, some of these crazy truth table things make way more sense. So the last couple days we have been talking about reasoning. I know not everyone has finished up the reasoning activities, but we are going to move on today. Tomorrow depending on how today goes, I am planning to have a work day for those who need to finish it up. Before we get going on today’s assignment, there is just a little notation I want to introduce you to. I am going to leave it up on the Board during the class period for you to reference back to. (quickly go over notation on attached powerpoint)

Lesson Plan Guide

TE 407 – Fall 2007 7/14 08.27.07

Student Reads the description from the worksheet.

Again, feel free to ask questions as we go about notation. Ok so for today’s activity We are going to step into the shoes of world renowned pilot Ellen Wright, a descendent of the world famous Wright brothers. Ellen is flying along and she runs into engine trouble she emergency lands on an Island. She opens up her guide book and finds the following description. Can _____ you read me the description of the Island? Thank you. Alright, so your task for today is to work with your group and finish reading the story work through the truth tables. Let’s now get into our groups from the last couple days. Take five minutes silently to read completely through the worksheet, and then begin working through it with your group. Remember to make sure you answer all the questions not just the tables.

Explore – Description of Task(s)

As the students begin to explore the task they will group their desks up with the students they had been working with the previous days.

Exact question that you will pose to students to begin the exploration.

Lesson Plan Guide

TE 407 – Fall 2007 8/14 08.27.07

The rules for group work are as follows:

1. Look like a group a. This means all

desks are facing each other and no one in your group is up and wandering.

2. Sound like a group a. This means they

will be talking about mathematics with the members of THEIR group.

3. Act like a group a. This is sort of all

encompassing, but mainly this means that they will all be working and writing down as they go.

Possible Solution #1: Students accurately fill in the truth table, but can’t determine which is true. I don’t know They all said that two are truth tellers and one is a liar. Miss Frederixon, we figured out that either they are all lying or all telling the truth. Two women telling the truth and one woman lying.

What is something we know about these women? Well let’s look back at the story, what is something else they said besides about the bus stop and the road. Let’s focus on that statement for a second. Think about what we know about the people on this island and what it means if all three said the same thing. (Walk away from the group) So if they are all telling the truth what is something we would have to see in our truth table? Good do we see that?

Lesson Plan Guide

TE 407 – Fall 2007 9/14 08.27.07

No so they are liars. A spot where they all are telling a lie, which is the first row. Possible Solution #2: Student was able to complete exercise one, but is unsure how to handle there is two columns for each person Well I filled out this table, but I don’t understand how to read it. That problem was different though, this one each person has two columns. They all are truthtellers or liars. No. Possible Student Solution #3: Students are completely unsure

What do you think you would be looking for in the truth table to find when this is the case? Good. So what is getting us hung up on this problem? Well what did you do in problem one. Well what do we know about the people on the island. Alright well thinking about that can a person tell both truths and lies? Ok so using that information think about what that says about some of the rows on the truth table.

Lesson Plan Guide

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of how to set up the truth table. We said what all the variables represent.

In every other truth table what was the first thing that was done, before we even filled out the table. Good, so let’s work on that, and then try to figure out what you think the headers will be. If you and your group can’t come up with anything then call me back over. But try to figure it out from your notes and power point slides before you do.

Summarize/Share and Discuss Presentation mode – Sharing solutions, teacher-led discussion, student led discussion, etc. Students are positioned back into their assigned seats.

What will you say or do to set up the discussion of the big math ideas? Remember our rules for sharing we talked about earlier in the week.

Each group explains what they did.

What is similar and what is different between these groups ideas?

Is there anything you would like to add to their statements based on what you wrote down?

Any other questions for them?

Lesson Plan Guide

TE 407 – Fall 2007 11/14 08.27.07

Well using the example we just filled in the truth table and determined the bus stop is here and the road goes to the capital.

Since all the women made the same statement “two of us are truth tellers and one is a liar”, then all the women are either truth tellers or liars. Since two women never made a true statement at the same time, they are all lying. This means the bus stop is here and the road goes to the capital, since that is the only time all three women lied.

Can_____ group come up and put there truth table for number one on the board. While you do it explain how you figured out what you were doing. How did you know? Very good. Does anyone else have any questions for this group? (Let students have discussion if there are questions). Now can someone put up the truth table for number two for

Lesson Plan Guide

TE 407 – Fall 2007 12/14 08.27.07

Well we knew that each symbol meant a different thing so as we read through the categories we just followed what we talked about with trues and false.

We already know the capital is in the mountains, so the bus to the beach is not to the capital. Since no person can lie and tell the truth at the same time, line four is the only possibility. This means that B1 goes to the capital. Well they used the boxes at the top and the notation to tell them what to do. Then they reasoned through what it meant to figure out which bus to take.

me? As you put it up please talk us through how you knew what was true and what was false. Ok. And what bus did you determine she took? Very good. Can someone tell me how what they did is similar to what the previous group did? Good. Does anyone have anything they are confused about or want to add? Alright and can someone put up number three for me and explain

Lesson Plan Guide

TE 407 – Fall 2007 13/14 08.27.07

Well I determined the headings by the woman told her “Computer 1 is not connected to the Internet, which means that the notation is this. The man told her, “Computer 2 has an Internet connection, but computer 3 does not,” which is noted like this. Finally the last man said “If computer 2 has an Internet connection, then so does computer 1. Computer 3 is not connected to the Internet,” which is noted like this. Then we filled out the truth table. Man two cannot make a false statement and a true statement, so all rows where he makes both can be eliminated. If man one tells the truth, then the woman is a truth teller since she said man one was. If man one tells a lie, then the woman is a liar since she said man one is a truth teller. This means their statements must match, so if he tells the truth so must she. You can then eliminate all rows where their statements don’t match. This leaves only the

how you figured out your headings? Thank you can you explain to us how you determined who had internet?

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fourth row. From this we can determine that computer 1 has the internet.

Thank you, does anyone have any questions for that last group? Alright you have the last couple minutes to finish up, and get your papers in to me. I need them today, so you can’t leave without giving them to me.

Summary Statement: (May change based on what actually happens in class) You guys did a good job working today. Tomorrow we are going to have a work day for those of you who are behind. At the end of the hour tomorrow I want all the worksheets we have done this week and homework assignments on my desk.

Homework: If you haven’t finished up any of the assignments, then finish them up for homework.