Logic+and+Reasoning

====Integrating Media into a Standards Based Curriculum Spring 2013 Justin Field ==== Media Enhanced Unit Plan Course: Geometry Honors Unit C: Logical Reasoning __** Lesson 1: Inductive Reasoning **__ Objective: Use inductive reasoning to identify patterns and counterexamples in order to make, prove, and disprove conjectures.

__** ISTE NETS and Performance Indicators for Students: **__ 2. Communication and Collaboration: d. Contribute to project teams to produce original works or solve problems

__**MD Technology Literacy Standards for Students: **__ Standard 3.0: Technology for Learning and Collaboration - Use a variety of technologies for learning and collaboration B. Encourage collaboration: a. Use technology tools to work collaboratively within a school community.

__**Technology Skills needed to complete lesson: **__ Ability to create, access, and manipulate a Google document. Ability to edit a word document and a geometer sketchpad document.

a. Think-pair-share is used to have students respond to two prompts: 1. what is the product of an even and an odd number? 2. Given 1, 4, 9, what is the next number in the pattern? b. Students will view video on how to construct Sierpinski's triangle using Microsoft Word in order to construct their own copy to be saved in their student folder. They will then answer the following prompt: "what pattern do you notice between the shaded triangles in each figure? What pattern do you notice between the unshaded triangles? Using your pattern, how many unshaded triangles would be in the 20th iteration of Sierpinski's Triangle?" c. Students will begin a Unit C: Logical Reasoning notesheet which will be added to throughout the unit in order to create a tool to refer back to for studying and completing geometric proofs throughout the unit and course. They will add the terms "conjecture" and "inductive reasoning" to this sheet. d. Students will practice making conjectures by filling in the blanks in various pattern examples. e. Students will answer prompts related to truth value and counterexamples. "Determine if each statement is true or explain why it is false: 1. All teachers are taller than students 2. 10+3=13" f. Students will practice deciding if statements are true or give counterexamples to show if they are false __**Media Activity **__
 * __<span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">1. What the students are doing __**

g. Within a group students will choose one of two activities. "Activity A: building and measuring triangles" or "Activity B: building and measuring circles." Students will view the video and follow the directions given in the video. They will be asked to build three different sizes of the figure they have chosen and add a image of each to a group Google document. As a group they should make a statement and determine what counterexample would have to be shown to prove that the statement is false. If they have chosen Activity A, they should come to the conclusion that all circle diameters go into the circumference 3.14159 times and if they have chosen Activity B then they should come to the conclusion that all triangle's angles have a sum of 180 degrees. Groups that finish early should look for other observed patterns that occur between their figures. At the end of the activity the class should conduct an online gallery walk through each group's Google document and conclusions. h. The class should end with a summary to clarify what inductive reasoning is (drawing conclusions based on patterns), what a conjecture is? what a counterexample is? and what observed patterns have been noticed through the group investigations during the lesson? i. Each student should answer the end assessment questions listed the 4th section below to assess their understanding the lesson's material.

<span style="font-family: Arial,Helvetica,sans-serif;">This lesson could be taught in a classroom or a lab setting with minimal modifications so long as the students or at least in groups had access to a computer. If they are in a lab then the lesson can precede as above with the students working on a notesheet and using the computer as appropriate. If they are in the classroom, the students should be situated so that each student or each group has access to a lap top. If there is only one lap top per group then extra time should be allotted so that all students have an opportunity to build their shapes during the group activity or the number of shapes built could be reduced to each member only constructing one so that the group had a total of three shapes which would still be enough to come to a conclusion about the observed pattern.
 * __<span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">2. Suggestions for Classroom/lab setting __**

<span style="font-family: Arial,Helvetica,sans-serif;">During the class discussion portions of the lesson, think pair share should be utilized so that all students are held accountable for their participation and it differentiation occurs as the students have an opportunity to think on their own as well as hear ideas from a partner and the whole class. During the Sierpinski's triangle activity and group activity a instructional video is utilized to differentiate the activity so that students can watch, rewind, or fast forward through the instructions. The group activity is differentiated because students can work together to create their figures and come to conclusions. Groups that finish early can also look for other patterns that occur in their data and extend the activity to include other conclusions.
 * __<span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">3. How the lesson is being differentiated __**

<span style="font-family: Arial,Helvetica,sans-serif;">Students will be assessed based on the results of their group activity and their answer to and end assessment question " 1. What is the next term in the pattern .5, 1, 1.5, _ 2. T/F, if false provide a counterexample All the students drew isosceles triangles All triangles must be isosceles.
 * __<span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">4. How students will be assessed: __**

Technology contributes to the students' understanding of the content by allowing them to view and follow instructions in an individualized manner through instructional videos. Also by using geometer sketchpad they can easily build and manipulate geometric objects to draw conclusions in ways that are more difficult and time consuming without technology, Finally, they can use a Google document as a place to work collaboratively with a group of their classmates.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">5. How technology will contribute to students' understanding of content **

As mentioned above, computers are necessary for the above lesson. In a classroom setting it would be recommended that the students had access to laptops individually or at least one per group. Group sizes could vary based on the availability of the technology. One alternate suggestion would be to use TI Nspire calculators which can perform the same operations as geometry sketchpad and show the videos in the front of the classroom while walking around and assisting groups as needed in the absence of laptops. In this case, a Google document could be replaced by a large poster board piece of paper where each group member could draw their shape and measurements and the group could write their conclusion at the bottom of the poster.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">6. Suggestions for implementation of technology in classroom or lab setting **

Technology was chosen to differentiate the lesson and support collaboration between groups. Instructional videos were chosen because when students are learning a new technology they need time to process what they are being asked to do. The ability to pause and rewind a video allows them to go back to steps they might have missed during a class discussion. Geometer sketchpad or a TI Nspire calculator in its absence was chosen for students to build geometric objects because the goal of the lesson is for them to observe patterns. Using this technology, they can easily build and measure geometric objects in order to discover patterns whereas if they had to do these things by hand, it could consume the lesson. Finally, a Google document provides a long lasting space for collaboration that can be stored on a class homepage or wiki and referenced throughout the year.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">7. Why technology was chosen and why the activity enhances the overall outcome of the activity **

__** Lesson 2: Conditional Statements **__ <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Objective: <span style="background-color: #ffff00; font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Identify and write conditional statements, their converses, inverses and contrapositives, in order to analyze their truth value.

<span style="font-family: Arial,Helvetica,sans-serif;">5. Digital Citizenship: b. Exhibit a positive attitude towards using technology that **supports** collaboration, **learning,** and productivity.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">ISTE NETS and Performance Indicators for Students: **

Standard 3.0: Technology for Learning and Collaboration - Use a variety of technologies for learning and collaboration 1. Select and use technology tools to enhance learning: a. Use technology tools including software and hardware in order to learn new content or reinforce skills.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">MD Technology Literacy Standards for Students: **

Ability to create and access a Khan Academy Account. Ability to use Khan Academy Cognitive Tutor.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">Technology Skills needed to complete lesson: **

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">1. What the students are doing a. Introduce the students to "tessellations" in order to motivate them and prepare a case where a conditional statement will be necessary by showing pictures of tessellations and asking students to think-pair-share on their observations. b. Define tessellation as a class c. Discuss whether a equilateral triangle will tessellate and form a conditional statement based on the situation "If a figure is an equilateral triangle then it will tessellate". Introducing terminology of "hypothesis" and "conclusion" d. Introduce converse, inverse, and contrapositive forms of a conditional statement and exam the truth value of each in the case of a equilateral triangle. Write out each form. e. Guide the students through writing a conditional statement for "rain makes the sidewalk wet" and giving its inverse, converse, and contrapositive forms." Examine the truth value in each case. f. Have students try independently or with a partner (differentiation) to write the four statement forms for "A three sided polygon is a triangle." and examine the truth value in each case. Then introduce the vocabulary "bi-conditional" noting that all four forms of the phrase are true and the statement "a polygon is called a triangle if and only if it has three sides" can be therefore made. Students should also be introducted to negations of statements. __** Media Activity **__ <span style="font-family: Arial,Helvetica,sans-serif;">g. take students to the computer lab or have them work on laptops to complete section in Khan Academy cognitive tutor labeled "logical reasoning." Have students add instructor as a coach so that progress and activity can be tracked. <span style="font-family: Arial,Helvetica,sans-serif;">h. Have students follow directions for the end assessment question " <span style="font-family: Arial,Helvetica,sans-serif; line-height: 1.5;">Write the Conditional, Converse, Contrapositive, and Inverse of the following statement and decide whether or not it is a biconditional statement: "All rectangles have 4 congruent angles."

<span style="font-family: Tahoma,sans-serif; font-size: 12pt; line-height: 1.5;">2. Suggestions for Classroom/lab setting <span style="font-family: Arial,Helvetica,sans-serif;">The lesson should begin in a classroom setting for initial introduction to the topic and guided practice portion and then transition to a computer lab for the Khan Academy activity. An alternative would be to give each student or pairs of students a laptop in order to complete activity. If computers are not available, an instructor may choose to display Khan Academy questions using the instructor computer and having students independently answer questions on their own paper. The desired arrangement in order for differentiated instruction to take place would be for each student to be at their own computer so that they can answer questions independently and click "hint" when necessary.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">3. How the lesson is being differentiated <span style="font-family: Arial,Helvetica,sans-serif;">During the Khan Academy portion students can answer questions on their own and are given the option to ask the cognitive tutor for hints or even watch a video if they are having difficulty. Students should be held accountable for completing a certain number of problems at instructors judgement based on the overall skill level of the class. Otherwise students may "play around" watching videos and trying other areas of the tutor if they are not directed as to how much of the logical reasoning module they should have completed prior to the end of the lesson.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">4. How students will be assessed <span style="font-family: Arial,Helvetica,sans-serif;">Students will be assessed based on their results in the Khan Academy tutor and their answer to the end assessment question at the end of the lesson as given in step h of "what students are doing section"

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">5. How technology will contribute to students' understanding of content <span style="font-family: Arial,Helvetica,sans-serif;">Technology will allow for differentiated independent practice for students to be challenged to construct their own forms of conditional statements. They will be able to ask for hints or complete more problems at their own pace based on their ability level.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">6. Suggestions for implementation of technology in classroom or lab setting. <span style="font-family: Arial,Helvetica,sans-serif;">Students should be taken to the computer lab or given laptops for the Khan Academy portion of the lesson. If neither option is available, the Khan Academy may be used as independent practice/class discussion section.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">7. Why technology was chosen and why the activity enhances the overall outcome of the activity Technology was chosen to give students individualized differentiation and an extension activity for them to complete prior to the end of the lesson. The Khan Academy is free cognitive tutoring software that they can create an account for and complete on their own.

Lesson 3: Deductive Reasoning: <span style="background-color: #ffff00; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">Objective: Use deductive reasoning in order to verify truth value of given premises.

2. Communication and Collaboration: b. Communicate information and ideas effectively to multiple audiences using a variety of media and formats.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 12pt;">ISTE NETS and Performance Indicators for Students: **

<span style="font-family: Arial,Helvetica,sans-serif;">5. Digital Citizenship: b. Exhibit a positive attitude towards using technology that **<span style="font-family: Arial,Helvetica,sans-serif;">supports **<span style="font-family: Arial,Helvetica,sans-serif;"> collaboration, **<span style="font-family: Arial,Helvetica,sans-serif;">learning, **<span style="font-family: Arial,Helvetica,sans-serif;"> and productivity.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">MD Technology Literacy Standards for Students: **

Ability to create and use an Edmodo class account. Ability to participate in online quizzes and to create a blog post.
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">Technology Skills needed to complete lesson: **

__<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">1. What the students are doing __ <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">a. students work individually or with a partner to complete opening activity "Greetings Earthlings from Planet Yercon Activity" where they will take three statements " If you are a zintoid, then you are a quorg, If you are a meerk, then you are a ving, If you are a quorg, then you are a wiklop." and answer questions to uncover logic behind the laws of syllogism and detatchment devoid of a real situation. b. Students are formally introduced to law of detatchment and syllogism using vocabulary of hypothesis and conclusion. These laws provide a basis for "deductive reasoning" or reasoning by drawing conclusions based on a premise. c. Students are given examples of situations and asked to determine whether they are inductive or deductive reasoning based on prior knowledge of inductive reasoning from lesson 1 and contrasting it with newly introduced deductive reasoning. d. Students are guided through creating conclusions based on laws of detatchement by using the statement "If Alice studies then she will get an A." Students are asked to identify the hypothesis and conclusion and guided in a class discussion to conclusions that can be drawn given the situation 1. Alice studies and 2. Alice got an A. Students should recognize that Alice getting an A does not imply that she studies (she could have cheated.) e. Students are guided through law of syllogism "If Alice studies then Alice will get an A." and " If Alice gets an A then she will be happy." Students are asked what they can deduce if Alice studies (that she will be happy). f. Students will participate in an Edmodo quiz by analyzing a situation and deciding if it is a. true by the law of detatchement, b. true by law of syllogism or c. inconclusive. Situations will include some mathematical and some non mathematical examples g. Students will create two conditional statements that form a syllogism and give two conjectures below. Students will then respond to two other classmates and draw conclusions based the given situation // Example: Student will create the statement If you eat junk food you will gain weight, If you gain weight then you will need new clothes. Followed by the following two conjectures: a. Martha eats Junk food conclusion// //and b. John needs new clothes.// Then a classmate will respond to the prompts which in this case would be a. Martha will need new clothes based on the law of syllogism and b. John's situation is inconclusive based on the laws of logic learned today. h. Students will be assessed by answering the following end assessment question: " <span style="font-family: Arial,Helvetica,sans-serif; line-height: 1.5;">Use the laws of detachment and syllogism to draw the appropriate conclusions. Identify which law you are using. Statement A: If two angles form a linear pair then they are supplementary and If two angles are supplementary then they add to 180 degrees. Choose: Syllogism/Detachment, Conclusion: _"
 * Media Activity**

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">2. Suggestions for Classroom/lab setting <span style="font-family: Arial,Helvetica,sans-serif;">The lesson can begin in a classroom transition to the computer lab for the media portion of the lesson. Another option is to have students use lap tops or Edmodo app on their ipod/cell phone as school policies allow.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">3. How the lesson is being differentiated <span style="font-family: Arial,Helvetica,sans-serif;">The lesson is differentiated by students being able to work individually or with a partner during opening activity. They also can choose their situation and which classmates prompts to respond to during the independent practice portion of the lesson.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">4. How students will be assessed <span style="font-family: Arial,Helvetica,sans-serif;">Students will be assessed based on their answers to the Edmodo activity and their response to the end assessment question at the end of the lesson.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">5. How technology will contribute to students' understanding of content <span style="font-family: Arial,Helvetica,sans-serif;">Teacher will be given instant feedback during the Edmodo quiz as to the classes grasp on the laws of syllogism and detatchement. The students will also get to review and write their own statements. They will be able to read other classmates responses if needed prior to posting their own response. In this way, technology will make the lesson more interactive and differentiated.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">6. Suggestions for implementation of technology in classroom or lab setting <span style="font-family: Arial,Helvetica,sans-serif;">As mentioned above, the media activity can be performed in a computer lab, with lap tops, or using the Edmodo app on ipods and cell phones as they are available to students.

<span style="font-family: Tahoma,sans-serif; font-size: 12pt;">7. Why technology was chosen and why the activity enhances the overall outcome of the activity The technology chosen will give the instructor long lasting data points as to student understanding of the lesson based on quiz results, blog posts, and responses to blog posts. It will put all student work in one easily accessible location for students and instructor to review throughout the course.

Formative Assessment : 1. Given above "End Assessment questions at the end of each lesson." <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">2. The following are daily quizzes to be given at the beginning of each lesson as a beginning formative assessment **
 * <span style="font-family: Tahoma,sans-serif; font-size: 12pt;">Summative Assessment: **