Heather+Sauer


 * WEEK 7**

= Daily Lesson GAME Plan = || Algebra II Block (lower-level) – Periods 6 & 7 17 students |||| **Unit:** Linear Systems ||
 * **Lesson Title:** It’s a Wrap! Movie-making to Review Systems of Equations |||| **Related Lessons:** Systems of Equations, Solving by Graphing, Substitution, and Elimination, Graphs in 3-Dimensions ||
 * **Grade Level:** 11th and 12th grade
 * == GOALS == ||
 * **Content Standards:**


 * “Describe relationships and make generalizations about patterns and functions” (CSDE, 2005, p. 2).
 * “Manipulate equations, inequalities and functions to solve problems” (CSDE, 2005, p. 2).
 * “Represent and analyze linear and nonlinear functions and relations symbolically and with tables and graphs” (CSDE, 2005, p. 2).
 * “Model real data graphically using appropriate tools, technologies and strategies” (CSDE, 2005, p. 5). ||
 * **ISTE NETS-S**


 * Creativity and innovation
 * Communication and collaboration
 * Research and information fluency
 * Critical thinking, problem solving, and decision making
 * Technology operations and concepts


 * Instructional Objectives:**

Students will create a slide show/movie to explain, and make connections between, the concepts involved with linear systems. They will take pictures or find images online, record their voices, and edit their presentation using Windows Movie Maker.


 * NOTE:** This learning experience will take the place of a traditional end-of-unit review and test. The evaluation of the students’ artifacts will serve as the summative assessment of learning in the unit. ||
 * == ACTION == ||
 * **Before-Class Preparation:** I will need to take a class period to present to my students a completed slide show on Windows Movie Maker. Then, I will guide them through some of the features and have them work as a class to create a short slide show, complete with video, audio, and editing (timing, transitions, and credits). Students will use Flip Video, a digital camera, and the audio recording software on my laptop to create the files needed for the class demonstration. Then, students will brainstorm as a class to generate a list of other technologies that can be used (cellular phones, tablets, etc.) ||
 * **During Class** ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 45 minutes (1 period)

90-135 minutes (2-3 periods)

45 minutes (1 period) |||| Students will be shown a checklist for the content criteria on their slide show/video on linear systems:
 * What is a linear system? What is a solution?
 * Describe the types of solutions
 * Show the three methods to solve
 * Write a word problem to relate to your equations. Explain.
 * Show how a system of inequalities is different that a system of equations.
 * Make connections!

I will explain to students that they will use photography, online images, video, audio, or any combination to create a slide show or movie that addresses the criteria on the checklist. Students will be allowed to choose a partner to work with. In their pairs, students will select a system of equations – they can write one themselves, or take one from the book. I will explain to them that the system they choose will guide their work – they will use the same system to demonstrate the three methods of solving, as well as to complete the pieces involving the word problem and linear inequality. Students will be asked to copy down the checklist, and I will encourage them to write down other things they can include to help make connections or expand upon concepts. For the remainder of the period, students will brainstorm a plan of action for the assignment. Every student will receive a copy of the evaluative rubric.

At the beginning of each class, I will guide a discussion on progress (as noted below). Students will work with their partners in the media center to create their slide show/video. At the end of each period, students will email me their file for review.

Students will present their slide shows/videos. Following each presentation, I will guide students to provide constructive feedback. Once all the presentations have been shown, students will work in their pairs to fill out a rubric based upon their own performance. || Pencils, Paper, Checklist, Rubric, media center/computers, Windows Movie Maker software, audio/visual recording devices ||
 * **Note student groupings, environmental modifications needed, etc:**

Students will work in pairs to complete this assignment. There will be one group of three, because there are an odd number of students. Because students will need quiet space to record audio or video, I will book the media center at my school instead of the math computer lab; this will allow my students enough room to spread out and work. Once they are ready to start working with Windows Movie Maker, they can use the computers in the media center. ||
 * == MONITOR == ||
 * **Ongoing Assessment(s):**

I will monitor pairs of students and check progress frequently. The checklist will help guide my conversations with students, and I will encourage students to write down questions that they have on the checklist, so when I am able to consult with each pair, students can get clarification. At the beginning of each period, the class will reconvene, I will share select samples of student work so far, and we will briefly discuss obstacles and successes. Throughout the whole learning experience, I will remind students to use their rubrics to guide their progress.


 * Accommodations and Extensions:**

For my students with learning strategies teachers, I will give them advance notice of this assignment, and explain to their teachers and paraprofessionals the expectations for the assignment. I will continue to communicate with the special education teachers and paraprofessionals to ensure that the students are on-track and clear about the assignment.

Students will be encouraged to include additional information about linear systems in their presentation – they can choose to include information that they learned about (but was not a required component in the project), or they can elect to conduct further research on solving systems in three dimensions (although the students have worked with graphs of three dimensions, they have not solved any of these types of systems, which are more advanced).


 * Back-Up Plan:**

This assignment is not reliant upon the Internet, and I cannot foresee any issues regarding accessibility of technology. Regardless, the project can be done by hand; students can use graph paper, rulers, lined paper, and posterboard to meet the criteria of the assignment. ||
 * == EVALUATE AND EXTEND == ||
 * **Be specific and include the evaluation that you will use for this lesson:**

Student understanding will be assessed formatively through class discussion and interviews of students in their pairs. I will also review progress of the artifact and help students to adjust as needed.

The rubric below will be used as a summative assessment for the unit on linear systems. ||


 * || === Digital Storytelling: Linear Systems ===

Teacher Name: **Heather Sauer** Student Name: ________________________________________  || || **WEEK 6** Algebra II Block (lower-level) – Periods 6 & 7 17 students |||| Unit: Linear Systems ||
 * CATEGORY  ||  **4 **  ||  **3 **  ||  **2 **  ||  **1 **  ||
 * **Mathematical Understanding ** || Explanations demonstrate evidence of conceptual understanding. || Explanations demonstrate partial evidence of conceptual understanding. || Explanations demonstrate incorrect understanding of concepts. || Explanations do not reference mathematical concepts. ||
 * **Accuracy ** || Each method of solving is used correctly. The solution is correct. || Each method of solving is used correctly. There are 1-2 errors that may/may not lead to an incorrect solution. || At least one method of solving is used correctly. The correct solution is reported through at least one method. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">None of the methods of solving are used correctly OR the correct solution is not reported. ||
 * **<span style="font-family: "Arial","sans-serif"; font-size: 14.66px;">Connections ** || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">At least 3 connections are made within the presentation. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">At least 2 connections are made within the presentation. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">At least 1 connection is made within the presentation. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">No connections are made within the presentation. ||
 * **<span style="font-family: "Arial","sans-serif"; font-size: 14.66px;">Visual ** || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">The visual material is clear and neat. Transitions are made at appropriate times. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">The visual material is at least 80% clear and neat. Transitions may be slightly off. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">The visual material is at least 60% clear and neat. Transitions may be off by a few seconds. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">The visual material is less than 60% clear and neat. The visual portion does not align with the audio. ||
 * **<span style="font-family: "Arial","sans-serif"; font-size: 14.66px;">Audio ** || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">Narration is clear to understand. The narrator(s) speak(s) in complete sentences and use(s) appropriate mathematical vocabulary. No slang is used. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">Narration is clear to understand. The narrator uses appropriate mathematical vocabulary. No slang is used. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">Narration is mostly clear to understand. The narrator uses some appropriate mathematical vocabulary. || <span style="font-family: "Arial","sans-serif"; font-size: 12px;">Narration is difficult to understand OR appropriate mathematical vocabulary is not used. ||
 * = Daily Lesson GAME Plan = ||
 * Lesson Title: Graphs in 3 Dimensions |||| Related Lessons: Systems of Equations, Systems of Inequalities, Linear Programming ||
 * Grade Level: 11th and 12th grade
 * == GOALS == ||
 * **Content Standards:**


 * Create the appropriate visual or graphical representation of real data.
 * Use a variety of coordinate systems and transformations to solve geometric problems in 2 and 3 dimensions using appropriate tools and technologies.
 * Develop and evaluate mathematical arguments using reasoning and proof. ||
 * **ISTE NETS-S**


 * Creativity and innovation
 * Communication and collaboration
 * Critical thinking, problem solving, and decision making
 * Technology operations and concepts


 * Instructional Objectives:**

Students will graph in three dimensions and sketch planes in coordinate space. They will collaborate using educational networking (Edmodo) to explore ideas related to three-dimensional graphs/equations in three variables. ||
 * == ACTION == ||
 * **Before-Class Preparation:**

I have recently created an Edmodo website, as well as groups for each class. I will present the Edmodo site to the students during class, making sure to point out the various features and demonstrate navigation of the site. Students will receive the code specific to their class and must register with the site, either at school or at home. I need to allow time to get all students registered before the activity below. I also need to reserve the computer lab for the activity on day 2.

I will meet with my paraprofessional prior to the Edmodo activity to show him what the students will be doing and explain what I will be looking for in student responses, so that he will be prepared to help his students with the assignment. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 45 minutes

45 minutes |||| Students will be given a vocabulary prediction worksheet featuring the following vocabulary: “ordered triples”, “coordinate space”, and “trace”. They will work for five minutes in their base groups to write their predictions for what each vocabulary word/phrase means. Next, the class will reconvene and share their ideas. I will present the lesson, “Graphs in Three Dimensions”, and model graphing points and planes in coordinate space. Following each example, students will work independently to do practice problems, after which volunteers will draw their points/planes on the SMART board. Students will be presented with a real-world connection problem in which they must interpret a technological representation of a bicycle helmet. At the end of the lesson, students will write (in their own words), the actual definitions of each vocabulary term on their prediction worksheets.

After reviewing the homework from the previous night and addressing any concerns/questions, the class will move to the computer lab. Students will work individually to log on to the Edmodo site, read the questions I have posted on their class’s page, and either respond to a question or create a thought-provoking question of their own. Students will be given a rubric so that they understand what constitutes a “good” comment and response. After they post their comment, students will be encouraged to explore the site further and write down some ideas on how they can use the site to benefit/extend their learning, as well as suggestions on how I can use it in class to help them learn. For homework, students will be required to contribute a response to another students’ comment.


 * POSTS/QUESTIONS:**

1. How would you graph “y = -2” in coordinate space? How would your graph compare to that on a coordinate plane? Explain.

2. Does every plane have three traces? Explain how you know.

3. A student says she can find the z-intercept of a plane by substituting “0” in for “z” in the equation of a plane. Is this student correct? Explain.

4. Explain one thing that confuses you about 3-dimensional planes. How will you overcome this obstacle? Explain.

5. Describe (in detail) a way that 3-dimensional planes are used in the real world.

6. What more would you like to learn about this topic? Why would you like to know? How can you find this information? || Vocabulary Prediction worksheets, SMART board, graph paper

Computer lab, Internet access (Edmodo site), Discussion comment/response rubric ||
 * **Note student groupings, environmental modifications needed, etc:**

Students will work individually, in their base groups, and as a whole class. (Specified above) ||
 * == MONITOR == ||
 * **Ongoing Assessment(s):**

Along with my in-class paraprofessional, I will monitor students during their computer lab time and clarify any misunderstandings or confusion. Because we have not yet used Edmodo, or educational networking in general, I will guide students by using the rubric, thoughtful questioning, and praise. Students have done a fair amount of writing with me, but I will remind them of my standards for academic writing; students will be encouraged to use Microsoft Word to type out their responses so that they can check their work for spelling or grammatical errors.


 * Accommodations and Extensions:**

This lesson may very well lead to follow-up learning or extensions, depending on the content of the discourse on the website. I will set aside the lab period on the third day to allow for further exploration of a topic that students might want to pursue.


 * Back-Up Plan:**

If the Internet/network is down, I can project the questions on the SMART board and students may write their responses by hand. Then, they can either post their comments at home, or use the Edmodo application on their cellular phones to respond during class. ||
 * == EVALUATE AND EXTEND == ||
 * **Be specific and include the evaluation that you will use for this lesson:**

Student understanding will be assessed formatively through class discussion, student practice work, and written explanations on the vocabulary prediction sheets.

The rubric below will be used to the quality of comments/responses and understanding of the content. ||
 * || === Educational Networking: Comments and Responses ===
 * || === Educational Networking: Comments and Responses ===

Teacher Name: **Heather Sauer** Student Name: ||  ||


 * CATEGORY || **4** || **3** || **2** || **1** ||
 * **Comment** || Comment answers the question and includes a detailed explanation that supports the answer. || Comment answers the question and includes a detailed explanation does not adequately support the answer. || Comment answers the question. The explanation is minimal, but provides at least partial support of the answer. || There is no comment and/or no explanation. ||
 * **Response** || Response provides constructive feedback and encourages further discussion. Details are given to support the feedback. || Response provides constructive feedback to the author of the comment. Details are given to support the feedback. || Response provides constructive feedback to the author of the comment. || Response provides no feedback, or feedback that is not constructive. ||
 * **Spelling/Grammar** || There are 0-1 spelling/grammar mistakes in comments/ responses. || There are 2-3 spelling/grammar mistakes in comments/ responses. || There are 4-5 spelling/grammar mistakes in comments/ responses. || There are over 5 spelling/grammar mistakes in comments/ responses. ||
 * **Mathematical Understanding** || Explanation demonstrates evidence of conceptual understanding. || Explanation demonstrates partial evidence of conceptual understanding. || Explanation demonstrates incorrect understanding of concepts. || Explanation does not reference mathematical concepts. ||

**WEEK 5** Algebra II Block (lower-level) |||| **Unit:** Linear Systems ||
 * = = Daily Lesson GAME Plan = ||
 * **Lesson Title:** Linear Programming Application |||| **Related Lessons**: Systems of Equations, Systems of Inequalities ||
 * **Grade Level:** 11th and 12th grade
 * = == GOALS == ||
 * **Content Standards:**
 * Model real-world situations and make generalizations about mathematical relationships using a variety of patterns and functions.
 * Relate the behavior of functions and relations to specific parameters and determine functions to model real-world situations.
 * Model real data graphically using appropriate tools, technologies and strategies. ||
 * **ISTE NETS-S**
 * Creativity and innovation
 * Communication and collaboration
 * Research and information fluency
 * Critical thinking, problem solving, and decision making
 * Technology operations and concepts

Students will write their own linear programming application problem. They will define the problem in two variables, write the restriction statements (at least four), and write the objective function. Students will use Winplot to graph and explain their solution. ||
 * Instructional Objectives:**
 * = == ACTION == ||
 * **Before-Class Preparation:**

Bookmark websites including definitions, information, and examples related to linear programming. Also, bookmark the following interactive tutorial for graphing linear programming problems on Winplot: [] Reserve computer lab for the first and last days of the lesson. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 30 minutes

60 minutes

45 minutes |||| Students will be presented with the problem. They will receive a guided note-taking worksheet to structure their research on linear programming. Students will work individually to conduct Internet research to define //linear programming//, //constraints//, //objective function//, and //feasible region//. They will include an example of a real-world linear programming application that they found.

The class will regroup and share their findings. I will guide them through the process to solving a basic linear programming application. Students will work in collaborative groups to solve three linear programming application problems of varying difficulty.

Students will work in their groups to create a linear programming application word problem. They will type it up in Microsoft Word and include a graphic. Next, each student will independently go through the Winplot interactive tutorial. Each student will create a Winplot graph to represent their own word problem. They will then find the vertices using the graphing calculator and solve their problem.


 * NOTE* This class has a block (lab) period every other day. The entire lesson should take three to four 45-minute periods. || Computer Lab, Internet with Bookmarked websites

Graphing calculators, rulers, graph paper

Computer lab, Internet, Winplot tutorial website, headphones, graphing calculators ||
 * **Note student groupings, environmental modifications needed, etc:**

Students will work in groups of three, pre-selected by the teacher. ||
 * = == MONITOR == ||
 * **Ongoing Assessment(s):**

Check for understanding by conferencing with each group as they progress through their research, practice examples, and development of their problem. Facilitate where necessary, asking guiding questions and offering different viewpoints. At the beginning of each class period, reconvene as a whole class to discuss progress.


 * Accommodations and Extensions:**

Student grouping will be homogeneous, and students will be encouraged to make their problem as difficult as they can, within their comfort level. Students may reference linear programming examples when they design their problem.

Students who are more advanced will be asked to create a more complex problem by including more constraints and/or more complex details within the problem.


 * Back-Up Plan:**

If the Internet/network is down, students may conduct their research using the course text. The graph can be made by hand, and by using graphing calculators. (Students will be allowed extra time to do work by hand). If the Winplot tutorial website is not working, I will demonstrate the material from the tutorial on the SMART board for the whole class. ||
 * = == EVALUATE AND EXTEND == ||
 * **Be specific and include the evaluation that you will use for this lesson:**

Student understanding will be assessed formatively when I collect, review, and provide feedback on the guided note-taking sheets.

The rubric below will be used to assess student understanding of linear programming on a summative basis: ||

**Math - Problem Solving : Linear Programming Application Rubric**

 * CATEGORY || **4** || **3** || **2** || **1** ||
 * **Mathematical Concepts** || Application problem demonstrates complete understanding of the mathematical concepts used to create the problem. || Application problem demonstrates substantial understanding of the mathematical concepts used to create the problem. || Application problem demonstrates some understanding of the mathematical concepts needed to create the problem. || Application problem demonstrates very limited understanding of the underlying concepts needed to create the problem OR is not written. ||
 * **Completion** || Problem includes all information needed to determine variables, constraints, and the objective function. || Problem is missing at least one necessary component, but all information is shown within the student work. || Problem contains all necessary components, but when graphed, does not result in a feasible region. || Problem does not include sufficient information ; it cannot be solved. ||
 * **Mathematical Errors** || 90-100% of the steps and solutions have no mathematical errors. || Almost all (85-89%) of the steps and solutions have no mathematical errors. || Most (75-84%) of the steps and solutions have no mathematical errors. || More than 75% of the steps and solutions have mathematical errors. ||
 * **Technology/Graph** || Graph is clear and greatly adds to the reader's understanding of the procedure(s). || Graph is clear and easy to understand. || Graph is somewhat difficult to understand. || Graph is difficult to understand or are not used. ||
 * **Strategy/Procedures** || Typically, uses an efficient and effective strategy to solve the problem(s). || Typically, uses an effective strategy to solve the problem(s). || Sometimes uses an effective strategy to solve problems, but does not do it consistently. || Rarely uses an effective strategy to solve problems. ||
 * **Strategy/Procedures** || Typically, uses an efficient and effective strategy to solve the problem(s). || Typically, uses an effective strategy to solve the problem(s). || Sometimes uses an effective strategy to solve problems, but does not do it consistently. || Rarely uses an effective strategy to solve problems. ||