Microsoft Word - 81613 SCHOOL OF EDUCATION.docx

School of Education

LESSON PLAN ORGANIZER

Identification of the class

Subject: Coordinate Algebra

Time frame (min. and period):4th period 70 minutes

Grade:8th grade honors

Number of students:18

National, State or NETS standards

(Write out complete standard. CCGPS, GPS, NGSS or NETS)

CCGPS: MCC9-12.A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Rationale for instruction

(State rationale given to students for how this instruction will benefit them. Readiness, interest, learning style, developmental level.

Topic: Graph solutions of two-variable inequalities.

Rationale: Students must be able to graph solutions of two-variable inequalities.

Essential Question:

· How do I graph a system of linear equalities in two variables?

Materials/equipment/technology/preparation (List materials, worksheets, formative or summative assessment instruments, and list web sites if needed.

*hw: homework

· Smart board

· Student handouts (hw worksheet and Graphing Inequalities Task worksheet)

· Pen, Pencil, colored pencils or markers

· Document camera

Daily objectives

(State in operational, measurable terms; objective should be directly linked to evaluation procedures. If you are working with a small group or one-to-one, individual goals may be appropriate; 1-3 goals per lesson.)

*SWBAT: Students will be able to

1. SWBAT: identify some solutions to the inequality

2. SWBAT: identify the solutions for the system

3. SWBAT: identify coordinates that are not solutions to the system.

Assessment/Evaluation/Monitoring

(Description of how you will evaluate student achievement of lesson objectives; attach any quizzes, questions used for assessment, or seatwork worksheets).

· SWBAT: graph a system and identify coordinates that are solutions to the system and coordinates that are not a solution to the system on a worksheet with coordinate planes as I walk around and observe them through an informal assessment.

(continued)

Lesson Plan Organizer (continued)

Instructional sequence

(Estimate amount of time per section.)

Start of class period (10 min.) Required tasks

Collection of homework

Warm-up activity

*TW: teacher will

Beginning lesson (intro or connecting to previous day) (5 -10 min.)

Procedures Motivation “Hook” Objective Overview

Purpose of lesson

Middle (20 - 40 min.) Key essential question(s) Modeling

Informal check for understanding (should be done throughout lesson)

Guided Practice

Independent Practice

· The concept of systems of inequalities was introduced the day before. To ensure that students have some understanding teacher will be informally checking through verbal responses and written responses as the teacher walks around the room.

Level of instruction (acquisition, practice, or generalization): Implementation Plan (bulleted outline)Procedures Identified

· Students will enter the classroom and sit in their assigned seats. (seating chart attached)

· Welcome the class

· TW ask students to get homework out so she can check and make sure everyone has completed the assigned work.

· TW inform students to turn to the side in which contains word problems. TW inform the students that we will review the word problems then return to the front side that contains the systems of inequalities after we finish the packet from yesterday. Today we will be reviewing word problems and looking at systems of inequalities again.

(hw answer key attached below)

· TW will show the answers to the six word problems under the document camera and review any in which students have questions over.

· TW remind the class that tomorrow is your major quiz over solving systems by graphing, a table, substitution, elimination, and word problems so when we come in tomorrow we need to own our knowledge in order to do well on the quiz This means make sure you study!!

(Hw answer key attached below.)

· Once word problems have been reviewed and the teacher has reminded the class of the major quiz the following day the TW then ask students to keep out their homework and turn to the Graphing Inequalities Task packet that they were working on yesterday.

(Graphing Inequalities Task Answer Key Packet attached below.)

· TW place #5 graph that was done the previous day under the document camera. (This is beneficial for the visual learners.)

· TW ask students rather we talked about question 5 c.) yet or not. If so teacher will move on to question 5 d.) and if not teacher will ask students: Is a coordinate on either line a solution?

· Answer: Yes, coordinates on the line are solutions to the system.

· TW then ask why the coordinates on these lines are a solution for this system but not the lines on the graph that was done before this one?

· Answer: Because these lines are solid due to the in the inequalities rather than in the other inequalities.

· TW be sure to use the correct academic language in order for students to effectively learn the vocabulary associated with the content being taught.

(Research provides a strong case for systematic instruction in vocabulary. Marzan (2001), concludes that the most effective components of vocabulary learning are: a.)students must encounter words in context more than once to learn them, b) Instruction in new words enhances learning words in context, c) One of the best ways to learn a new word is to associate an image with it, d) Direct vocabulary instruction works, e) Direct instruction on words that are critical to new content produces the most powerful learning (Marzano, R.J., 2001). )

.

· TW ask: How would you change the inequality

so that it would shade below the line?

· Answer: If you change the, the graph will shade below.

· After a student answers TW then do an informal check for understanding by asking students to stand on chair if they agree or sit on floor if they disagree.

· TW ask: How would you change the inequality

so that it would shade above the line?

· Answer: If you change, the graph will shade above the line.

· After a student answers TW then do another informal check for understanding by asking students to stay seated if they agree or do jumping jacks if they disagree.

· TW the slide the packet to show #6 in the Graphing Inequalities Task packet on the document camera. While doing this teacher will instruct class to get two color pencils or highlighters of different colors and look at #6.

· TW then inform students that she wants them to graph the new equations from ‘d’ and ‘e’ on the coordinate grid below.

· TW remind students to use one color for one equation and the other color for the other equation.

· TW will give students a tip: Graph one equation and shade the region in which its coordinates are solutions in one color. Then graph the other equation and shade the region in which its coordinates are solutions in the other color.

· TW allow students adequate time (2-4 minutes) to graph the system and shade the areas that represent the solutions to the inequalities.

· TW will take a student’s artifact and display it under the document camera in order to discuss what the shaded regions represent and why the colors do NOT overlap.

· TW first ask: What do the coordinates in the upper right hand shaded area represent?

· Answer: This shaded area or color (will vary) represents the solutions to the inequality, but not the other.

· Summarize this answer to make it your own and so that you will understand when you are looking over it when you study.

· Students will be summarizing information being discussed throughout the lesson. According to Marzano (2001), “to effectively summarize, students must delete some information, substitute some information, and keep some information and in order to do this, students must analyze the information at a fairly deep level (p. 30-31).

· TW ask: So, what do the coordinates in the lower left hand area represent?

· Answer: This shaded area or color (will vary) represents the solutions to the inequality, but not the other.

· TW then ask: Why do the colors NOT overlap for this system?

· Answer: There is no coordinate that is a solution to both inequalities. Therefore, the system has no solution.

· Teacher uses comprehension and application level questions from Bloom’s Taxonomy. Marzano (2001) states, “higher level questions produce deeper learning than lower level questions (p. 107).

· TW confirm with students that they understand why the system has no solution.

· TW then prompt the students to put pencils and everything down and look up towards their direction.

· TW state don’t answer out loud just think about this questions I’m about to ask. TW then ask: Is there any way we can just look at the inequality and just tell rather we are going to shade above or below it?

· TW allow students to ponder on the question while instructing them watch as she writes.

· TW inform the students to state out loud rather they think it’s above or below the line as she writes the inequality.

Closing (5 -10 min.) Wrap up

Review of key points/EQ/objectives

Bridge to future learning

Collection of papers/materials, etc.

NOTE: This entire section is to be scripted! List the questions or prompts you will use for formative assessment.

· TW then write equations below and allow students to verbally express whether they believe the solutions are above or below the inequality.

1. Answer: below

2. Answer: above

3. Answer: above

4. Answer: above

5. Answer: below

6. Answer: below (TW remind students that on this particular problem when you divide

· TW ask students if they can draw a conclusion yet.

· TW pick a student who raises their hand to explain their conclusion or rationale. If a student does not volunteer teacher will explain how to determine where to shade by just looking at the inequality.

· Example answer: To determine what part is shaded, look at the equation that is solved for y, and pay attention to the inequality sign. If it is y>... then it is shaded above. If it is y<... then it is shaded below.

· TW then state: Everyone pull your homework you did last night back out. Let’s test our hypothesis on how to determine what part to shade on your homework!

· TW go through homework (attached below) with students and determine if their hypothesis is correct. While checking hypothesis teacher will also discuss any homework questions with students.

· If time allots TW have students go back to the Graphing Inequalities Task packet and look at the back part.

· TW direct students to focus their attention below the part that states “use these graphs to invent your questions”.

· TW will walk through each graph and help students write inequalities for each. ( answers attached below)

· TW review key points on systems by asking students:

· How do we determine if the line is dashed or not?

Answer: By looking at signs in the inequality.

· How do we determine rather we shade above or below the inequality?

Example answer: To determine what part is shaded, look at the equation that is solved for y, and pay attention to the inequality sign. If it is y>... then it is shaded above. If it is y<... then it is shaded below.

· How many solutions does an inequality have?

Answer:

· What does it mean if there is no overlapping in a system?

Answer: There is no coordinate that is a solution to both inequalities. Therefore, the system has no solution

1. After reviewing the key concepts of how to graph a system of linear equalities in two variables the teacher will then pass out homework. Teacher will inform them of what number it should be in their notebook.

1. TW instruct students to complete front and back in order to be well prepared for the major quiz tomorrow.

1. TW also remind students that on their word problems she wants them to define their variables, write their system, and write a sentence for their word problems.

1. TW will then instruct students to Study, Study, Study!! Have a good day

References

Marzano, R. J. (2001). Classroom assessment and grading that work. Alexandria, VA: Association for Supervision and Curriculum Development.

Lesson Plan Organizer (continued)

Solo/Co-teaching considerations for accommodations/modifications

Did we…

Address any non-content- related IEP goals

Address appropriate

content-related IEP goals

Consider needs of individual students for assignments and classwork (modalities, developmental pathways)

Discuss how to provide accommodations/ modifications without alienating students with disabilities

ESOL

Notes:

Solo/Co-teaching considerations

(Who teaches what? Who prepares what? Who is responsible for grading which assignments?)

Did we plan for…

Seating

Roles in instruction

Roles in discipline

Classroom movement patterns

Instructional strategies

Did we consider including…

Mnemonics

Graphic organizers

Cooperative learning strategies

Progress monitoring

Peer-assisted learning strategies

Notes:

· Classroom seating is determined by a seating chart at the beginning of every Unit.

· Cooperative learning will occur if given the opportunity for group work.

· Progress monitoring will occur during the individual work.

· Peer-assistance will be allowed during the time in which they are allotted to come up with the graph of each inequality.

Additional considerations:

(Do we need other resources? How will we know we have succeeded? )

Things to consider: Yes No

Yes Do we have an alternate plan if technology does not work or is unavailable? I.e., usb drive

· I would use the white board and markers to review homework and graph systems of inequalities .

Yes Has your collaborating teacher and supervisor approved this lesson?

Yes Do you have a plan to remediate and assess students who are absent?

· They can come during A-squared for remediation and assessment if absent.

Yes Do you have a plan to reteach challenging material if your students are not successful (assessment)?

· If a few students in each class are not successful they can come during A-squared, but if it seems like the whole class does not understand the material then I can re-teach the lesson in a different way the following day.

Key for Graphing Inequalities Task

1. Graph the inequality y > -½ x + 5. What are some solutions to the inequality?

2. Graph the inequality y < x + 2. What are some solutions to the inequality?

3. Look at both graphs.

The main purpose of this exercise is to allow students to discover visually and conceptually where the solutions to the inequalities lie on the graph.

a. Are there any solutions that work for both inequalities? Give 3 examples.

There are many solutions that work for both, including: (-2, 7), (4, 4), (7, 3)

b. Are there any solutions that work for 1 inequality but not the other? Give 3 examples and show which inequality it works for.

There are many solutions that work for one inequality but not the other.

2. Graph both inequalities on the same coordinate system, using a different color to shade each.

a. Look at the region that is shaded in both colors. What does this region represent?

The region shaded in both colors represents the solutions to the system.

b. Look at the regions that are shaded in only 1 color. What do these regions represent?

The regions shaded in one color represent solutions that work for one inequality, but not the other.

c. Look at the region that is not shaded. What does this region represent?

The region that is not shaded represents combinations that are not solutions to either inequality.

5. Graph the following system on the same coordinate grid. Use different colors for each.

x + y ≥ 3

y ≤ -x + 5

a. Give 3 coordinates that are solutions to the system.

Answers may vary.

b. Give 3 coordinates that are not solutions to the system.

Answers may vary.

c. Is a coordinate on either line a solution?

Yes, coordinates on the line are solutions to the system.

d. How would you change the inequality x + y ≥ 3 so that it would shade below the line?

If you change the > to < , the graph will shade below.

e. How would you change the inequality y ≤ -x + 5 so that it would shade above the line?

If you change < to > , the graph will shade above the line.

6. Graph the new equations from ‘d’ and ‘e’ above on the same coordinate grid. Use blue for one graph and red for the other.

a. What do the coordinates in blue represent?

Each color represents solutions to one inequality, but not the other.

b. What do the coordinates in red represent?

See above.

c. Why do the colors not overlap this time?

There is no coordinate that is a solution to both inequalities. Therefore, the system has no solution.

Lesson Plan Rubric

Target (4 pts)

Acceptable (3 pts)

Needs Improvement (2 pts)

Unacceptable (1 pt)

Mechanics (1.000, 12%)

Writing contains 1-2 errors in spelling, punctuation, and grammar.

Writing contains 3-4 errors in spelling, punctuation, and grammar, but writing follows normal conventions.

Writing contains (5-6) spelling, grammar and punctuation errors that interfere with comprehension

Writing contains more than six spelling, grammar and punctuation errors.

Targeted Standards/Objectives/Learning Theories (1.000, 12%)

All standards/theories are identified and are a focus of instruction and assessment throughout lessons.

Standards/theories are implied throughout, but some are not specifically shown as being part of instruction or assessment.

Standards/theories seem to be addressed, but they are vague within lesson plans.

Standards/theories are not addressed in any meaningful way.

Curriculum -Framing and Engagement (1.000, 12%)

*Questions address the standards identified in the by asking students to analyze, theorize, and contemplate the implications, connections, and reasons behind and in support of the content within the standards.*Lessons are written to maximize student engagement

*Questions address the standards identified and describe higher-order thinking as well as content knowledge and skills.*Lessons are written to maximize student engagement.

*Questions are related to standards addressed. They only target lower-level elements of the standards.*Student engagement activities may be questionable.

*Questions are only tangentially related to the standards. Their support of the targeted standards is unclear.*Student engagement is questionable and most likely absent from the lesson.

Assessment Plan (1.000, 12%)

Lessons look at multiple ways of assessment. Assessment tools are included.

Lessons generally look at multiple ways of assessment. Assessment tools are included.

Lessons seldom look at multiple ways of assessment. Assessment tools are included.

Assessment is not included as part of lessons plans.

Procedures: Student Work/Artifacts (1.000, 12%)

Work is complete, authentic, meaningful, and resembles the kinds of work people do in real life. A description (1 page) of specific behaviors, knowledge, and/or products that relate to standards is included in the form of a photo or student work sample.

Work is complete, authentic, generally meaningful, and resembles the kinds of work people do in real life. A general description (1 page) of specific behaviors, knowledge, and/or products that relate to standards is included in the form of a photo or student work sample.

Work is complete, authentic, vaguely meaningful, and resembles the kinds of work people do in real life. A vague description (1 page or less) of specific behaviors, knowledge, and/or products that relate to standards is included in the form of a photo or student work sample.

Work does not resemble authentic work in a discipline in any way. Lessons are missing or do not follow the correct formatting.

Procedures: Student Work/Artifacts (1.000, 12%)

Lessons take diverse learners into consideration and provide well-defined and thoughtful accommodations.

Lessons provide some accommodations to support a diversity of learners.

Lessons support some learning styles but do little to support any special needs.

Lessons do not provide any accommodations to support multiple types of learners.

Procedures: Technology Integration (1.000, 12%)

Technology deepens students' understanding of important concepts, supports higher-order thinking skills, and develops students' lifelong skills. The technology enhances student learning, increases productivity, and promotes creativity.

Technology in lessons help students understand concepts and develop skills. The technology enhances student learning, increases productivity, or promotes creativity.

Technology in lessons seems to be added without much thought to how it supports and deepens student skills and understanding.

Lessons could be taught more effectively without the current use of technology as it is described in my Unit Plan.

Overall Procedures (1.000, 12%)

Lessons have well thought-out, detailed instructions and procedures that make lessons more understandable for students.

Lessons have instructions and procedures that serve as an effective guide for implementation.

Lessons have instructions and procedures, but some areas are unclear, making implementation difficult.

Lessons lack clarity and are not an effective guide for implementation.