TITLE: Expressions and Equations with Like Terms
TASK DEVELOPER: Amal Saad
TEXT: New Views in Mathematics Course 1
CONTENT AREA AND GRADE: Application of Math - Grade 10
TARGET TEACHING DATE: May 7,8,9, 2007
SCHOOL: John F. Kennedy High School

STANDARDS:

PATTERNS AND ALGEBRA - GRADE 9-12

STANDARD 4.3 PATTERNS AND ALGEBRA: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

Strand D. Procedures: Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

1. Evaluate and simplify expressions.

  • Add and subtract polynomials

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PERFORMANCES:
  1. The students will take detailed notes as the lesson is presented.
  2. The students will write key words in their notebook.
  3. The students will complete the assigned classwork problems on the classwork sheet provided. This sheet will be collected at the end of the class period.
  4. The students will complete the homework assignment related to this lesson.

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SETTING:

Real World Setting: Home improvement

You are a builder. You are faced with a goal. You must plan to build a house that is 1 1/2 times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house. Write an expression for the area of the land surrounding the house. If X = 30 feet,

a. What is the area of the house?

b.What is the area of the entire property?

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SMARTSKILLS:

Level I: Acquiring Data - Data students will acquire in this standards-based task:

  • Vocabulary: Expressions, Equations, Like Terms, Unlike Terms, Factor, Coefficient.
  • Concepts: Simplifying/Expressions.

Level II: Visualizing Information - Data from Level I that are visualized as information in this standards-based task: The like terms and unlike terms are to be grouped.

  • Organizing: The similarities and differences of the like terms and the unlike terms.

Level III: Applying Knowledge - Visualized information from Level II that is applied knowledge in this standards-based task:

  • Solving problems: by finding the value of the variable in the equations.

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PREFERENCES:

Student Involvement - The students will complete the task individually,as a cooperative group, as an action team, or in a whole class group setting

Instruction - Activities will be organized and delivered by a teacher facilitating a set of hands-on activities.

Use of Resources - The students will provide classroom materials such as pencils, paper, notebooks and homework time.

Customer for Student Work - The student will present their work as evidence of task completion to teachers and their parents.

Assessment of Student Work

The following people will be involved in assessing student work generated to complete the task: the student's teacher and their peers.

Reporting Results - The assessment results will be reported as a letter grade for class work and a number grade for the test.

Timeline - The estimated time needed to plan, teach, and score this task is one to three class periods.

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ACTIVITIES:

Teaching for Understanding in Mathematics

Activity 1: The teacher reviews yesterday's lesson and assigns a problem that was not finished
(Estimated time: 3 minutes)

  • Step 1: Ask the students to define like terms and give an example.

  • Step 2: Ask the students to define unlike terms and give an example.

  • Step 3: Check the homework on yesterday's lesson..

Materials: Notebooks, pencils
Student product or performance: Students produce their homework and give examples of like terms and unlike terms.
Links or connections between different parts of the lesson: The ability to find like term and unlike term will be needed to simplify expressions.
Scoring: teacher records if homework was completed.

Activity 2: Activating Prior Knowledge
Estimated time: 10 minutes

  • Step 1: Warm up activity : Have students evaluate unsimplified expressions.
  • Step 2: Rearrange the terms so that like terms are grouped together.
  • Step 3: Combine like terms.

Note: Many examples can be taken from the Text Book: New Views in Mathematics Course 1 published by Merv Edwards, David Gold, & Dr. Albert Mamary. Expressions and Equations with Like Terms is in section 7.3 of this text and there are many fine examples on pages 386 and 387

Activity 3: The teacher presents the task for the day.

  • Step 1:Teacher will present lesson and assist students as necessary to ensure that the lesson is understood.
  • Step 2: Student will listen, ask questions, copy down the notes, try example problems, complete assigned classwork problems, volunteer to place problems on the board, submit classwork for assessment, and copy down the homework assignment to be completed by the next class meeting.
  • Step 3: Notes examples

Example 1: Simplify 7x - 3x - x.

Example 2: Simplify 7 - 8x - 9y - x - 3.

Example 3: Simplify 5 - 6( 4c - 2 ) - 3c.

  • Step 4: Classwork - Students will work independently and in pairs on various problems. The work will be completed on a classwork sheet. This sheet will be collected at the end of class, graded, and returned to students the following class session. The following problems will be assigned for classwork from the text book as described above.

Pages 391 (1 - 20 ) All.

  • Step 5: Boardwork - Students will volunteer or be asked to place several problems on the blackboard. In this way, the teacher can check the student's work as well as the student's peers.
  • Step 6: Homework - The following problems will be assigned for homework, to be completed by the next class meeting.

Page 392 W.EX (1-20) All.

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BENCHMARKING:

Student Performance One:

Students can create their own examples (about 5 Questions) of simplifying expressions and they themselves evaluate their expressions. These examples should be based on the activities 1 through 5.

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SCORING:

Scoring: Students will be scored based on the rubric below. In addition to this, student understanding will be assessed based on answers to questions presented during the lesson and throughout the class period, by observing class work as it is being performed, by observing work placed on the blackboard, by assessing the class work that will be collected at the end of class, and by reviewing and assessing the homework that will be due the following class meeting.

New Jersey High School Mathematics Rubric
Extended Constructed Response
Level 4The response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The representations are correct. The explanation and/or justification is logically sound, clearly presented, fully developed, supports the solution, and does not contain significant mathematical errors. The response demonstrates a complete understanding and analysis of the problem.
Level 3

The response indicates application of a reasonable strategy that may or may not lead to a correct solution. The representations are essentially correct. The explanation and/or justification is generally well developed, feasible, and supports the solution. The response demonstrates a clear understanding and analysis of the problem.

Level 2

The response indicates an incomplete application of a reasonable strategy that may or may not lead to a correct solution. The representations are fundamentally correct. The explanation and/or justification supports the solution and is plausible, although it may not be well developed or complete. The response demonstrates a conceptual understanding and analysis of the problem.

Level 1

The response indicates little or no application of a reasonable strategy. It may or may not have the correct answer. The representations are incomplete or missing. The explanation and/or justification reveals serious flaws in reasoning. The explanation and/or justification may be incomplete or missing. The response demonstrates a minimal understanding and analysis of the problem.

Level 0The response is completely incorrect or irrelevant. There may be no response, or the response may state, "I don't know."
Notes: Explanation refers to the student using the language of mathematics to communicate how the student arrived at the solution.

Justification refers to the student using mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates and theorems.

Essentially correct representations may contain a few minor errors such as missing labels, reversed axes, or scales that are not uniform.

Fundamentally correct representations may contain several minor errors such as missing labels, reversed axes, or scales that are not uniform.
Source: http://www.mdk12.org/mspp/high_school/structure/algebra/index.html

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METACOGNITION:

Cognitive Information: I will collect the following information by asking the questions to students in class and summarizing their verbal responses.

  1. Describe what skills you needed to complete this task.
  2. Explain how you solved the goal, problem, or issue in this task.

Attitude Information: I will collect the following information by asking the questions to students in class and summarizing their verbal responses.

  1. Do you feel that you are good in simplifying expressions?
  2. Did you find this task to be difficult?
  3. Did you enjoy the task?

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RESULTS:

Results: Most of the students (85%)were placed in the level 4 and level 3 learning categories, demonstrating a solid understanding of the subject matter. 10% of students were placed at level 2, demonstrating incomplete understanding of the subject matter. The above results were determined by assessing answers to questions presented during the lesson and throughout the class period, by observing classwork as it was being performed, by observing work placed on the blackboard, and by assessing the classwork that was completed the following class period.

Improvement: The next time this lesson is presented, I would place any level 2 learners next to level 3 or level 4 learners and assign some problems to be worked in pairs. This should improve the comprehension of the lower level learners.

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