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Lesson Plan for Student Achievement 2010 -2011

Teacher:Damyon Ray Course: Integrated Math II

Department:Mathematics Unit: Algebra

Date: Nov 29th – Dec 10th, 2010Topic: Quadratics

  1. What is the curriculum standard / objective?

Students will be able to factor and graph quadratic equations and solve quadratics equations in four ways: factoring, completing the square, quadratic formula, and graphing.

  1. What do I want students to know (content & concepts) and be able to do (skills) by the end of the lesson? (Objectives)

LESSON 1: Students willfactor quadratic expressions in various ways. (Completed)

  • Students will be taught how to factor trinomials, binomials and monomials.
  • Students will be taught how to solve quadratic equations using factoring.

LESSON 2: Students will be able to solve quadratic equations using factoring

LESSON 3: Students will be able to solve quadratics by completing the square.

LESSON 4: Students will be able to solve equations using the quadratic formula

LESSON 5: Students will be able to graph quadratic functions using three methods.

  • Axis of symmetry
  • Vertex form (Completing the Square)
  • Intercept form

LESSON 6: Students will be able to solve quadratic functions by graphing.

  1. How will I formatively assess students’ knowledge of content, concepts and skills?

LESSON 1: Students will be formally assessed with written assignment pg. 260 #23 – 61 odd, students will come to the board to work out problems.

LESSON 2: Students will be formally assessed with written assignment pg. 261 #59, 66, 79, 22, 97 and 91 (in that order). These questions are specifically designed to increase in difficulty to assess whether the student can transfer what they have learned to real experiences.

LESSON 3: Students will be assessed with a written assignment pg. 286 #23, 27, 31, 39, 45, 47, 52, 56, 57, 85, & 87 (skill and word concepts).

LESSON 4: Students will be formally assessed by completing pg. 295 #17, 27, 40, 56, 57, & 65 – 67, 75, pg. 261 # 22, 91, and 97(skill and word concepts).

LESSON 5: Students will do pg. 253#17 – 19, 20, 25, 27, 30, 32, 36, & 50.

LESSON 6:Students will play Quadratics Jeopardy covering all the topics of Quadratics. Students will complete in groups, but must answer every question and hand in their work at the end of class.

  1. How will I summatively assess students’ level of mastery of the content, concepts and skills?

Students will be given a cumulative assessment at the end of the topic.

  1. What are the key vocabulary words that I want students to be able to use during this lesson?

LESSON 1: Monomial – an expression with only one term

Binomial – expression with two terms

Trinomial – an expression with three terms

Factoring – process to write a trinomial as a product of binomials

LESSON 2: Quadratic Function has the form ax2 + bx + c = 0, where a 0, this is called the Standard form of the equation.

Zero Product Property – Let A and B be real numbers or algebraic expressions. If AB = 0, then A = 0 or B = 0.

LESSON 3: Completing the Square – a process that allows you to write an expression of the form x2 +bx as the square of a binomial.

LESSON 4: Quadratic Formula – Let a, b, and c be real numbers such that a = 0. The solutions of the quadratic equation ax2 + bx + c = 0 are:

LESSON 5: Quadratic Function has the form y =ax2 + bx + c, where a0

Parabola – the U-shaped graph of a quadratic function

Vertex – the lowest and highest point on the graph of a quadratic function.

Axis of symmetry – the vertical line through the vertex that makes the graph symmetric.

LESSON 6: N/A

  1. Describe the sequences of events in the lesson. (Focus on a high level of student engagement and remember to ask yourself if you have included the (1) Do Now activity; (2) a Motivate and Activate activity; (3) Opportunity for movement; (4) Reading &Writingactivities; (5) Review; (6) How students will get written information on the content, concepts and skills; (7) Checks for understanding; (8) Gender-based activities (9)Technology (10)Research based instructional strategies; and (11) a Closure activity.)

LESSON 2solving Quadratic Equations by factoring

1)DO NOW – Find the value of x

Teacher will ask students to explain which value is the actual answer, 5 is since it is positive.

Teacher will ask students to explain which value is the actual answer, 11 is since it is positive.

2)MOTIVATE AND ACTIVATE

Students will discuss how to solve the Do Now problem and will give methods of approach on how to solve the equation. Teacher will review with students the correct procedures to the problem.

Students will take notes via PowerPoint on the special patterns of factoring and the steps to factor quadratics.

Students will write the instructions to a verbal model

3)MOBILITY

Students will move about in their groups.

4)READING AND WRITING

Students will be given three challenging word problems which will incorporate prior learning experiences and also a chance to apply the Verbal Model approach to problem solving. Students will complete pg. 261 # 22, 91, and 97.

5)REVIEW

Students will review the steps to factoring during the Do Now activity and also how to solve equations.

6)AQUIRY OF INFORMATION ON THE CONTENT, CONCEPTS AND SKILLS

Students will work on assignment, pg. 261 #59, 66, 79, 22, 97 and 91 (in that order).

Students will practice various types of problems w/ assistance of a VIP both in regular skill and drill problems and conceptual problems.

7)CHECKS FOR UNDERSTANDING

Students will come to the board to work out problems as a proof of understanding and mastery of schools.

The teacher will use go throughout the classroom and mark students work as they move on.

Students will be encouraged to ask questions, and teacher will ask thought provoking questions to prompt students to think on their own.

8)GENDER BASED ACTIVITIES

When appropriate students will split into gender pairs/groups (only four boys in the classroom)

9)TECHNOLOGY

Students will come up and use the Promethean Board

10) RESEARCHED BASED INSTRUCTIONAL ACTIVITIES

Students will be expected to discover patterns and techniques via a collaborative effort by building on their experiences together.

11) CLOSURE ACTIVITIES– Students will the review steps to solve a quadratic equation.

LESSON 3Completing the square

1)DO NOW– c

x + 4 = 8i

x = 4 + 8i or x = 4 – 8i

CLASS ACTIVITY– SEQUENCE OF EVENTS

2)MOTIVATE AND ACTIVATE– (5 min)

Students will discuss how to solve the Do Now problem and will give methods of approach on how to solve the equation. Teacher will review with students the correct procedures to the problem.

Students will review the homework assignment given over the weekend.

Teacher will review with students the steps to Completing the Square

3)AQUIRY OF INFORMATION ON THE CONTENT, CONCEPTS AND SKILLS

Students will work on assignment, pg. 286 #23, 27, 39, 45, 47, 52, 55, 57, 85, & 87 (skill and word concepts).

Students will practice various types of problems w/ assistance of a VIP both in regular skill and drill problems and conceptual problems.

The teacher along with the students will complete the square of the standard form of a quadratic equation to derive the quadratic formula, .

4)CLOSURE ACTIVITIES – Students will the review steps to Completing the Square.

SUMMARY OF STUDENT AND TEACHER ENGAGEMENT DURING CLASS

5)MOBILITY

Students will come to the Promethean Board to work out problems.

6)READING AND WRITING

7)REVIEW

Students will review how to solve radical equations and simplify Complex numbers in the Do Now. This will be needed when the students start using the quadratic formula in the next lesson.

8)CHECKS FOR UNDERSTANDING

Students will come to the board to work out problems as a proof of understanding and mastery of schools.

The teacher will use go throughout the classroom and mark students work as they move on.

Students will be encouraged to ask questions, and teacher will ask thought provoking questions to prompt students to think on their own.

9)GENDER BASED ACTIVITIES

When appropriate students will split into gender pairs/groups (only four boys in the classroom)

10)TECHNOLOGY

Students will come up and use the Promethean Board

11) RESEARCHED BASED INSTRUCTIONAL ACTIVITIES

Students will be expected to discover patterns and techniques via a collaborative effort by building on their experiences together.

LESSON 4The Quadratic Formula

1)DO NOW– Solve the following equation by completing the square, ax2 + bx + c = 0 →

CLASS ACTIVITY– SEQUENCE OF EVENTS

2)MOTIVATE AND ACTIVATE– (5 min)

Students will discuss how to solve the Do Now problem and will give methods of approach on how to solve the equation. Teacher will review with students the correct procedures to the problem.

Students will take notes from a PowerPoint Activity on the Quadratic formula.

3)AQUIRY OF INFORMATION ON THE CONTENT, CONCEPTS AND SKILLS

Students will work on assignment, pg. 295 #17, 27, 40, 56, 57, & 65 – 67, 75.

Students will practice various types of problems w/ assistance of a VIP both in regular skill and drill problems and conceptual problems.

Students will work on Construction Activity, pg. 261 # 22, 91, and 97 (skill and word concepts).

4)CLOSURE ACTIVITIES – Students will write out the quadratic formula (exit ticket).

SUMMARY OF STUDENT AND TEACHER ENGAGEMENT DURING CLASS

5)MOBILITY

Students will come to the Promethean Board to work out problems.

6)READING AND WRITING

Students will be given three challenging word problems which will incorporate prior learning experiences and also a chance to apply the Verbal Model approach to problem solving. Students will complete pg. 261 # 22, 91, and 97. Students will have the ability to solve using the three methods given in class, factoring, completing the square, or quadratic formula.

7)REVIEW

Students will review how to solve quadratic equations using different methods.

8)CHECKS FOR UNDERSTANDING

Students will come to the board to work out problems as a proof of understanding and mastery of skills.

The teacher will use go throughout the classroom and mark students work as they move on.

Students will be encouraged to ask questions, and teacher will ask thought provoking questions to prompt students to think on their own.

9)GENDER BASED ACTIVITIES

When appropriate students will split into gender pairs/groups (only four boys in the classroom)

10)TECHNOLOGY

Students will come up and use the Promethean Board

11) RESEARCHED BASED INSTRUCTIONAL ACTIVITIES

Students will be expected to discover patterns and techniques via a collaborative effort by building on their experiences together.

LESSON 5Graphing quadratic Equations

1)DO NOW– Graph the equation y = 3x + 4(6 min)

Students will have to find the slope of the equation, m = 3 and the intercept of the equation b = 4 using slope-intercept form y = mx + b, students can then use a t-table to find the rest of the points, and then plot the graph through the points.

x / -1 / 0 / 1
y / 1 / 4 / 7

CLASS ACTIVITY– SEQUENCE OF EVENTS

2)MOTIVATE AND ACTIVATE– (30 min)

Students will discuss how to solve the Do Now problem and will give methods of approach on how to graph the linear equation. Teacher will review with students the correct procedures to the problem.

Teacher and students will discuss linear graphs, and will be introduced to quadratic equations.

Students will take notes from a PowerPoint Activity on graphing Quadratics.

In the PowerPoint Lesson, students will perform a concurrent activity along with the presentation. First they will be directed to a site, to learn the basics of graphing calculators,

Students will then perform the Activity on pg. 249 Investigating Parabolas.

3)AQUIRY OF INFORMATION ON THE CONTENT, CONCEPTS AND SKILLS(14 min)

The teacher will come and see how the graphs of the students graphing calculators look and will compare them with his own.

Students will continue taking notes from the PowerPoint to learn how to graph in standard form and how to apply it in a real world context.

Students will work on assignment, pg. 253 #20-25 and/or complete the assignment for homework.

Students will come to the board to work out the problems.

4)CLOSURE ACTIVITIES – Students will find the axis of symmetry of y = x2 – 4x + 7

SUMMARY OF STUDENT AND TEACHER ENGAGEMENT DURING CLASS

5)MOBILITY

Students will come to the Promethean Board to work out problems.

6)READING AND WRITING

Students will be given an Activity to do in class that will require the students to correctly read and comprehend the instructions to effectively complete the assignment.

7)REVIEW

Students will review how to solve quadratic equations using different methods.

8)CHECKS FOR UNDERSTANDING

Students will come to the board to work out problems as a proof of understanding and mastery of skills.

The teacher will use go throughout the classroom and mark students work as they move on.

Students will be encouraged to ask questions, and teacher will ask thought provoking questions to prompt students to think on their own.

9)GENDER BASED ACTIVITIES

When appropriate students will split into gender pairs/groups (only four boys in the classroom)

10)TECHNOLOGY

Students will come up and use the Promethean Board

11) RESEARCHED BASED INSTRUCTIONAL ACTIVITIES

Students will be expected to discover patterns and techniques via a collaborative effort by building on their experiences together.

LESSON 5(A)Graphing quadratic Equations

1)DO NOW– Does the graph of the equation y = -3x2– x – 4 open up or down? (6 min)

The graph opens down because a < 0.

CLASS ACTIVITY– SEQUENCE OF EVENTS

2)MOTIVATE AND ACTIVATE– (30 min)

Students will discuss how to solve the Do Now problem and compare it to what they learned in the previous lesson. Teacher will review with students the correct procedures to the problem.

Students will continue taking notes from the PowerPoint Activity on graphing Quadratics, in this lesson the students will learn about graphing in Vertex Form and in Intercept form.

3)AQUIRY OF INFORMATION ON THE CONTENT, CONCEPTS AND SKILLS (14 min)

The teacher will show the students how to put a quadratic equation in standard form (y = ax2 + bx + c, a 0) into vertex form y = a(x – h)2 + k, a 0. The teacher will also show how transformations take place in this form via Geometer’s Sketchpad.

The teacher will show the students how to put a quadratic equation in standard form (y = ax2 + bx + c, a 0) into Intercept form y = a(x – p)(x – q), a 0. The teacher will show how in this form students can find the intercepts (roots or solutions) of the equation to graph it

Students will work on assignment, pg. 253 #17 – 19, 26, 27, 30, 32, 33, 36, & 50.

Students will come to the board to work out the problems.

4)CLOSURE ACTIVITIES – Students will find write out the formulas for the Vertex and Intercept form of Quadratic equations.

SUMMARY OF STUDENT AND TEACHER ENGAGEMENT DURING CLASS

5)MOBILITY

Students will come to the Promethean Board to work out problems.

6)READING AND WRITING

Students will be given an Activity pg. 254 # 50 to do in class that will require the students to correctly read and comprehend the instructions to effectively complete the assignment.

7)REVIEW

Students will review how to solve quadratic equations using different methods.

8)CHECKS FOR UNDERSTANDING

Students will come to the board to work out problems as a proof of understanding and mastery of skills.

The teacher will use go throughout the classroom and mark students work as they move on.

Students will be encouraged to ask questions, and teacher will ask thought provoking questions to prompt students to think on their own.

9)GENDER BASED ACTIVITIES

When appropriate students will split into gender pairs/groups (only four boys in the classroom)

10)TECHNOLOGY

Students will come up and use the Promethean Board

11) RESEARCHED BASED INSTRUCTIONAL ACTIVITIES

Students will be expected to discover patterns and techniques via a collaborative effort by building on their experiences together.

LESSON 6Assessment

  1. What homework assignment will I give to students?
  2. (What questions do I want answered about my teaching and or student learning during the lesson?) Reflections

  • Introduce lesson effectively

  • Did the students remain on-task for the duration of the lesson?

  • Was the opportunity provided for movement during the lesson?

  • Did the gender activity assist the male students?

  • Was opportunity for reading and writing during the lesson?

  • Was the closure meaningful?

  • Did the lesson reflect a balance of skills, conceptual understanding and problem solving?

  • Were the students actively engaged in the lesson?

  • Were students able to make connections to other ideas in their lives?

November 2010