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Ready-Set-Tech: A Menu for "The Real Numbers
 A Menu for "The Real Numbers

This project is designed to integrate the Internet into a major unit of study in the Mathematics A course for New York State. It utilizes the Web site www.regentsprep.org as a tool to practice operations with radicals and to incorporate real-world applications with the Pythagorean Theorem. Four lessons in this unit create a "menu" to which students relate the Real Number System. The "appetizers" serve as a means for the students to recognize the foundations of the unit, which is differentiating between rational and irrational numbers. The "main course" shows students the integration of all the types of real numbers through performing operations. Lastly, the dessert, applying the Pythagorean Theorem to solve real world problems, is an analogy of how "sweet" success is when the unit finally comes together and they can successfully solve problems on their own.

These activities are used for both homework and class work assignments to enable the students to work both independently and cooperatively. Select activities will be graded as quizzes. The outline below shows how to incorporate "The Menu" into a two week unit of study on the Real Number System. These materials and lessons could be adapted to use with other textbooks as well.

 Stephanie Gabrielli Stephanie Gabrielli is in her second year of teaching at Clarkstown High School in West Nyack, New York. She teaches Regents level mathematics and has previously been awarded an IMPACT II Adaptor Grant. She is continuously in pursuit of projects that engage her students and foster mathematical learning, with the support and encouragement of her department chairperson, Dr. Mary Ann Gavioli. Subject: Mathematics Grade Level: 9 Time: 13 lessons, approximately 2 weeks Materials: Computers with Internet access, copies of pdf worksheets, textbook Merrill: Integrated Mathematics or similar text along with teacher-developed practice worksheets.

Objectives:

Students will:

1. Learn the difference between rational and irrational numbers.

2. Articulate knowledge of radicals by completing problems and answering short answer questions.

3. Apply the Pythagorean Theorem to solve real world problems.

4. Restate and define major key words and concepts of the unit.

Web sites:

• http://regentsprep.org/Regents/
math/fpyth/PracPyth.htm

Outline:

Lesson 1:

•  Objective: Students will be able to define, discuss, and calculate rational and irrational numbers. (Defining the Real Number System, converting decimals to fractions and vice versa including repeating decimals, using the scientific calculator, approximating square roots to the nearest tenth, concept of principal root).

•  Worksheet 1,2,3:

•  Odds in class as guided practice.

•  Pair-work for student activity.

•  Homework :

•  Additional problems from the text book.

Lesson 2:

Objective: Students will be able to continue to define, discuss, and calculate rational and irrational numbers.

•  Selected problems as guided practice.

•  Selected problems on black board as student activity.

Lesson 3:

Objective: Students will be able to simplify radicals.

•  Selected problems as guided practice.

•  Selected problems on black board as student activity. Students will put solutions on black board.

Lesson 4:

Objective: Students will be able to complete a mixed practice of simplifying radicals.

•  Worksheet #1 as guided practice / student activity

•  Selected problems from text book as student activity.

•  Homework:

Lesson 5:

Objective: Students will be able to add and subtract radicals.

•  Selected problems as guided practice.

•  Selected problems on black board as student activity.

Lesson 6:

Objective: Students will be able to continue to add and subtract radicals.

•  Quiz (20 minutes)

•  Worksheet. Selected problems as guided practice.

•  Selected problems as student activity. Students will put solutions on blackboard.

Lesson 7:

Objective: Students will be able to complete a mixed practice with radicals.

•  In class activity to be completed as pair-work in computer lab:

Activity 3: “Main Course: Mixed Practice with Scrumptious Radicals”

•  Additional problems from worksheet as student activity.

Lesson 8:

Objective: Students will be able to develop and use the Pythagorean Theorem in solving problems.

•  In class activity to be completed as pair-work in computer lab:

Activity 4: “Dessert: The Pleasing Pythagorean Theorem”

•  Additional problems from worksheet 4/evens, if necessary.

•  Additional problems from worksheet #5/5-9, if necessary.

Lesson 9:

Objective: Students will be able to review all work to date with radicals.

•  Selected problems from numerous worksheets: students to work in pairs.

Lesson 10:

Objective: Students will be able to divide square roots and rationalize the denominator.

•  Selected problems as guided practice.

•  Selected problems on black board as student activity.

Lesson 11:

Objective: Students will be able to complete a mixed practice with radicals.

•  Finding the area and perimeter of geometric shapes (squares, rectangles, triangles) with radical measurements.

•  Simplifying radicals: problems involving a combination of addition, subtraction, multiplication and division.

•  Word problems with the Pythagorean Theorem.

Lesson 12:

Objective: Students will be able to review for unit test: The Real Number System.

•  “Miss G's ‘Challenger' Review Game.” Students complete problems independently. The students request which problems they would like explained on the blackboard. Teacher chooses the student volunteers to go to the board. If correct, that student gets the prize (candy/bonus points). If the solution is incorrect, another student can “challenge” the other and redo the problem. If correct, that student will “steal” the points. If there are any further questions students explain their solutions.

Lesson 13:

Objective: Students will be able to display mastery of skills on The Real Number System Unit.

•  Test (all period)

Standards:

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real world settings, and by solving problems through the integrated study of number systems, geometry, algebra and data analysis.

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