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06_13_07 abegra1 - simplify radicals.doc

Lesson Prepared by: Austin Anderson

Subject: Algebra I

Date: June 13, 2007

Approximate Time: 50 minutes

Objective(s):

The students will…

1. simplify radical expressions (1d)
2. add and subtract radical expressions (1d)

Materials:

• students have pencils, notebooks, and textbooks
• whiteboard and dry-erase markers & eraser
• notecards prepared with equivalent (unsimplified) radical, (simplified) radical, and decimal expressions (enough for each student to receive three cards)

Schedule:

1. warm-up
2. intro
3. examples & explanations:
   1. factoring out perfect squares
   2. rationalizing denominator
4. matching activity
5. closure

Warm-Up:

Find (a) the square and (b) the square root ( ) of each of the following numbers (using calculators if necessary):

2. 1
3. 20

Set:

Volunteers share responses to warm-up. Discuss. (Note no real square root of ). Does anyone know another name for the square root symbol? (radical) Can anyone think of a reason why we might use square root? Show example of a ladder against a wall, using Pythagorean Theorem to measure how high up the wall the ladder reaches. There are special rules that we use to simplify square roots (or radicals), and that is what we are going to learn today.

Procedures:

1. Orally review square numbers from  to  and repeat several times. Ask students to write them down, in order, forwards and backwards.
2. Lecture: To simplify a square root:
   1. Factor out perfect squares. We can factor radicals as long as both factors keep the radical sign over them.
   2. Take the square root of the perfect square.
3. Examples and try now:
4. Ask students to convert previous numbers to decimal equivalents (using calculators). Discuss the difference between rational and irrational numbers.
5. Teacher passes out notecards prepared with equivalent (unsimplified) radical, (simplified) radical, and decimal expressions. Students are to trade cards until they have a matching hand, where all three cards are equivalent to each other. No student should have more than three cards at a time!
6. Lecture: After simplifying each radical, if the square root left is the same for each term, then we can combine like terms.
7. Examples and try now:

Closure:

Verbally quiz students on the rules for simplifying radicals. Discuss the difference between square and square root. Discuss the difference between simplify and solve. Restate objectives. In the next lesson, we are going to continue working with radicals, adding and subtracting them.

Assessment/Evaluation:

Informal: Teacher circulates the room to observe student responses on “try now” guided practice, assessing their ability to simplify given expressions with accuracy. Teacher also observes card-matching activity and takes note of students who seem to be struggling with the objectives.

Formal: Students are formally assessed on homework, as well as the upcoming quiz and unit test, for their ability to simplify radical expressions accurately, and their grades are recorded in the grade book.