hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN

More documents

Recommendations

Info

$hvvrq 6\vwhpv ri &rqlf 6hfwlrqv - NCPN$

INSTRUCTION Recursion is a new topic for students. Tell students that recursion is demonstrated in the following joke: Pete and Repeat sat on a fence. Pete fell off. Who was left? Repeat. Pete and Repeat . . . Tell students that recursion can also be seen where two mirrors are placed almost parallel to each other. The image in a mirror is an infinite sequence of reflections, each a little smaller version than the previous, disappearing into the distance. Ongoing Assessment Show students the explicit formula for this problem also as a reminder of the exponential functions which were studied in Chapter 6. Diversity in the Classroom Visual Learner Direct students to an Internet site which will allow them to interactively play the classic puzzle “The Towers of Hanoi.” Instruct students to begin with one disc, and continue on through five discs. Tell students to record the minimum number of moves that are required for each number of discs. Ask students to identify the resulting sequence and to describe the recursive nature of the game. 9.1 Patterns 393
INSTRUCTION Example 2 Return to the spreadsheet used at the beginning of class. Remind students of the formulas that they created to represent the amount of savings in Maryanne’s account. Ask students to classify the formulas as being recursive or explicit. Ask students to identify which method of defining a sequence they prefer if given a choice. Ask students to justify their answers. Think and Discuss Answers 1. No, the value of a 1 is not known. 2. Answers will vary. Sample answer: a sequence is an ordered list of numbers such as 2, 4, 6, 8, 10, … 3. An explicit formula is given by a rule that does not depend on other terms of the pattern. A recursive formula generates terms of the pattern based on previous terms. 4. The formula is explicit since a n does not depend on a previous term. 5. Substitute 8 for n in the expression and simplify. R.E.A.C.T. Strategy Applying Introduce students to the classic handshake problem. Challenge students to determine how many handshakes would take place in a roomful of 20 people. Ask students to justify their answers and to identify if they used an explicit or recursive formula when solving the problem. 394 Chapter 9 Sequences and Series
Page 1 and 2: LESSON OBJECTIVES 9.1 Patterns •
Page 3: LESSON PLANNING Vocabulary sequence
Page 7 and 8: Answers to Math Applications Math A
Page 9 and 10: INSTRUCTION Tell students that the
Page 11 and 12: INSTRUCTION Ongoing Assessment Show
Page 15 and 16: INSTRUCTION Tell students that the
Page 17 and 18: Problem Solving Before solving this
Page 21 and 22: INSTRUCTION Students might incorrec
Page 23 and 24: WRAP UP To ensure mastery of object
Page 25 and 26: Mixed Review Additional Answers 35.
Page 27 and 28: INSTRUCTION Ask students to express
Page 29 and 30: WRAP UP To ensure mastery of object
Page 31 and 32: MATH LAB Activity 1 PREPARE • An
Page 33 and 34: Math Applications Solutions and Not
Page 41 and 42: Vocabulary Review arithmetic mean (
Page 43 and 44: 1 2 10 , 922 1 2 ∞ 1 ∑

hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?