Lesson 50 Say the base and exponent for that group. Note: Students - PDF document

Lesson 50 Say the base and exponent for that group. Note: Students will need a calculator (Signal.) 3 10 . with π function for exercise 2. • How many 10s are in the other group? (Signal.) 3. Say the base and the exponent for that Exercise 1 group. (Signal.) 3 10 . EXPONENTS • So 10 3 × 10 3 = 10 6 . In Groups • What’s another way of showing 10 6 ? (Signal.) 3 × 3 10 10 . Textbook practice e. So if the base number is shown 6 times, a. Open your textbook to lesson 50, the exponents must add up to 6. part 1. √ f. If the base is shown 6 times, what must • (Teacher reference:) the exponents add up to? (Signal.) 6. • If the base is shown 9 times, what must 6 10 × 10 × 10 × 10 × 10 × 10 = 10 6 the exponents add up to? (Signal.) 9. (10 × 10) × (10 × 10 × 10 × 10) = 10 2 4 6 10 × 10 = 10 • If the base is shown 5 times, what must the exponents add up to? (Signal.) 5. 6 10 × 10 × 10 × 10 × 10 × 10 = 10 6 • (Repeat step f until fj rm.) (10 × 10 × 10) × (10 × 10 × 10) = 10 3 3 6 10 × 10 = 10 Textbook practice • You’ve learned how to express repeated a. Find part 2. √ multiplication as a base and exponent. • For each item, you’ll write the complete b. The fj rst equation shows a set of 10s. equation with exponents. • What’s the base? (Signal.) 10. b. Problem A. The multiplication shows 8 The base is 10. The base is shown 6 seven times. times. • Say the base and exponent for all the 8s. • So what’s the exponent? (Signal.) 6. (Signal.) 7 8 . 6 So the whole set is 10 . So no matter how the 8s are multiplied c. Below is the same set of 10s in 2 groups. together, the exponents must add up to 7. The groups are multiplied together. How • You can see the groups set off with many 10s are multiplied in the fj rst group? parentheses. (Signal.) 2. • Touch the fj rst group. √ 2 So that group equals 10 . Tell me the base and exponent you’ll write • Say the base and exponent for that group. for the fj rst group. (Signal.) 2 8 . (Signal.) 2 10 . • Next group. • Look at the next group. √ Tell me the base and exponent. How many 10s are in the second group? (Signal.) 3 8 . (Signal.) 4. • Last group. • Say the base and exponent for that group. • Tell me the base and exponent. (Signal.) 4 10 . (Signal.) 2 8 . 6 is 2 So another way to show 10 10 • The exponents are 2 and 3 and 2. Do the 4 times 10 . exponents add up to 7? (Signal.) Yes. 6 • What’s another way of showing 10 ? • So the whole equation is (Signal.) 2 × 4 10 10 . 8 7 = 8 2 × 8 3 × 8 2 . • (Repeat step c until fj rm.) c. Say the equation. (Signal.) d. The next box shows the same set of 10s 7 = 2 × 3 × 2 8 8 8 8 . in different groups. • Write that equation. Pencils down when • How many 10s are in the fj rst group? you’re fj nished. √ (Signal.) 3. Lesson 50 297

50 • (Write on the board:) • So what do you solve for? (Signal.) [50:1A] Circumference. e. Circle C. What is given? (Signal.) 7 = 2 × 3 × 2 a. 8 8 8 8 Circumference. • So what do you solve for? (Signal.) • Here’s what you should have. Diameter. d. Write the complete equation for problem f. Circle D. What is given? (Signal.) B. Pencils down when you’re fj nished. Diameter. (Observe students and give feedback.) • So what do you solve for? (Signal.) • (Write on the board:) [50:1B] Circumference. g. Circle E. What is given? (Signal.) b. 7 5 = 7 3 × 7 2 Circumference. • So what do you solve for? (Signal.) • Here’s what you should have. Diameter. e. Write the complete equation for the rest h. Work problem A. Use the π key on your of the items in part 2. Pencils down when calculator. Pencils down when you’re you’re fj nished. fj nished. (Observe students and give feedback.) (Observe students and give feedback.) f. Check your work. Read each equation. • (Write on the board:) [50:2A] • Equation C. (Signal.) 9 = 4 × 2 × 3 9 9 9 9 . • Equation D. (Signal.) 4 = 2 × 2 5 5 5 . a. C = π d • Equation E. (Signal.) 8 = 3 × 3 × 10 10 10 2 _ _ 10 . ( 1 ) ( ) 1 π 11 = π d π g. Raise your hand if you got everything _ 11 right. √ π = d 3 . 50 m Exercise 2 • Here’s what you should have. CIRCUMFERENCE/DIAMETER • The circumference is 11 meters. What problem did you work on your calculator? Textbook practice (Signal.) 11 ÷ π . a. Find part 3. √ • What’s the diameter? (Signal.) 3 . 50 b. You’re going to work problems that start meters. with the equation for the circumference of i. Work problem B. Pencils down when a circle. you’re fj nished. • What’s the name for 3 . 14? (Signal.) Pi. (Observe students and give feedback.) • Say the equation for the circumference of • (Write on the board:) [50:2B] a circle. (Signal.) C = π D. • For some problems, you’ll fj nd the b. C = π d diameter. For others, you’ll fj nd the C = π (4 . 5) circumference. c. Touch circle A. √ 14 . 14 yd • What is given, the circumference or the diameter? (Signal.) Circumference. • Here’s what you should have. • So you solve for the diameter. • The diameter is 4 . 5 yards. • What do you solve for? (Signal.) Diameter. • What problem did you work on your d. Circle B. What is given, the circumference calculator? (Signal.) π × 4 . 5. or the diameter? (Signal.) Diameter. • What’s the circumference? (Signal.) 14 . 14 yards. [ 14 . 13 if 3 . 14 is used.] 298 Lesson 50

50 j. Work the rest of the problems in part 3. • (Write to show:) [50:3B] Pencils down when you’re fj nished. (Observe students and give feedback.) ( _ _ a. m = p ( m p ) ) p p k. Check your work. l. Problem C. The circumference is 2 . 08 feet. • Here’s what you should have: M = M over • What problem did you work on your P times P . calculator? (Signal.) 2 . 08 ÷ π . c. Problem B: There are 3 . 5 pounds of fm our • What’s the diameter? (Signal.) 0 . 66 feet. for every pound of sugar. How many m. Problem D. The diameter is 29 inches. pounds of fm our are used if 10 pounds of • What problem did you work on your sugar are used? calculator? (Signal.) π × 29. • Tell me which unit the problem asks • What’s the circumference? (Signal.) 91 . 11 about. (Pause. Signal.) Pounds of fl our. inches. [ 91 . 06 if 3 . 14 is used.] • Skip 5 lines. Start with the simple n. Problem E. The circumference is 0 . 8 equation PF = PF, and complete the centimeters. rate equation. Pencils down when you’re • What problem did you work on your fj nished. calculator? (Signal.) . 8 ÷ π . (Observe students and give feedback.) • What’s the diameter? (Signal.) 0 . 25 • Check your work. centimeters. • (Write on the board:) [50:3C] Exercise 3 ( pf ) b. pf = ps _ RATE EQUATIONS ps Reverse Order Textbook practice • Here’s what you should have: PF = PF a. Find part 4. √ over PS times PS. • These are problems you solve with rate d. Write letter equations for problems in C equations. and D. Leave space below each equation. • Last time you wrote the equations so Pencils down when you’ve done that they start with the unit that answers the much. question. (Observe students and give feedback.) b. Problem A: A machine produces pencils • Problem C. Read the equation that begins at the rate of 120 pencils per minute. How with W. (Signal.) W = (W / M) M. long will it take the machine to produce • Problem D. Read the equation that begins 40 pencils? with CM. (Signal.) CM = (CM / Y) Y. • Raise your hand when you know which e. Now work all the problems in part 4. unit the problem asks about. √ Answer each question with a number and • Which unit? (Signal.) Minutes. a unit name. Pencils down when you’re • (Write on the board:) fj nished. [50:3A] (Observe students and give feedback.) f. Check your work. a. m = m • Problem A. How long will it take to • Start with the simple equation M = M, produce 40 pencils? (Signal.) 1 / 3 minute. and complete the rate equation. Pencils • Problem B. How many pounds of fm our are down when you’ve done that much. used? (Signal.) 35 pounds. (Observe students and give feedback.) • Problem C. How many women work in the • Check your work. factory? (Signal.) 160 women. 299 Lesson 50