Exploring Powers of 10 Very small and large numbers Tasks 1 & 2

1. Exploring Powers of 10Very small and large numbersTasks 1 & 2

2. M8N1 Powers and Roots M8N1 Students will understand different representations of numbers including square roots, exponents, and scientific notation. Elements: a. Find square roots of perfect squares.b. Recognize the (positive) square root of a number as a length of a side of a square with a given area.

3. M8N1 Powers and Roots Course 2 SPONGE: SEPT.8 Simplify. 1.62 2. 72 3. 112 4. 152 36 49 121 225

4. M8N1 Powers and Roots Course 2 Learn to express and evaluate numbers using powers and roots.

5. Powers and Roots Course 2 M8N1 Insert Lesson Title Here Vocabulary perfect square square root radical sign

6. Powers and Roots Course 2 M8N1 Recall that a power is a number represented by a base and an exponent. The exponent tells you how many times to use the base as a repeated factor. Exponent 2 3 Base A square with sides that measure 3 units each has an area of 3 · 3, or 32. Notice that the area of the square is represented by a power in which the base is the side length and the exponent is 2. A power in which the exponent is 2 is called a square.

7. Powers and Roots M8N1 3.6 12 3.6 12 Course 2 Additional Example 1A & 1B: Finding Squares Model each power using a square. Then evaluate the power. B. (3.6)2 A. 122 A = lw A = lw A = 12 · 12 Substitute. A = 3.6 · 3.6 Substitute. Multiply. Multiply. A = 144 A = 12.96 The square of 12 is 144. The square of 3.6 is 12.96.

8. Powers and Roots M8N1 11 5.2 11 5.2 Course 2 Insert Lesson Title Here Try This: Example 1A &1B Model each power using a square. Then evaluate the power. B. (5.2)2 A. 112 A = lw A = lw A = 11 · 11 Substitute. A = 5.2 · 5.2 Substitute. Multiply. Multiply. A = 121 A = 27.04 The square of 11 is 121. The square of 5.2 is 27.04.

9. Powers and Roots M8N1 The square root of a number is one of the two equal factors of the number. Four is a square root of 16 because 4 · 4 = 16. The symbol for a square root is √ , which is called a radical sign. Course 2 A perfect square is the square of a whole number. The number 49 is a perfect square because 49 =72 and 7 is a whole number. The number 6.25 is not a perfect square.

10. M8N1 WORKPERIODCMP2 INVESTIGATION 2.2 TEXTBOOK,PAGE 2.1-2.2, PAGES 19-21 GROUP WORK, 2.2, A, B AND D MATERIALS DOT PAPER PENCILS TEXTBOOK

11. CLOSING:SEPT. 8 Students will model answers to questions in Investigation 2 Complete group Reflection sheet for self evaluation HOMEWORK: TEXTBOOK PAGE 24, 10-18 SQUARING OFF

12. Powers and Roots M8N1 Reading Math √16 = 4 is read as “The square root of 16 is 4.” Course 2 Sept.10 Element: a-f Most calculators have square-root keys that you can use to quickly find approximate square roots of nonperfect squares. You can also use perfect squares to estimate the square roots of nonperfect squares.

13. Powers and Roots M8N1 A. √40 √ √36 < 49 √40 < 6 < 40 < 7 √ 40  6 √ 40  6.32455532033 √ Use a calculator to approximate √40. Course 2 Additional Example 2A: Estimating Square Roots Estimate each square root to the nearest whole number. Use a calculator to check your answer. Find the perfect squares nearest 40. 36 < 40 < 49 Find the square roots of 36 and 49. 36 is nearer in value to 36 than to 49. Check 6 is a reasonable estimate.

14. Powers and Roots M8N1 B. √79 √ √64 < 81 √79 < 8 < 79 < 9 √ 79  9 √ 79  8.8881944 √ Use a calculator to approximate √79. Course 2 Additional Example 2B: Estimating Square Roots Estimate each square root to the nearest whole number. Use a calculator to check your answer. Find the perfect squares nearest 79. 64 < 79 < 81 Find the square roots of 64 and 81. 79 is nearer in value to 81 than to 64. Check 9 is a reasonable estimate.

15. Powers and Roots M8N1 √ √16 < 25 √22 < 4 < 22 < 5 √ 22  5 √ 22  4.690415759 √ Use a calculator to approximate √22. Course 2 Insert Lesson Title Here Try This: Example 2A Estimate each square root to the nearest whole number. Use a calculator to check your answer. A. √22 Find the perfect squares nearest 22. 16 < 22 < 25 Find the square roots of 16 and 25. 25 is nearer in value to 22 than to 16. Check 5 is a reasonable estimate.

16. Powers and Roots M8N1 √ √49 < 64 √53 < 7 < 53 < 8 √ 53  7 √ Use a calculator to approximate 53  7.2801098828 √ √53. Course 2 Insert Lesson Title Here Try This: Example 2B Estimate each square root to the nearest whole number. Use a calculator to check your answer. B. √53 Find the perfect squares nearest 53. 49 < 53 < 64 Find the square roots of 49 and 64. 53 is nearer in value to 49 than to 64. Check 7 is a reasonable estimate.

17. Powers and Roots M8N1 The length of each side of the square is √125 . < √121 < √125 √144 11 < < 12 √125 √125  11 Course 2 Additional Example 3: RecreationApplication A Coast Guard boat searching for a lost sailboat covers a square area of 125 mi2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. 121 < 125 < 144 Find the perfect squares nearest 125. Find the square roots of 121 and 144. 125 is nearer in value to 121 than to 144. Each side of the search area is about 11 miles long.

18. Powers and Roots M8N1 The length of each side of the square is √168 . < √144 < √168 √169 12 < < 13 √168 √168  13 Course 2 Insert Lesson Title Here Try This: Example 3 A tent was advertised in the newspaper as having an enclosed square area of 168 ft2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot. Find the perfect squares nearest 168. 144 < 168 < 169 Find the square roots of 144 and 169. 168 is nearer in value to 169 than to 144. Each side of the tent is about 13 feet long.

19. Powers and Roots M8N1 4. √52 √15 Course 2 Insert Lesson Title Here Closing Sept. 10 Evaluate each power. 1. 162 2. (3.5)2 Estimate each square root to the nearest whole number. Use a calculator to check the reasonableness of your answers. 3. 5. A square dining room table has an area of 20 ft2. What is the length of each side of the table, to the nearest tenth? 256 12.25 7 4 4.5 ft