1. FeatureLesson Course 2 Lesson Main Determine if and where Will and Pedro will meet if they start driving from the same intersection. Pedro travels 2 blocks east, 2 blocks south, 2 blocks east, and 2 blocks north. Will starts traveling 2 blocks north, 4 blocks east, and 2 blocks south. Yes, they will meet 4 blocks east. LESSON 3-1 Estimating with Fractions and Mixed Numbers Problem of the Day 3-1

2. FeatureLesson Course 2 Lesson Main Questions about homework? 34. An astronomical unit (AU is approximately 9.3 X 10 7 mi. Pluto is about 39 AU from the sun. Write the distance in miles using both scientific notation and standard form. (39 AU)(9.3 x 10 7 mi/AU) = 362.7 x 10 7 distributive property = 3.627 x 10 9 move the decimal point 2 places to the left, so add 2 to exponent Scientific notation: 3.627 x 10 9 Standard notation: 3,627,000,000

3. FeatureLesson Course 2 Lesson Main More on exponents 2 3 = 222 = 8 2 2 = 22 = 4 2 1 = 2 What is the pattern so far? Dividing the product by 2 (which is the base) 2 0 = 1 What if I want to divide by 2 again? ½ What would the exponent be then? (See pattern above) 2 -1 = ½

4. FeatureLesson Course 2 Lesson Main More on exponents Now try it yourself with 3 as the base 3 3 = 333 = 27 3 2 = 33 = 9 3 1 = 3 3 0 = 1 3 -1 = 1/3 Exponent Rules: 1)If an exponent is zero, the answer is 1. 2) If an exponent is negative, the answer is a fraction (NOT a negative number)

5. FeatureLesson Course 2 Lesson Main LESSON 3-1 (For help, go to Lesson 1-1.) Estimating with Fractions and Mixed Numbers Check Skills You’ll Need 1. Vocabulary Review How is estimating with compatible numbers different from estimating by rounding? Use compatible numbers to estimate each quotient. 2. 49.8 ÷ 6.8 3. 21.05 ÷ 5.29 4. 25.27 ÷ 2.99 5. 52.6 ÷ 8.8 6. 19.4 ÷ 10.1 Check Skills You’ll Need 3-1

6. FeatureLesson Course 2 Lesson Main LESSON 3-1 Estimating with Fractions and Mixed Numbers Solutions 1. When you estimate by rounding, you round the number to the nearest unit. When you use compatible numbers, you look for numbers that are easy to compute mentally. 2. 7 3. 4 4. 8 5. 6 6. 2 Check Skills You’ll Need 3-1

7. FeatureLesson Course 2 Lesson Main LESSON 3-1 Estimating with Fractions and Mixed Numbers Quick Check Definition 3-1 We use benchmarks to estimate fractions. It is a convenient number used to replace fractions less than 1. We use 0, ½ or 1 to estimate fractions.

8. FeatureLesson Course 2 Lesson Main LESSON 3-1 Use benchmarks to estimate +. 4747 4545 4747 4545 + Use benchmarks to estimate each fraction. Then add. 1212 1212 + 1 = 1 Estimating with Fractions and Mixed Numbers Quick Check Additional Examples 3-1

9. FeatureLesson Course 2 Lesson Main LESSON 3-1 5 – 3 = 2Round each mixed number. Then subtract. Estimate 5 – 2. 1919 5656 5 – 2 1919 5656 Estimating with Fractions and Mixed Numbers Quick Check Additional Examples 3-1

10. FeatureLesson Course 2 Lesson Main LESSON 3-1 Estimate 6 6. 1818 5858 6 7 = 42Round each mixed number. Then multiply. 6 1818 5858 Estimating with Fractions and Mixed Numbers Quick Check Additional Examples 3-1

11. FeatureLesson Course 2 Lesson Main LESSON 3-1 Estimate 26 ÷ 8. 1414 2323 26 ÷ 8 1414 2323 27 ÷ 9 = 3Use compatible numbers. Use 27 for 26 and use 9 for 8. 1414 2323 Estimating with Fractions and Mixed Numbers Quick Check Additional Examples 3-1

12. FeatureLesson Course 2 Lesson Main Estimate. 1. +2.4 – 1 3.2 64. 43 ÷ 10 3535 1212 LESSON 3-1 1818 3434 2323 3 5656 1 10 7878 1313 184 Estimating with Fractions and Mixed Numbers Lesson Quiz 3-1

13. FeatureLesson Course 2 Lesson Main Adding and Subtracting Fractions Lesson 3-2

14. FeatureLesson Course 2 Lesson Main LESSON 3-2 (For help, go to Lesson 2-3.) Find each missing number. 2. =3. =4. = ?8?8 4?4? 8 16 ? 10 4545 1616 Adding and Subtracting Fractions Check Skills You’ll Need 1. Vocabulary Review Two fractions that name the same amount are called ?. Check Skills You’ll Need 3-2

15. FeatureLesson Course 2 Lesson Main LESSON 3-2 2. = =3. = =4. = = 4545 4 x 2 5 x 2 8 10 8 16 8 ÷ 2 16 ÷ 2 4848 1616 1 x 4 6 x 4 4 24 Adding and Subtracting Fractions Solutions 1. equivalent Check Skills You’ll Need 3-2

16. FeatureLesson Course 2 Lesson Main When adding and subtracting fractions, the first step is to check that the denominators of all the addends are the same.

17. FeatureLesson Course 2 Lesson Main LESSON 3-2 Find +. 2727 3737 Keep the denominator the same. 2727 3737 + = 2 + 3 7 Add the numerators. The answer is close to the estimate. 5757 = 2727 3737 + 1414 1212 3434 +, or Estimate Adding and Subtracting Fractions Quick Check Additional Examples 3-2

18. FeatureLesson Course 2 Lesson Main When adding and subtracting fractions, the first step is to check that the denominators of all the addends are the same. What if the denominators are not the same? (Hint: equivalent fractions)

19. FeatureLesson Course 2 Lesson Main LESSON 3-2 Find +. 5959 1616 5959 1616 + 1212 1212 + 0, or Estimate The LCD is 18. 5959 5 2 9 2 = 10 18 1616 1 3 6 3 3 18 The LCD is 18. + = = + 13 18 Add the numerators. The answer is close to the estimate. Adding and Subtracting Fractions Quick Check Additional Examples 3-2

20. FeatureLesson Course 2 Lesson Main LESSON 3-2 3434 The LCD is 16. 3434 3 4 4 = 12 16 3434 1 16 3434 3434 – – 0, or Estimate 1 16 1 16 1 16 – = = – 11 16 Subtract the numerators. The board is now in. thick 11 16 Check for Reasonableness The answer,, is close to the estimate,. The answer is reasonable. 11 16 3434 A carpenter begins with a board that is in. thick. She removes in. from its thickness. How thick is the board now? 1 16 Adding and Subtracting Fractions Quick Check Additional Examples 3-2

21. FeatureLesson Course 2 Lesson Main Find each sum or difference. 1. + 2. – 3. + 4. – 3535 LESSON 3-2 4545 11 12 10 12 5656 3434 2323 7878 2525 1 1 12 7 12 1 5 24 Adding and Subtracting Fractions Lesson Quiz 3-2

22. FeatureLesson Course 2 Lesson Main Homework: Lesson 3-1: pp. 122 – 123, #s 1, 2, 12 - 44 evens Lesson 3-2: pp. 128-129, #s 26-46 evens Get quiz signed (Lesson 2-1 to 2-4) 3-1