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

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) = x 10 7 distributive property = x 10 9 move the decimal point 2 places to the left, so add 2 to exponent Scientific notation: x 10 9 Standard notation: 3,627,000,000

FeatureLesson Course 2 Lesson Main More on exponents 2 3 = 222 = = 22 = = 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

FeatureLesson Course 2 Lesson Main More on exponents Now try it yourself with 3 as the base 3 3 = 333 = = 33 = = = = 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)

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 ÷ ÷ ÷ ÷ ÷ 10.1 Check Skills You’ll Need 3-1

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 Check Skills You’ll Need 3-1

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.

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

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

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

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

FeatureLesson Course 2 Lesson Main Estimate – ÷ LESSON Estimating with Fractions and Mixed Numbers Lesson Quiz 3-1

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

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 ? 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

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

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.

FeatureLesson Course 2 Lesson Main LESSON 3-2 Find Keep the denominator the same = Add the numerators. The answer is close to the estimate = , or Estimate Adding and Subtracting Fractions Quick Check Additional Examples 3-2

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)

FeatureLesson Course 2 Lesson Main LESSON 3-2 Find , or Estimate The LCD is = The LCD is = = Add the numerators. The answer is close to the estimate. Adding and Subtracting Fractions Quick Check Additional Examples 3-2

FeatureLesson Course 2 Lesson Main LESSON The LCD is = – – 0, or Estimate – = = – Subtract the numerators. The board is now in. thick Check for Reasonableness The answer,, is close to the estimate,. The answer is reasonable 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

FeatureLesson Course 2 Lesson Main Find each sum or difference – – 3535 LESSON Adding and Subtracting Fractions Lesson Quiz 3-2

FeatureLesson Course 2 Lesson Main Homework: Lesson 3-1: pp. 122 – 123, #s 1, 2, evens Lesson 3-2: pp , #s evens Get quiz signed (Lesson 2-1 to 2-4) 3-1