Comparing and Ordering Rational Numbers. ESSENTIAL QUESTION How do you compare and order rational numbers? Prep for 6.NS.3.7a
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1 L E S S O N. Comparing and Ordering Rational Numbers 6.NS..7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Also 6.NS..7, 6.NS..7b? ESSENTIAL QUESTION How do you compare and order rational numbers? EXPLORE ACTIVITY Prep for 6.NS..7a Equivalent Fractions and Decimals Fractions and decimals that represent the same value are equivalent. The number line shows equivalent fractions and decimals from 0 to 1. A B Complete the number line by writing the missing decimals or fractions. Use the number line to find a fraction that is equivalent to 0.. Explain C Explain how to use a number line to find a decimal equivalent to 1 7. D Use the number line to complete each statement. 0. = = 0.7 = 1. = Reflect 1. Communicate Mathematical Ideas How does a number line represent equivalent fractions and decimals?. Name a decimal between 0. and 0.. Lesson. 9
2 Ordering Fractions and Decimals You can order fractions and decimals by rewriting the fractions as equivalent decimals or by rewriting the decimals as equivalent fractions. Math On the Spot EXAMPLE 1 6.NS..7, 6.NS..7a A Order 0., _, 0.8, 1_, 1_, and 0. from least to greatest. Animated Math STEP 1 STEP Write the fractions as equivalent decimals. 1_ = 0. 1_ = 0. _ = 0.7 Use the number line to write the decimals in order < 0. < 0. < 0. < 0.7 < 0.8 The numbers from least to greatest are 0., 1_, 0., 1_, _, 0.8. Personal Math Trainer Online Assessment and Intervention B Order 1 1, _, and 0. from least to greatest. STEP 1 STEP STEP YOUR TURN Write the decimal as an equivalent fraction. 0. = 0 = 7 0 Find equivalent fractions with as the common denominator = = = 1 0 Order fractions with common denominators by comparing the numerators. < 1 < 0 The fractions in order from least to greatest are, 1, 0. The numbers in order from least to greatest are 1 1, 0., and _. Order the fractions and decimals from least to greatest. _. 0.8,, 0.1, 7 is a multiple of the denominators of all three fractions. Unit 1
3 Ordering Rational Numbers You can use a number line to order positive and negative rational numbers. EXAMPLE 6.NS..7a, 6.NS..7b Five friends completed a triathlon that included a -mile run, a 1-mile bike ride, and a 1_ -mile swim. To compare their running times they created a table that shows the difference between each person s time and the average time, with negative numbers representing times less than the average. Math On the Spot Runner John Sue Anna Mike Tom Time above or below average (minutes) 1_ _ Image Credits: ImageState Royalty Free/Alamy Order the numbers from greatest to least. STEP 1 STEP Write the fractions as equivalent decimals. 1_ = _ = 1. Use the number line to write the decimals in order Average Time 1.9 > 1. > 0. > -1. > -.0 The numbers in order from greatest to least are 1.9, 1., 1_, -1 1_, -.0. Reflect. Communicate Mathematical Ideas Describe a different way to order the numbers. YOUR TURN. To compare their bike times, the friends created a table that shows the difference between each person s time and the average bike time. Order the bike times from least to greatest. Biker John Sue Anna Mike Tom Time above or below average (minutes) _ Math Talk Mathematical Practices Who was the fastest runner? Explain. Personal Math Trainer Online Assessment and Intervention Lesson. 61
4 Guided Practice Find the equivalent fraction or decimal for each number. (Explore Activity 1) = =. 1 =. 0.9 = = = 7. = = 9. 6 = 8 Use the number line to order the fractions and decimals from least to greatest. (Example 1). 0.7, 1_, 0., and 1_ The table shows the lengths of fish caught by three friends at the lake last weekend. Write the lengths in order from greatest to least. (Example 1) Lengths of Fish (cm) Emma Anne Emily _ 1 _ List the fractions and decimals in order from least to greatest. (Example 1, Example ) 1.., _, , 16, 0.7, , 1_ 1, 0.,, _ 1. _, 7, _, _ 8, 16, 0.6, _ 17.., _, , _ 8, , 1 1_, 1 1_, , 0., 0., 0.? ESSENTIAL QUESTION CHECK-IN 1. Explain how to compare 0.7 and _ 8. 6 Unit 1
5 Name Class Date. Independent Practice 6.NS..7, 6.NS..7a, 6.NS..7b. Rosa and Albert receive the same amount of allowance each week. The table shows what part of their allowance they each spent on video games and pizza. a. Who spent more of their allowance on video games? Write an inequality to compare the portion spent on video games. Video games Personal Math Trainer Online Assessment and Intervention Pizza Rosa 0. _ Albert 1_ 0. b. Who spent more of their allowance on pizza? Write an inequality to compare the portion spent on pizza. c. Draw Conclusions Who spent the greater part of their total allowance? How do you know?. A group of friends is collecting aluminum for a recycling drive. Each person who donates at least. pounds of aluminum receives a free movie coupon. The weight of each person s donation is shown in the table. Weight (lb) Brenda Claire Jim Micah Peter _ 8 a. Order the weights of the donations from greatest to least. b. Which of the friends will receive a free movie coupon? Which will not? c. What If? Would the person with the smallest donation win a movie coupon if he or she had collected 1_ pound more of aluminum? Explain. Lesson. 6
6 . Last week, several gas stations in a neighborhood all charged the same price for a gallon of gas. The table below shows how much gas prices have changed from last week to this week. Gas Station Change from last week (in cents) Gas and Go Samson Gas Star Gas _ Corner Store Tip Top Shop 7 _ 8 a. Order the numbers in the table from least to greatest. b. Which gas station has the cheapest gas this week? c. Critical Thinking Which gas station changed their price the least this week? FOCUS ON HIGHER ORDER THINKING Work Area. Analyze Relationships Explain how you would order from least to greatest three numbers that include a positive number, a negative number, and zero. 6. Critique Reasoning Luke is making pancakes. The recipe calls for 0. quart of milk and. cups of flour. He has _ 18 8 quart of milk and 8 cups of flour. Luke makes the recipe with the milk and flour that he has. Explain his error. 7. Communicate Mathematical Ideas If you know the order from least to greatest of negative rational numbers, how can you use that information to order the absolute values of those numbers from least to greatest? Explain. 6 Unit 1
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