Lesson 8.5 PROBLEM SOLVING
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1 Name Problem Solving Comparison Problems with Fractions Essential Question How can you use the strategy draw a diagram to solve comparison problems with fractions? PROBLEM SOLVING Lesson 8.5 Numbers and Operations Fractions 4.NF.B.4c MATHEMATICAL PRACTICES MP1, MP2 Unlock the Problem The deepest part of the Grand Canyon is about 1 1_ 6 miles deep. The deepest part of the ocean is located in the Mariana Trench, in the Pacific Ocean. The deepest part of the ocean is almost 6 times as deep as the deepest part of the Grand Canyon. About how deep is the deepest part of the ocean? Read the Problem What do I need to find? I need to find Solve the Problem Draw a bar model. Compare the depth of the deepest part of the Grand Canyon and the deepest part of the ocean, in miles Image Credits: (r) superstock rf/superstock What information do I need to use? The deepest part of the Grand Canyon is about _ miles deep. The deepest part of the ocean is about _ times as deep. How will I use the information? I can to compare the depths. Write an equation and solve. m is the deepest part of, in miles. Write an equation. Write the mixed number as a fraction. Multiply. Write the fraction as a whole number. So, the deepest part of the ocean is about _ miles deep. Chapter 8 481
2 Try Another Problem Mountains are often measured by the distance they rise above sea level. Mount Washington rises more than 1 1 miles above sea 10 level. Mount Everest rises about 5 times as high. About how many miles above sea level does Mount Everest rise? Read the Problem Solve the Problem What do I need to find? What information do I need to use? How will I use the information? So, Mount Everest rises about _ miles above sea level. How did drawing a diagram help you solve the problem? Math Talk MATHEMATICAL PRACTICES 7 Look for Structure What strategy could you use to find the height of Mount Everest? Image Credits: (t) Karl Maret/Corbis 482
3 Name Share and Show MATH BOARD 1. Komodo dragons are the heaviest lizards on Earth. A baby Komodo dragon is 1 1_ feet long when it 4 hatches. Its mother is 6 times as long. How long is the mother? Unlock the Problem Use the Problem Solving MathBoard. Underline important facts. First, draw a bar model to show the problem. Math WRITE Show Your Work Then, write the equation you need to solve. Finally, find the length of the mother Komodo dragon. The mother Komodo dragon is _ feet long. 2. SMARTER What if a male Komodo dragon is 7 times as long as the baby Komodo dragon? How long is the male? How much longer is the male than the mother?. The smallest hummingbird is the Bee hummingbird. It has a mass of about 1 1_ grams. A Rufous hummingbird s mass is 2 times the mass of the Bee hummingbird. What is the mass of a Rufous hummingbird? 4. Sloane needs _ hour to drive to her grandmother s house. It 4 takes her 5 times as long to drive to her cousin s house. How long does it take to drive to her cousin s house? Chapter 8 Lesson 5 48
4 MATHEMATICAL PRACTICES M On Your Own Use the table for 5 and Payton has a variety of flowers in her garden. The table shows the average heights of the flowers. MATHEMATICAL PRACTICE 1 Make Sense of Problems What is the difference between the height of the tallest flower and the height of the shortest flower in Payton s garden? Flower Height tulip 11_ 4 feet daisy 21_ 2 feet tiger lily 1_ feet sunflower 7_ 4 feet Math WRITE Show Your Work 6. SMARTER Payton says her average sunflower is 7 times the height of her average tulip. Do you agree or disagree with her statement? Explain your reasoning. 7. DEEPER Miguel ran 1 miles on Monday. On Friday, 10 Miguel ran times as far as he did on Monday. How much farther did Miguel run on Friday than he did on Monday? Personal Math Trainer 8. SMARTER The table shows the lengths of different types of turtles at a zoo. Turtle Name Type of Turtle Length Tuck Common Snapping Turtle 1 1 _ 6 feet Lolly Leatherback Sea Turtle 5 5 _ 6 feet Daisy Loggerhead Sea Turtle 1 _ 2 feet For numbers 8a 8d, select True or False for each statement. 8a. Daisy is 4 times as long as Tuck. True False 8b. Lolly is 5 times as long as Tuck. True False 8c. Daisy is times as long as Tuck. True False 8d. Lolly is 2 times as long as Daisy. True False 484
5 Name Problem Solving Comparison Problems with Fractions Practice and Homework Lesson 8.5 COMMON CORE STANDARD 4.NF.B.4c Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Read each problem and solve. 1. A shrub is 1 2_ feet tall. A small tree is times as tall as the shrub. How tall is the tree? t is the height of the tree, in feet. t = 1 2_ t = 5_ t = 15 shrub tree 1 2_ 1 2_ 1 2_ 1 2_ t = 5 So, the tree is 5 feet tall. 5 feet 2. You run 1 _ miles each day. Your friend runs 4 4 times as far as you do. How far does your friend run each day?. At the grocery store, Ayla buys 1 1_ pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy? 4. WRITE Math Draw a bar model that shows a pen is 4 times as long as an eraser that is 1 1_ inches long. Chapter 8 485
6 Lesson Check (4.NF.B.4c) 1. A Wilson s Storm Petrel is a small bird with a wingspan of 1 1_ feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor? (It may be helpful to draw a model.) 2. The walking distance from the Empire State Building in New York City to Times Square is about 9 mile. The walking distance from 10 the Empire State Building to Sue s hotel is about 8 times as far. About how far is Sue s hotel from the Empire State Building? (It may be helpful to draw a model.) Spiral Review (4.OA.B.4, 4.NF.A.2, 4.NF.B.d, 4.NF.B.4c). Write an expression that is equal to 4. At a bake sale, Ron sells 7_ of an apple pie 2 1_ 4. 8 and 5_ of a cherry pie. Altogether, how much 8 pie does he sell at the bake sale? 5. Write one measurement that is between 6. Write a composite number that is less than 5. inch and 7_ 16 8 inch on a ruler. 486 FOR MORE PRACTICE GO TO THE Personal Math Trainer
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