Represent and Interpret Data

Transcription

1 Represent and Interpret Data Home-School Connection Topic 1 Dear Family, Your student is learning to analyze and create line plots to display a set of data measurements in fractions of a unit. He or she will solve real-world problems using measurement data displayed in a line plot. Complete the following activity with your student to reinforce his or her ability to record data and create a line plot representing the data. Pencil Length Data and Line Plot Materials: 10 pencils of various lengths, inch ruler Step 1 Have your child gather 10 used pencils. Step Have your child measure and record the length of each pencil to the nearest 1 inch. Step 3 Work together and use the data collected to complete a frequency table and a line plot such as those below. Value Tally Frequency Pencil Lengths Length (in inches) 7 1 Observe Your Child Ask your child which pencil length occurs most often. Which pencil length occurs least often? Discuss how to answer these questions by looking at the line plot.

2 Nombre Representar e interpretar datos De la escuela al hogar (en español) Tema 1 Estimada familia: Su niño(a) está aprendiendo a analizar y crear diagramas de puntos para mostrar un conjunto de datos de mediciones en fracciones de una unidad. Resolverá problemas de la vida diaria usando datos de mediciones representados en un diagrama de puntos. Complete esta actividad con su niño(a) para reforzar su capacidad de anotar datos y crear un diagrama de puntos que represente los datos. Datos de longitud de lápices y diagrama de puntos Materiales 10 lápices de distinta longitud, regla de pulgadas Paso 1 Pida a su niño(a) que busque 10 lápices usados. Paso Pídale que mida y anote la longitud de cada lápiz a la 1 pulgada más cercana. Paso 3 Trabajen juntos y usen los datos reunidos para completar una tabla de frecuencias y un diagrama de puntos como los que se muestran. Valor Conteo Frecuencia Longitudes de los lápices Longitud (en pulgadas) 7 1 Observe a su niño(a) Pregúntele qué longitud es la más frecuente. Qué longitud es la menos frecuente? Comenten cómo responder a esas preguntas mirando el diagrama de puntos.

3 1. A punch bowl has a capacity of 8 quarts. How many cups can the punch bowl hold? A 16 cups B 4 cups C 3 cups D 48 cups. Burt has 986 paperback books. He wants to put these books on storage shelves. Each shelf can hold 50 paperback books. How many shelves will Burt need to hold all of the books? A 0 B 19 C 18 D How many unit cubes are needed to make a model of a rectangular prism that is 9 units long, 5 units wide, and 3 units high? A 17 unit cubes B 135 unit cubes C 174 unit cubes D 70 unit cubes 4. Which expression is NOT equal to 0 1? A 5, B 4, 5 Daily Review In the North Woods Middle School chorus, 3 8 of the members are 11 years old. Of the 11-year-old chorus members, 5 are boys. What fraction of all the chorus members are 11-year-old boys? 6. Write the product of 5 9 and 5 as a mixed number. 7. Find the perimeter of the rectangle below in inches. 4 ft yd 8. Beth and Dave are hiking on a mile trail. When they stopped for a picnic lunch, they had hiked 5 8 miles of the trail. How much farther do they have to hike after lunch to complete the trail? 9. Find the area of a square with a side length of 7 1 inch. C 4, 1 5 D 1 10, D 11

4 Vocabulary 1. A line plot shows data along a number line. Collected information is called data. Each dot in a line plot represents one value in a data set. Which numbers have dots plotted above them? Number of Miles Walked Number of Miles Reteach to Build Understanding If a number is much greater or less than the rest of the numbers in the data set, that number is called an outlier. On the line plot above, which number could be an outlier? The table and line plot show the time that students spent on homework last week. Time Spent on Homework (in hours) Time Spent on Homework Number of Hours 3. Use the table to find how many students spent exactly 5 hours on homework last week. Use the line plot to find the number of dots above 5. students dots 4. Count the dots above 4 1, 43 4, and 5 to find the number of students that spent 5 or fewer hours on homework last week. students 5. Use the line plot to find the number of students that spent more than 5 hours on homework last week. students 6. Is there an outlier in the data? If so, what is it? On the Back! 7. Use the Time Spent on Homework line plot to solve. Which two times spent on homework occurred most often? R 11

5 Deforestation Math and Science Activity 1-1 Did You Know? Many of Earth s forests have vanished because of deforestation. Deforestation is the removal of all trees in a forest. Humans clear forests for farming, grazing animals, lumber, paper products, and building towns. Deforestation changes the ecosystem. It damages and erodes soil. Deforestation causes a loss of homes and food for animals and plants. And, it affects the water cycle. Answer the following questions using the line plots. ➊ The Clear-Away Tree Company buys forestland, cuts down trees, and then sells the cleared land. They used a line plot to show the number of acres they cleared each day for two weeks. What was the greatest number of acres cut in one day? What was the least? Acres of Trees Cut per Day Number of Acres ➋ Scientists want to know if clearing the forest affects a population of macaws. They measure the decrease in habitat area for 14 different macaw populations and make a line plot with the data. What is the smallest decrease in area? What is the greatest? Can you tell from the line plot how many macaws live in each habitat? 1 4 Acres of Macaw Habitat Lost Number of Acres ❸ Extension The LuvTreez organization works to prevent deforestation. They buy acres of forestland that they turn into protected parks. Every time they make a purchase, they record it. The line plot shows the data. How many purchases have they made so far? What is the total number of acres purchased? Forestland Purchases Number of Acres Math and Science Activity 11

6 1. The dot plot represents the number of children enrolled, by age, at a preschool. Select all the statements that are true. Number of Children Daily Review 1-4. Kevin and Jen are buying carpeting for a bedroom with an area of 9 square feet. The carpeting costs $3.89 per square foot, plus $0.45 per square foot for padding and $0.50 per square foot for installation. The sales tax on their purchase is $ What is the total amount that Kevin and Jen will pay? Age in Years There are 30 children enrolled. 14 children are at least 4 years old. 5 children are 3 years old. There is one outlier. 11 children are older than 3 1 years old and younger than 5 years old.. Earth takes days to complete one orbit around the Sun, while Venus takes 4.7 Earth days. How many more Earth days is the Earth s orbit than that of Venus? A Earth days B Earth days C Earth days D Earth days 3. Five Black Angus cows weigh about 6,000 pounds. About how many tons do the cows weigh? A 3 tons B 5 tons C 6 tons D 10 tons D 1 5. The table shows the distances that Victoria walked on a treadmill last week. Day Tuesday Thursday Saturday Distance 1,600 m 3.5 km.7 km What is the total distance, in kilometers, Victoria walked on these three days? 6. Estimate the product. Then find the exact product. ( ) ( ) Estimate: Exact product: 7. A rectangular prism is 5 feet long, 3 feet wide, and 8 feet high. What is the volume of the prism?

7 Vocabulary 1. A frequency table shows how many times a data value occurs in a set of data. This table shows the Miles Walked data for 14 students. 4, 1, 3,,, 4, 4,, 3, 4, 4, 7,, 4 A tally mark is made for each data value. The total number of tally marks is written in the Frequency column. Reteach to Build Understanding 1- Miles Walked Tally Frequency 1 l 1 llll 4 3 ll 4 llll l 6 7 l 1 How many students walked 4 miles?. The cats in Sandy s Pet Shop have the weights shown in the table. Order the weights from least to greatest. Check to be sure you have listed each item in the table. The list should have 10 numbers in it. Weights of Sandy s Cats (in lb) Cat Weight (pounds) Tally Frequency 3. Make a frequency table to show the data in the list. Make a tally mark for each weight in the list. Count the tally marks to find each frequency. Write each number in the Frequency column. 4. Make a line plot. First, label the number line. Since the data ranges from 5 through 9 pounds, a reasonable number line is from 0 to 10 pounds. Next, make a dot for each value in the data set. Then write a title. On the Back! Title: 0 1 Pounds 5. Make a frequency table and line plot for the following data: Quiz Scores: 9, 10, 8 1, 8, 8, 9, 10, 91, 9, 9, 81, 71, 81, 9, 9 R 1

8 1. Which fraction is NOT equivalent to 5 6? A B 3 C 5 30 D Which expression can be used to find the volume of the figure? Daily Review The table shows the amount of time Morgan spent doing homework each school night over the past three weeks Make a line plot for this data set. Time Spent on Homework A 5 B 10 C 0 D Camden lives 1 mile from school. He has walked 3 of the way to school. How many feet does he have left to walk? A 587 feet B 1,08 feet C 1,760 feet D 3,50 feet 4. Which is the quotient of 58, 7? A 7 58 B 7 7 C 8 7 D Number of Hours 6. Luke has,150 milliliters of water in his bottle. Katherine has 1.85 liters of water in her bottle. Who has more water? Explain. 7. A container holds 6 cups of yogurt. The nutrition label reads that a serving size is 1 3 cup. How many servings are in the container? 8. A rectangular plaza measures 3 8 mile by 4 5 mile. What is its area? D 13

9 Vocabulary 1. A sum is the answer to an addition problem. Sums give totals of values. A difference is the answer to a subtraction problem. Differences tell how much more one value is than another. A product is the answer to a multiplication problem. Products give the total number of items in groups of the same size. Find each sum, difference, or product = = = = = = Reteach to Build Understanding 1-3. On a line plot, each data value is shown as a dot above a number line. What do the 3 dots above 3 4 indicate? There were days with rainfall of inch. Rainfall Over 7 Days Inches 3. Use the frequency table to find the total amount of rainfall for the 7-day period. Since there were days with 1 4 inch of rain, multiply 1 4 times. The product is the total amount of rainfall for those two days. 1 4 = 4 or Write the product in the Multiplication column in the table. Rainfall (inches) Frequency Multiplication = = = = Complete the rest of the table. Multiply each rainfall amount by the frequency. 4. Add all four products in the Multiplication column to find the total amount of rain for the 7-day period = inches The total rainfall for the 7-day period was On the Back! 5. Make a frequency table for the data in this line plot. Find the total amount of rainfall over weeks. R 13 inches. Rainfall Over Weeks Inches

10 1. The dot plot shows the shoe sizes for a group of women Women s Shoe Sizes Size Select all the statements that are true about this group of women. 4 women are in the group. The shoe size that occurs most often is 7 1. Fewer than 9 women wear shoes that are size 8 or greater. Size 10 is an outlier. The number wearing size 8 shoes is the same as the total number wearing sizes 8 1 and 9.. Jessica has 1 1 hours to take a test. She spends 65 minutes answering the questions. How much time does she have to check her work? A 1 hour B 30 minutes C 5 minutes D 10 minutes 3. Find the quotient. 1 1, 5 A 60 1 C 5 5 B 1 D 60 Daily Review The line plot shows the number of hours the employees of a small company worked on one day. Time Worked by Employees Hours What was the total number of hours worked by the 15 employees? 5. A set of 9 books has 5,487 pages. Estimate the number of pages in each book, if each book has the same number of pages. 6. A window box the shape of a rectangular prism is 7 inches long and 4 inches wide. It holds 168 cubic inches of dirt. What is its height? 7. Rashon measured the length of the hallway in his school to be 0 yards 5 feet. How many inches long is the hallway? D 14

11 Reteach to Build Understanding 1-4 Vocabulary 1. To critique reasoning is to examine an explanation, determine whether it makes sense or not, and correct it, if necessary. Since 6 10 = 600, then = Explain the flaw in this reasoning. Multiplying by 10 moves the decimal point two places to the right, with zeroes annexed as needed. So, =.. In Adrian s town, it rained 15 times last month. Adrian measured and recorded the amount of rain that fell each day. The amounts are shown in the line plot. Adrian did the following work to find the total rainfall last month. (3 0.5) + (5 0.5) + ( 0.75) + (3 1) + ( 1.5) = = 11.5 How can you find the number of days of measurements? I can count the on the line plot. There are dots. Add the first whole numbers in the parentheses to find the number of days that Adrian used. Did she use the correct number of days? = 3. In Adrian s work, each expression represents the amount of rainfall for that measurement. Check Adrian s work. Is it correct? Explain.. Adrian wrote the product of 3 1 as. Days of Rainfall Last Month Inches 4. Find the correct total amount of rainfall last month. inches On the Back! 5. The month before last, there was a total of 7.75 inches of rain. Adrian stated that this was 3.5 inches less rain than last month. How can you critique her reasoning? R 14

12 California Condor Recovery Did You Know? California condors are vultures. As scavengers, they are an important part of the ecosystem. During the 0th century, the California condor population dropped dramatically due to poaching, lead poisoning, and habitat destruction. In 198, only birds remained in the wild. In 1987, a captive breeding program began. In 199, the first few condors were released into the wild. Math and Science Activity 1-4 Weights of Condor Eggs Ounces Scientists working for a captive breeding program measure the weights of several condor eggs. Use the line plot to answer the questions. ➊ What is the difference in weight between the lightest and the heaviest eggs? ➋ Marta says that at least half of the eggs weigh ounces or more. Is her reasoning correct? Explain. ➌ Drew says that 10 is an outlier. Do you agree? Explain why or why not. ➍ Extension Drew wrote the expression ( 83 4 ) + ( 91 ) + ( ) + ( ) + 10 to find the total weight of the condor eggs. Is his expression correct? Explain. Math and Science Activity 14