Line Plots. Objective To provide experience creating and interpreting line plots with fractional units. Assessment Management

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1 Line Plots Objective To provide experience creating and interpreting line plots with fractional units. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Identify equivalent fractions. [ and Numeration Goal ] Identify fractions on a number line. [ and Numeration Goal 6] Add fractions and mixed numbers with like and unlike denominators. [Operations and Computation Goal ] Create a line plot. [Data and Chance Goal ] Analyze a data set. [Data and Chance Goal ] Key Activities Students make a line plot to display and analyze a data set measurements in fractions a unit. Students use equivalent fractions and operations fractions including addition and subtraction to solve problems involving information presented in line plots. Materials Math Journal, pp. and A Fraction Cards (Math Journal, Activity Sheets ) Student Reference Book, pp. 9 (optional) calculator Probability Meter Poster (optional) Operations with Multidigit Whole s and Decimals Math Journal, p. B Students practice solving problems involving operations with multidigit whole numbers and decimals. Math Boxes Math Journal, p. Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem. [ and Numeration Goal 6 and Operations and Computation Goal ] Study Link Math Masters, p. Students practice and maintain skills through Study Link activities. READINESS Identifying Fractions on a Line Math Masters, p. Students label fractions on number lines. ETRA PRACTICE Plotting Rain Gauge Data Math Master, p. Students read measures from pictures rain gauges, plot the data on a line plot, and then answer questions about data landmarks. Advance Preparation For Part, students need Fraction Cards (Math Journal, Activity Sheets ), which were cut out and used in Lesson -. 9 Unit Exponents and Negative s

2 Getting Started Mental Math and Reflexes Have students rename fractions as decimals and as percents. Suggestions: _.; % _. ;. %.; % _.; %.; % _.;.%.;.%. 6 ; % _.; % Math Message Sort the Fraction Cards to find the cards equivalent to, _, _, _, and. Use your slate to record the number cards in each group. Be ready to justify your choices. Study Link 9 Follow-Up Have partners compare answers and resolve differences. Teaching the Lesson Math Message Follow-Up (Math Journal, Activity Sheets ) WHOLE-CLASS Draw a number line on the Class Data Pad, and label the benchmarks, _, _, _, and. Label the line plot Sorting Fraction Cards, the x-axis Fractions, and the y-axis Cards. Place the title, Sorting Fraction Cards, above the number line, allowing enough room for data to be added for a line plot. Tell students that the number line will be used to create a line plot displaying the results the equivalent-fraction card sorting activity. Ask students to share the results their card sorting and justify their choices as you record the results on the Class Data Pad. Cards Sorting Fraction Cards Fractions Possible questions to ask include the following: How many cards show a fraction equivalent to? eight: _, _,,, 6_ 6, _, _, 6_ 6 How do you know these fractions are all equivalent to? Sample answers: The front each these cards is fully colored. The numerator is equal to the denominator in each fraction. How many cards show a fraction equivalent to _? seven: _, _, _ 6 _,, _, 6_, _ 6 How do you know these fractions are all equivalent to _? Sample answers: The denominator in each these fractions is twice the numerator. The number spaces shaded blue on each these cards is equal to the number spaces that are white. How many cards show a fraction equivalent to _? three: _, _, _ How many cards show a fraction equivalent to _? three: _, 6_, 9_ How many cards show a fraction equivalent to? three: _, _, _ 6 Cards Sorting Fraction Cards Fractions Lesson 9

3 Ask volunteers to label the fractions _, _, _, and _ on the line plot. Ask students to explain their reasoning for the placement each fraction as it is recorded. Cards Sorting Fraction Cards Fractions Have students continue to sort the Fraction Cards to find those that are equivalent to the fractions for eighths that were just added to the number line. Continue discussing students findings as you complete the line plot. Ask: How many cards did you find for each new fraction we marked on the number line? There are cards for each: _ is equal to _ 6 _, is equal to 6_ 6, _ is equal to _, and _ is equal to _ 6 6. How can you use the line plot to find the total number cards sorted? Count all the s in the line plot. Using a Line Plot to Analyze Data (Student Reference Book, pp.9 ) WHOLE-CLASS Cards minimum Sorting Fraction Cards median mean Fractions mode and maximum Refer students to Student Reference Book, pages 9 to review data landmarks, if necessary. Have students use slates to record information about the data on the Sorting Fraction Cards line plot. Ask students to share their thinking as they analyze the data. As they determine the various landmarks, label them on the line plot on the Class Data Pad. Which number on the line plot has the most equivalent fractions? whole, or What do we call the landmark for the value or values that occur with the greatest frequency in a set data? mode What is the maximum value in the set data? What is the minimum value in the set data? What is the range data displayed on the line plot? How did you find the range? I subtracted the minimum from the maximum: =. What is the median? _ How did you find the median? I started at each end and then worked toward the center until I found the middle number. How many cards do we have in our data set? If the blue shading on the cards represents blue liquid in a beaker, for how many beakers do we have data? What landmark would tell us how much liquid each beaker would have if the liquid were distributed equally among all the beakers? mean If you actually had these beakers liquid, what would you do to distribute the liquid equally among all beakers? Sample answer: I d pour liquid from the beakers with more liquid into the beakers with less liquid until the liquid levels in all the beakers were equal. How do you find the mean for a set data? Sample answer: Add all the data values, and then divide the sum by the number data values. 9 Unit Exponents and Negative s

4 Finding the Mean PARTNER Ask students to work with a partner to find the sum the data values using various strategies. _ Ask students to share their strategy for finding the sum. Date Student Page Time Line Plots and Data in Fractional Units Use the data in the table below to create a line plot. Rainfall in the Driest U.S. Cities City and State Annual Rainfall () City and State Annual Rainfall () Yuma, Arizona _ Alamosa, Colorado _ Las Vegas, Nevada _ Reno, Nevada _ Bishop, California _ Winslow, Arizona _ Bakersfield, California _ El Paso, Texas _ Adjusting the Activity Students who need a visual model to find the sum the fractions may benefit from using the Fraction Cards. Have students match cards that together add to a sum whole. For example, _ and _ add to whole. Using this method, all cards except for one the _ cards has a match to make whole. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Students then use a calculator to find the mean the set data. Students may convert _ to a decimal and then use the calculator to divide the sum by to find the mean. Ask students to round the quotient in the calculator display to the nearest hundredth.. / =., or about. Ask: Between which two fractions on your line plot does. fall? Between _ and _ Which fraction on your line plot is. closest to? How do you know? Sample answer:. is closest to _ because _ =.6, and.6 -. =.. This is less than the distance between. and., which is.. Students then use estimation to determine an approximate placement on the line plot for the mean the set data. + Phoenix, Arizona _ Winnemucca, Nevada _ Source: National Climatic Data Center. Place an on the line plot below to represent the annual rainfall in each the driest cities in the United States. Label the line plot with the mixed numbers for the data. Rainfall in the Driest U.S. Cities Cities 6 Annual Rainfall () Now analyze the data from the table and line plot to answer the questions about the annual rainfall in the driest U.S. cities.. What is the minimum amount annual rainfall?. What is the range annual rainfall?. What is the mode annual rainfall?. What is the median annual rainfall? _ 6 _ 6. What is the combined annual rainfall for the driest cities?. What is the mean annual rainfall for the driest cities? 6. Math Journal, p. 9-_EMCS_S_MJ_G_U_6.indd // :6 PM Adjusting the Activity Students who need a visual model to estimate the placement the mean on the line plot may benefit from referring to the Probability Meter Poster. After determining the approximate location the decimal on the decimal side the probability meter, students look on the opposite side the meter to determine the fraction that is closest to the one found on the line plot. Students should notice that. is greater than. and less than.6, and that it is closer to.6. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Date Time Line Plots and Data in Fractional Units cont. The table below shows rainfall for days in one the driest cities. Organize the data in a line plot. Then analyze the data to answer questions about the plotted rainfall. Rainfall Data Day 6 9 Rainfall () Student Page _. Label the approximate locations on the line plot for _, _, _, _, _, 6_, and _. Displaying and Analyzing Data on a Line Plot (Math Journal, pp. and A) PARTNER Students work with a partner. Have students solve the problems on journal pages and A involving plotting data points on a line plot with fractional units and analyzing the data with landmarks. Circulate and assist. 9. Plot the rainfall data from the table. Days Rainfall Data 6 Rainfall (). Identify the following landmarks for the rainfall data: a. mode: 6_ or _ b. range: _ c. median: 6 d. mean (as a decimal, rounded to the nearest hundredth inch):. Math Journal, p. A 9-_EMCS_S_MJ_G_U_6.indd A // :6 PM Lesson 9

5 Date Time Operations with Multidigit Whole s and Decimals. Use the standard algorithm to complete the multiplication problem shown at right.. $, is shared equally among people. Student Page a. Write an open number sentence to show how much money each person gets., = m b. Will a reasonable estimate for the quotient be in the tens, hundreds, or thousands? In the hundreds c. Each person gets $.. In a store, Denny picks out jeans for $.9 and a shirt for $6.9. He has $ with him. a. Does he have enough money to buy the jeans and shirt? no b. If not, how much more money does he need? $.. a. The correct digits for the product are given. Write the decimal point in the product without actually multiplying =.6 b. Explain how you decided where to place the decimal point. Sample answer:.9 is almost, so I knew that the product would be close to 9.. a. Explain how you could use the shading in the grid to find the quotient.6.. Sample answer: The shading shows groups. in.6. b. What whole number division problem has the same quotient? Sample answer: 6 + º,, º º Ongoing Learning & Practice Operations with Multidigit Whole s and Decimals (Math Journal, p. B) INDEPENDENT Students practice solving problems involving operations with multidigit whole numbers and decimals. Math Boxes (Math Journal, p. ) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skills in Problem 6 previews Unit. Math Journal, p. B 9-_EMCS_S_MJ_G_U_6.indd B // : PM Ongoing Assessment Recognizing Student Achievement Math Boxes Problem Use Math Boxes, Problem to assess students ability to add fractions with unlike denominators and to use benchmarks to compare fractions. Students are making adequate progress if they can compare the fraction _ to _ and find the sum the two fractions. Some students may be able to compare the fraction to _. [ and Numeration Goal 6 and Operations and Computation Goal ] Date Math Boxes Student Page Time. Write the following number in standard notation. Nine billion, one hundred two million, three thousand, sixty-two 9,,,6. Shade _ the fraction stick. a. Is this more or less than _? b. Is this more or less than _? c. _ + _ = _ less more. Fill in the blanks. a. ( ) + ( ) = ( + ). b. ( ) = (.) ( ) 6 9 c. ( + ) = (6 ) + (6 ) d. (9 ) (9 ) = ( ). Write the next two numbers in each pattern. _ 9_ a. _, _, _,, b. 6,,,, 96 c. 6,,,, 6_ d. _, _, _,, _ A large jar drink mix holds. kg. How much drink mix will jars the same size hold? kg 6. 6 stamps per package. How many in... a. _ a package? b. _ 6 a package? c. _ 9 a package? d. _ a package? e. _ a package? stamps stamps stamps stamps stamps Math Journal, p. 9-_EMCS_S_MJ_G_U_6.indd // : PM 9 Unit Exponents and Negative s

6 Study Link (Math Masters, p. ) INDEPENDENT Home Connection Students practice making line plots with fractional increments using insect data. Differentiation Options Name Date Time STUDY LINK Scouting for Insects Some insects are harmful to farmers crops. The insects listed in this table are harmful to alfalfa crops. Farmers scout their crops and randomly collect sample plants. They regularly observe the plants and gather data to determine if the insect population is growing or remaining stable. The table shows the result one farmer s insect scouting. Plot and label the lengths the insects from the scouting sample on the line plot below. Use the line plot to find the following data landmarks:. Minimum insect length Study Link Master Type Insect Average Length Insect () Insects Alfalfa Weevil _ Larvae Fall Armyworm _ Meadow Spittlebug _ Pea Aphid _ 6 Potato Leafhopper _ 6. Maximum insect length. Range insect lengths. Median insect length _. Mean insect length READINESS Identifying Fractions on a Line (Math Masters, p. ) SMALL-GROUP Min Insects Insect Lengths Average Length () Students label fractions on number lines. Math Masters, p. ETRA PRACTICE Plotting Rain Gauge Data (Math Masters, p. ) SMALL-GROUP Min -_EMCS_B_MM_G_U_69.indd // 9: AM Students use rain gauge data to practice creating a line plot with fractional increments and then answer questions about the landmarks the data set. Name Date Time Identifying Fractions on a Line Label each number line with the correct fractions.. Teaching Master Name Date Time Plotting Rain Gauge Data Teaching Master Rainfall ().. 6 Example: Read the rain gauge pictured above and place an on the line plot to show how much rain has been collected.. Read each rain gauge to find out how much rain fell each day. Write the amount rain on the line below the gauge. Sun Mon Tue Wed Thu Fri Sat. Draw and label the following points on this number line. The first one is done for you. A: _ B: _ C: _ D: _ E: _ B C A D E. Jay, Kay, and Mae are in a -mile walk-a-thon. So far, Jay has walked _ mi, Kay has walked _ mi, and Mae has walked _ mi. Draw and label points on the number line below to show their approximate locations. Jay Kay Mae _. Use the number line to make a line plot recording daily rainfall for week. Label the tick marks on the number line. Place an to represent each rain amount. Days _ Daily Rainfall _ Rainfall (). Analyze the rain gauge data to answer the questions below. _ a. What is the mode amount rain that fell each day? _ Math Masters, p. b. What is the range the rainfall during the week? _ Math Masters, p. -_EMCS_B_MM_G_U_69.indd // 9: AM -_EMCS_B_MM_G_U_69.indd /6/ : PM Lesson 9

7 Name Date Time Identifying Fractions on a Line Label each number line with the correct fractions..... Draw and label the following points on this number line. The first one is done for you. A: _ B: _ C: _ D: _ E: _ A Copyright Wright Group/McGraw-Hill. Jay, Kay, and Mae are in a -mile walk-a-thon. So far, Jay has walked _ mi, Kay has walked _ mi, and Mae has walked _ mi. Draw and label points on the number line below to show their approximate locations.

8 Name Date Time STUDY LINK Scouting for Insects Some insects are harmful to farmers crops. The insects listed in this table are harmful to alfalfa crops. Farmers scout their crops and randomly collect sample plants. They regularly observe the plants and gather data to determine if the insect population is growing or remaining stable. The table shows the result one farmer s insect scouting. Type Insect Average Length Insect () Insects Alfalfa Weevil Larvae Fall Armyworm Meadow Spittlebug Pea Aphid Potato Leafhopper 6 _ 6 Plot and label the lengths the insects from the scouting sample on the line plot below. Use the line plot to find the following data landmarks:. Minimum insect length. Maximum insect length. Range insect lengths. Median insect length. Mean insect length Insect Lengths Insects Copyright Wright Group/McGraw-Hill Average Length ()

9 Name Date Time Plotting Rain Gauge Data Rainfall () Example: Read the rain gauge pictured above and place an on the line plot to show how much rain has been collected.. Read each rain gauge to find out how much rain fell each day. Write the amount rain on the line below the gauge. Sun Mon Tue Wed Thu Fri Sat Copyright Wright Group/McGraw-Hill. Use the number line to make a line plot recording daily rainfall for week. Label the tick marks on the number line. Place an to represent each rain amount. Days Daily Rainfall Rainfall (). Analyze the rain gauge data to answer the questions below. a. What is the mode amount rain that fell each day? b. What is the range the rainfall during the week?

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