Sunrise-Sunset Line Graphs

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1 Sunrise-Sunset Line Graphs Objectives To guide children as they analyze data from the sunrise-sunset routine; and to demonstrate how to make and read a line graph. 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 Find the maximum, imum, and range using data from the Sunrise and Sunset Record. [Data and Chance Goal 2] Draw conclusions from a line graph. [Data and Chance Goal 2] Draw line segments on a line graph. [Geometry Goal 1] Key Activities Children make a line graph of the Length-of- Day data they have collected so far. Adding to the graph will be part of the yearlong weekly sunrise-sunset routine Playing Beat the Calculator (Multiplication) Math Journal 1, p. 156 Student Reference Book, p. 279 calculator Children practice multiplication facts. Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip Math Masters, p. 398 [Operations and Computation Goal 3] Math Boxes 5 12 Math Journal 1, p. 126 Children practice and maintain skills tough Math Box problems. ENRICHMENT Math Masters, p. 162 Student Reference Book, p. 234 Children calculate changes in world population as they read and interpret data from a chart and line graph. EXTRA PRACTICE Heights of 8-Year-Old Children Student Reference Book, pp and 235 half-sheet of paper Children find landmarks for a set of data. Key Vocabulary line graph Materials Math Journal 1, pp. 27 and 125 Home Link 5 11 Math Masters, pp. 159 and 160 transparency of Math Masters, p. 159 Place-Value Book straightedge slate Home Link 5 12 Math Masters, p. 161 Children practice and maintain skills tough Home Link activities. Advance Preparation Make copies of Math Masters, pages 159 and 160 and position them next to the Sunrise-Sunset wall chart and the class Sunrise and Sunset Record. Teacher s Reference Manual, Grades 1 3 pp Lesson

2 Getting Started Mathematical Practices SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8 Content Standards 3.OA.7, 3.MD.1 Mental Math and Reflexes Dictate decimals while children display them with their Place-Value Books. In decimal numbers greater than 1, the decimal point is read as and. Suggestions: fifty-tee hundredths 0.53 two and thirty-five hundredths 2.35 four-hundredths 0.04 twenty and seven-hundredths one and four-tenths 1.4 forty and nine-tenths 40.9 For each number, ask questions such as the following: Which digit is in the tenths place? What is the value of the digit x? How many hundredths are there? Math Message Look at your Sunrise and Sunset Record on journal page 27. Which day was the longest day so far? Which was the shortest? How much longer was the longest day than the shortest day? Write the answers on your slate. Home Link 5 11 Follow-Up Partners or small groups take turns reading the number sentences in Problems 1 8 aloud to the class. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Children share strategies for finding the difference between the lengths of the longest and shortest days. Time Making a Line Graph of the Lengths of Days (Math Journal 1, pp. 27 and 125; Math Masters, pp. 159 and 160) ELL PROBLEM SOLVING WHOLE-CLASS 1 13 Sunrise and Sunset Record Time of Sunrise Time of Sunset Length of Day In today s lesson, the data from the Sunrise and Sunset Record is going to be transferred to a Length-of-Day line graph. Draw an enlarged date box on the board. (Model it after the ones on the bottom of the Length-of-Day graph.) Using a transparency of Math Masters, page 159, show children how to copy the dates from journal page 27 to the date boxes below the grid on journal page 125. Explain that the slash separates the month and the day. Explain the scale on the vertical (upright) axis. The labels represent the lengths of days in hours and utes. The heavy horizontal rules indicate whole hours. To support English Language learners, label the graph with the terms vertical axis and horizontal axis. Math Journal 1, p _EMCS_S_SMJ_G3_U01_ indd 27 4/18/11 3:00 PM 380 Unit 5 Place Value in Whole Numbers and Decimals

3 Teaching Master Adjusting the Activity ELL Write the word whole on the board and explain its meaning. Whole hours means entire or complete hours. This will prevent children from hearing and thinking the word hole. 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 Length-of-Day Line Graph 30 Each interval between consecutive whole hours is divided into six equal parts, each part representing 10 utes. The halfway point between consecutive whole hours is labeled 30. Show the class how to graph the length of day above the first date. Children make a dot in the appropriate place on the vertical rule above the first date box. This dot will most likely fall between two consecutive 10-ute marks. Children continue to graph the lengths of days from journal page 27 onto the grid on journal page 125. Use the overhead to demonstrate correct graphing technique Links to the Future Math Masters, p. 159 The activities in this lesson are an early exposure to creating and using line graphs. Creating and using line graphs is a Grade 4 Goal. After everyone has graphed all the data, ask children to use their straightedges to connect consecutive dots. The graph created is a line graph. The line graph is a representation of the data that the children are collecting. Children can look for patterns in the data table and in the data on the line graph. Spend a few utes sharing observations about the graph. For example: Find the highest point on the graph. Which date corresponds to this point? Is that the longest day so far? The longest day of the year, the summer solstice, is around June 21. Find the lowest point on the graph. Which date corresponds to this point? Is that the shortest day so far? The shortest day of the year, the winter solstice, is around December 21. What does it mean when the lines connecting the points go down? The days are getting shorter. What does it mean when the lines go up? The days are getting longer. Is there a turning point at which the lines change direction (either up or down)? At each solstice NOTE Math Masters, page 159 is similar to journal page 125. Teaching Master Length-of-Day Line Graph continued Math Masters, p. 160 Lesson

4 5 12 Math Boxes 1. Color 0.08 of the grid. 3. Which is more? 1.36 or or or or Time 2. What is the maximum number of points? 25 What is the mode? 25 points 4. One side of this square is 4 cm long. Perimeter = Number of Points 4 cm cm Point Totals A B C D E Players Tell children that from now on, whenever they record the sunrisesunset data for a certain day, they will also plot the length of that day on their line graphs. NOTE By the time children finish Math Journal 1, the Sunrise and Sunset Record, page 27, and the Length-of-Day line graph, page 125, will most likely be complete. In Math Journal 2, children will find a new Sunrise and Sunset Record on page 279, and a new Length-of-Day line graph on pages 280 and 281. Children should continue to enter data on these pages. The classroom copies of Math Masters, pages 159 and 160 positioned next to the Sunrise-Sunset chart, will serve as the yearlong record of the children s data. Each week, as children record the data in their journals, one child should record the data on the classroom copies of the journal pages Write the number that has 4 in the tenths place 0 in the hundredths place 6 in the ones place 9 in the thousandths place Math Journal 1, p This polygon has 12 sides. Name the shape. dodecagon Ongoing Learning & Practice Playing Beat the Calculator (Student Reference Book, p. 279; Math Journal 1, p. 156) SMALL-GROUP _EMCS_S_SMJ_G3_U05_ indd 126 1/26/11 9:17 AM Children develop automaticity with multiplication facts by playing Beat the Calculator. Have children add a check mark on the Fact Power Table (journal page 156) for each fact that they solve correctly when playing the role of the Brain. For Fact Power Table directions, see Lesson 4-5. For game directions, see page 279 in the Student Reference Book. HOME LINK 5 12 Family Note Home Link Master Subtraction & Multiplication Practice Ask your child to explain the counting-up and trade-first subtraction methods. Please return this Home Link to school tomorrow Ongoing Assessment: Recognizing Student Achievement Exit Slip Use an Exit Slip (Math Masters, page 398) to assess children s progress toward demonstrating automaticity with multiplication facts tough Children record the facts from the Fact Power Table for which they earned at least one check mark. Children are making adequate progress if they record at least 15 facts from the unshaded portion of the record sheet. Some children may record more than 15 facts. [Operations and Computation Goal 3] Make a ballpark estimate. Subtract and show your work. Check to see if your answer makes sense. 1. Use the counting-up method Use the trade-first method Multiplication. Write facts that you know. Sample answer: 450 (Ballpark estimate) Sample answer: 450 (Ballpark estimate) Answers vary facts 4. 3 facts 5. 4 facts 4 2 = 8 Math Masters, p. 161 Unit Math Boxes 5 12 (Math Journal 1, p. 126) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skill in Problem 6 previews Unit 6 content. Writing/Reasoning Have children write an answer to the following: For Problem 3, explain how you know which number in each pair is more. Sample answer: I wrote the pairs of numbers one under the other. Then I compared each digit starting with the ones. If they were the same, I compared the tenths. If they were the same, I compared the hundredths. If the digits weren t the same, the larger digit was in the larger number. EM3MM_G3_U05_ indd 161 1/7/11 3:29 PM 382 Unit 5 Place Value in Whole Numbers and Decimals

5 Home Link 5 12 (Math Masters, p. 161) Home Connection Children practice multidigit subtraction using two different strategies. They write multiplication facts they know. 3 Differentiation Options ENRICHMENT (Math Masters, p. 162; Student Reference Book, p. 234) 5 15 Min To further explore interpreting data on a line graph, have children answer questions on Math Masters, page 162 using data from the World Population Table and the graph on Student Reference Book, page 234. Teaching Master Use the data about world population on Student Reference Book, page 234 to help you answer the questions below. 1. About how many people were added to the world population between 1500 and 1804? How many years is that? 304 years 2. About how many people were added to the world population between 1804 and 1960? How many years is that? 156 years 3. About how many people were added to the world population between 1960 and 1999? How many years is that? 39 years 500,000,000 2,000,000,000 3,000,000, Compare your answers for Questions 1, 2, and 3. What do you notice about population growth? Sample answer: Population is increasing more rapidly in recent years. 5. Look at the World Population Graph. What does the line graph illustrate, or show, about world population? Sample answer: The population has grown much larger and faster in the last 500 years than in the previous 1,500 years. 6. Use the World Population Table to predict when the world population will reach 8,000,000,000. Explain. Use the back of this page, if needed. Sample answer: About 24 years. 1 billion more people were added from 1987 to 1999; that s 12 years. In 24 years, 2 billion would be added. Math Masters, p. 162 EXTRA PRACTICE Heights of 8-Year-Old Children (Student Reference Book, pp and 235) PARTNER Min To provide additional practice in finding data landmarks, have children detere the maximum 148 cm, imum 107 cm, range 41 cm, mode 126 cm, and median 126 cm for the Heights of Third Graders data set on page 235 in the Student Reference Book. Children record their answers on a half-sheet of paper. They may refer to pages in their Student Reference Books as needed. Data Bank There are more than 6 billion people in the world today. The table and graph below show how the world s population has grown. By the year 2050, the world will have about 10 billion people. World Population Table Population Population 1000 B.C. 50,000, ,000,000,000 A.D ,000, ,000,000, ,000, ,000,000, ,000, ,000,000, ,000,000, ,000,000,000 Source: United Nations Population Division World Population Student Reference Book, p. 234 Lesson

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