# Bar Graphs with Intervals Grade Three

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1 Bar Graphs with Intervals Grade Three Ohio Standards Connection Data Analysis and Probability Benchmark D Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; e.g., each = 10 bicycles or the intervals on an axis are multiples of 10. Indicator 3 Read, interpret and construct bar graphs with intervals greater than one. Mathematical Processes Benchmarks I. Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others. J. Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language. Lesson Summary: Students explore a variety of bar graphs using familiar contexts. They read, interpret, and construct bar graphs with intervals of two, five and ten. Activities include diverse groupings of students, opportunities for oral and written communication and informal assessment. The concepts can be extended across the curriculum to teach or reinforce skills. Estimated Duration: Four hours Commentary: Students should have frequent experiences with collecting, representing and analyzing data. Students build on prior knowledge of bar graphs and learn that intervals are necessary to represent large sets of data. In order to determine intervals which are appropriate, students must have an informal sense of the range of data. Modeling and practicing the decision-making process to identify an interval is essential to building understanding. Pre-Assessment: Distribute a copy of Pre-Assessment, Attachment A, to each student. Have students complete the worksheet independently to assess their competency of reading and interpreting a bar graph with intervals of one and their understanding of intervals. Circulate to observe and assist as needed. Ask questions to have students explain their understanding of bar graphs: 1. What does this bar graph show? (ways to go to school) How did you know that? (title: Ways We Come to School ) 2. What do the vertical numbers show? (number of students) How did you know? (label by the numbers: Number of Students ) 3. What do the words on the bottom show? (different ways students go to school) How did you know? (label: Types of Transportation ) 4. How can we tell how many students walk to school? (Look at the walk column to see how far the bar goes and at what numbered line the bar stops.) 1

6 Bar Graphs with Intervals Grade Three 25. Pair the students. Distribute one-inch grid paper (or a copy of Blank Grid, Attachment J) to each student. Students work together to read, discuss, brainstorm ideas and construct the graph (each student must make a graph). Write this list on the board or chart paper for students to use as a checklist: Title of graph Label horizontal axis (for the columns) Category or Intervals horizontal axis Label vertical axis (for the rows) Category or Intervals vertical axis Bars shaded to show data 26. Circulate to observe, assist, and ask leading questions to guide the construction of the graph. Have students explain what they are drawing and why. 27. Have students visit other groups to see various ways of making a bar graph and to get ideas if they are not sure what to do. When all groups are finished, have each group display their graph telling how they constructed it. Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). Provide students with counters to represent the quantity at each interval. For example, the graph shown uses an interval of three. Allow students to place three counters between each interval to represent concretely. Collect data from newspapers or magazines using numbers through 1,000 and have students create graphs and choose appropriate intervals. Extensions: Opportunities for graphing occur each day in the classroom such as 1. Keep a graph of the weather and adding to it daily over the course of a month, season or year. 2. Create and display a birthday graph to show all students birthdays. 3. Have students conduct surveys of classmates, tally the information and create bar graphs (e.g., favorite pizza toppings, favorite cartoon shows, favorite candy bars, eye color, favorite school subject, favorite pets, etc.) 4. Use data in other subject areas and (e.g. science experiments, population, land area) have students create bar graphs to compare/contrast the information. Home Connections: Collect data from home and create a bar graph such as: types of shoes, coins in a bank, different clothing items (shirts, pants, shorts, etc.), types of books, etc. Have students find displays (such as cereal boxes or from media) that show bar graphs with intervals greater than one. 6

7 Bar Graphs with Intervals Grade Three Interdisciplinary Connections: Content Area: Science Standard: Scientific Inquiry Benchmark: B. Organize and evaluate observations, measurements and other data to formulate inferences and conclusions. Indicators: 3. Read and interpret simple tables and graphs produced by self/others. 5. Record and organize observations (e.g., journals, charts and tables). Being able to graph and interpret data correctly is an important skill necessary for scientific inquiry. Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: chalkboard, chalk, overhead transparency of Attachments A, E, H, and J, overhead markers For the student: counters, crayons, grid paper, pencils Vocabulary: axis bar graph horizontal interval vertical Technology Connections: Use computer encyclopedias or online sources to collect data about given topics. Students can then use available computer software to create bar graphs. Research Connections: Burns, Marilyn. About Teaching Mathematics: A K-8 Resource. Sausalito, Ca: Math Solutions Publications, Sousa, David A. How the Brain Learns: A Classroom Teacher s Guide. Reston, VA.: NASSP,

8 Bar Graphs with Intervals Grade Three General Tips: Prior to class: Reproduce a class set of: 1. Pre-Assessment, Attachment A 2. Post-Assessment, Attachment B 3. Number Lines, Attachment E 4. Bar Graph with Intervals of Two, Attachment F 5. Bar Graph with Intervals of Five, Attachment G 6. Bar Graph with Intervals of Ten, Attachment H 7. Blank Grid, Attachment J, if needed (one inch grid paper may be used) Make transparencies of: 1. Pre-Assessment, Attachment A 2. Number Lines, Attachment E 3. Bar Graph with Intervals of Ten, Attachment H 4. Blank Grid, Attachment J, or one-inch graph paper Attachments: Attachment A, Pre-Assessment Attachment B, Post-Assessment Attachment C, Post-Assessment Part B Answer Key Attachment D, Post- Assessment Scoring Rubric Attachment E, Number Lines Attachment F, Bar Graph with Intervals of Two Attachment G, Bar Graph with Intervals of Five Attachment H, Bar Graph with Intervals of Ten Attachment I, Bar Graph with Intervals of Ten Answer Key Attachment J, Blank Grid 8

9 Bar Graphs with Intervals Grade Three Attachment A Pre-Assessment Name Date Part A Directions: Look at the bar graph. Answer the questions. Write number sentences to show how you solved problems. 1. What does this bar graph show? 2. Which type of transportation is used the most? 3. Which type of transportation is used the least? 4. How many students ride a bus to school? 5. How many students walk to school? 6. How many bus riders and car riders are there? 7. How many more students come to school by car than by walking? 8. How many fewer students come to school by car than by bus? 9. How many students are in this class? 9

10 Attachment A (continued) Pre-Assessment Part B Give the value for each point. 10. Point C = 11. Point A = 12. Point T = 13. Point C = 14. Point A = 15. Point T = 10

11 Attachment B Post-Assessment Name Date Part A: Use this bar graph to answer the questions. Write number sentences to solve problems. 1. Which pet was the least common? 2. Which type of pet was the most common? 3. How many dogs are shown on the graph? 4. How many fish are shown on the graph? 5. How many more cats are shown than birds? 6. How many fewer rabbits are shown than birds? 7. Which pet is more popular, a dog or cat? How many more are shown? 8. How many pets in all? 9. Why are there only even numbers on the vertical axis? 11

13 Attachment B (continued) Post-Assessment Part C: Use the following information to make a bar graph. Use the checklist to make sure you include all parts. Washington School collected pennies to help people in need. In one day, these amounts were collected: Kindergarten, 48 pennies Grade 1, 65 pennies Grade 2, 21 pennies Grade 3, 54 pennies Grade 4, 72 pennies Grade 5, 44 pennies CHECKLIST Title of Graph Label horizontal axis (for the columns) Category or Intervals horizontal axis Label vertical axis (for the rows) Category or Intervals vertical axis Bars shaded to show data 13

15 Attachment D Post-Assessment Scoring Rubric The following rubric may be used to assess progress on the post-assessment worksheet, Parts A and B: 3 - Contains accurate and complete responses. Interprets information correctly and uses this information to correctly solve problems of comparison. 2 Contains mostly accurate responses with few errors. Interprets information correctly and uses correct process for solving problems, but may have errors in calculations for comparison problems. 1 Contains some accurate responses but displays difficulty interpreting the value of some bars or difficulty choosing the correct process or calculations for some comparison problems. 0 - Response shows major gaps in understanding. Response shows inadequate interpretation of information or incorrect process for problem solving. Intervention and additional practice are necessary for understanding concepts. The following rubric may be used to assess progress on the post-assessment worksheet, Part C: Title and Axes Adequate Understanding (3) Partial understanding (2) Limited understanding (1) Titles graph and labels axes correctly. Titles graph correctly, but omits or incorrectly labels one axis. Titles graph incorrectly or omits title. Omits or incorrectly labels one axis or both axes. Intervals and Categories Labels one axis correctly showing intervals of 10. Labels one axis correctly with categories. Uses intervals of 10, but not correctly (does not start at 0 or skips some numbers) or omits category. Fails to use intervals of 10 or omits labels for intervals or category. Bar Values Shades bars correctly to show value. Shades most bars correctly with 1-2 errors. Shades most bars incorrectly with 3 or more errors. Readability Constructs and labels graph neatly and graph is readable. Constructs and labels graph in an acceptable manner. Constructs and labels graph, but graph is not readable. Use the information to identify areas of weakness and to determine the need for further instruction and intervention. 15

16 Attachment E Number Lines Name Date Directions: Give the values of each point. Draw in the points given and label them. 1. Point A = Point T = Place point M at 3. Place point H at Point A = Point R = Point P = Place point G at 4. Place point S at 28. Place point H at Point E = Point S = Point I = Place point L at 54. Place point T at 21. Place point V at 38. Place point R at 33. Place point A at 46. Place point N at

17 Attachment E (continued) Number Lines Instructional Procedures 1. Pass out a copy of Number Lines, Attachment E, to each student. Have students look at all three number lines and ask how these differ (#1 counts by 2 s, #2 counts by fives, #3 counts by 10 s). Explain to the class that sometimes all the points on a number line do not show what number they are equal to, and we need to use the scale to determine the value of the point. 2. Have students begin with #1. Discuss the intervals used on this number line (intervals of two). Write the word intervals on the board. Emphasize that the numbers are evenly spaced on the number line. 3. Have students fill in the answers on the worksheet as the class responds to the questions. Use a transparency of Number Lines, Attachment E, on the overhead to display the answers to the class. Use the following questions, to lead the discussion of determining the value and placement of given points: How many numbers would be between 0-2? (one, the number 1) What is the value of point A? (6) Can we determine the value of point T? (yes, it is 9, because it is halfway between 8 and 10) Point M equals three. Where would we put point M? (halfway between 2 and 4) Point H equals 11. Where should we put H? (halfway between 10 and 12) What did we spell? (MATH) Have students check their neighbor s work to assure that all students placed the points correctly. 4. Have students look at #2. Discuss the intervals used on this number line (intervals of five). Ask: How many whole numbers would be between zero and five? (four: 1, 2, 3, 4) Explain that we could draw in four little marks to get an idea of where each whole number would be. Have students draw these marks in between 0-5 to give them a spatial sense of the numbers between the intervals. What is the value of point A? (15) Can we determine the value of point R? (yes, it would be 9 because it is very close to 10) What would be the value of point P? (17, because it is a little less than halfway between 15 and 20) Point G equals 4. Where should we put point G? (a little before the 5) Point S equals 28. Where should we put point S? (a little more than halfway between 25 and 30) Point H equals 22. Where should we put point H? (past 20, but not quite halfway to the 25) What did we spell? (GRAPHS) Have students compare work to assure all students correctly displayed the points. 17

18 Attachment E (continued) Number Lines Instructional Procedures 5. Have students look at #3. Discuss the intervals used on this number line (intervals of ten). Ask: How many numbers would be between 0-10? (nine: 1, 2, 3, 4, 5, 6, 7, 8, 9) Have students draw a mark halfway between zero and ten. What number would this be? (5 because five is one-half of ten) Have students draw in four evenly spaced marks between 0-5, and four more evenly spaced marks between five and ten. Explain that now our intervals are larger and it is difficult to determine exact numbers for the points between the interval marks.) What is the value of point E? (25, halfway between 20 and 30) What is the value of point S? (it looks very close to 60, so it is most likely 59, but 58 would also be acceptable) What is the value of point I? (acceptable answers would be 7, 8 or 9) 6. Have students work with a partner to complete #3. Encourage them to discuss the placement of each point with their partner. Circulate to observe and assist. a. When finished, have students place points on the number line on the overhead. Have class use thumbs up for agreement or thumbs down for disagreement then allow the students time to correct any mistakes on their papers. b. Have students check their partner s work to assure correct placement of letters. What word did the letters spell? (INTERVALS) c. Let students discuss what an interval is (the difference in the values used as spacing on the graph). 7. In their math journal or on paper, have students write their own definition for the word interval. a. Instruct them to draw a number line from 0 70 with intervals of 10. b. Have them put points on the number line and name the points with the letters of their first name. c. Under the number line, have them tell what each letter equals. (Example: Pat may have P = 8, A = 22, T = 35.) d. Students may share their name number line with their partner. Choose several students to share their number lines with the class by drawing them on the board. e. Have students share with the class their definition of interval. Accept all reasonable answers. 18

19 Attachment F Bar Graph with Intervals of Two Name Date Directions: Look at the bar graph. Answer the questions. Write number sentences to show how you solved problems. 1. What does this bar graph show? 2. Which type of weather occurred most often? 3. Which type of weather occurred the least? 4. How many partly cloudy days were there in October? 5. How many sunny days were there? 6. How many days were there with no rain? 7. How many more sunny days than rainy days were there? 8. How many fewer cloudy days than partly cloudy days were there? 9. How many days are in October? Does this graph show the same number of days? How do you know? 19

21 Attachment H Bar Graph with Intervals of Ten Name Date Directions: Use the graph to answer the questions. Show all work. 1. What does this bar graph show? 2. Which kind of fast food is the favorite? 3. Which kind of fast food is the least favorite? 4. About how many students liked chicken nuggets the best? 5. About how many more students liked pizza than tacos? 6. About how many fewer students liked tacos than cheeseburgers? 7. About how many students liked cheeseburgers and chicken nuggets? 8. About how many third-graders are shown on this graph? 9. Why do the numbers on the vertical axis all end with 0? 21

22 Attachment I Bar Graph with Intervals of Ten Answer Key Name Date Directions: Use the graph to answer the questions. Show all work. 1. What does this bar graph show? Third-graders favorite fast foods 2. Which kind of fast food is the favorite? Cheeseburgers 3. Which kind of fast food is the least favorite? Submarine sandwich 4. About how many students liked chicken nuggets the best? About how many more students liked pizza than tacos? (21-23) (15-17) = (4-8) students 6. About how many fewer students liked tacos than cheeseburgers? (44-46) (15-17) = (27-31) students 7. About how many students liked cheeseburgers and chicken nuggets? (44-46) + (36-38) = (80-84) students 8. About how many third-graders are shown on this graph? (44-46) + (15-17) + (36-38) + (21-23) + (8-10) = ( ) third-graders 9. Why do the numbers on the vertical axis all end with 0? Because the scale shows intervals of ten, and counting by tens will always end with zeroes. 22

23 Attachment J Blank Grid Name Date 23

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