Mathematics Lesson Plan Graphing the Demographics

Transcription

1 Mathematics Lesson Plan Graphing the Demographics Created by Angel Greenley Grade 4 Approximate Duration: 120 minutes Stage 1 Desired Results Established Goals: MT Mathematics Standard 6 Benchmark 1: Collect, organize and display data. MT Mathematics Standard 6 Benchmark 2: Construct, read and interpret displays of data, including graphs IEFA: Essential Understanding 1: There is great diversity among the 12 tribal Nations of Montana in their languages, cultures, histories and government. Each Nation has a distinct and unique cultural heritage that contributes to modern Montana. IEFA: Essential Understanding 2: There is great diversity among individual American Indians as identity is developed, defined and redefined by entities, organizations and people. Understandings: Students will understand that Each tribal Nation of Montana has its own unique set of statistics Statistics of tribal Nations vary as widely as demographics of counties around Montana Students will be able to Create graphs (bar graphs, double bar graphs and circle graphs) based on statistics of a particular tribal Nation in Montana Interpret data from the graphs created and use it to analyze that tribal Nation s statistics Determine an appropriate scale and interval for bar and double bar graphs based on the data Essential Questions: To what extent are tribal Nations similar? Different? How do the statistics for the county you live in compare to individual tribal Nations? Students will know The scale and interval that you choose for a particular graph will vary the appearance of that data. Different graphs are used for different purposes. Stage 2 Assessment Evidence Performance Tasks: Completed Bar graph and journal entry, Completed double bar graph and journal entry, Double bar graph assessment sheet Other Evidence: Participation in class discussions. Individual questioning of students. Page 1 of 8 10/23/2008

2 Mathematics Lesson Plan Graphing the Demographics Stage 3 Learning Plan Learning Activities: This is a unit on graphing and can be presented in any order and independent of each other. Bar Graph: Number of Farms Background Information: A bar graph is a graph that uses bars to show data that can be counted. The scale is determined by the range of the data and the size of the graph is dependent upon the intervals chosen. All bar graphs need the following information to be considered correct: Title, Key or Legend, x and y-axes labels as well as accurate data. Begin by accessing prior knowledge of students by asking what a bar graph is and when is it best used. Choose one of the pamphlets for all students to look at. (See Resource Section to access pamphlets). As students look at the pamphlet, discuss the information about the tribal Nation found on page 2. Students will be making a graph of the number of farms on each tribal Nation. Discuss with students first steps to making a graph. The data ranges from 42 farms to 931 farms. We need to decide what our interval for the graph should be. Take suggestions from students, having them justify their response. ( or would both be acceptable). Once students have determined an interval, ask for suggestions concerning the scale of the graph. Have students justify their reasoning for each suggestion. (possible intervals could be 50 or 100). Allow students to choose their own intervals (even if they seem too small to you). During this time, students can revise their intervals based on what their graph looks like. For example, if a student has chosen 10 and starts to build the axis, they will find that it is too small of an interval and can revise it at that point. Discuss the different intervals students have chosen. Ask students if anyone revised their axis once they started and what led to the decision to change it. Next, look at the pamphlet you have been viewing with students. Discuss how to determine the height of each bar based on the intervals chosen. (For example, Rocky Boy has 42 farms if the intervals are 100 apart, students need to understand how to estimate where 42 would be.) Have students draw the bar on the x-axis for the tribal Nation you are working with. Have students put the other names of the tribal Nations along the x-axis and then graph the data of the tribal Nations Look at a different pamphlet and discuss the height of the bar and estimation strategies used. Page 2 of 8 10/23/2008

3 As students are ready, give them information for the rest of the tribal Nations and have them graph the information. Once students have completed their graphs, lead students through a discussion of other things that the bar graph might need to make it complete. (Title, labels on the axes, a legend, etc.) Have students find a partner who had chosen a different interval and discuss the similarities and differences between the graphs. Have students share their graphs with the whole class. Again, ask students what the similarities and differences are between the graphs. How does the interval affect the way the data looks? Is the data still the same information? What are the advantages to having a smaller interval? What are the disadvantages? What are the advantages of having a larger interval? Disadvantages? What if you set your interval at 500, is that a good choice? Why or why not? By looking at the graphs of farms on different tribal Nations, what are some things we can say about the tribal Nations? Why do you think there is such a wide range of number of farms reported for the many tribal Nations? (size of nation; landscape of nation; climate, etc.) Assessment: Have students look at the data for your county and add that information to their bar graph. (Data is on the attached reference sheet). Journal question: How does our county s data regarding number of farms compare to (closest tribal Nation)? Why do you think this is true? Make three factual statements about your bar graph. (For example, Flathead Nation has the greatest amount of farms.) Double Bar Graph: Tribal Members Living on Reservation/Total Tribal Members Background Information: A bar graph that displays two different shaded bars to compare the two sets of data. The scale is determined by the range of the data and intervals are dependent upon the size of the graph. Begin by accessing prior knowledge of students by asking what a double bar graph is and when is it best used. Choose one of the pamphlets for all students to look at. (See Resource Section to access pamphlets). As students look at each pamphlet, discuss the information about each tribal Nation found on page 2. Have students look at the attached data sheet to find the information about number of tribal members living on a reservation and the total tribal members. Students will be making a double bar graph of tribal members living on each reservation vs. total tribal members for each tribal Nation. Discuss with students first steps to making a graph. The data ranges from 3311 Page 3 of 8 10/23/2008

4 people to 12,755 people. We need to decide what our interval for the graph should be. Take suggestions from students, having them justify their response. (0-13,000 or 0 14,000 would both be acceptable). Once students have determined an interval, ask for suggestions concerning the scale of the graph. Have students justify their reasoning for each suggestion. (possible intervals could be 1000 or 2000). Allow students to choose their own intervals (even if they seem too small to you). During this time, students can revise their intervals based on what their graph looks like. For example, if a student has chosen 100 and starts to build the axis, they will find that it is too small of an interval and can revise it at that point. Discuss the different intervals students have chosen. Ask students if anyone revised their axis once they started and what led to the decision to change it. Next, look at the pamphlet you have been viewing with students. Discuss how to determine the height of each bar based on the intervals chosen. (For example, Rocky Boy has 5656 tribal members enrolled if the intervals are 1000 apart, students need to understand how to estimate where 42 would be.) Have students draw the bar for the tribal Nation you are working with. Have students put the other names of the tribal Nations along the x-axis and then graph the data of the tribal Nations. Be sure that students understand how to create a double bar graph. Have students discuss similarities and differences between bar graphs and double bar graphs. Look at a different pamphlet and discuss the height of the bar and estimation strategies used. As students are ready, give them information for the rest of the tribal Nations and have them graph the information. Once students have completed their graphs, have them share with a partner who had a different interval. Have students discuss the similarities and differences between the graphs. Have students share their graphs with the whole class. Again, ask students what the similarities and differences are between the graph. How does the interval affect the way the data looks? Is the data still the same information? What are the advantages to having a smaller interval? What are the disadvantages? What are the advantages of having a larger interval? Disadvantages? What if you set your interval at 50, is that a good choice? Why or why not? By looking at the graphs of tribal members living on the reservation vs. total tribal members of the different tribal Nations, what are some things we can say about the tribal Nations? Why do you think there is such a wide range of number of tribal members reported for the many tribal Nations? Assessment: Students will create a double bar graph based on data given about number of employees for each tribal Nation. Note to Teacher: A rubric for the double bar graph is attached. This can be used for you as to aid in assessing the graph, or can be handed out to students with the assessment sheet so that students have a Page 4 of 8 10/23/2008

5 check list of criteria that they will be assessed on. Materials/Resources Needed: Cm or ½ inch graph paper (several sheets per student) tribal Nation pamphlets These can be obtained by downloading them from and clicking on American Indian Data, then American Indian Reservation Fliers Montana Counties data sheet & Tribal Nations population data sheet (see attached) Coloring instruments Ruler Page 5 of 8 10/23/2008

6 Number of Farms by County Beaverhead Big Horn Blaine Broadwater Carbon Carter Cascade Chouteau Custer Daniels Dawson Deer Lodge Fallon Fergus Flathead Gallatin Garfield Glacier Golden Valley Granite Hill Jefferson Judith Basin Lake Lewis & Clark Liberty Lincoln McCone Madison Meagher Mineral Missoula Musselshell Park Petroleum Phillips Pondera Powder River Powell Prairie Ravalli Richland Roosevelt Rosebud Sanders Sheridan Silver Bow Stillwater Sweet Grass Teton Toole Treasure Valley Wheatland Wibaux Yellowstone Information from National Agriculture Statistics Service Total Populations Blackfeet Rocky Boy Native American Populations Fort Belknap Flathead Fort Peck Crow Northern Cheyenne Tribal Members Living on reservation Total tribal members enrolled 15, ,755 11, Information from Census and Economic Information Center Department of Commerce Page 6 of 8 10/23/2008

7 Name: Look at the following information. You are going to use it to create a double bar graph and answer questions regarding the data. Tribal Nation 2005 Total Employees 2006 Total Employees Blackfeet Crow Flathead Fort Belknap Fort Peck Northern Cheyenne Rocky Boy s ) What is the range of your data? 2) Choose an interval for your graph and write it here. Explain why you chose the above interval for your graph. 3) What interval would not be a good choice? Why not? Now create your double bar graph on a separate piece of paper. When you are finished write three mathematical statements regarding your graph on the lines below. Page 7 of 8 10/23/2008

8 Rubric for Double Bar Graph Student Name: Criteria Point Awarded Comments Title on Graph Key/Legend Appropriate Intervals Bars Labeled with tribal names y-axis labeled x-axis labeled Data graphed accurately for each tribal Nation (7 total points possible) Total (out of 13) ** Each criteria is worth 1 point unless otherwise noted** Student Name: Criteria Point Awarded Comments Title on Graph Key/Legend Appropriate Intervals Bars Labeled with tribal names y-axis labeled x-axis labeled Data graphed accurately for each tribal Nation (7 total points possible) Total (out of 13) ** Each criteria is worth 1 point unless otherwise noted** Page 8 of 8 10/23/2008