SHARECROPPING MATH PROJECT 5 th Grade 5 to 7 day unit

Transcription

1 SHARECROPPING MATH PROJECT 5 th Grade 5 to 7 day unit Georgia Content Standards M5N3. Students will further develop their understanding of the meaning of multiplication and division with decimal fractions and use them. a. Model multiplication and division of decimal fractions by another decimal fraction. b. Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimal fractions. c. Multiply and divide with decimal fractions including decimal fractions less than one and greater than one. d. Understand the relationships and rules for multiplication and division of whole numbers also apply to decimal fractions. M5N5. Students will understand the meaning of percentage. b. Apply percentage to circle graphs. M5M1. Students will extend their understanding of area of fundamental geometric plane figures. f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes. M5D2. Students will collect, organize, and display data using the most appropriate graph. M5P1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving. M5P4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.

2 M5P5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena. Objectives - Students will simulate the process of sharecropping over a four-year period. - Students will understand the amount of land an acre represents. - Students will calculate the area and perimeter, in square feet, of land plots measured in acres. - Students will multiply and divide using decimal numbers. - Students will calculate a percentage of a given whole and represent this as both a percentage and a fraction. - Students will create pie charts and represent portions of the charts as both fractions and percentages. - Students will create bar graphs that show change in quantity over time. - Students will identify the difficulties of life as a sharecropper. - Students will identify the benefits of sharecropping to plantation owners. - Students will calculate interest as a percentage and understand how interest charged on balances due adds to the balance itself and grows over time. Essential Questions - What is the process of sharecropping? - How much land is an acre? - Why is land measured in acres? - What did a sharecropping contract look like and entail? - How did plantation owners benefit from sharecropping? - Why was it difficult for many sharecroppers to get out of debt? - How is interest calculated? - How are percentages of a whole calculated? - How is a pie chart created and interpreted? - How is a bar graph created and interpreted? - How is a double bar graph created and interpreted?

3 Materials - Four Sharecropper Land Grids for each sharecropper - One set of Supply Order Forms ( ) for each sharecropper - One Sharecropping Contract for each sharecropper - One Sharecropping Account sheet for each sharecropper - One Land Use Data sheet for each student - One Plantation Owner Accounting sheet for each plantation owner - One Plantation Owner Land Grid (2 pgs) for each plantation owner - Sample Supply Order Form to show students - Sample Sharecropper Land Grid to show students - Sample Graphs to show students Lessons Day 1 Divide students into groups of 4 6. Make sure that each group has at least one student who is particularly strong. This student will be the plantation owner. If time allows, have each student create a fictitious family. They can be former slaves looking for a way to get by or poor white farmers whose livelihoods were destroyed during the Civil War. Once students are in their simulation groups, explain the sequence of the simulation and what will be required of them. Show students examples of graphed land, a completed supplies form, and the bar and pie graphs they will be creating. Make sure students are aware that they will be required to present their project on the last day of the simulation. Give the plantation owner in each group one sharecropping contract for each future sharecropper on his/her plantation. Instruct the plantation owner to decide on a name for his/her plantation (fill this in on each sharecropper contract) and an amount of land to lease to each of the sharecroppers. The PO may choose.11,.12,.13,.14, or.15 of the total 250 acres (for amounts of 27.5, 30, 32.5, 35, and 37.5 acres, respectively). This decision may be based on the number of family members each sharecropper has if this has been determined, with larger families receiving more land because they have more hands to work it. Each sharecropper should receive a different amount of land. After the PO has written the appropriate decimal amounts on the sharecropping contracts and given one to each group member, the contracts need to be completed with both the sharecroppers and PO s names and signatures in the appropriate blanks. All signed contracts will be held by the plantation owner. If a sharecropper wishes to see the contract later on, s/he must ask the plantation owner for it. (Plantation

4 owners should be given a folder in which to keep these contracts. This folder will stay in the classroom to prevent it from being lost or damaged.) Once all contracts are signed, each sharecropper should calculate his given portion of land. Explain to students that an acre is a measure of land area and is equivalent to 43,560 square feet. It can take any shape, but for this project students should stick with polygonal shapes for their land. Give each student the created sharecropper land grid or a sheet of enlarged graph paper (with at least 40 squares) on which to draw their land allotment. Instruct sharecroppers to use pencil to create a bird s-eye view of their land plot, which already includes a small house (1/4 acre). Students who include a garden for growing vegetables should make the garden ¼ of an acre. Give each plantation owner the two-page plantation owner land grid, which contains 250 squares, and instruct them to draw in the land plots of their sharecroppers. After students have done so, instruct sharecroppers to divide up their farmable land into subplots for grazing (1 acre per work mule), corn, and cotton. Students may decide to raise all cotton, all corn, or divide their land up in any way they wish. Plantation owners should copy the land distribution of their sharecroppers on the plantation plot map. Next, all students should calculate the area and perimeter of their plots in feet; plantation owners will be calculating the area and perimeter of their plantations, as well as those of their sharecroppers plots (to check them ). A square-shaped acre of land is approximately feet long on each side. After calculating the total area and perimeter, both sharecroppers and landowners need to calculate the area and perimeter of the subplots for grazing, cotton, and/or corn. Plantation owners should add these together to calculate the total square footage that is being used for each purpose and record these numbers on their data sheet. Finally, students should calculate the percentage of area that is being used for grazing, cotton, and/or corn, respectively, by writing the proportion in fraction form (acres of corn over total acreage, etc.) and then dividing to obtain a decimal. Acres are easier to start with, but students could also calculate this using square feet in order to show that the percentage is the same either way. Rather than doing these calculations for each sharecropper, plantation owners instead calculate the percentages of land being used for each sharecropper and for the PO s own purposes. Students need to retain all of these figures in their land use data sheets for later use in creating graphs. Day 2 Students will begin their first year of sharecropping by purchasing the clothing, seeds, and food they will need for the year using the Supply Order Form for Cottonseed and

5 corn kernels for planting have been priced per dozen acres. Make sure students note that they will need to compute the price per acre and then multiply it by the number of acres they will plant. They may choose to either plant a vegetable garden or buy vegetables, buy a cow (and sacrifice an extra ½ acre of land to grazing) or buy milk, butter, and cheese, etc. They must either rent work mules and a plow or purchase them. Renting is cheaper up-front, but purchasing them outright means paying $375 less for each of the next three years. Sharecroppers may or may not choose to buy meat or vegetables. However, make sure students are aware that not feeding their families properly will result in malnourishment and could lead to other negative consequences. After sharecroppers have determined their needs for the year and calculated their total purchase, they need to check this number with the plantation owner for reasonableness. If the plantation owner agrees, the sharecropper will then subtract any amount that she can pay in cash from the total and write this on the appropriate line. Next, both the PO and the sharecropper will calculate the 11% interest due on any amount bought on credit and add this to the supplies amount to determine the total due at the beginning of the next year. The PO needs to keep this supplies sheet and record the appropriate amounts on his accounting form. After buying the necessary supplies, the sharecropper farms and harvests. During the first year, no unusually good or bad events happen. Students should harvest their crops using the average of 1.5 bales of cotton per acre and 27.1 bushels of corn per acre. They then have to calculate their total earnings by translating 1.5 bales of cotton per acre to pounds of cotton (1 bale is 500 lbs.) and calculating a price of $0.09 per lb. Corn is sold for $0.43 per bushel. Students who harvest cotton need to remember that the sharecropper contract stipulates a $4 charge for ginning each cotton bale and deduct this amount from their earnings. After tabulating their earnings, sharecroppers will ask the plantation owner to calculate his 47% cut of the harvest and will check his calculation for reasonableness. After deducting this amount, sharecroppers will need to pay the PO back for his initial $475 loan (or as much of it as possible) before repeating this process for the second year, Before starting 1877, students have the opportunity to change the percentages of land they are using for corn and cotton and should draw and calculate this on a new sheet of grid paper. Ask all sharecroppers to raise their hands when they have completed the second year and are ready to buy supplies for After two years of hard work, every sharecropper will receive a random good or bad event that will affect them the next year. These range from drought, locusts, and sickness in the family to an excellent harvest, beneficial find in the field, or inheritance. At this point, look over the sharecropper s supply sheet from the previous years and note if he bought an adequate supply and variety of food. If not, the sharecropper must

6 draw from a selection of negative events that all result in sickness or death in his family. If the sharecropper is not at fault, he may draw from the random selection of events. Sharecroppers who finish the years 1876 and 1877 on Day 2 should continue to While they are waiting for sharecroppers to do calculations, plantation owners can begin creating pie graphs that show their total land distribution for each year (corn/cotton/grazing/other/unused) and/or a pie graph for each year that shows the percentage (and fractional equivalent) of income earned from each sharecropper. Day 3 Sharecroppers should continue to farm and harvest during the years 1877 and 1878, completing the four year cycle. Any students who finish earlier than their peers should begin creating a pie graph for each year showing how their plot of land is split up in both percentages and fractions. Students who finish that task can begin creating a pie graph for each year that shows the distribution of their income between cotton and corn, again in both percentages and fractions. Plantation owners will make a double bar graph for each sharecropper showing the money earned from each sharecropper each year, separated into bars for corn and cotton. Day 4 All students should be finished or nearly finished with the four-year harvest cycle. Students who are not yet finished should continue working but leave at least half the class to work on their graphs; students who have finished the graphs noted in Day 3 should proceed to making bar graphs showing their corn and cotton yields over the 4-year period (in bushels and lbs, respectively). Students who still finish early can extend their learning by creating a double bar graph that shows the amount of money they earned each year from both corn and cotton (each in a separate bar) and/or a line graph showing their income (or debt) over the four years. Plantation owners should finish their double bar graphs and make a single bar graph showing the total income earned from sharecroppers for each of the four years. Plantation owners who finish early can also create a line graph showing their income over the four year period. If there is still extra time, they should help students in their group. Day 5 Students will finalize and quickly present their work. All papers and graphs should be stapled together into a booklet form or contained neatly in a folder. Sharecroppers will submit the following as their final product: - Gridded map of land plot, complete with measurements in acres and feet and clearly showing the initial division of land for cotton, corn, grazing, and other purposes. - Completed Land Use Data Sheet - Supply Order Forms for each year

7 - Sharecropping Account table - All calculations performed during the simulation - Any new maps created by changing the use of land, including new calculations of square footage - Pie chart for each year showing the distribution of land as a percentage and fraction - Pie chart for each year showing the income earned from cotton and corn as a percentage and fraction - Two bar graphs covering all four years, each showing the yield of either corn or cotton - Optional: double bar graph showing corn and cotton income for each year over the four year period and/or line graph showing total income/debt over the four year period Plantation Owners will submit the following as their final product: - Gridded map of plantation, complete with measurements in acres and feet and clearly showing the initial division of land for cotton, corn, grazing, and other purposes. - Completed Plantation Owner Accounting Sheet - All sharecropper contracts - All calculations performed during the simulation - Pie chart for each year showing the distribution of land as a percentage and fraction - Pie chart for each year showing the income earned each sharecropper as a percentage and fraction - Bar graph showing total income earned from all four sharecroppers each year - Double bar graph for each sharecropper showing corn vs. cotton income for each year - Optional: line graph showing total income over time Assessment - Informal formative assessment of student work on a day-to-day basis - Project graded as a summative assessment according to rubric for completion, accuracy, and effort