The River of Life TEACHER NOTES SCIENCE NSPIRED. Science Objectives. Math Objectives. Materials Needed. Vocabulary.
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1 Science Objectives Students will calculate the volume of blood in their own bodies. Students will analyze and quantify some of the components of their blood. Math Objectives Students will use tabular data to accurately generate a scatter plot. Students will generate a linear regression model, use the function to perform calculations, and interpolate a value on the regression model. Materials Needed TI-Nspire or TI-Nspire CAS unit for each student Vocabulary plasma erythrocytes leukocytes milligram microliter About the Lesson This lesson involves generating a linear regression model for human blood volume vs. body weight. As a result, students will: Algebraically calculate their own blood volume. Interpolate on the regression model to determine their blood volume. TI-Nspire Navigator System Screen Capture to monitor student progress. Live presenter allows students to show their graphs to the class. TI-Nspire Technology Skills: Download a TI-Nspire document Open a document Move between pages Entering and graphing data using multiple applications Tracing, interpolating, predicting Tech Tips: Make sure the font size on your TI-Nspire handhelds is set to Medium. You can hide the function entry line by pressing / G. Lesson Materials: Student Activity The_River_of_Life.pdf The_River_of_Life.doc TI-Nspire document The_River_of_Life.tns 2011 Texas Instruments Incorporated 1 education.ti.com
2 Discussion Points and Possible Answers Create a new TI-Nspire document. 1. Add a Lists & Spreadsheets page. 2. Name Column A weight, and Column B pints. 3. In cell A1, enter the number 60, then continue to enter values in this column adding 24 to the previous number until you reach In cell B1, enter the number 5, and increase it by 2 in each succeeding cell until you have reached 25. The weights are in pounds, and the pints are the number of pints of blood in the human body. Double-check to make sure you have the same number of items in each column. 5. According to the data table, what is the relationship between body weight and blood volume? Answer: As body weight increases, blood volume increases. 6. a. What is the change in weight from data point to data point? Answer: 24 pounds b. Is the ΔX the same between each two consecutive x-values? Answer: Yes 7. a. What is the change in blood volume from data point to data point? Answer: 2 pints b. Is the ΔY the same between each two consecutive y-values? Answer: Yes 2011 Texas Instruments Incorporated 2 education.ti.com
3 8. Now, graph the data by inserting a Data & Statistics page. 9. Select weight as the x-value and pint as the y-value. 10. Use this graph to figure out approximately how much blood YOU have in your body. There is more than one way to do this, so play around until you find a method that works for you. Hint: It might be a good idea to have a "best-fit" line on your graph. 11. Next, insert a Graphs page, graph your data again, and figure out a way to determine your blood volume using this page. After you have finished experimenting with weight and blood volume, move on to the questions that accompany this activity. 12. What is the significance of your answers to #10 and #11? Answer: It means the graph will be linear. 13. What is the formula for determining the volume of blood if you know your weight? Answer: Pints = 0.083*weight (y=0.083x) 14. a. Using the regression model (best-fit line) you produced, estimate the volume of blood you have in your body. Answer: Answers will vary. b. How did you make your estimation? Answer: Several methods: putting their weight into the equation and solving for pints; tracing along the regression line; etc. 15. How much blood would there be in a person who had a mass of 75 kg? Hint: there are about 2.2 pounds in one kilogram. Answer: 15.6 pints 16. Estimate the weight in pounds of a person who has 11.5 pints of blood in his body. Answer: 139 pounds 2011 Texas Instruments Incorporated 3 education.ti.com
4 17. How much blood would a 7-pound newborn baby have? Answer: 0.6 pints 18. If this weight/blood volume relationship were true for other animals, too, how many gallons of blood would there be in a horse that had a mass of 500 kg? Answer: 11.4 gallons 19. Estimate the weight of a person who has two gallons of blood in his body. Answer: 193 pounds 20. If you decided to donate blood at the blood bank, you would donate one pint. Using your own weight, calculate the percentage of your blood you would be donating. Answer: Answers will vary. Lower percentage for heavier people. 21 a. If 52% of your blood is water, what is the volume of water circulating in your blood vessels right now? Answer: Answers will vary. b. Which of the two main blood components contains the water? Answer: Plasma 22. Sodium is an abundant ion in the bloodstream. Normally, there are about 2400 milligrams of sodium in one liter of blood. If one liter of blood is about the same volume as two pints of blood, approximately how much sodium do you have flowing through your blood vessels right now? Express your answer in both milligrams and grams. Sample Answers: Answers will vary Texas Instruments Incorporated 4 education.ti.com
5 23. One of the most important functions of the blood is to transport oxygen to all of your cells, and the cells that take care of this for you are called erythrocytes, or red blood cells. Red blood cells are by far the most numerous cells in the blood, averaging about 4.5 x 10 6 cells per microliter (1000 microliter = 1ml; 1000ml = 1L). How many microliters are there in one liter? Using this information, calculate the approximate number of red blood cells you have in your body right now. Sample Answers: Answers will vary 24. Leukocytes, or white blood cells, are another type of blood cell in your body. Human blood contains about 7.0 x 10 3 WBC's per microliter. Calculate the approximate number of leukocytes you have in your body right now. Sample Answers: Answers will vary. 25. White blood cells function mainly in defending you against infections. Explain why the number of white blood cells in a person s body may tend to fluctuate a lot more than the number of red blood cells does. Answer: WBC numbers tend to increase when a person is sick or injured. TI-Nspire Navigator Opportunity: Screen Capture See Note 1 at the end of the lesson. Wrap Up Assessment Formative assessment will consist of questions embedded in the TI-Nspire document. The questions will be graded when the document is retrieved. The Slide Show can be utilized to give students immediate feedback on their assessment. TI-Nspire Navigator Notes Note 1: Screen Capture Screen Capture can be used to monitor student progress Texas Instruments Incorporated 5 education.ti.com
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