Scientific Notation

1. Scientific Notation Unit 1, Concept 6

2. Materials • Scientific Notation POGIL printouts (3 teams work) • Scientific Notation Practice worksheet (1 per student)

3. Key Ideas • Rules of Significant figures • Rules of 0’s • Addition/subtraction • Multiplication/division • CLO: I can do arithmetic operations and report the results to the correct number of significant figures using a POGIL activity and independent practice

4. Do Now • Calculate the density of a silver statue with a mass of 105 g, and a volume of 10 cm3.

5. Do Now • Calculate the density of a silver statue with a mass of 105 g, and a volume of 10 cm3. Density = mass/volume = 105 g/10 cm3 = 10.5 g/cm3

6. Objective • I can do arithmetic operations and report the results to the correct number of significant figures using a POGIL activity and independent practice

7. Homework • Complete the Significant Figures Practice Worksheet. Due Thursday/Friday

8. Agenda • Do Now, Objective (7 min) • Accuracy and Precision (10 min) • Introduction to Significant Figures (10 min) • Team Activity: POGIL (40 min) • Significant Figures Review (15 min) • Exit Ticket (5 min)

9. Agenda • Do Now, Objective (7 min) • Accuracy and Precision (10 min) • Introduction to Significant Figures • Team Activity: POGIL • Significant Figures Review • Exit Ticket

10. Accuracy vs. Precision • Accuracy refers to how close a measured value is to the true value.  are you correct? • Precision refers to how close a series of measurements are to one another.  are your measurements the same every time?

11. Accuracy vs. Precision

12. Precise Instrumentation Less Precise More precise

13. What makes one piece of lab equipment more precise than another? • A piece of lab equipment is more precise than another if it has smaller increments (spaces between numbers) (Ex: A graduated cylinder with 0.5 mL increments is more precise than a graduated cylinder with 1 mL increments)

14. What makes one measurement of more precise than another? • A value with more digits (#’s) is more precise. (3.52 is more precise than 3.5)

15. Accuracy and precision: the target example Accurate and precise

16. Accuracy and precision: the target example Precise, but not accurate

17. Accuracy and precision: the target example Neither accurate, nor precise

18. Accuracy and precision: the target example Accurate, but not precise

19. Agenda • Do Now, Objective (7 min) • Accuracy and Precision • Introduction to Significant Figures (10 min) • Team Activity: POGIL • Significant Figures Review • Exit Ticket

20. Uncertainty and Significant Figures • Every measurement is an estimate of the actual value because every measurement contains a degree of uncertainty or error. • Error does not mean “mistake”. • Error (uncertainty) is the variance between individual measurements that happens when repeated measurements are made on the same sample or object.

21. Uncertainty • Example:four students weighed a dime ($0.10) multiple times using different types of balances. The measurements in Set I contain two digits. The first digit (the one’s place) is called the reproducible digit and the second digit in the tenth’s place (0.1) is called the doubtful digit.

22. Agenda • Do Now, Objective (7 min) • Accuracy and Precision • Introduction to Significant Figures • Partner Activity: POGIL (40 min) • Significant Figures Review • Exit Ticket

23. Introduction to POGIL • Today we will be doing our first POGIL activity • You will be working in groups of 3 to facilitate your own learning around significant figures • In a POGIL activity, you will look at data to come to your own understanding of a concept • You and your group members will figure out the answers for yourselves, and be able to explain it to Ms. B!

24. POGIL • POGIL Group Roles • Reader: you will read all information aloud • Facilitator: you will lead your group in discussion for each question/task • Recorder: you will write down all important information, and answers to questions

25. POGIL: Significant Figures • Complete parts B, C, and D of your POGIL activity sheet • By the end of this activity you will understand • Uncertainty • Significant Figures • Rounding with Sig Figs • Calculations with Sig Figs

26. Part B - Uncertainty • An increase in precision DECREASES uncertainty

27. Part C – Significant Figures • Non-zero numbers are ALWAYS significant • Rules of Zeros • Zeros between non-zeros are ALWAYS significant • Zeros in the coefficient of scientific notation are ALWAYS significant • Zeros after a decimal point are ALWAYS significant • Trailing 0’s are not significant • Leading 0’s are not significant

28. Part D – Rounding & Calculations with Significant Figures

29. Rules of Significant Figures • When multiplying/dividing measurements, the answer must contain the same number of Sig Figs as the measurement with the least Sig Figs 108.4 mi/3.5 gal = 30.97142857 mpg = 31 mpg

30. Rules of Significant Figures • When adding/subtracting measurements, the answer must contain the same number of decimal places as the starting measurement with the least amount of decimal places. 7.6 mL + 125 mL = 132.6 mL = 133 mL

31. Agenda • Do Now, Objective (7 min) • Accuracy and Precision • Introduction to Significant Figures • Partner Activity: POGIL • Significant Figures Review • Exit Ticket (5 min)

32. Exit Ticket • Complete the Exit Ticket at your desk, and hand it to Ms. Bergman as you leave class. • NO calculators!

33. 45 Minute Version of Lesson • No POGIL

34. Materials • Scientific Notation Practice worksheet (1 per student) • Exit Ticket (1 per student)

35. Key Ideas • Rules of Significant figures • Rules of 0’s • Addition/subtraction • Multiplication/division • CLO: I can do arithmetic operations and report the results to the correct number of significant figures using a notes and independent practice

36. Do Now • Calculate the density of a silver statue with a mass of 105 g, and a volume of 10 cm3.

37. Do Now • Calculate the density of a silver statue with a mass of 105 g, and a volume of 10 cm3. Density = mass/volume = 105 g/10 cm3 = 10.5 g/cm3

38. Objective • I can do arithmetic operations and report the results to the correct number of significant figures using notes andindependent practice

39. Homework • Complete the Significant Figures Practice Worksheet. Due Thursday/Friday

40. Agenda • Do Now, Objective (7 min) • Accuracy and Precision (7min) • Uncertainty (5 min) • Significant Figures (10 min) • Independent Practice (10 min) • Exit Ticket (3 min)

41. Accuracy vs. Precision • Accuracy refers to how close a measured value is to the true value • Precision refers to how close a series of measurements are to one another.

42. Accuracy vs. Precision

43. Accuracy and precision: the target example Accurate and precise

44. Accuracy and precision: the target example Precise, but not accurate

45. Accuracy and precision: the target example Neither accurate, nor precise

46. Accuracy and precision: the target example Accurate, but not precise

47. Precise Instrumentation Less Precise • lab equipment is more precise when it has smaller increments (spaces between numbers) More precise (Ex: A graduated cylinder with 1mL increments is more precise than a graduated cylinder with 10 mL increments)

48. Precise Measurements • Numbers with more digits (places) aremore precise. • 3.52 is more precise than 3.5 • 2.14 is more precise than 2.1

49. Agenda • Do Now, Objective (7 min) • Accuracy and Precision (7min) • Uncertainty (5 min) • Significant Figures (10 min) • Independent Practice (10 min) • Exit Ticket (3 min)

50. Uncertainty and Significant Figures • Measurements have uncertainty because you never know the EXACT value • Uncertainty is the variance between individual measurements that happens when repeated measurements are made on the same sample or object.