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C: 22 September 2011. Take Out Homework : W eek 3 #1-5 and Lab Report Objective : You will be able to: differentiate between accurate and precise measurements determine the number of significant figures in any value

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C: 22 September 2011

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C: 22 September 2011

  • Take Out Homework: W eek 3 #1-5 and Lab Report

  • Objective: You will be able to:

    • differentiate between accurate and precise measurements

    • determine the number of significant figures in any value

  • Do now: Calculate the mass of a pure copper penny (density = 8.92 g/cm3) with a volume of 0.20 cm3.


Agenda

  • Do now

  • Track objective mastery

  • Go over homework

  • Accuracy vs. precision notes and examples

  • Practice problems

  • Significant figures rules and examples

  • Clicker practice problems

    Homework: Week 3 Homework #6-10: Fri.


Track Objective Mastery

  • Objective 8 (Density) Exit Ticket

  • Unit 1 Pretest B Objectives 5-12

  • Where have you improved most?!


Density Exit Ticket

II. b. Calculate the volume of a piece of gold (density = 19.32 g/cm3) that has a mass of 5.00 grams.


Expectations

  • During notes and example problems: silently write them into your notebook

    • Raise your hand to ask questions or make comments


Reading a graduated cylinder


Precision and Accuracy

  • precision: how close a series of measurements are to each other.

  • accuracy: how close a series of measurements are to the actual or true value.


Volume of a sample of water(Actual volume: 5 mL)

  • 2.0 mL, 2.1 mL, 1.9 mL

  • 4.0 mL, 5.0 mL, 6.0 mL

  • 1.2 mL, 5.5 mL, 10.6 mL

  • 4.9 mL, 5.0 mL, 5.0 mL


Mass of copper cylinder (g)

Three students made multiple weighings of a copper cylinder, each using a different balance. The correct mass of the cylinder had previously been determined to be 47.32 grams. Comment on the accuracy and precision of each student’s measurements.


  • Comment on the accuracy and precision of these basketball free-throw shooters:

    • a. 99 of 100 shots are made

    • b. 99 of 100 shots hit the front of the rim and bounce off

    • c. 33 of 100 shots are made, the rest miss.

SWBAT determine the precision and accuracy of data.


On Your Own

  • How are accuracy and precision similar?

  • How are accuracy and precision different?

  • Give an example of a data set that is very precise but not accurate. (Hint: You’ll have to write down the “real” answer, too.)


Percent Error: a measurement of how accurate your data are

  • So, if the actual value is 5.0 grams, but your average mass was 4.6 grams, what is your percent error?

  • What if your average volume was 25.0 mL, but the actual value is 23.9?


  • An engineer was responsible for calculating amount of water that overflowed from a dam. He measured all of the water runoff going into the reservoir (1.2 million cubic feet per year), the rainfall (860 cubic feet per year), and the capacity of the reservoir (3.8 million cubic feet). He did some fancy calculations. He reported to his boss that the overflow from the dam would be 350,246.2544330 cubic feet per year.

  • What’s wrong here?


Significant Figures

  • How to determine how accurate a number is

  • How to determine how much to round an answer


I. Significant Figuresaka: Significant Digits

  • A. Nonzero integers count as significant figures

    • Ex. Any number that is NOT zero (1, 2, 3, 4, 5, 6, 7, 8, 9)

    • 345

    • 597.2

    • 145.456

SWBAT identify and round a number to the correct number of significant figures.


  • Zeros

    • B. Leading zeros that come before all the nonzero digits do NOT count as significant figures

    • Ex: 0.0025 has two sig. fig. The zeros are “leading” and do not count.

    • 0.23

    • 0.0004

    • 0.03564

SWBAT identify and round a number to the correct number of significant figures.


  • C. Captive zeros are between nonzero digits and DO count as sig. fig.

  • Ex: 1.008 has four sig. fig. The zeros are captive and DO count.

  • 10,004

  • 1.000006

  • 1,000,000,000,000,567

SWBAT identify and round a number to the correct number of significant figures.


  • D. Trailing zeros are to the right end of the number and DO count as sig. fig. if the number contains a decimal point.

  • Ex.: 100 has only one sig. fig. because the trailing zeros DO NOT have a decimal point.

  • Example: 1.00 has three sig. fig. because the trailing zeros DO have a decimal point.

SWBAT identify and round a number to the correct number of significant figures.


More practice: Trailing zeros

  • 1.000000

  • 3,000,000

  • 3.00000

  • 30.00

  • 300

  • 300.


  • E. Exact numbers

    • Any number found by counting has an infinite number of significant figures.

    • Ex: I have 3 apples. The 3 has an infinite number of significant figures.

    • 50 people

    • 100 baseballs

SWBAT identify and round a number to the correct number of significant figures.


Which are exact numbers?

  • The elevation of Breckenridge, Colorado is 9600 feet.

  • There are 12 eggs in a dozen.

  • One yard is equal to 0.9144 meters.

  • The attendance at a football game was 52,806 people.

  • The budget deficit of the US government in 1990 was $269 billion.

  • The beaker held 25.6 mL of water.

SWBAT identify and round a number to the correct number of significant figures.


Clicker Use

  • Always pick up and use only your assigned clicker: You are responsible for it!

  • Remain silent while the question is being read and while you answer – only answer for yourself!

  • Never laugh at, mock or ridicule the proportion of students answering incorrectly.

  • Listen carefully as the answer is explained.


How many significant figures? 256

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 647.9

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 647.0

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 321.00

  • 2

  • 3

  • 4

  • 5

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 4005

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? nine

  • 1

  • 2

  • 3

  • infinite

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 200.

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 200.0

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 0.009009

  • 2

  • 4

  • 6

  • 7

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? -500

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? -500.

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures? 1.3x1032

  • 1

  • 2

  • 3

  • 4

SWBAT identify and round a number to the correct number of significant figures.


How many significant figures?

  • A student’s extraction procedure yields 0.0105 g of caffeine.

  • A chemist records a mass of 0.050080 g in an analysis.

  • In an experiment, a span of time is determined to be 8.050 x 10-3 s.

  • Rewrite 8.050 x 10-3 so it has three significant figures.

SWBAT identify and round a number to the correct number of significant figures.


Assignment

  • In your lab notebook, find the density stations from yesterday.

  • Next to each value you measured, write the number of significant figures in a circle.

    • Ex: 12.35 cm 4


Exit Ticket


Homework

  • Week 3 Homework #6-10: Fri.


C: 23 September 2011

Rounding

Take Out Homework: Week 3 Homework #1-10

  • Objective: You will be able to:

    • round values to the correct number of significant figures

  • Do now: How many significant figures?

    • a. 0.00045

    • b. 0.00040

    • c. 0.0004050


Agenda

  • Do now

  • Go over homework

  • Accuracy/Precision, Sig. Fig. “Exit” Ticket

  • Rounding Notes and Examples

  • Practice Problems

  • Exit Ticket

    Homework: Week 3 Homework #11-14: Mon.


“Exit” Ticket

  • Precision/Accuracy

  • Sig. Fig.


Rounding

  • The answer to a calculation can not be any more accurate than the least accurate value in that calculation.

  • When multiplying or dividing, round to the least number of significant figures given in the problem.


Example 1

  • An iron block with side lengths 10.5 cm by 22.6 cm by 2.5 cm has a mass of 4655 grams. Calculate the density of iron.


Example 2

  • The density of mercury is 13.53 g/cm3. Calculate the volume taken up by 5.0 grams of mercury.


Problems

  • Calculate the mass of a cube of silver with side length 5.0 cm. Silver has a density of 10.49 g/cm3.

  • Calculate the density of a stack of gold coins with mass 1100 grams and volume of 51.76 cm3.


Exit Ticket

  • Rounding


Homework

  • Week 3 Homework #11-14: Monday


C: 28 September 2011

  • Objective: You will be able to:

    • round a calculation to the correct number of sig. fig.

    • plan a procedure and data table for a lab on the density of pennies

  • Do now: Round to TWO sig. fig:

    a. 0.003563725

    b. 5,723


Agenda

  • Do now

  • Tracking Objectives – Rounding

  • Rounding Worksheet

  • Pennies lab: Plan procedure

  • Design a data table

    Homework: Quiz Friday: Objectives 8-11


Tracking Objectives

  • Rounding Exit Ticket: Objective 11


Rounding Practice (10 min.)

  • Quietly, on your own

  • If you have a question, you may consult your partner or raise your hand to ask me a question.

  • When you are done, have me check your work.

  • Then, complete the exit ticket on your own.


With your lab group (20 min.)

  • In your notebook:

    • Copy the research questions

    • Make two hypotheses (one for each research question)

  • On the poster paper as a group:

    • Write your complete and detailed procedure


Gallery Walk (8 min.)

  • With a marker, read another group’s procedure.

  • Make constructive comments in writing

    • “How big is the graduated cylinder?”

    • “I like how you were specific about what to change in each trial!”

  • Then, visit another group’s poster and do the same thing.


Together:

  • Construct the procedure we will all follow from the best elements of everyone’s group posters.


As a lab group

  • Design your data table for next class!


Homework

  • Quiz Friday: Objectives 8-11

  • Finish Procedure


A: 27 September 2011

  • Objective: You will be able to:

    • determine the relationship between mass and volume of pennies.

    • compare the density of pre- and post-1982 pennies.

  • Do now: Round to THREE sig. fig:

    a. 0.003549248

    b. 356,908,256


Agenda

  • Do now

  • Tracking Objectives

  • Carry out your procedure and collect data!

  • Finish calculations

    Homework: Finish Unit 1 Pretest B: tomorrow

    Be sure all your density calculations are done.

    Objectives 8 through 11 quiz tomorrow


Track Quiz and Exit Ticket

  • Did you get less than a 3 or 4 on Objectives 1 through 4?

    • Come for extra help after school!

    • Re-take a quiz on that objective after school or next time we have a quiz.

    • Your goal is to earn a 3 or a 4 for EVERY objective!!


Carry out your procedure

  • Split up the work to be most efficient.

  • Work carefully.

  • Estimate the last digit on the graduated cylinder.

  • Neatly record your data in a table in your notebook.

  • Make sure your station looks as neat when you are finished as it did when you started!


Equipment

  • 250 mL beaker

  • vinegar

  • 100 mL graduated cylinder

  • electronic balance

  • water


Homework

Be sure all your density calculations are done.

Objectives 8-11 Quiz Thursday (study exit tickets!)

We’ll finish this lab tomorrow!


C: 30 September 2011

  • Objective: You will be able to:

    • show what you know about objectives 8-11.

  • Do now:

    • Look at your tracking sheet Quiz grades for objectives 1-4. Write down the number of any objectives you have not yet earned a 3 or 4 on.


Agenda

  • Do now

  • Track Rounding (Obj. 11) exit ticket 2

  • Objectives 8-11 Quiz!

  • Make up Objectives 1-4 Quizzes

  • Work on lab graph, analysis and conclusion

    Homework: Week 4 Homework p. 1: Mon.

    Lab graph, analysis and conclusion: due Monday


Properties

  • Intensive: the property does NOT depend on the amount of stuff you have

    • ex: temperature

  • Extensive: the property DOES depend on the amount of stuff you have

    • ex: mass

  • Use your data to determine if density is an intensive property or an extensive property!


Track Rounding (Obj. 11)

  • You can erase/cross out your first exit ticket score if you earned a higher score!


When you finish your quiz…

  • Raise your hand and tell me if you need to retake any objective 1-4 quizzes.

  • Once you are done with quizzes, work on graphing your data, writing an analysis and conclusion

    • Look at the lab handout for all the details!

    • Work on this silently until everyone is done with their quizzes.


Need help on the lab?

  • Need extra help before you retake a quiz?

  • Work with me after school Monday!


Homework

  • Lab notebook: Monday

  • Week 4 Homework p. 1: Mon.


C: 29 September 2011

  • Homework: Density of Pennies Procedure

  • Objective: You will be able to:

    • determine the relationship between mass and volume of pennies and compare density

    • Convert between scientific and regular notation.

  • Do now: Read through your procedure. Write down one question you have about it to share with your lab group.


Agenda

  • Do now

  • Carry out your procedure and collect data!

  • Finish calculations and graph data

  • Graph Data

  • Scientific notation notes and practice

    Homework: Week 4 Homework page 1: Mon.

    Pennies lab analysis and conclusion: Monday

    Objectives 8 through 11 quiz tomorrow


By 9:15…

  • Collect your data and organize it into the nicest table you have ever made

    • See the lab handout for more details.

  • Graph both data sets on one set of axes – this should be the nicest graph you have ever made

    • See the lab handout for more details.

  • Complete the analysis and conclusion in your lab notebook.


Scientific Notation


Homework

Pennies lab analysis and conclusion: Friday

Objectives 8 through 11 quiz tomorrow


  • The sample of gold contained 1,200,000,000,000,000,000,000,000,000 atoms.

  • How do we keep track of ALL those zeros?

  • In chemistry, some numbers are HUGE!


III. Rules for Sig. Fig. in Mathematical Operations

  • A. Multiplication and Division

    • The number of sig. fig. in the results should be the same as the number of sig. fig. in the least precise measurement used in the calculation.

    • Example: 4.56 x 1.4 = 6.38  6.4


  • B. Addition and Subtraction

    • The result should have the same number of decimal places as the least precise measurement used in the calculation.

    • Example: 12.11 + 18.0 + 1.013 = 31.123  31.1 (one decimal place)


  • 13 x 1.000 = 13.000 =

  • 23.45 x 400 = 9380 =

  • 5000 / 3.12 = 1602.56410256…


  • 14 + 3.567 = 17.567

  • 56.2 + 23.988 = 80.188

  • 100 – 1.9995 = 98.0005


IV. Rounding

  • Calculate first, then round

  • Example: round 4.348 to two sig. fig.

    • 4.3

    • Never round until your final answer!


Converting between SI units

  • notes from the board

SWBAT convert between units in the SI system.


SI Unit Prefixes


Steps to Conversions

  • Identify and write your known and unknown.

  • Choose an equality.

  • Make a fraction

  • Put units to cancel on the bottom

  • Put units to remain on the top

  • Cancel units and compute

  • Report answer with units!


Practice Problems

  • 1 liter = 1000 milliliters

  • How many liters are equal to 550 milliliters?

  • How many milliliters are equal to 3.5 liters?

  • How many liters are equal to 45,000 milliliters?

  • How many milliliters are equal to 354 liters?

SWBAT convert between units in the SI system.


  • 1 meter = 100 cm, 1 kilometer = 1000 meters

  • How many meters are equal to 500 centimeters?

  • How many centimeters are equal to 850 meters?

  • How many meters are equal to 37.5 kilometers?

  • How many centimeters are equal to 5.8 kilometers?

SWBAT convert between units in the SI system.


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