# Unit 1: Nature Of Science UNIT 1: NATURE OF SCIENCE Chapter 1.3: Measurement, pg 14-20 Chapter 1.4: Presenting Scientific Data, pg 22-25 Chapter 1.2: Using a Scientific Approach, pg 7-11 Progression of Objectives 1 & 2 Accuracy and Precision Random and Systematic Errors Significant figures Counting sig figs Calculating with sig figs Measurement Base Units

Prefixes Writing measurement Number Uncertainty Units Nature of Science Pure science aims to come to a common understanding of the universe Scientists suspend judgment until they have a good reason to believe a claim to be true or false Evidence can be obtained by observation or

experimentation Observations followed by analysis and deductioninference(pic) Experimentation in a controlled environment Observations vs. Inferences 1 Observations vs. Inferences 2 Observations vs. Inferences 3 Purpose of Evidence Evidence is used to develop theories, generalize data to

form laws, and propose hypotheses. Theory well-tested explanation of things or events based on knowledge gained from many observations and investigations Can theories change? What about if you get the same results over and over? Law a statement about what happens in nature and that seems to be true all the time Tell you what will happen, but dont always explain why or how something happens Hypothesis explanatory statement that could be true or false, and suggests a relationship between two factors. Talk about these images in terms of precision and

accuracy. When collecting evidence or data Which is more important: accuracy or precision? Why?? Define both terms. Sketch four archery targets and label: High precision, High accuracy High precision, Low accuracy Low precision, High accuracy Low precision, Low accuracy Percent Error - Accuracy The percent error is used when comparing the final measured

value to a well-accepted or well-known value. The percent error is defined as: Once the percent error or percent difference is known, the error analysis may proceed. Error analysis is the description of why two measured quantities differ. Usually, this discussion is about a final measured value and why it differs from a well-accepted or known value. Two main contributors factor into accounting for the discrepancy between the final measured value and the known value these are accuracy and precision. Standard Deviation - Precision Used to tell how far on average any data

point is from the mean. The smaller the standard deviation, the closer the scores are on average to the mean. When the standard deviation is large, the scores are more widely spread out on average from the mean. When thinking about the dispersal of measurements, what term comes to mind? Std Dev Link The bell curve which represents a normal distribution of data shows what standard deviation represents.

( ) One standard deviation away from the mean in either direction on the horizontal axis accounts for around 68 percent of the data. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations representing about 99 percent of the Find Standard Deviation 2 (

x ) n Find the variance. a) Find the mean of the data. b) Subtract the mean from each value. c) Square each deviation of the mean.

d) Find the sum of the squares. e) Divide the total by the number of items. Take the square root of the variance. Recording the COMPLETE Measurement 1. Measurement a. Write what you know b. Include degree of freedom 2. Uncertainty (random error) a. Half of the smallest division on the scale b. Determined by the measuring device 3. Units

a. Use metric unless otherwise instructed b. Common SI units: meters, liters, grams 1. The Measurement When you report a number as a measurement, the number of digits and the number of decimal places tell you how exact the measurement is. What is the difference between 121 and 121.5?

The total number of digits and decimal places tell you how precise a tool was used to make the measurement. 1. The Number: Degree of Freedom Record what you know for sure Guess or estimate your degree of freedom (your last digit) 1. The Measurement: DOF cont. 1. The Measurement: DOF cont.

2. The Uncertainty No measure is ever exact due to errors in instrumentation and measuring skills. Therefore, all measurements have inherent uncertainty that must be recorded. Two types of errors: 1. Random errors: Precision (errors inherent in apparatus) a. Cannot be avoided b. Predictable and recorded as the uncertainty c. Half of the smallest division on a scale 2. Systematic errors: Accuracy (errors due to incorrect use of equipment or poor experimental design) a. Personal errors reduced by being prepared

b. Instrumental errors eliminated by calibration c. Method errors reduced by controlling more variables Precision vs. Accuracy Precision based on the measuring device Accuracy based on how well the device is calibrated and/or used How big is the beetle? Measure between the head and the tail! Between 1.5 and 1.6 in

Measured length: 1.54 +/- .05 in The 1 and 5 are known with certainty The last digit (4) is estimated between the two nearest fine division marks. Copyright 1997-2005 by Fred Senese How big is the penny? Measure the diameter. Between 1.9 and 2.0 cm Estimate the last digit.

What diameter do you measure? How does that compare to your classmates? Copyright 1997-2005 by Fred Senese Is any measurement EXACT? 3. Units - Systems of Measurement We collect data two ways: Quantitative and Qualitative

Why do we need a standardized system of measurement? Video Link Scientific community is global. An international language of measurement allows scientists to share, interpret, and compare experimental findings with other scientists, regardless of nationality or language barriers. 3. Units - Metric System & SI The first standardized system of measurement: the Metric system

Developed in France in 1791 Named based on French word for measure based on the decimal (powers of 10) Systeme International d'Unites (International System of Units) Modernized version of the Metric System Abbreviated by the letters SI. Established in 1960, at the 11th General Conference on Weights and Measures. Units, definitions, and symbols were revised

and simplified. 3. SI Base Units Physical Quantity Unit Name Symbol length meter m

mass kilogram kg time second s volume

liters, meter cubed L, m3 temperature Kelvin K 3. SI Prefixes Prefix Symbol giga

G mega M kilo k hecto h deka dk no prefix means: deci d centi c

milli m micro nano n Numerical Multiplier 1,000,000,000 1,000,000 1,000 100 10 1

0.1 0.01 0.001 0.000001 0.000000001 Exponential Multiplier 109 106 103 102 101 100

101 102 103 106 109 Significant Figures Indicate precision of a measured value 1100 vs. 1100.0 Which is more precise? How can you tell? How precise is each number? Determining significant figures can be tricky.

There are some very basic rules you need to know. Most importantly, you need to practice! Counting Significant Figures The Digits Digits That Count Example Non-zero digits ALL

4.337 4 Leading zeros (zeros at the BEGINNING) NONE 0.00065 2

Captive zeros (zeros BETWEEN non-zero digits) ALL 1.000023 7 Trailing zeros (zeros at the END) ONLY IF they follow a significant figure AND

there is a decimal point in the number Leading, Captive AND Trailing Zeros Combine the rules above Scientific Notation ALL 89.00

but 8900 0.003020 but 3020 7.78 x 103 # of Sig Figs 4 2 4 3 3

Calculating With Sig Figs Type of Problem MULTIPLICATION OR DIVISION: Find the number that has the fewest sig figs. That's how many sig figs should be in your answer. ADDITION OR SUBTRACTION: Example 3.35 x 4.669 mL = 15.571115 mL rounded to 15.6 mL 3.35 has only 3 significant figures, so

that's how many should be in the answer. Round it off to 15.6 mL 64.25 cm + 5.333 cm = 69.583 cm rounded to 69.58 cm Find the number that has the fewest 64.25 has only two digits to the right of digits to the right of the decimal point. the decimal, so that's how many The answer must contain no more should be to the right of the decimal in digits to the RIGHT of the decimal the answer. Drop the last digit so the point than the number in the problem.

answer is 69.58 cm. Dimensional Analysis My friend from Europe invited me to stay with her for a week. I asked her how far the airport was from her home. She replied, 40 kilometers. I had no idea how far that was, so I was forced to convert it into miles! : ) This same friend came down with the stomach flu and was explaining to me how sick she was. Im down almost 3 kg in two weeks! Again, I wasnt sure whether to send her a card or hop on a plane to see her until I converted the units.

Usain Bolt ran the 100. meter dash in 9.58 seconds. If he was racing a car that was driving 25 miles per hour, who would win? Staircase Method Draw and label this staircase every time you need to use this method, or until you can do the conversions from memory Staircase Method: Example Problem: convert 6.5 kilometers to meters

Start out on the kilo step. To get to the meter (basic unit) step, we need to move three steps to the right. Move the decimal in 6.5 three steps to the right Answer: 6500 m Staircase Method: Example Problem: convert 114.55 cm to km Start out on the centi step To get to the kilo step, move five steps

to the left Move the decimal in 114.55 five steps the left Answer: 0.0011455 km Big Fat Fractions Conversion Factor: a fraction that relates the original unit and the desired unit. Conversion factor is always equal to 1. Numerator and denominator should be equivalent measurements.

When measurement is multiplied by conversion factor, original units should cancel 5 Steps to BFF 1. Look at what youre starting with. 2. Identify the desired units. 3. Find the conversion. 4. Decide which conversion factor will allow you to cancel the appropriate units. 5. Multiply and divide as needed and check sig figs.

BFF: Example Convert 6.5 km to m First, we need to find a conversion factor that relates km and m. We should know that 1 km and 1000 m are equivalent (there are 1000 m in 1 km) We start with km, so km needs to cancel when we multiply. So, km needs to be in the denominator 1000 m 1 km

BFF: Example Multiply original measurement by conversion factor and cancel units. 1000 m 6.5 km 6500 m 1 km BFF: Example Convert 3.5 hours to seconds If we dont know how many seconds are in an

hour, well need more than one conversion factor in this problem 60 minutes 60 seconds 3.5 hours 12600 seconds 1 hour 1 minute round to appropriat e number of sig figs (2) Answer :13000 seconds Purpose of Evidence

Evidence is used to develop theories, generalize data to form laws, and propose hypotheses. Theory well-tested explanation of things or events based on knowledge gained from many observations and investigations Can theories change? What about if you get the same results over and over? Law a statement about what happens in nature and that seems to be true all the time Tell you what will happen, but dont always explain why or how something happens Hypothesis explanatory statement that could be true or false, and suggests a relationship between two factors.

Chapter 1.4: Presenting Scientific Data, pg 22-25 (Objective 3) Graph visual display of information or data Scientists graph the results of their experiment to detect patterns easier than in a data table. Line graphs show how a relationship between variables change over time Ex: how stocks perform over time Bar graphs comparing information collected by counting Ex: Graduation rate by school Circle graph (pie chart) how a fixed quantity is

broken down into parts Ex: Where were you born? Parts of a Graph Parts of a Graph Title: Dependent Variable Name vs. Independent Variable Name X and Y Axes X-axis: Independent Variable Y-axis: Dependent Variable Include label and units Appropriate data range and scale.

Data pairs (x, y): plot data, do NOT connect points. Best Fit Line to see general trend of data. Ch 1.2: Using a Scientific Approach, pg 7-11 (Objectives 4&5) Set of investigation procedures General pattern May add new steps, repeat steps, or skip steps

Group Discussion Questions 1&6 What is the scientific method and its goal? 2&7 What is a hypothesis and how is it formed? 3&8 What are the types of variables in a controlled experiment and how are they different? 4&9 What is the difference between scientific theory and scientific law? 5&10 What is a scientific model and how are they useful? Bubble Gum Example

1. Problem/Question: How does bubble gum chewing time affect the bubble size? 2. Gather background info 3. Hypothesis: The longer I chew the larger the bubble. 4. Experiment 1. Independent variable chew time 2. Dependent variable bubble size 3. Controlled variables type of gum, person chewing, person measuring, etc. 5. Analyze data 1 minute 3 cm bubble, 3 minutes 7 cm bubble30 minutes 5 cm 6. Conclusion there is an optimum length of

chewing gum that yields the largest bubble 7. What next? Now try testing Mark Schemes (Objectives 4&5) Rubric used to assess IB labs 9th graders will only focus on 2 parts of the rubric: Exploration and Analysis Exploration Exploration Checklist ____ Focused research question or problem-- may include a clear hypothesis

____ Introduction describes current knowledge on topic and provides clear overview of this

investigation ____ Independent variable (I.V.) & Dependent variable is (D.V.) are identified and quantitative ____ Controlled variable(s) is/are identified and justified ____ Materials list is provided ____ Safety, ethical or environmental considerations are described ____ Method describes how the I.V. will be manipulatedshould include description of sample sizes, trials & replicates ____ Method describes how controlled variables are held constantneeds to be clear and concise ____ Describe apparatus & setup and/or provides a diagram/picture with annotations including materials specific to the investigation

____ If applicable, cite reference for standard collection procedureuse CBE/CSE, MLA or APA ____ Methods are not written in person-point-of-view ____ Method describes how the D.V. will be measured ____ Method describes how data will be collected/measured ____ Method provides for collection of sufficient data points (5 recommended) ____ Method provides for replication of data points (3-5 replicates per data point / consistent results are met) Analysis Analysis Checklist ____ all relevant raw data has been includedboth quantitative & qualitative ____ uncertainties of measures are identified

____ data is collected into tables with: I.V. values and trials/replicates are identified Cells contain only one value Values are aligned (by decimal point) ____ data tables contain headingsboth table title and columns/rows ____ all measurements contain units and uncertainties (written in the column heading) ____ measures and uncertainties have the same significance (same place) ____ all raw data has been completely processed (e.g. calculations, graphed and statistical analyses

performed) ____ sample calculations are present & clearly explained standard calculations need not be shown but referenced (e.g. sum, mean, & standard deviation) ____ calculations show propagation of uncertainty (addition/subtraction vs. multiplication/division)____ a suitable format (graphs/tables) shows the relationship between I.V. & D.V. ____ graphs/tables have proper titlesidentifying the variables included in the table ____ graphs have appropriate scales, labeled axes with units & uncertainties and accurately plotted data A suitable best fit line/curve with appropriate equation is present ____ tables/graphs have annotations describing graphical relationships ____ statistical analyses of error is incorporated when prompted (e.g. standard deviation, error bars, max./min. slopes) Homework Outline the design of a lab relating two variables Correlation statistical link or association between

two variables EX: families that eat dinner together have a decreased risk of drug addiction, Causation one factor causing another EX: smoking causes lung cancer Be sure your variables are measurable and have some sort of causal relationship. Include a title, question, hypothesis, materials, and procedure Read Pink Packet