Science Tools and Skills - Notes

Science Tools and Skills

Chapter 1: Thinking Like a Scientist

• Introduction:
  • Christopher Columbus's voyage challenged the belief that the Earth was flat.
  • Scientific inquiry helps us understand nature's rules.
• Nature of Science (1.1)
  • Science involves observing nature, identifying patterns, and making predictions.
  • Example: Farmers predicting harvest season based on observations.
  • Science also involves connecting seemingly unrelated things.
  • Example: The relationship between the tides and the Moon.
  • Science inquiry: Studying the natural world to understand science; acquiring knowledge by studying the natural world
  • Science is both a body of knowledge and a way of thinking
  • Life sciences: Study of living things (anatomy, zoology, botany, taxonomy).
  • Physical sciences: Study of nonliving things (geology, astronomy, physics, chemistry).
  • The scientific revolution: Observing, analyzing, and modeling nature mathematically.
  • Mathematics: A universal language for scientists.
• Scientific Inquiry (1.2)
  • Alfred Wegener: Proposed the theory of continental drift, initially rejected but later supported by evidence.
  • Pangaea: A supercontinent that Wegener assumed all the continents were once connected. In 1915, Wegener published his book about Pangaea and the continental drift.
  • Plate tectonics: The structure of Earth's surface and its changes.
  • Galileo Galilei & Francis Bacon: Founders of the scientific method.
  • Scientific method steps:
    • Make Observations.
    • Ask a Question.
    • Hypothesize.
    • Do an Experiment.
    • Make Measurements.
    • Collect Data.
    • Interpret Data.
    • Draw Conclusions.
    • Communicate Your Results.
  • The method offers the blue print for scientific investigations, but scientists do not always follow these exact steps every time they make a discovery. Some advances in science occurred due to plain accidental discoveries.
  • Science Inquiry Skills:
    • Hypothesize: Provide a reasonable explanation of an observation that can be repeatedly tested by an experiment.
    • Ask Questions.
    • Observe: Using senses (sight, hearing, touch, smell, and taste}.
    • Use Numbers.
    • Compare and Contrast.
    • Estimate.
    • Classify.
    • Design Models.
    • Predict.
    • Measure.
    • Plan Experiments.
    • Communicate.
    • Record Data.
    • Schematize/Draw Results.
    • Analyze Data.
    • Infer: Finding the logical interpretation based on previous knowledge.
    • Research.
    • Relate Data.
  • Cricket Chirping Example:
    • Observation: Crickets chirp faster on some nights.
    • Question: Does chirping depend on the weather (temperature)?
    • Hypothesis: Crickets chirp faster when it is warmer.
  • Experiment: Testing a hypothesis. Plan and design an experiment that can be repeated over and over again to minimize errors.
    • Controlled Experiment: Uses control and experimental groups.
    • Control Group: Standard for comparison; doesn't receive the variable being tested (e.g., no pesticide).
    • Experimental Group: Receives the variable (e.g., pesticide).
    • Variable: The condition you're testing (e.g. temperature).
    • Data: Facts, figures, and evidence collected through observation.
    • Qualitative Data: Descriptions (color, sound, shape).
    • Quantitative Data: Measurements and numbers.
  • Analysis: Cricket Chirping Example (Table 1.2):
    • Results show more chirps at higher temperatures.
    • Conclusion: Warmer temperatures cause faster chirping.
  • Communication: Sharing results in a classroom or with other scientists.
    • Allows testing, challenging, or disproving hypotheses.
• Activities:
  • Activity 1: Explore which colors absorb more heat.
    • Hypothesis: Dark colors absorb more heat than light colors.
    • Procedure: Place different sheets of paper under the sun, measure the temperature and record the data in a table.
    • Interpret Data: From experiment to test hypothesis.
  • Activity 2: Explore what affects the size of shadows.
    • Hypothesis: The distance between an object and a light source affects the size of an object's shadow.
    • Procedure: Place a cube on the table and measure the height of the cube's shadow as it appears on the wall. Record the data in a table.
    • Interpret Data: From experiment to test hypothesis.
  • Activity 3: Design an experiment to test the effect of fertilizers on the growth of tomato plants.
  • Activity 4: Design an experiment to test if adding sugar to water keeps cut flowers fresh.
• Scientific Facts, Laws, and Theories (1.3)
  • Facts: Verifiable, descriptive statements that don't change (e.g., "Fish live in water"). Are always supported by observations, tests, experiments, and studies.
  • Phenomenon: An observable fact (e.g., evaporation of water).
  • Law: A hypothesis that has been repeatedly tested and not contradicted. (e.g. Law of Universal Gravitation that explains why coins drop to the ground when you release them)
  • Theory: A group of well-tested and verified hypotheses (e.g., the theory of plate tectonics).
  • Scientific Inquiry: New discoveries may contradict existing hypotheses, laws, or principles.
  • Scientific Theories: Not fixed; are refined and redefined as new evidence is gathered.

Chapter 2: Tools of Scientific Inquiry: Manipulating Powers

Manipulating Powers (2.1)

• Powers of Small Numbers (up to 10):
  • Representing the number of times a number is multiplied by itself in short form.
  • Example: $2 \times 2 \times 2 = 2^3$ (2 raised to the power 3).
    • Base: The number being raised to a power (e.g., 3 in $3^4$).
    • Exponent: Indicates how many times the base is used as a factor (e.g., 4 in $3^4$).
    • Power: The product obtained (e.g., $3^4 = 81$).
  • $X^n$: x Raised to the power of n. Also called nth power of x. can be read differently: $x^2$ (x squared) and $x^3$ (x cubed).
  • Powers of 10: Important in science.
    • $10^1 = 10$
    • $10^2 = 100$
    • $10^3 = 1,000$
    • $10^6 = 1,000,000$
    • $10^n = 100…00$ (1 followed by n zeros).
  • $10^0 = 1$
• Negative Powers of 10:
  • Pattern:
    • $10^3 = 1,000$
    • $10^2 = 100$
    • $10^1 = 10$
    • $10^0 = 1$
    • $10^{-1} = 0.1 = 1/10$
    • $10^{-2} = 0.01 = 1/10^2 = 1/100$
    • $10^{-3} = 0.001 = 1/1,000 = 1/10^3$
    • $10^{-n} = \underbrace{0.00000…1}_{n \text{ zeros}} = 1/10^n$
• Multiplying Powers of 10 :
  • Adding exponents
    • $10^n \times 10^m = 10^{n + m}$
    • $10^n / 10^m = 10^{n-m}$

Scientific Notation (2.2)

• Expressing Large Numbers:
  • Used for very large or very small numbers.
    • Speed of light: 299,792,458 m/s.
  • Expressed as $M \times 10^n$:
    • M: Mantissa (number between 1 and 10).
    • n: Exponent.
    • Example:
      • speed of light in vacuum can be written as $3 \times 10^8 m/s$
      • The mass of cesium is $2.21 \times 10^{-22} g$
• Steps to Represent a Large Number using Scientific Notation:
  1. Identify mantissa.
  2. Count decimal places to move the decimal point
  3. Write the final answer as $mantissa \times10^{exponent}$
• Expressing Small Numbers in Scientific Notation:
  • Like large numbers, small numbers can also be expressed in scientific notation.
  • However, the power in this case is a negative number.
  • When 10 is raised to an n-th power (where n is a negative number), the result is always smaller than 1, and it is written with ❘n| zeros. $Mantissa \times 10^{-n}$.
  • To represent a small number in scientific notation, follow these steps:
    1. Identify what the mantissa of the number is going to be.
    2. Count the number of decimal places to move the decimal point to get the mantissa from your original number.
    3. Write down the final answer as mantissa multiplied by $10$ raised to the appropriate exponent.

Scientific Notation in Arithmetic (2.3)

• Multiplication and Division:
  • Multiplying:
    1. Multiply mantissas.
    2. Multiply exponents ($10^n \times 10^m = 10^{n + m}$).
    3. Write down the expression as the expression multiplied by the exponent
  • Dividing:
    1. Divide mantissas.
    2. Divide exponents ($\frac{10^n}{10^m} = 10^{n-m}$).
    3. Multiply mantissa with exponent.
  • If necessary, change the resulting number into scientific notation.
    • Always pay attention to the sign of exponents.
• Adding and Subtracting:
  • The numbers with the same power of 10 are easily added and subtracted.
  • Thousands are easily added to thousands ($m×10^3 +n×10^3$
  • Millions are easily added to millions ($m×10^6 +n×10^6$
  • Note that a number can be written in any power of 10 you choose.
    • For example: $60,000,000=6.0×10^7 =60×10^6 =6,000×10^4 =60,000×10^3$
• Exponents of Exponents:
  • What is $(10^5)^3$, $(10^5)^{-3}$, or $(10^m)^n$ where m and n are integers?
    • $(10^m)^n = 10^{n \times m}$ that is $(10^5)^3= 10^{5 \times 3} = 10^{15}$
• Fractional Exponents:
  • The nth root or radical of a certain number x is a number y whose nth power equals x. $\sqrt{x}$ and cube roots. Examples:
    • $\sqrt{100} = 10$, since $10 \times 10 = 100$
    • $\sqrt{1,000,000} = 1,000$
    • $\sqrt[n]{10^n} = (10^n)^{1/2} = 10^{n/2}$

Working With Units (2.4)

• Measurements: Act of quantitatively describing a physical property using numbers and an associated unit.
• System of measurement: Is a collection of units of measurements for different physical quantities.
• Two Main Systems of measurement used worldwide:
  • The US customary measurement system
  • The International System of units referred to as the SI system , also know as the metric system
• Base Units:
  • There are seven SI base units:
    • Meter (m): Length.
    • Kilogram (kg): Mass.
    • Second (s): Time.
    • Kelvin (K): Temperature.
    • Ampere (A): Electric Current.
    • Mole (mol): Amount of substance.
    • Candela (cd): Luminous intensity.
  • A unit named after a scientist is written as lowercase however its symbol is written as a capital letter
• Working with Simple Units:
  • Prefixes are added to base units to express dimensions or quantities, that are too big or too small to be expressed using standard units. Also prefixes enables the expression using either a very small fraction of the standard unit, called a sub-multiple, or to use the unit many times, called a multiple
    • Example: kilometer is a unit of length that has one thousand meters $(1,000)$
      • Multiple:
      • mega- (M): $10^6$
      • kilo- (k): $10^3$
      • hecto (h): $10^2$
      • deca(da): $10$
    • Submultiples:
      • deci- (d): $10^{-1}$
      • centi- (c): $10^{-2}$
      • milli- (m): $10^{-3}$
      • micro- (\mu): $10^{-6}$
      • nano- (n): $10^{-9}$
      • pico- (p): $10^{-12}$

Working With Simple Units (2.4.2)

• Changing prefixed units into base units or the other way round, is called unit conversion.
• One way to convert units is to use cross multiplication
  • Unit conversion methods:
    * Converting Prefixed and Base Units Using Cross Multiplication
    * Converting Prefixed and Base Units by Multiplying by "one"
    * Conversion Factors

Converting Complex Units

• Conversion of speed units: involves units of distance and time.
  *Conversion of volume and area units: involves cubic meters $(m^3)$