Chapter 2: Mathematics and Models in Science

Science 8Matesick

Meters and Liters and Grams, OH MY!•What do you know about

the metric system of measurement?

Read the paragraph below……• Jo an worked as a scientific researcher in the field of genetics. She

designed experiments that provided evidence: certain families can be at a higher risk for specific disease. Joan learned that genetics has had a great impact on how society treats diseases.

• Let’s define the bold terms.• What is one activity that a scientific researcher does?

Lesson 1: Scientific Measurement• The metric system is a standard measurement system based on the

number 10.• Modern scientists use a version of the metric system called International

System of Units (SI).• Using the SI as the standard system of measurement allows scientists

to compare data and communicate with each other about the results of scientific investigations.• Mass• Length • Volume• Density• Temperature• Time

Why do Scientist Use a Standard Measurement System?•Metric come from the

Greek word metron (to measure)• Easy to use because we can

convert between units.• This is used in the SI as the

standard of measurement.• This allows other scientists to

communicate and compare data!

• Common Prefixes

Prefix Meaning Example

Kilo (k) 1000 Kilometer

Hecto (h) 100 Hectometer

Deka (da) 10 Dekameter

Base (no prefix)

1 Meter

Centi (c) .01 Centimeter

Milli (m) .001 Millimeter

Micro () .000001 Micrometer

Nano (n) .000000001 Nanometer

Stair-Step Method (Metric Prefixes)

Length• Length is the distance from one point to another.• The basic SI unit for measuring length is the meter (m).•We use a meter-stick to measure larger distances.•Metric rulers can measure smaller distances by using a

centimeter (cm) or a millimeter (mm).• A unit larger than a meter is a kilometer. A kilometer is 1000

meters.•Conversions

• 1 km= 1000 m• 1 m= 100 cm• 1 m = 1000 mm• 1 cm= 10 mm

Mass• Mass is the measure of the

amount of matter in an object.• The basic SI unit for measuring

mass is the kilogram (kg).• Smaller objects (apples, bottles,

calculators) will be measured in grams(g), or milligrams (mg)

• Scales measure WEIGHT.• This is the force of gravity acting

on an object. (9.8 m/s2)• The SI unit for measuring weight

is the newton (N).• Weight changes as gravity

changes.

Volume• Volume is the amount of space taken up by an object or

substance.• The basic SI unit for measuring volume is the cubic meter (m3).• Other units include the liter (L), milliliter (mL), and cubic

centimeter (cm3).• The liter and milliliter are used to measure liquids.• The cubic meter and cubic centimeter are used to measure solids.

• Solids are measured and then calculated.• Liquids are poured into graduated cylinders.• Irregular solids are measured by water displacement.• Put water into a graduated cylinder and record the volume.• Add the irregular solid.• Record the new volume.• The difference in the water volumes will be the volume of the

irregular solid.

Density

•Density is the measure of how much mass is contained in a given volume.• The SI unit for density is kilograms per cubic meter

(kg/m3), but scientists commonly use grams per milliliter (g/mL or grams per cubic centimeter (g/cm3).• The FORMULA to find density is: D

Using Density• The density of a PURE

substance is always the same, no matter how much of a substance you have!• A pure substance is any

substance with a definite, unchanging chemical composition.

•Water has the density of 1.0 g/cm3

Densities of Common Substances

Substance Density (g/cm3)

Gold 19.3

Gasoline 0.7

Milk 1.03

Water 1.0

Iron 7.8

Air 0.001

Ice 0.9

Aluminum 2.7

Time• Time is the measurement of “how

long”• The basic SI unit of time is the

second (s)• When would we need to use time

in science?• Can we break the second down

into smaller measurements?• In what way is time (seconds)

different from the rest of the metric system?

Temperature • Temperature is the measurement of the speed of the molecules in the air.• The SI unit for measuring

temperature is Kelvin (K).• The Kelvin scale starts at 0 K

(absolute zero) and only goes up.

Conversions for Temperatures0 C 273 K100 C 373 K

Lesson 2: Mathematics and Scientific Thinking

What Math Skills Do Scientists Use?

• Good math skills are essential as scientists collect and analyze data about their subject.• When collecting data, scientists use math skills that include

estimation, accuracy and precision, and significant figures

Estimation

•An estimate is an approximation of a number based on a number of reasonable assumptions.• Useful when it is impossible to count every individual or

object.• Useful when something cannot be measured directly.

Accuracy and Precision

• Accuracy refers to how close the measurement is to the true or accepted value.• Precision refers to how close a group of measurements are to

each other.• When making measurements, the more decimals that you mark- the more precise

you will be!

• By repeating measurements with high-quality tools, scientists obtain the most accurate and precise results possible.

Significant Figures• Significant figures

communicate how precise measurements are.• The significant

figures in a measurement include all digits measured exactly, plus one estimated digit.

What Math Tools Do Scientists Use?

•Scientists use many math tools to analyze data. Some of these tools include mean, median, mode and range. Scientists also use percent error and other math tools to determine if the values of data points are reasonable.

Reasonable and Anomalous Data•Does our data make sense?•Human/ equipment error can cause anomalous data–

data that do not fit with the data set.• If there is a data point or calculation that is different from

others, a scientist will examine the data for errors.• Investigating the reason for anomalous data can lead

scientists to new discoveries!

Percent Error• Some properties of substances never change!• The percent difference between the true value of a

substance and its experimental value is called the percent error.• A low value means that the experimental results were accurate.• A high value means that the experimental results were not

accurate!• Calculating the percent error shows how reliable data and

the methods for collecting it are.• Make sure that you remove any minus sign in your calculations!

Lesson 3: Using Graphs in Science

Kinds of Data

•Graphs can illustrate different types of data.• Identify trends•Make predictions•Recognize inconsistent (anomalous) data

•Categorical Data grouped into categories•Numerical Data ranges of number

Kinds of Graphs•First let us remember VARIABLES:• Independent: the scientists is in control of this•Dependent: changes as a result of the independent

variable•Variables are what are displayed on graphs!•Line graphs are used to show numerical data.• Line graphs show changes over time!

•Bar graphs can show numerical and categorical data.

Linear Graphs• Linear graphs show that

points are plotted and connected in a straight line. • This means that there is a

direct relationship between the variables.• If one variable increases, the

other increases as well.• If one variable decreases, the

other decreases as well.• THESE ARE CONSTANT CHANGES

Nonlinear Graphs

• Nonlinear graphs show data points that do not fall along a straight line.• There is no direct

relationship between the variables.

Outliers• A point that is not part of a trend is called an outlier.•When graphs do not have a clear trend, it means that the

variables are not related.

Lesson 4: Models and Systems

• Input

•Output

How Do Scientists Use Models?•A model is a representation of an object or a process.• Examples:

• Scientists use models to test their ideas about things they cannot observe directly.• Small• Large

• Types:• Physical• Three-Dimensional• Not- Physical

What are the Characteristics of a System?•Models are often used to represent systems.•A system is a group of parts that work together to carry

out a function.•All systems have at least one input, at least one process,

and at least one output.• Examples:•Microwave•Word Processor• Sno-Cone Machine• Car Engine

• Feedback is output that changes a system in some way.• Can be positive or negative.

How Do Models Help Scientists Understand Systems?

• Scientists build models to represent a process. They test whether the input and the output from the model match the input and the output of the system in the natural world.• They predict changes as a result of feedback or input changes.

• Some systems that scientists study are simple. • Only have a few parts or few steps

• Some systems are more complex.• Many parts and variables can interact in complex systems.• These are sometimes difficult to model, so scientists may model a specific part of

the system that they wish to study.• Example: predict where a hurricane will make landfall

• May model winds that affect the hurricane’s path.

• Often scientists use computers to keep track of the variables.

Testing Assumptions

• Scientists start models by testing assumptions.• Compare input and output of the model to the input and output in

the natural world. • If they match, then the assumptions are correct.• If they do not match, scientists must change one or more assumptions.

• The revised model more accurately represents the natural world.

TEST EACH OTHER

• Write 10 questions about models and systems.• Once everyone has completed this, we will exchange and take turns

answering questions.

Lesson 5: Safety in the Science Laboratory