Chapter # 1 Lecture - p p1-12

Biology 198

Chapter # 1 Lecture - pp1-12Lecture Presentations for Integrated Biology and Skills for Success in ScienceBanks, Montoya, Johns, & Eveslage

Welcome time.1Getting StartedHeres some paperwork!Pass out any paper suppliessyllabus, text, etc.2Course OverviewThree different areas of study, wrapped up into one courseMathBiologyBiochemistryLecture, Exams, Labs, and On-lineHow to determine your gradeSyllabusCourse Objectives(Review syllabus, etc.. Pass out course objectives and review.)3Expectations for the courseCommunityWorking with othersin class, in lab, in study groupsLearningComplete all assignments for deep comprehensionRespectFellow students, instructors and self

When we all do better, we all do better. If you know the topic under discussion, practice your skills as a coach or teacherhelp others in class or in study groups that you set up. Be patient with yourselfthere is always a delay from the exposure of a new idea to the comprehension of the new idea. And then celebrate your learning and the learning of your fellow students. Attend all classes, and be on time. Come prepared with a positive attitude. Review your work and your notes, and review the text everyday. Complete all assignments to the best of your ability, and ask for help when you need it. When your grade is in the computer, its too late to ask for help.4Mathematical PracticesMaking sense of problems and persevere in solving themReasoning abstractly and quantitativelyConstructing viable arguments and critiquing the reasoning of othersModeling with mathematicsUsing appropriate tools strategicallyAttending to precisionLooking for and making use of structureLooking for and expressing regularity in repeated reasoningThis class is not a spectator sport, nor is it a competitive sport (at least its not when we are in this room, learning material). Take risks with your workdont be afraid to make mistakes (some of the greatest triumphs have come as a result of a mistake). PERSEVEREdont give up. We will be using these mathematical practices to analyze the biological worldreasoning, modeling, finding regularity/patterns and all the other practices will be invaluable in our pursuit of knowledge.5Guiding Principles for the CourseLooking at seemingly simple things deeply

Conceptual understanding

Practical Applications

Contextualized Some of the material may appear to be simplethere will be an activity that we will complete today that may seem simple, but it has great consequences. The trick is to gain a deep conceptual understanding of the process, then you can apply it to complex situations with ease. We will be taking seemingly simple processes and putting them into new situations. When someone does not have a strong foundation to stand on, problems can arise when facing challenges. This course will provide to you the tools you will need to understand many of the complex concepts found in the biological world.6Setting up your BinderText Section

Lab Section

On-line Section

Objectives

(Pass out text, etc.)7Week 1 Course ObjectivesTake a moment to review this weeks objectives.

Questions?(Answer questions as necessary.)8Lecture 1Arithmetic and the AtomBy the end of the lecture this week, students will be able to:1.Explain the importance of math in science.2.Describe the subatomic particles, their places in the atom, and their charges.3. Apply the commutative and associative properties of addition to problems.4.Use the distributive property to simplify and/or solve problems.5. Determine the charge on an atom or an ion.6. Combine like terms to simplify expressions.7.Perform mathematical operations in the correct order.8. Simplify and perform mathematical operations on fractions.

(Allow students to review this list. There are some objectives listed on the syllabus that wont be thoroughly covered by the lectures. Such objectives will not be on the tests in the math portion of the course.)9Math and ScienceScience is math applied to the real world.

Science asks testable questions and is based on empirical dataif you cant gather data on it, its not science.

And, of course, you cant analyze the data without mathNumbers tell the story of our world, you just have to know what they say.Science and math are very closely related. Science is about collecting data. If you cant collect empirical data on the topic, its not science. Its the class down the hallphilosophy or religion. Not that theres anything wrong with those classes, its just that science is BASED ENTIRELY on data. And, you cant understand the data without knowing what the numbers saythats where math comes in.10Making a ModelUsing the beads given to you, create a model for the following problems:

1) 5 6 = 2) 5 + -6=3) -5 + -5 =4) -5 -5 = 5) -5 5 = 6) -5 + 5 = 7) 4 7 =8) 4 + -7 =

Which of these problems give the same result?Be prepared to present (on the doc cam) your model when asked.Models help us understand the real world, and help us see things that are sometimes abstract, or something you cant normally see and touch. In this activity, make a model for these problems. (The end goal here is to have students reach the consensus that it is better to convert all subtraction problems to ADDING THE OPPOSITE. Walk around and ask students about their models. When one has a good model that converts a subtraction problem to ADDING THE OPPOSITE, ask that student to share out when its time.) PLEASE ALLOW STUDENTS TO EXPLORE THEIR MODELS FOR 15 MINUTES, AND THEN PRESENT ONE OR TWO THAT YOU HAVE APPROVED. USE THE DOC CAM FOR WHOLE CLASS SHARE OUTS.11SubtractionAdding the OppositeThis activity hopefully brought you to the conclusion that subtraction can be very confusingit is much easier to add the opposite.

5 6 becomes 5 + -6 -5 -5 becomes -5 + +5 or just -5 + 5-5 5 becomes -5 + -5 (notice nothing changes about the first term)4 7 becomes 4 + -7

Commutative and Associative Properties of AdditionThe Commutative Property of addition:For any two numbers a and b, a + b = b + a

The Associative Property of addition:For any three numbers a, b, and c, (a + b) + c = a + (b + c) How many of you commute to school? What does that mean to commute? (Move around . . . ) What is an associate? (Someone you interact with, like the numbers within the parenthesis.) Notice that the associative property (of addition) is applicable only when the operation between all three numbers is addition.13Application to the Real WorldThe Three Subatomic ParticlesWithin an atom, there are three types of subatomic particles: protons, neutrons and electrons.Protons and neutrons are found in the nucleusso they are called the nucleons.Protons are positive in charge.Neutrons are neutral, or have no overall charge.Together, protons and neutrons determine the mass of the atom.Electrons have a negative charge and are found around the nucleus. Electrons have a very small mass and are considered to be negligible when determining the mass.A submarine travels under water. SUB means under. In this case, it would be UNDER THE SIZE OF AN ATOM. Chemistry will be explored more during next weeks lecture. This is a brief intro.14Application to the Real WorldThe Three Subatomic Particles (Cont.)It is impossible to draw the atom to scale while still being able to see the subatomic particles.

The nucleus, with its protons and neutrons, is actually very small and exceedingly dense. The electrons are moving extremely fast. The electrons should be the size of a pinpoint since protons and neutrons have a mass around 2,000 times larger than the electrons.15Application to the Real WorldThe Three Subatomic Particles (Cont.)Determine the mass of the following atoms:5 protons, 6 neutrons and 5 electrons ________1 proton, 1 neutron and 0 electrons________11 protons, 12 neutrons and 10 electrons________Determine the charge of the following atoms:5 protons, 6 neutrons and 5 electrons ________1 proton, 1 neutron and 0 electrons________9 protons, 10 neutrons and 10 electrons________

5+6=111+1=211+12=235+-5=01+0=19+-10=-1(Allow for 1-2 minutes for students to work on the problems.) When determining the mass of an atom, we only use the protons and the neutrons. When determining the charge, we only are concerned with the protons and electrons. Why is the 10 in the last problem negative? (Because it represents electrons and electrons have a negative charge.) So, you can have a positive charge OR a negative charge. Can you have a negative mass? (No)16Trends in the Periodic TableWrite an equation for each scenario.Noble Gases do not readily form compounds (they dont bond).Argon has 18 protons and 18 electrons. What is its charge?Alkali Metals (column 1) tend to lose 1 electron when they bond.Sodium has formed an ionic compound and now has11 protons and 10 electrons. What is its charge?The halogens (non-metals in column 7) tend to gain 1 electron when they bond.Chlorine has formed an ionic compound and now has 17 protons and 18 electrons. What is its charge?18-18=011-10=117-18=-1Combining Like TermsOnly terms that are alike can be combined. This doesnt mean you cant add terms that arent alike, you just cant combine them.Combine the terms, when possible:1. 5 hippos + 2 hippos2. 5 hippos + 2 giraffes3. 6x + 34. 6x + 3x5. 6x2 + 3x6. 6x2 + 3x2

7 hippos5 hippos + 2 giraffes, cant simplify anymore6x + 39x6x2 + 3x9x2 Take some time to work on these in a small group and share with your group your answers. (Allow for small group timeabout 5 minutes. Then, share out as a class. One student can demonstrate 1 and 2. Another student can demonstrate 3 and 4. A third student can do 5 and 6.)18Addition of FractionsYou can only combine LIKE TERMS

When you multiply by 3/3, is the value really changed? What about 2/2?We cannot combine 1 half and 1 third, but we can combine 3 sixths and 2 sixths.Viewing the denominator as a unit helps with addition of fractions.

Notice that the first term is multiplied by 3/3. What does 3/3 simplify to? (One) Multiplying anything by one does not really change the value of the term. We chose 3/3 and 2/2 because it would give us like terms in the denominator. One sure-fire way to do this is to choose the denominator of the other term.19Fractions, Decimals and PercentsPlace the following values on the number line:1 , 4 , -2 , 0 , 66.6% , -1.3 3 3 3 3

| | | | | | | | | | | | | | | -1 0 1 2 3

2 = 2 3 = two thirds = 0.6 = 66.6 = 66.6%3 1001 = 1 4 = one fourth = 0.25 = 25 = 25%4 1000313233343(Allow time for students to draw the number line and place the values on it. Show the students how each mark is one third of a unit. Take some time to discuss the answers with the students.) Two thirds is the same as two divided by three. Notice the bar above the six. What does the bar indicate? (Ask students until a correct response is given.) How many years are in a century? What does per cent mean? Since the per denotes the operation of division and cent means one hundred, per cent means divided by (or out of) one hundred.20The Area Model for MultiplicationMultiplication can be modeled by finding the area of a rectangle. Here we see 3 x 7

3 7You can view this problem as 3 x 7 or 7 x 3, these are equivalent expressions.What would the units be on the answer of 21? (Have a discussion about why the units on the 21 must be units squared because units times units is units squared.)21Area Model of Multiplication for FractionsThis model can also be applied to fractions. Here we see

1

1Here we would only fill in one of the small blocks, which is one sixth (square units).

Notice that the sum of each side is one. So, what is the total area of all of the squares? (Discuss until one is answered, then lead the students to six sixths is also a correct answer.) By drawing ONE SQUARE UNIT, the numerator and denominator become more obvious. Can you imagine if we only had drawn one half and one third? It would be more difficult to determine the answer. What would the answer be if the question were one half times two thirds? (Ask for a student to write the answer on the board, or the instructor can write it.) This is a geometric solutiona solution in picture form.22Multiplying FractionsA more traditional method . . .

This is a more traditional method to solve this problem. Could we combine the numerator and denominator like this if the operation were addition? (No!) We would need to make the denominators the same so that we could add like terms. (See next slide.)23The Cancellation Property of DivisionAnything divided by itself is one.

Multiplying by one (the same value in the numerator and the denominator) does not change the value.

Similarly, one can cancel a common factor from the numerator and the denominator.

Anything divided by itself is one. This is easier to see when numbers are used, but can be tricky when variables enter the picture. Notice that no matter what the value, the answer is still one. Notice in the second bulletwhen you multiply by one, the overall value does not change. Anything multiplied by one remains itself. It may be in a slightly different form, but the values are equivalent. With this in mind, the third bullet becomes more clearthree divided by three cancels to one, leaving five times one, divided by seven times one, or just five divided by seven.24A Common MistakeMultiplication is very different from addition, and these expressions are not equivalent.

The expression on the left cannot be simplified any further. Plug in values (numbers) for r, b and a to check if this is a correct statement.

Be very careful when working with fractions, and canceling out factors. Canceling factors does not apply in this situation. (Ask a student to share out his/her or share an example that you choose.)25The Distributive PropertyThe area model of multiplication also explains the distributive property a b c dThe sides are (a + b) and (c + d).

(a + b) (c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd

acadbcbdThe sides are a+b and c+d. To find the area of the rectangle, we will multiply the sides. The arrows show how the numbers are distributedlike cards being dealt to each player, the numbers are first distributed outside the parenthesis, then to the numbers in the parenthesis. 26

Adding the Opposite AND The Distributive PropertyAvoid confusion by using the ADD THE OPPOSITE technique to distribute the negative sign.

5x (5 3x) = 5x + -(5 + -3x) = 5x + -5 + 3x = 8x + -5

The like terms can be combined.(Walk through the steps.) First, change all subtraction signs to add the opposite. Next, distribute the negative sign that is outside of the parenthesis. Be carefulthis negative sign will make each term inside the parenthesis into the opposite of what it is. +5 to -5. -3x to +3x. Finally, like terms can be combined.27Tracking UnitsThere are very few true numbers in science. Most values will have units, and these values should always be written with their unit.5cm + 5cm = ____________5cm 5cm = ____________5cm x 5cm = ____________5cm 5cm = ____________

10cm25cm20cm1(Allow for 1-2 minutes of work time for students to complete the problems.) Whats the answer to the first one? Why can we combine the numbers together? (Combining like terms) Whats the answer to the second one? Is it important to keep the units on a zero? (Answers will vary.) Whats the answer to the third one? How did you know what units to use? (cm times cm = cm squared) Whats the answer to the fourth one? Why arent there any units on this one? (Anything divided by itself is one.) Lets look at the last one. What happens to the cm units? (They get cancelled out.) Did you change the value? (Noit was simply converted to meters. Its still the same distance. (Draw 5cm on the board and label it 5cm and 0.05m.)28Squaring a Number5 cm x 5 cm= (5 cm)2= 52 cm2= 25 cm2

Notice how the exponent was distributed to both the 5 and the cm inside the parenthesis.

What are some other perfect squares?If we were to draw this out, what would it look like? (Ask for a student to draw it on the board, or draw it yourself. Draw a square with sides of 5cm and 25 square units inside.) What kind of number is 25? (A perfect square) 29PEMDASMost people are familiar with:Please Excuse My Dear Aunt SallyRemember this rule for the order of operations while you simplify these expressions:

3x(4 3)5 (-4) 2-2x (3x + 5)

9m2(3m 5x + 2y)-7x 5x

3x2 + 8n2-2x2 + -6 12x2

3xyz(5xy 2z) - 3(2+5x)2 + x2 5x

Highlight that multiplication and division are preformed at the same time as you move from left to rightand so are addition and subtraction. Allow students to work in groups and share answers out when they are finished.Answers (in order): 3x, -11, -5x 5, 27m3 45m2x + 18 m2y, -12x, 3x2 + 8n2, -14x2 6, 15 x2y2z 6 xyz2, -74x2 5x 12 30Work Time ReviewTry these problems on for size! (No calculators, except #3.)1.5 -3 =-4 3 = -5 + -3 =2.An atom has a mass of 25amu (atomic mass units) and a charge of positive 2. If the atom has 12 protons, how many neutrons and electrons does it have? (Write an equation that shows the number of neutrons and an equation that shows the number of electrons.)3.Which has the greatest value: , 67%, or 0.8?4.Simplify: 3x(2x 2)-5x (2 7x)5.What property says that a + b = b + a ?6.Simplify:3 + 2 5 _ 3 4 5 9 4(Allow time for students to work on these problems, then ask for students to show their work, as time allows.)Answers:8, -7, -8Neutrons = 13. Electrons = 10.3. Converted all to decimals 0.67, 0.75, 0.8 (so, 0.8 is the greatest).6x2 6x, 2x 2 Commutative Property of Addition23/20 or 1 3/20, -7/3631Exit Quiz and HomeworkExit QuizCopy the questions, then answer.Place your name/date/class day & time in the upper right hand corner.1. 5 6 = 7 -4 = -4 + -3 =2.A particular phosphorus atom has 15 protons, 16 neutrons, and 18 electrons. What is its mass and charge?3. Simplify:(4x)(3x 2) -2 (3x + 5) 4.Put these numbers in order, from least to greatest: 55%, 1/2, 0.54 and -3/2HomeworkRead and take notes on the Introduction and Chapter 1. Start Chapter 2.Review your notes, the syllabus and course objectives from class. (Be sure you understand the objectives for the week.)(There are some objectives that are only covered in the text. These are important, but will not be on the tests within the math section. Pass out a half sheet of paper and have the students complete and turn in as they exit the class. Whether or not notes may be used is up to the instructor.)32