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Chapter # 1 Lecture - p p1-12

Lecture Presentations for Integrated Biology and Skills for Success in Science Banks , Montoya, Johns, & Eveslage. Chapter # 1 Lecture - p p1-12. Getting Started. Here’s some paperwork!. Course Overview. Three different areas of study, wrapped up into one course Math Biology

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Chapter # 1 Lecture - p p1-12

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

  2. Getting Started • Here’s some paperwork!

  3. Course Overview • Three different areas of study, wrapped up into one course • Math • Biology • Biochemistry • Lecture, Exams, Labs, and On-line • How to determine your grade • Syllabus • Course Objectives

  4. Expectations for the course • Community • Working with others—in class, in lab, in study groups • Learning • Complete all assignments for deep comprehension • Respect • Fellow students, instructors and self

  5. Mathematical Practices • Making sense of problems and persevere in solving them • Reasoning abstractly and quantitatively • Constructing viable arguments and critiquing the reasoning of others • Modeling with mathematics • Using appropriate tools strategically • Attending to precision • Looking for and making use of structure • Looking for and expressing regularity in repeated reasoning

  6. Guiding Principles for the Course • Looking at seemingly simple things deeply • Conceptual understanding • Practical Applications • Contextualized

  7. Setting up your Binder • Text Section • Lab Section • On-line Section • Objectives

  8. Week 1 Course Objectives • Take a moment to review this week’s objectives. • Questions?

  9. Lecture 1—Arithmetic and the Atom • By 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.

  10. Math and Science • Science is math applied to the real world. • Science asks testable questions and is based on empirical data—if you can’t gather data on it, it’s not science. • And, of course, you can’t analyze the data without math • Numbers tell the story of our world, you just have to know what they say.

  11. Making a Model • Using 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.

  12. Subtraction—Adding the Opposite • This activity hopefully brought you to the conclusion that subtraction can be very confusing—it 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

  13. Commutative and Associative Properties of Addition • The 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)

  14. Application to the Real World—The Three Subatomic Particles • Within an atom, there are three types of subatomic particles: protons, neutrons and electrons. • Protons and neutrons are found in the nucleus—so 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.

  15. Application to the Real World—The Three Subatomic Particles (Cont.) • It is impossible to draw the atom to scale while still being able to see the subatomic particles.

  16. Application to the Real World—The Three Subatomic Particles (Cont.) • Determine the mass of the following atoms: 5 protons, 6 neutrons and 5 electrons ________ 1 proton, 1 neutron and 0 electron s ________ 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=11 1+1=2 11+12=23 5+-5=0 1+0=1 9+-10=-1

  17. Trends in the Periodic Table Write an equation for each scenario. • Noble Gases do not readily form compounds (they don’t 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 has 11 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=0 11-10=1 17-18=-1

  18. Combining Like Terms • Only terms that are alike can be combined. This doesn’t mean you can’t add terms that aren’t alike, you just can’t combine them. Combine the terms, when possible: 1. 5 hippos + 2 hippos 2. 5 hippos + 2 giraffes 3. 6x + 3 4. 6x + 3x 5. 6x2 + 3x 6. 6x2 + 3x2 7 hippos 5 hippos + 2 giraffes, can’t simplify anymore 6x + 3 9x 6x2 + 3x 9x2

  19. Addition of Fractions • You 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.

  20. Fractions, Decimals and Percents • Place 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% 3 100 1 = 1 ÷ 4 = one fourth = 0.25 = 25 = 25% 4 100 0 3 1 3 2 3 3 3 4 3

  21. The Area Model for Multiplication • Multiplication can be modeled by finding the area of a rectangle. Here we see 3 x 7 3 7 • You can view this problem as “3 x 7” or “7 x 3”, these are equivalent expressions.

  22. Area Model of Multiplication for Fractions • This model can also be applied to fractions. Here we see 1 1 • Here we would only fill in one of the small blocks, which is one sixth (square units).

  23. Multiplying Fractions • A more traditional method . . .

  24. The Cancellation Property of Division • Anything 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.

  25. A Common Mistake • Multiplication 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.

  26. The Distributive Property • The area model of multiplication also explains the distributive property a b c d The sides are (a + b) and (c + d). (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd

  27. Adding the Opposite AND The Distributive Property • Avoid 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.

  28. Tracking Units • There 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 = ____________ 10cm 0cm 25cm2 1

  29. Squaring a Number • 5 cm x 5 cm= (5 cm)2= 52cm2= 25 cm2 • Notice how the exponent was distributed to both the 5 and the cm inside the parenthesis. • What are some other perfect squares?

  30. PEMDAS • Most people are familiar with: Please Excuse My Dear Aunt Sally • Remember 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 – 12x23xyz(5xy – 2z) - 3(2+5x)2 + x2 – 5x

  31. Work Time Review Try 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: ¾ , 67%, or 0.8? 4. Simplify: 3x(2x – 2) -5x – (2 – 7x) 5. What property says that a + b = b + a ? 6. Simplify: 3+25 _ 3 4 5 9 4

  32. Exit Quiz and Homework • Exit Quiz—Copy 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 -3/2 Homework • Read 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.)

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