Transcript of UNIT 1: LINEAR FUNCTIONS With a review of Algebra 1 Basics.
- Slide 1
- UNIT 1: LINEAR FUNCTIONS With a review of Algebra 1 Basics
- Slide 2
- LESSON 1: ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL NUMBERS IN
EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES
- Slide 3
- DAY 1 To Turn in: Signed, Filled out Last page of the Syllabus
(torn off) Warmup ( At your desk, By yourself, Silently ): 2
minutes Jot down examples of all of the different types of numbers
you can think of, and name the type for each that you write. Think
of any numbers you can! For example: 3 a prime number, 2.3 a
decimal number, but also a rational number
- Slide 4
- DAY 1 PRAYER
- Slide 5
- DAY 1 Share some responses! Types of numbers: Where do our
numbers come from? Sets of numbers - what are all of the different
types of numbers? 1. Natural numbers 2. Whole numbers 3. Integers
4. Rational Numbers (think ratios fractions) 5. Irrational Numbers
6. Real Numbers 7. Whats next? stay tuned
- Slide 6
- DAY 1 Whiteboard practice! Be sure to write clearly on the
boards. Please write LARGE and CLEAR! 1. True/False: An integer is
a rational number. 2. True/False: A rational number is an integer.
3. True/False: A number is either rational or irrational, but NOT
both.
- Slide 7
- DAY 1
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- Rules/Procedures on white board, write the most important rule
to you in any classroom 1. Top three rules on the front wall 2.
OVERALL: Raise Your Hand! 3. A time for listening, a time for
talking Responsibility for actions regardless of intent 1. Late
better have a pass or a tardy slip! 2. Materials have textbook,
notebook, binder, graphing calc, pencils, pens every day! if not,
deduction in Demeanor grade 3. Homework on time and completed, not
partial if not, no credit must be responsible, ask for help after
school, at lunch, etc.
- Slide 9
- DAY 1 4. Cell Phones even if they beep this year, Im taking
them. Responsibility turn them off! If not, I will keep them for
two days (more if repeat offender) 5. Backpacks/other belongings
outside if not, Ill confiscate them 6. Changing Rooms light chatter
ok, but should be silent upon entering any of the buildings or
classroom so as not to disturb other meetings and classes 7.
Emergencies remain calm! Stay SILENT and listen to teacher. Why is
this also important in a drill?
- Slide 10
- DAY 1
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- Homework worksheets ALL PROBLEMS!
- Slide 12
- LESSON 1: DAY 2 ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL
NUMBERS IN EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES
- Slide 13
- DAY 2 To turn in: Homework worksheet packet pages 11, 15, 16
Bellwork: In pairs, write out the following texts sent by Mr. Speer
in complete, full-English-word sentences. 1.Omg I wz wrking out nd
I saw ths prsn nd thy wr dncing on th st in a graff cstme lol!
2.Wuz gr8 2 c u but omg g2g ttyl 3.Dd u c that txt frm 2zdy?
WTF.
- Slide 14
- DAY 2 Bellwork continued: Please translate the following
sentences into a text of no more than 10 characters. 1.The sum of a
number and twelve is forty. 2.The product of ten and a number, r,
is twice as much as twenty. 3.You start saving for college by
putting $20 into a savings account and add $5 each month. How many
months will it take to reach $500? Assume no interest.
- Slide 15
- DAY 2
- Slide 16
- Class Logistics SUPPLIES CHECK! Syllabus Grade breakdown,
assignment submission, emailing, late work
- Slide 17
- DAY 2 Rules/Procedures on white board, write the most important
rule to you in any classroom 1. Top three rules on the front wall
2. OVERALL: Raise Your Hand! 3. A time for listening, a time for
talking Responsibility for actions regardless of intent 1. Late
better have a pass or a tardy slip! 2. Materials have textbook,
notebook, binder, graphing calc, pencils, pens every day! if not,
deduction in Demeanor grade 3. Homework on time and completed, not
partial if not, no credit must be responsible, ask for help after
school, at lunch, etc.
- Slide 18
- DAY 2 4. Cell Phones even if they beep this year, Im taking
them. Responsibility turn them off! If not, I will keep them for
two days (more if repeat offender) 5. Backpacks/other belongings
outside if not, Ill confiscate them 6. Changing Rooms light chatter
ok, but should be silent upon entering any of the buildings or
classroom so as not to disturb other meetings and classes 7.
Emergencies remain calm! Stay SILENT and listen to teacher. Why is
this also important in a drill?
- Slide 19
- DAY 2
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- Vocabulary to know and use often: 1.Term 2.Coefficient
3.Constant Term - An expression that is a number, variable, or the
product of both. The numerical factor of a term. A term with no
variables.
- Slide 21
- DAY 2
- Slide 22
- Homework worksheets ALL PROBLEMS!
- Slide 23
- LESSON 1: DAY 3 ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL
NUMBERS IN EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES
- Slide 24
- DAY 3 TO TURN IN: NOTHING, KEEP HOMEWORK ON DESK
- Slide 25
- DAY 3 PRAYER
- Slide 26
- DAY 3
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- When solving a word problem, 1.Figure out what your variable is
look for key phrases like "What is," "Find, or "Solve for What are
the measurable pieces of information in the problem? 2. Set up an
expression or equation using the variable(s). 3. Solve the
equation(s).
- Slide 28
- DAY 3 Word Problems to solve With your group, try the word
problems on the sheet. Lets do the first one together.
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- DAY 3 Homework worksheet ALL PROBLEMS!
- Slide 30
- LESSON 1: DAY 4 ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL
NUMBERS IN EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES
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- DAY 4 TO TURN IN: NOTHING TODAY TAKE OUT NOTES
- Slide 32
- DAY 4 PRAYER
- Slide 33
- DAY 4 - REVIEW FROM WEEK ON WHITEBOARDS
- Slide 34
- DAY 4 - REVIEW FROM WEEK Vocabulary to know and use often:
1.Term 2.Coefficient 3.Constant Term - An expression that is a
number, variable, or the product of both. The numerical factor of a
term. A term with no variables.
- Slide 35
- DAY 4
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- Inequality Solution and Graph Practice Problems on Document
Camera in Class Notebook
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- DAY 4 Homework worksheet ALL PROBLEMS! QUIZ MONDAY on First
week topics.
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- LESSON 2: DAY 1 STRUCTURE AND PATTERNS OBJECTIVE: SWBAT MAKE
USE OF STRUCTURE AND PATTERNS TO GENERALIZE FORMULAE
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- DAY 1 To Turn In: Nothing. Warmup: Please have all of your
required materials placed in the basket underneath your desk. Dress
Code Check! Quiz time! You may have your calculator.
- Slide 41
- DAY 1 - Turn quizzes in to your class tray. - Please remain
silent until ALL quizzes are turned in. (15 min) - After the Quiz:
You may begin your Homework for tonight.
- Slide 42
- DAY 1 OBJECTIVE: SWBAT MAKE USE OF STRUCTURE AND PATTERNS TO
GENERALIZE FORMULAE WHAT DOES THIS MEAN? LETS TRY SOME!
- Slide 43
- DAY 1 Staircases Activity: Given the first two
block-staircases, can you determine how many blocks comprise the
third staircase? The 6-step staircase? The 50-step staircase? How
about the n-step staircase?
- Slide 44
- DAY 1 How can we determine the number of blocks in each
staircase?
- Slide 45
- DAY 1 Homework (ALL Due Thursday) 1. READ and take notes
(Cornell) on pages 4-6 of textbook. Include the "Got It?" questions
and their solutions in your notes. 2. DO page 7-9 #8-15 All, 25-31
All
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- LESSON 2: DAY 2 STRUCTURE AND PATTERNS OBJECTIVE: SWBAT MAKE
USE OF STRUCTURE AND PATTERNS TO GENERALIZE FORMULAE
- Slide 47
- DAY 2 To Turn In: Nothing. Take out your notes on the Staircase
Problem from yesterday and compare solution ideas at your pod.
- Slide 48
- DAY 2
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- Skeleton Towers Activity: Given the first three skeleton
towers, can you determine how many blocks comprise the 4 th
skeleton tower? The 5 th skeleton tower? The 10 th skeleton tower?
How about the nth skeleton tower?
- Slide 50
- DAY 2 How can we determine the number of blocks in each
skeleton tower? Extension: How about Skeleton Castles? How many
blocks are in the nth skeleton castle?
- Slide 51
- DAY 2 Homework (ALL Due Thursday) 1. Homework from yesterday 2.
DO page 7-9 #16-24 All, 37- 40 All 3. (Optional: Determine how many
blocks are in the nth skeleton castle?)
- Slide 52
- LESSON 2: DAY 3 STRUCTURE AND PATTERNS OBJECTIVE: SWBAT MAKE
USE OF STRUCTURE AND PATTERNS TO GENERALIZE FORMULAE
- Slide 53
- DAY 3 Keep at desk: All HW problems from Monday and Tuesday
Reminders: 1. Be in the room by the bell! 2. Complete the HW come
for Qs! 3. Bags NOT ON the piano 4. I am assessing you on
participation and presentation be willing to answer!
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- DAY 3 PRAYER
- Slide 55
- DAY 3 One final pattern: THINK/WRITE What are the next two
figures in the pattern? (2 min) PAIR How many blocks are in the 100
th pattern? (3 min) SHARE What is the rule for this pattern? (rule
means formula or equation)
- Slide 56
- DAY 3 Linear patterns have the same rate of change from data
point to data point Rate of change = SLOPE What does this mean? -
The difference between each output value is the same RELATIVE TO
the difference in each input value - We can always start a linear
pattern problem by trying to find the SLOPE.
- Slide 57
- DAY 3 EXAMPLE: Linear Data problem InputOutput 2 10 4 14 6 18 8
22 12 30 +4 +8? +2 +4 ? We only pay attention to the data values
that have the same difference in input values, so (12,30) does not
factor into the creation of our pattern here.
- Slide 58
- DAY 3 Exit Ticket (on a half sheet): Lesson Check page 7 #1-4,
7
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- DAY 3 HOMEWORK: Due TOMORROW, FRIDAY Textbook pg 8-9 #32-36
All, 41-45 All
- Slide 60
- LESSON 3: DAY 1 MULTIPLE REPRESENTATIONS OF LINEAR FUNCTIONS
OBJECTIVE: SWBAT CONVERT BETWEEN A TABLE, GRAPH, AND EQUATION OF A
LINEAR FUNCTION
- Slide 61
- DAY 1 Keep at desk: ALL HW Problems Peer HW Review Time!
Correct or incorrect, FULL solutions = check PLUS Correct or
incorrect, decent effort = check mark Some problems blank = check
MINUS Just answer is written, no work shown, problems missing=
X
- Slide 62
- LESSON 3: DAY 1 MULTIPLE REPRESENTATIONS OF LINEAR FUNCTIONS
OBJECTIVE: SWBAT CONVERT BETWEEN A TABLE, GRAPH, AND EQUATION OF A
LINEAR FUNCTION
- Slide 63
- DAY 1 From HW: #34 Multiple Representations of Functions
Graphical Graph, Picture, Chart Numerical Table of Values Algebraic
Equation, Function Rule Verbal Explanation, Application
- Slide 64
- DAY 1 What about this one? # of M&Ms eaten Calories gained
16 7 12 5 4 1 9 3.5 24 11 -Difficult, why? -Try plotting on W.B. -
So lets organize the data values by organizing inputs from least to
greatest.
- Slide 65
- DAY 1 NOW, try it! # of M&Ms eaten Calories gained 4 1 9
3.5 12 5 16 7 24 11 -There is still not a clear pattern. -How can
we tell if there is a pattern?
- Slide 66
- DAY 1 # of M&Ms eaten Calories gained 4 1 9 3.5 12 5 16 7
24 11
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- DAY 1 # of M&Ms eaten Calories gained 4 1 9 3.5 12 5 16 7
24 11
- Slide 68
- DAY 1 FINAL Problem: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g
17.42 g
- Slide 69
- DAY 1 HOMEWORK: Due Monday 1. READ pages 60-64 of your textbook
on functions and take notes on important concepts, vertical line
test, and function notation 2. Use the example problems on pages
60-64 to DO page 64 #1-4, 3. HW Quiz next class?
- Slide 70
- LESSON 3: DAY 2 MULTIPLE REPRESENTATIONS OF LINEAR FUNCTIONS
OBJECTIVE: SWBAT CONVERT BETWEEN A TABLE, GRAPH, AND EQUATION OF A
LINEAR FUNCTION
- Slide 71
- DAY 2 Keep on desk: Homework (notes and problems) - Using your
notes only, HW Quiz! Need half sheet of paper, numbered 1-3. - Turn
HW Quiz in to class tray and remain quiet while classmates finish.
(Write down and begin HW!)
- Slide 72
- DAY 2 Last Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42
g
- Slide 73
- DAY 2 Last Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42
g Problem: We didnt all get the same slope, but our data looked
linear on the graph. Welcome to the real world! Not a perfect fit.
We must now find a way to model the data as best as we can.
- Slide 74
- DAY 2- LINEAR REGRESSION EQUATIONS Lets use our calculators! To
plot the data on your calculator: Click HereClick Here for step by
step instructions. Take notes on these!
- Slide 75
- DAY 2 - LINEAR REGRESSION EQUATIONS This Week: Mass (g) 14.71 g
11.32 g 21.85 g 19.87 g 17.42 g
- Slide 76
- This Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42 g DAY
2 - LINEAR REGRESSION EQUATIONS
- Slide 77
- DAY 2 FUNCTIONS - A function is a relation in which each
element of the domain corresponds with exactly one element of the
range. - A relation is a set of pairs of inputs and outputs.
- Slide 78
- DAY 2 FUNCTIONS As with any machine, we want to know exactly
what happens when we input a specific piece of data. If you pressed
the print button on the printer, and the printer might print OR it
might turn off, that printer would not be very effective. This is a
relation, but NOT a function. (Ex 2)
- Slide 79
- DAY 2 FUNCTIONS - To determine if it is a function: 1.
Numerically (table) refer to last slide. If each distinct input
only points to ONE output, it is a function. 2. Graphically the
vertical line test. (next slide) 3. Algebraically That is our
mission this whole year! (When I plug in ANY value to the function,
do I get a MAXIMUM of ONE possible output?)
- Slide 80
- DAY 2 FUNCTIONS - Vertical Line Test: to test if a graph is a
function - If a vertical line can be drawn that touches MORE than
one point on the graph, the relation is NOT a function. NO YES
- Slide 81
- DAY 2 HOMEWORK: Due Thursday 1. Study for QUIZ tomorrow on
Patterns, Multiple Representations, and Functions Basics 2.
Complete worksheet packet pgs 3 and 4 - all problems for tonight.
(Whole packet will be due Thursday)
- Slide 82
- LESSON 3: DAY 3 MULTIPLE REPRESENTATIONS OF LINEAR FUNCTIONS
OBJECTIVE: SWBAT CONVERT BETWEEN A TABLE, GRAPH, AND EQUATION OF A
LINEAR FUNCTION
- Slide 83
- DAY 3 Not due Today: Worksheet packet - Bellwork: Plot the data
points below on your calculator and find the equation of the
best-fit line. Include the correlation coefficient (r). XY 1.00
2.00 3.001.30 4.003.75 5.002.25 Reference yesterdays notes! What
does the r value mean?
- Slide 84
- DAY 3 1. In pairs, try Problem #2 on handout. 2. You will begin
the quiz with 21 minutes left in class.
- Slide 85
- DAY 3 HOMEWORK: Due Thursday 1. Finish the Chemistry worksheet
problem 2. Complete worksheet packet pgs 23 and 26 - all problems
for tonight. The whole packet will be due Thursday. Pages
3,4,23,26
- Slide 86
- LESSON 4: DAY 1 THE EQUATION OF A LINE OBJECTIVE: SWBAT
DETERMINE THE SLOPE-INTERCEPT FORM OF A LINE IN THE (X,Y)
COORDINATE PLANE KEEP AT YOUR DESK: HW WORKSHEETS
- Slide 87
- DAY 1 - Bellwork: Individually, Calculate the correlation
coefficient (r) for the following two scenarios from the in-class
problem last class: 1. Linear Regression for (Volume, Mass) using
the Displacement method 2. Linear Regression for (Volume, Mass)
using the cylinder formula method QUESTIONS: 1. Which of the two
methods fits better? 2. What does the slope mean? What are the
units of the slope?
- Slide 88
- DAY 1 HW Questions? Honors only: Write the equation of a line
connecting the points (-1,6) and (4,-4). Keep answer to
yourself.
- Slide 89
- DAY 1 Finding the Equation of a line Notes and Examples Try
some! Use page 78 #9-21 Odds to check yourself.
- Slide 90
- DAY 1
- Slide 91
- HOMEWORK: Due Monday 1. Finish worksheet on finding equations
of lines given two points ALL problems 2. READ pages 74-85 and take
notes on the sections Next Quiz: Next Tuesday Next Test: MONDAY,
AUGUST 31st!
- Slide 92
- LESSON 4: DAY 2 THE EQUATION OF A LINE OBJECTIVE: SWBAT
DETERMINE THE SLOPE- INTERCEPT FORM OF A LINE IN THE (X,Y)
COORDINATE PLANE KEEP AT YOUR DESK: HW WORKSHEET
- Slide 93
- DAY 2 - Bellwork (Alg 2): Solve for y in the following
equations. 1. 3y = 3x - 6 2. 10 y = 8 3. 2x + 5y = 10 4. 4 - 2x +
6y = 10 5. -2(x + 5) = 4(y - 4)
- Slide 94
- DAY 2
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- - HW Questions? - Reflection on Quizzes
- Slide 96
- DAY 2 EQUATION OF A LINE What information are you given? Two
points on the line (x,y) and (x,y) Slope and another point
(sometimes y-int) Equation in another form (Standard or Point-
Slope) Information (parallel/perp) leading to slope 1. Find the
SLOPE 1. Solve for y 2. Solve for b. (y-intercept y-coordinate) Use
one of the points you are given along with the SLOPE, and plug
those x,y,and m values into the equation y=mx+b. Substitute the
value for m and b into y=mx+b form. 2. Simplify the mx+b side of
the equation
- Slide 97
- DAY 2 - Pod-Races!
- Slide 98
- DAY 2 HOMEWORK: Due Thursday 1. READ pages 74-85 and take
notes, DO pages 86-87 #11-25 Odds, #30- 31, #33-41 Odds 2. Study
for Quiz tomorrow (Tuesday) on writing linear equations given
points, slope, y-intercept, or any other information. Next Test:
MONDAY, AUGUST 31st!
- Slide 99
- LESSON 5: DAY 1 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT
WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES HW DUE
THURSDAY
- Slide 100
- DAY 1 Honors only: Calculate the x- and y- intercepts of the
lines
- Slide 101
- DAY 1 GRAPHING LINES - Graph the line 2x-3y=6 - Steps for
graphing a line: 1. Change the equation into slope-intercept form.
2. Using the y-coordinate of the y-intercept (b), plot a point on
the y-axis for the y-int. 3. Using the rise and run values of the
slope, go up/down and left/right to the location of another point.
Plot a point there. 4. Connect the two points with a smooth line,
continuing the rise and run trend.
- Slide 102
- DAY 1 GRAPHING LINES - Example Problem: Graph the line that is
perpendicular to y=4x-3 and goes through the point (8,10)
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- DAY 1 GRAPHING LINES
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- AB DC
- Slide 105
- DAY 1 GRAPHING LINES A B D C
- Slide 106
- DAY 1 GRAPHING LINES - QUIZ TIME! - Clear your desks.
- Slide 107
- DAY 1 HOMEWORK: Due Thursday 1. READ pages 74-85 and take
notes, DO pages 86-87 #11-25 Odds, #30- 31, #33-41 Odds 2. READ
pages 114-115 and take notes, DO pages 118-119 #9-15 Odds, 39-41
all Next Test: MONDAY, AUGUST 31st!
- Slide 108
- LESSON 5: DAY 2 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT
WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES KEEP ON YOUR
DESK: HW PROBLEMS
- Slide 109
- DAY 2 GRAPHING LINES
- Slide 110
- Slide 111
- Finding Intercepts of equations. 1. Y-intercepts Where the
graph crosses the y-axis. - All y-intercepts have an x-coordinate
of 0. - To find the y-intercept in an equation, substitute 0 in for
x. - y-intercept: (0,b) 2. X-intercepts Where the graph crosses the
x-axis. - All x-intercepts have a y-coordinate of 0. - To find the
x-intercept in an equation, substitute 0 in for y. - X-intercept:
(a,0)
- Slide 112
- DAY 2 GRAPHING LINES Find the intercepts on our graphing
calculator! - Y-intercepts 1. Write the equation in the (Y=) menu.
Y=, then type in the equation 2. Graph the line. ZOOM then 6 OR
GRAPH 3. TRACE this allows you to type in an x-value and see its
corresponding y-value TRACE, then 0, then ENTER - X-intercepts 1.
Do steps #1-2 from above 2. 2 ND , then the TRACE button 3. Select
choice 2:ZERO 4. Scroll to the left of where the x-intercept is on
the graph using the left and right arrows, Press ENTER. 5. Scroll
to the right of where the x-intercept is on the graph using the
left and right arrows, Press ENTER. 6. Press ENTER one more time,
and the coordinates will display on the bottom of the screen.
- Slide 113
- DAY 2 GRAPHING LINES
- Slide 114
- DAY 2 HOMEWORK: Due Friday Review questions (optional): 1.
Pages 123-124 #1-8, 16-30 All Page 127 #1-20, 23-26, 31, 32, #37(on
calculator) 2. TEST REVIEW SESSION: After school today! 3. STUDY
FOR TEST MONDAY! Textbook sections 1-1, 1-2, 1-3, 1-4, 1-5, 2-1,
2-3, 2-4, and 2-8
- Slide 115
- LESSON 5: DAY 3 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT
WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES KEEP ON YOUR
DESK: HW PROBLEMS
- Slide 116
- DAY 3 Any Homework/Review Questions? (15 minutes)
- Slide 117
- DAY 3 The Stroop Test - In Psychology, The Stroop Test is named
after J. Ridley Stroop who discovered this idea in the 1930s. - The
Stroop Test measures two things: 1. Speed of Processing Theory 2.
Selective Attention Theory
- Slide 118
- DAY 3 The Stroop Test - Lets try it! - Today: Collect Data from
experiment - Tuesday: Part 2 of your Test will be an in-class
Performance Assessment of your data from the Stroop Test - You will
need to know: slopes, finding equation of a line, problem-solving
and interpretation of results, how to interpret a best-line on a
scatter plot
- Slide 119
- DAY 3 HOMEWORK: Not due, just review Review questions
(optional): 1. Pages 123-124 #1-8, 16-30 All Page 127 #1-20, 23-26,
31, 32, #37(on calculator) 2. STUDY FOR TEST MONDAY! Textbook
sections 1-1, 1-2, 1-3, 1-4, 1-5, 2-1, 2-3, 2-4, and 2-8 3. Try any
and all problems on Review Guide