unit 1: linear functions with a review of algebra 1 basics

UNIT 1: LINEAR FUNCTIONS With a review of Algebra 1 Basics

LESSON 1: ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL NUMBERS IN EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES

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

DAY 1 PRAYER

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

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.

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.

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?

Homework worksheets ALL PROBLEMS!

LESSON 1: DAY 2 ALGEBRA REVIEW OBJECTIVE: SWBAT USE REAL NUMBERS IN EXPRESSIONS, EQUATIONS, AND OTHER ALGEBRAIC DEVICES

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.

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.

Class Logistics SUPPLIES CHECK! Syllabus Grade breakdown, assignment submission, emailing, late work

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.

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?

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.

Homework worksheets ALL PROBLEMS!

DAY 3 TO TURN IN: NOTHING, KEEP HOMEWORK ON DESK

DAY 3 PRAYER

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).

DAY 3 Word Problems to solve With your group, try the word problems on the sheet. Lets do the first one together.

DAY 3 Homework worksheet ALL PROBLEMS!

DAY 4 TO TURN IN: NOTHING TODAY TAKE OUT NOTES

DAY 4 PRAYER

DAY 4 - REVIEW FROM WEEK ON WHITEBOARDS

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.

Inequality Solution and Graph Practice Problems on Document Camera in Class Notebook

DAY 4 Homework worksheet ALL PROBLEMS! QUIZ MONDAY on First week topics.

LESSON 2: DAY 1 STRUCTURE AND PATTERNS OBJECTIVE: SWBAT MAKE USE OF STRUCTURE AND PATTERNS TO GENERALIZE FORMULAE

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.

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.

DAY 1 OBJECTIVE: SWBAT MAKE USE OF STRUCTURE AND PATTERNS TO GENERALIZE FORMULAE WHAT DOES THIS MEAN? LETS TRY SOME!

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?

DAY 1 How can we determine the number of blocks in each staircase?

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

DAY 2 To Turn In: Nothing. Take out your notes on the Staircase Problem from yesterday and compare solution ideas at your pod.

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?

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?

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?)

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!

DAY 3 PRAYER

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)

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.

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.

DAY 3 Exit Ticket (on a half sheet): Lesson Check page 7 #1-4, 7

DAY 3 HOMEWORK: Due TOMORROW, FRIDAY Textbook pg 8-9 #32-36 All, 41-45 All

LESSON 3: DAY 1 MULTIPLE REPRESENTATIONS OF LINEAR FUNCTIONS OBJECTIVE: SWBAT CONVERT BETWEEN A TABLE, GRAPH, AND EQUATION OF A LINEAR FUNCTION

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

DAY 1 From HW: #34 Multiple Representations of Functions Graphical Graph, Picture, Chart Numerical Table of Values Algebraic Equation, Function Rule Verbal Explanation, Application

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.

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?

DAY 1 # of M&Ms eaten Calories gained 4 1 9 3.5 12 5 16 7 24 11

DAY 1 FINAL Problem: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42 g

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?

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!)

DAY 2 Last Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42 g

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.

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!

DAY 2 - LINEAR REGRESSION EQUATIONS This Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42 g

This Week: Mass (g) 14.71 g 11.32 g 21.85 g 19.87 g 17.42 g DAY 2 - LINEAR REGRESSION EQUATIONS

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.

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)

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?)

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

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)

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?

DAY 3 1. In pairs, try Problem #2 on handout. 2. You will begin the quiz with 21 minutes left in class.

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

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

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?

DAY 1 HW Questions? Honors only: Write the equation of a line connecting the points (-1,6) and (4,-4). Keep answer to yourself.

DAY 1 Finding the Equation of a line Notes and Examples Try some! Use page 78 #9-21 Odds to check yourself.

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!

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

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)

- HW Questions? - Reflection on Quizzes

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

DAY 2 - Pod-Races!

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!

LESSON 5: DAY 1 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES HW DUE THURSDAY

DAY 1 Honors only: Calculate the x- and y- intercepts of the lines

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.

DAY 1 GRAPHING LINES - Example Problem: Graph the line that is perpendicular to y=4x-3 and goes through the point (8,10)

DAY 1 GRAPHING LINES

DAY 1 GRAPHING LINES A B D C

DAY 1 GRAPHING LINES - QUIZ TIME! - Clear your desks.

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!

LESSON 5: DAY 2 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES KEEP ON YOUR DESK: HW PROBLEMS

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)

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.

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

LESSON 5: DAY 3 GRAPHING EQUATIONS AND INEQS OBJECTIVE: SWBAT WRITE AND GRAPH LINEAR EQUATIONS AND INEQUALITIES KEEP ON YOUR DESK: HW PROBLEMS

DAY 3 Any Homework/Review Questions? (15 minutes)

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

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

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

unit 1: linear functions with a review of algebra 1 basics

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