Algebra I CM third marking term

Algebra I CM third marking term

Algebra I CMthird marking termWicomico High SchoolMrs. J. Austin2009-2010Chapter 7 : System of EquationsWelcome to Algebra CM3 minutes

Seating Chart

Classroom Sets of Books

1Class FormatMiniQuiz: 10 minutesCognitive Tutor Program on Computer

GROUP A DAY 1

GROUP B DAY 2Textbook Lesson / Practice at Desk

GROUP B DAY 1

GROUP A DAY 2

Cognitive Tutor ProgramSelf-pacing program with immediate feedback.Log-in using your first name and last nameThe lesson will open and to begin you will click on the yellow box in the upper right-hand corner.The first lesson has eight sections of Solving EquationsOn the right-hand side of the screen, there are two drop-down menus. Transformations and ApplicationsUse the choices to solve the problemClick Done and the next problem will appearRED means incorrect. Use the UNDO button and try again.Systems of Linear EquationsTwo linear equations graphed on the SAME coordinate plane.

What are the THREE things that could happen?

They could CROSS or INTERSECT

They could NEVER CROSS or be PARALLEL

They could be ON TOP OF EACH OTHER or COINCIDESolving a System of Linear EquationsBy Solving a System of Linear Equations, we are asking:

Are there any Values for x and y that will satisfy or make BOTH equations TRUE?

Is there a POINT that will make BOTH equations TRUE?

What is the POINT OF INTERSECTION of these two lines?

Find the values for x and y that will make BOTH equations TRUE.

5Solving a System By Graphing 7.1Transform each equation to Slope-Intercept Form

For EACH of the TWO equations:PLOT the y intercept, b COUNT, rise over run using the Slope, m.DRAW the straight line.

Cognitive Tutor Packet: Intro to Systems

6Solving a System By Graphing 7.1Transform each equation into Slope-Intercept Form.

Solving a System By Graphing 7.1GROUP A:

Work SessionSolving Systems using the Graphing Method.

Textbook: Pg. 431 (1-28)

GROUP B:

Computer SessionCognitive Tutor Unit 19 Solving Equations

DAY 1Solving a System By Graphing 7.1GROUP B:



GROUP A:


DAY 2Solving a System By Substitution 7.2 Transitive Property A variable can be REPLACED with its equivalent.If two equations equal the SAME thing, they must then EQUAL each other. AND THEN The two equations are SET equal to each other

Textbook 7.2 Use Cognitive Tutor Packet #1 10Solving a System By Substitution EXAMPLE:

Now we know y=2.Substitute this into an equations to find x.

Solve the first equation for x.

Substitute the expression in for x in the second equation.

Now SOLVE for y.

Solving a System By Substitution GROUP A:

Work SessionSolving Systems using the Substitution Method.

Textbook: Pg. 439 (1-28)GROUP B:


DAY 1Solving a System By Substitution GROUP B:

Work SessionSolving Systems using the Substitution Method.

Textbook: Pg. 439 (1-28)GROUP A:


DAY 2Solving a System By Elimination 7.3Transitive Property Replace a variable with its equivalent.Set two expressions equal to each other, when they BOTH equal the same thing!Property of EqualityAdd or Subtract two equations to create a new equivalent equation.Transform the look of an equation by multiplication.Cognitive Tutor Packet #214Solving a System By Elimination 7.3Using Addition:

___________

Write the equations one above the other. Be sure the variables are lined up.Draw a line under them.Combine the Like-Terms to create a NEW equation.Solve for the variable.Substitute your answer into one of the equations to find the other variable.

Solving a System By Elimination 7.3Using Subtraction

_____________Write the equations one above the other. Be sure the variables are lined up.

Draw a line under them.

Subtract the Like-Terms to create a NEW equation.

Solve for the variable.

Substitute your answer into one of the equations to find the other variable.

Cognitive Tutor Packet #316Solving a System By Elimination 7.3GROUP A:



GROUP B:


DAY 1Solving a System By Elimination 7.3GROUP B:


Textbook: Pg. 443 444(1-35)

GROUP A:


DAY 2Solving a System By Elimination 7.4Using MultiplicationBefore Adding or Subtracting:

___________________

__________________

Write the equations one above the other. Be sure the variables are lined up.Multiply the top equation by 4.Multiply the lower equation by 7.Draw a line under them.Distribute through each equation.Combine or Subtract the Like-Terms to create a NEW equation.

Cognitive Tutor Packet #419Solving a System By Elimination 7.4 Using Multiplication Before Adding or Subtracting.What would you MULTIPLY by?

Solve the System.

Did you get the solution:Solve the System.

Did you get the solution:

Cognitive Tutor Packet #420Solving a System By Elimination 7.4GROUP A:


Textbook: Pg. 454 - 455 (1-34)

GROUP B:


DAY 1Solving a System By Elimination 7.4GROUP B:


Textbook: Pg. 454 - 455 (1-34)GROUP A:


DAY 2Special Types of Systems 7.5One Solution:Lines Intersect at one point.Lines have different slopes.Lines may be PERPENDICULAR if they cross at 90 angles.

No Solution:Lines do not intersect.Lines have the SAME slope and DIFFERENT y-intercepts.Lines are PARALLEL.

Many Solutions:Lines touch on every point.Lines have the SAME slope and SAME y-intercepts.Line COINCIDE.Special Types of Systems 7.5 How Many Solutions Does the System Have?.System:

System:

System:

Answer Choices:

One Intersecting LinesNone Parallel LinesMany Coinciding Lines

Special Types of Systems 7.5GROUP A:


Textbook: Pg. 462 463 (1-31)GROUP B:


DAY 1Special Types of Systems 7.5GROUP B:


Textbook: Pg. 462 463 (1-31)

GROUP A:


DAY 2Writing and Solving Systems Slope Intercept Form:

Total Cost scenarios with given rates of change.

The movie theater charges $8 per a ticket for its general customers. It offers a movie club discount of $5 per ticket if you join the club for a one-time fee of $15. How many movies would you have to go see to make joining the club beneficial? Write a system. Let x = the number of movie tickets y = total cost

Mixed Review: Pg. 465 (42-61)27Writing and Solving Systems Standard or General Form:Two different Items are given.

At a grocery store, a customer pays a total of $9.70 for 1.8 pounds of potato salad and 1.4 pounds of coleslaw. Another customer pays a total of $6.55 for 1 pound of potato salad and 1.2 pounds of coleslaw. How much do 2 pounds of potato salad and 2 pounds of coleslaw cost?Write the system. Let: x = cost of potato salad y = cost of coleslaw.

Mixed Review: Pg. 465 (42-61)28Writing and Solving SystemsHigh School Assessment Practice Questions:READ the question ALL the way through.

RE-READ and define the variables.

RE-READ and WRITE two equations to model the scenario.

DECIDE which METHOD you will use to solve the System of Equations.

SOLVE the System.

RE-READ the question. Use YOUR SOLUTION to CONSTRUCT a written ANSWER to the question. HSA Packet29Solving a System By Writing 7.5GROUP A:


Textbook: Pg. 458 (1-6)Pg. 464 ( 36-40)GROUP B:


DAY 1Solving a System By Writing 7.5GROUP B:


Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40)

GROUP A:


DAY 2Solving Systems of Linear Inequalities 7.6Graphing Linear Inequalities:Graph the first line.Shade the area defined by the first line.Graph the second line.Shade the area defined by the second line.The SOLUTUION to the System of Linear Inequalities is the AREA OF INTERSECTION. Re-shade the section of the graph that has been shaded by both of the equations.Solving Systems of Linear Inequalities 7.6GROUP A:


Textbook: Pg. 458 (1-6)Pg. 464 ( 36-40)GROUP B:


DAY 1Solving Systems of Linear Inequalities 7.6GROUP B:


Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40)

GROUP A:


DAY 2Solving Systems of Linear Inequalities 7.6 Chp 7 ReviewTwo linear functions graphed on a coordinate plane.They could CROSS, INTERSECTThey could NEVER CROSS, PARALLELThey could be ON TOP OF EACH OTHER, COINCIDE

Solving a System By Graphing 7.1Solving a System By Substitution 7.2 Solving a System By Elimination 7.3

Identifying the Point of IntersectionTesting a Solution to a System of EquationsSpecial Types of Systems

Writing and Solving Systems of Equations

Surveys and SamplingTAKE A SAMPLE:Types of SamplingSimple Random SamplingEvery person has an equally likely chance of being chosen and each is independent of the other.Stratified Random Sampling The population is divided into groups, then by groups every person has an equally likely chance of being chosen and each is independent of the other.Convenient SamplingOnly people in your area get to participateSelf-Selected SamplingOnly people who volunteer to answer your survey get to participate.Representative SamplingThe people who get to answer your survey match the gender and ethnicity of the population.

Survey ProjectSTEP 1: Create 5 questions about the given topic.

STEP 2: Create two questionnaires on a half-sheet of paper each.

STEP 3: Decide on your Sampling Technique and how your are going to conduct your survey.

STEP 4: Conduct your Survey of the school population.

STEP 5: You must have a minimum of 30 responses to make the survey VALID.

STEP 6: Compile your results in a table and with a Box-and-Whisker Plot.

STEP 7: Create a POSTER to display your survey, graphics, and findings.

STEP 8: Write a summary and conclusion based on your survey results.Exponential Functions Chp 8 introGraphing Exponential Functions 8.5Growth Functions:Graphing Exponential Functions 8.6Decay Functions:The Laws of Exponents 8.1The Laws of Exponents 8.2Negative Exponents 8.3Exponents and Scientific Notation 8.4Chapter 8 ReviewSimulationsTypes of DevicesDice or Number CubeSix numbers; evens/oddsSpinnersAny number of sections of EQUAL size can be madeCoinsTwo sides, heads/tailsDeck of Playing CardsThirteen cards; Four Suits; Two ColorsColored Chips in a BagAny number of chips and colors can be usedRandom Number Generator (TI-84 calculator)Ten digits, any number of choices can be made.Random Number TableTen digits, any number of choices can be made.

Setting Up SimulationsDecide which device will FIT your numbers.PercentageFractionSimple FractionDevicesDesign10%Spinner10 Chips in Bag10 sections;1 red chip, others blue25%Two coinsSpinner 4 sections; 4 chips30%10Chips in a BagSpinner3 of one color, rest another color35%noneNumber Generator35 choices out of 10050%Coins, Cards, Spinner, Die ,etc.2 sections, colors, sides, 66.6%Dice, Spinner, Chips in a Bag1 die, 4 numbers3 chips, 2 one color75%Two Coins, Spinner,4 Chips, Cards, 4 sections, 3 one outcome, 1 the other

50Polynomial Functions Chp 9.Constant Function NOT a POLYNOMIALLinear Function 1st degree polynomialQuadratic Function 2nd degree polynomialCubic Function 3rd degree polynomialQuartic Function 4th degree polynomialFifth Degree Function

Activity: Pg. 560 Graphing Polynomial FunctionsGreenGlobs Software Let students play the game using polynomial shots51Types of FunctionsEven Functions degree is even tails go in the same directionOdd FunctionsDegree is oddTails go in opposite directionsOne-to-One FunctionsEvery x and be paired with only one yContinuous FunctionsNo breaks in the curve. No jumps, skips, holes, oscillations,.Discrete FunctionsFractions are not possible as outcomes. A series of points that are NOT connected.Piece-wise FunctionsThe function is defined by two or more equations.Each piece of the function has a different equation.Step FunctionsA discrete function with horizontal lines that appear like steps going up or down the y axis.Finite FunctionsThe function is BOUNDED The function has a distinct domain and/or rangeInfinite FunctionsThe function has NO BOUNDSThe function has an unrestricted Domain and Range, - to

Polynomial Vocabulary 9.1Classifying Polynomials:Monomial one termBinomial two termsTrinomial three termsPolynomial many terms

Degree of a PolynomialAdding Polynomials 9.1Two Step Process:Align the like-termsCombine the coefficients

Remember: The exponents DO NOT CHANGE

54Subtracting Polynomials 9.1Three Step Process:1. Distributing the negative sign2. Align the like-terms3. Combining the coefficients

Remember: The exponents DO NOT CHANGE

Page 557 558 (1-35)

55Work Session 9.1 Adding and Subtracting Polynomials Pg 558 (38 42) evens

Problem SolvingAlgebra Tiles 9.2Activity: Page 561Multiplying Polynomials 9.2Distributive MethodMultiplying Polynomials 9.3Square a BinomialDifference of SquaresMultiplying Polynomials 9.3FOIL MethodWork Session Page 572 (1-37)Multiplying Polynomials 9.3Punnett SquarePage 573 #40 and #42The Zero Product Property 9.4Finding the Zeros of a FunctionPages 578 (1-48)

62The Zero Product Property 9.4Vertical Motion Formula

Rocket Project Begins63Factoring Polynomials 9.5GCF Factoring out the Greatest Common FactorFactoring Polynomials 9.5F O I L (first, outer, inner, last)

Multiply to get C and add to get B

Multiply to get C and Subtract to get B

Pages 586 ( 1-41)65Factoring Polynomials 9.5Work Session Page 587 (42 55)Factoring Polynomials 9.5Work Session Page 588- 589 (59 81)67Factoring Polynomials 9.6Slip- Slide-Divide Method

Using Algebra Tiles Pg. 592 (1-8)

Factoring Polynomials 9.6Slip- Slide-Divide Method

Work Session Page 596 ( 1-21)






Work Session Page 598 599 (58-81)

QUIZ Factoring Polynomials 9.6Page 599 (1-25)Factor Special Products 9.7Difference of SquaresPerfect Square TrinomialsFactor Special Products 9.7Work Session: Page 603 (1-39)Factor Special Products 9.7Work Session: Page 604 - 605 (46-76)Factor Polynomials CompletelyFactoring Out a Common BinomialFactoring By Grouping 2 by 2Factoring By Grouping 3 by 1Factor Polynomials CompletelyFactoring Out a Common BinomialFactoring By Grouping 2 by 2Factoring By Grouping 3 by 1

Work Session: Pg. 610 (1-42)Factor Polynomials CompletelyFactoring Out a Common BinomialFactoring By Grouping 2 by 2Factoring By Grouping 3 by 1

Work Session: Pg. 611 (43-66)Factor Polynomials CompletelyFactoring Out a Common BinomialFactoring By Grouping 2 by 2Factoring By Grouping 3 by 1

Work Session: Pg. 612 (68-89)QUIZ Factor Polynomials 9.8Page 613 (1-19)Chapter 9 ReviewGraphing Quadratic Equations 10.1General Form of a Quadratic Function: A indicates the width of the parabolaB is used to find the Axis of SymmetryC is the y-intercept

Parabola Shape:Positive holds water concave upNegative doesnt hold water concave down

Shifting of the Parabola:Vertical ShiftHorizontal ShiftSkinnyWideGraphing Quadratic Equations 10.2Finding the Axis of Symmetry

Finding the Vertex (maximum or minimum)

Graphing a Parabola:Dot in the vertical line for the Axis of SymmetryPlot the VertexPlot the y-intercept and its reflected point.Plot another point and its reflection.Draw a smooth curve connecting the points.

Graphing Quadratic Equations 10.2Work Session: Page 638 639 (1-37)Conic Form of a ParabolaPage 669 ReferenceGreen Globs Activity:Solve Quadratic By Graphing 10.3Solve Quadratics With Square Roots 10.4Solve Quadratic By: Completing the Square 10.5Solve Quadratics By: the Quadratic Formula 10.6Quadratic Formula:The Discriminate of the Formula 10.7Comparing Linear, Exponential, and Quadratic Functions 10.8Performing RegressionWork Session with Graphing Calculators:

Page 692-694 (1-3)Chapter 10 ReviewBenchmark Review # 3

Algebra I CM third marking term

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