Honors Algebra 1 Mr. Wells.

Honors Algebra 1 Mr. Wells

Day One: September 6th Objective: Discuss the syllabus and classroom procedures. THEN Interpret points and continuous graphs, understanding that a point conveys two pieces of information and that a continuous graph conveys trends. Introduction: Books, syllabus, homework sheet 1-1 to 1-2 (pgs 3 & 5, RscrcPg) Conclusion Homework: Fill out information sheet, last page of syllabus, extra credit tissues OR hand sanitizer, and 1-3 to 1-6 (pgs 6-7)

Support www.cpm.org www.hotmath.com My Webpage on the HHS website
Homework help and answers Resources (including worksheets from class) Extra support/practice Parent Guide Pay site All the problems from the book My Webpage on the HHS website Classwork and Homework Assignments Worksheets Extra Resources

Getting To Know You, Part 1
Find the other students who have the missing pieces of your graph. Every graph will have sections 1, 2, 3, and 4. Locate a group of desks to sit in (Not permanent). Choose a scenario for your graph from the list below. Make sure to discuss how the graph fits the scenario. A Runner in a timed race Temperature changing over time Babysitting earnings over time Label the x- and label the x- and y-axes. (For example you can use labels such as time, distance, height, years, months, minutes, water level, meters, yards, seconds, number of people, distance from the ground, volume, etc.)

Getting To Know You, Part 2

Area and Perimeter 40 units 75 square units
Perimeter: The distance around the edge of a figure Area: The number of square units the figure covers 40 units 75 square units 6

Day Two: September 7th Objective: Practice using the Cartesian coordinate system by labeling and reading points. Also, begin to identify linear patterns. 1-7 to 1-8 (pgs 8-9) Conclusion Homework: 1-9 to 1-14 (pgs 10-11)

Diamond Problems Use the pattern we discovered in the homework to complete the diamonds below. 15 10 ab 5 3 1 10 a b 8 11 a+b

y-axis goes up and down just like the tail in the letter
Coordinate Plane + y-axis goes up and down just like the tail in the letter y-axis Quadrant I Quadrant II – + x-axis Quadrant III Quadrant IV –

How to Plot or Name a point
A coordinate point describes a position on the Cartesian Plane. A point is always listed as: ( x , y ) Alphabetical The first number tells how far left (-) or right (+) The second number tells far down (-) or up (+) Example: Plot (-4,3) 4 left since it is negative 3 up since it is positive

Day Three: September 9th
Objective: Introduce X-Y tables and scatter plots as tools for organizing data and making predictions. Also the scaling of axes of a graph and the concept of dependent and independent measures. THEN How to extend a tile pattern and how to generalize the geometric description of the pattern. Homework Check 1-15 to 1-19 (pgs 12-14) Wells Time 1-31 to 1-32 (pg 18) Conclusion Homework: 1-21 to 1-30 (pgs 16-17) AND 1-34 to 1-39 (pgs 20-21)

Average The number that is found by dividing the sum of data by the number of items in the data set. Example: Ted is 4.1 feet tall, Greg is 5.3 feet tall, and Ally is 4.3 feet tall. Find their average height. Feet

1-31: Growing, Growing, Growing
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig # 1 2 3 4 5 100 Tiles 8 15 24 Generalize Pattern/Find a Rule:

1-31: Find a Convenient Shape
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig # 1 2 3 4 5 100 Tiles 8 15 24 3 35 10200 Generalize Pattern/Find a Rule:

1-31: Make a Convenient Shape
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig # 1 2 3 4 5 100 Tiles 8 15 24 3 35 10200 Generalize Pattern/Find a Rule:

1-32: New Tile Patern 19 3 7 24 Fig # 1 2 3 4 5 Tiles 11 15 19 79
1 2 3 4 5 Tiles 11 15 19 79 19 3 7 24 Generalize Pattern/Find a Rule:

5 1 6 1 3 5 7 9 11 13 LINEAR # OF TILES = Fig # *2, +1 +2 +2 +2 +2 +2
4 Tiles 1 6 1 3 5 7 9 11 13 +2 +2 +2 +2 +2 +2 LINEAR How is the pattern changing? The growth rate is consistent. From one figure to the next, 2 tiles are always added. # OF TILES = Fig # *2, +1 Rule?

5 1 6 1 4 7 10 13 16 19 LINEAR # OF TILES = Fig # *3, +1 +3 +3 +3 +3
2 3 4 Tiles 1 6 1 4 7 10 13 16 19 +3 +3 +3 +3 +3 +3 LINEAR How is the pattern changing? The growth rate is consistent. From one figure to the next, 3 tiles are always added. Rule? # OF TILES = Fig # *3, +1

Day 4: September 12th Objective: Solve a complex problem and develop a new problem-solving strategy called “Guess and Check.” Students will organize their guesses into a Guess and Check table. THEN Continue to develop our Guess and Check organizational strategies for traditional word-problems Homework Check 1-40 to 1-43 (pgs 22-24, RscrcPg) Wells Time 1-50 to 1-51 (pgs 26-27) Conclusion Homework: 1-44 to 1-49 (pgs 25-26) AND 1-54 to 1-58 (pg 29)

1-50: Bull’s-Eye Jamie hit 12 bulls-eyes and 38 outer-ring shots! 10
Guess: # of Bulls-eyes # of Outer-Ring Shots Total Points Check: (?=160) 10 50 – 10 = 40 7(10) + 2 (40) = 150  Too low 15 50 – 15 = 35 7(15) + 2(35) = 175  Too high 12 50 – 12 = 38 7(12) + 2(38) = 160  Yes, sir! Jamie hit 12 bulls-eyes and 38 outer-ring shots!

Rules for Guess and Check
In order to receive credit for a guess and check answer… There must be at least two bad guesses There must be organization (I recommend a a table) The final answer must have units

Day 5: September 13th Objective: Continue to develop our Guess and Check organizational strategies for traditional word-problems. THEN Assess Chapter 1 in a team setting. Homework Check 1-59 to 1-63 (pgs 30-31) Wells Time Chapter 1 Team Test 2-1 (pg 41) Conclusion Homework: 1-65 to 1-69 (pgs 31-32)

Day 6: September 14th Objective: Introduction to algebra tiles, which will start our work with algebraic expressions and equations. THEN Finding the perimeter of shapes while learning the difference between the dimensions (length and width) and area. Also, simplifying expressions by combining like terms. Homework Check 2-1 to 2-5 (pgs 41-42) Wells Time 2-12 to 2-14, 2-16 (pgs 44-45) Conclusion Homework: 2-6 to2-11 (pgs 42-43) AND 2-17 to 2-21 (pgs 45-46)

*Make sure all tiles are positive side up (negative [red] side down)*
Algebra Tiles *Make sure all tiles are positive side up (negative [red] side down)* 1 1 x x x2 Tile Area = 1 5 y y 1 x Unit Tile Area = x Area = x2 1 x Tile 5 Piece Area = 5 1 y Area = y Area = y2 y2 Tile xy Tile x y Tile y Area = xy

Algebra Tiles: Perimeter
*Make sure all tiles are positive side up (negative [red] side down)* Algebra Tiles: Perimeter 1 y 1 1 x 1 1 1 1 x x x x P = 4 5 5 y y y y 1 x P = 2x + 2 P = 4x 1 P = 12 y 1 y P = 2y + 2 P = y + y + y + y = 4y x x y P = 2x +2y

Answers to 2-13

Commutative Properties
Are two the expressions equivalent? Commutative Property of Addition: When adding two or more numbers together, order is not important Commutative Property of Multiplication: When multiplying two or more numbers together, order is not important Are there Commutative Properties for Subtraction and Division?

A symbol which represents an unknown.
Variable A symbol which represents an unknown. Examples: m x z y

Day 7: September 15th Objective: Introduction to algebra tiles, which will start our work with algebraic expressions and equations. THEN Finding the perimeter of shapes while learning the difference between the dimensions (length and width) and area. Also, simplifying expressions by combining like terms. Homework Check 2-22 to 2-26, 2-28 (pgs 47-48) Wells Time 2-34 to 2-40 (pgs 51-52) Conclusion Homework: 2-29 to 2-33 (pgs 49-50) AND 2-41 to 2-46 (pgs 53-54)

Combining like Terms Terms: Variable expressions separated by a plus or minus sign. Like terms: Terms with the same variable(s) raised to the same power. Combine Like Terms: Add the the numbers the liked terms are being multiplied by. Ex: Simplify the expression below: 6x2 + 4x x2 + 3x + 6 The x2 Tile The x Tile x2 x 5 x2 x 6 8x2 + 7x + 11 Unit Tiles 6+2 4+3 5+6

Substitution and Evaluation
Substitution: Replace each vairable with its indicated value. Evaluation: Simplify the expression with proper order of operations. Example: Evaluate the expression below if x = 3 and y = -2. P E MD AS

Legal Mat Move: Flipping
+ – To move a tile between the positive and opposite regions, it must be placed on the opposite side. Algebra

Rules for Showing Work with Mats
+ – In order to receive credit for a tile and mat problem… Copy at least the original mat and tiles Circle zeros, use arrows to show flipping, etc. It must be organized and clear. Draw a second table if necessary. Do NOT make a Picasso!

L.M.M. – Removing Zeros in Same Region
+ – To remove two tiles in the same region, the tiles must be of opposite signs (one positive and the other negative). Algebra

L.M.M. – Removing Zeros in Different Regions
+ – To remove two tiles in different regions, the tiles must be the same sign (both positive or both negative). Algebra

Day 8: September 16th Objective: Understanding different interpretations of “minus”. Also, simplifying algebraic expressions while determining whether expressions are the same or different. THEN Simplify algebraic expressions and determine which of two expressions is greater. Homework Check 2-47 to 2-51 (pgs 55-57, RsrcPg) Wells Time 2-57 a-d, to 2-58 (pgs 59-60) Conclusion Homework: 2-52 to 2-56 (pg 58) AND 2-59 to 2-63 (pgs 61-62)

Legal Mat Move – Balancing
+ – + – Adding (or subtracting) like tiles to (or from) the same region of both sides of the mat is allowed. Algebra ?

Day 9: September 19th Objective: Learning how to record work while simplifying algebraic expressions and determining which of two expressions is greater. THEN Solving equations for x and strengthening simplification skills. Homework Check 2-64 to 2-66, 2-67 a,b,c (pgs 63-64) Wells Time 2-73 to 2-76 (pgs 67-69) Conclusion Homework: 2-68 to 2-72 (pgs 66-67) AND 2-77 to 2-81 (pg 70)

2-65: Recording Your Work Right Side is Greater + – + – ? Left Right
Explntn Original Flip Remove 0’s Balance ? Right Side is Greater

2-75: Solving for x x = 3 + – + – = Explntn Original Flip Remove 0’s
CLT = Balance Balance Divide x = 3

Day 11: September 21st Objective: Solving equations for x and determining whether there are no solutions, one solution, or infinite solutions. THEN Assess Chapter 2 in a team setting. Homework Check 2-99 (pg 77), (pg 81), (pg 77) Wells Time Chapter 2 Team Test Conclusion Homework: to (pgs 78-79) AND to (pgs 82-83)

Using a Table to solve a Proportion Question
Toby uses seven tubes of toothpaste every ten months. How many tubes would he use in 5 years? 5 years = 5x12 = 60 months Months Tubes 10 7 x6 x6 60 42 ? 42 Tubes

Using a Table to solve a Proportion Question
Toby uses seven tubes of toothpaste every ten months. How long would it take him to use 100 tubes? Months Tubes 10 7 x14.286 x14.286 142.86 ? 100 Months

Using a Diagram to solve a Proportion Question
One more way to organize your work for 2-99 ÷ 1.8 15 x 1.8 7.83 = 0x 6 y = 27 20 14.1 10.8 36 x 1.8

Day 11: September 21st Objective: How to identify a rule for a pattern and state it in words. THEN Find rules for patterns and write rules algebraically using symbolic notation. Homework Check 3-1 to 3-3 (pgs 93-95) Wells Time 3-9 to 3-12 (pgs 97 to 98) Conclusion Homework: 3-4 to 3-8 (pgs 95-96) AND 3-13 to 3-17 (pg 99)

3-2: Finding Rules from Tables
Hard Dark Heptagon D Quadrilateral S Right Decagon

3-2: Finding Rules from Tables
-3 3 4 3 144 60 36

Silent Board Game -22 -2.5 -10 -1 11 -8.5 3x-4
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) -6 2 10 -2 1 5 -1.5 x Out (y) 26 -4 -22 -2.5 -10 -1 11 -8.5 3x-4 RULE: Multiply the x by 3 and then subtract 4

Silent Board Game Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) 9 -1 4 0.5 20 -5 7 3 x Out (y) 24 12 4 6 14 46 -4 20 2x+6 RULE: Multiply the x by 2 and then add 6

Silent Board Game 1 6 -7 -195 21 5 -2x+5
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) 2 11 -3 -½ 6 100 -8 5 x Out (y) -17 -5 1 6 -7 -195 21 5 -2x+5 RULE: Multiply the x by -2 and then add 5

Silent Board Game Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) -4 1.5 8 50 -2 6 12 x Out (y) 16 64 36 2.25 2500 4 144 x2 RULE: Multiply the x by itself (square x)

Silent Board Game -17 -23 -25 -4 -5 -3 -2x-3
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) 7 -0.5 10 11 -4 1 8 x Out (y) -2 5 -19 -17 -23 -25 -4 -5 -3 -2x-3 RULE: Multiply the x by -2 and then subtract 3

Different Representations
Table: Graph: Years (x) 1 2 3 4 5 Height (y) 17 21 25 5 9 13 -4 -4 -4 +4 +4 The change in height after one year Initial Height before planting y = 4x+5 4 5 RULE:

Day 13: September 23rd Objective: Graph data points from a pattern on the x->y coordinate plane. Learn how to use graphing technology to graph data points and equations. Learn the difference between a continuous and discrete graph. THEN Practice plotting points from an x->y table and practice setting up appropriate axes for a data set. Homework Check 3-18 to 3-22 (pgs , RsrcPg) Wells Time 3-32 to 3-35 (pgs 105 to 106) Conclusion Homework: 3-23 to 3-31 (pgs ) AND 3-36 to 3-40 (pgs )

Day 14: September 26th Objective: Complete a table (including decimals), plot the points, and draw the graph for a linear situation and equations. THEN Given a linear or quadratic equation, create x->y tables, scale axes, plot points, and draw complete graphs. Notebook Quiz 3-41 to 3-44 (pgs ) Wells Time 3-51 to 3-54 (pgs 112 to 113) Conclusion Homework: 3-45 to 3-49 (pgs ) AND 3-55 to 3-59 (pg 113)

Notebook Quiz 9/26 Provide the following on a sheet of paper to be turned in. You have 10 minutes. Homework: The solutions to a-d from assigned on September 15th Classwork: The answers to 1-51 (b) assigned on September 12th

Silent Board Game 13 5 -1 -9 1 -2x+1
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) -6 2 10 -2 1 5 -1.5 x Out (y) -3 -19 4 13 5 -1 -9 1 -2x+1 RULE: Multiply the x by -2 and then add 1

Silent Board Game -2 -3.25 47 -7 -3 0.5x-3
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) 2 11 -3 -½ 6 100 -8 5 x Out (y) 2.5 -4.5 -0.5 -2 -3.25 47 -7 -3 0.5x-3 RULE: Multiply the x by 0.5 and then subtract 3

Silent Board Game -16 -25 -28 3.5 2 5 -3x+5
Rules: Copy the table. In silence, study the input and output values and look for a pattern. Raise your hand if you know a missing cell. Find the rule in words and symbols. In (x) 7 -0.5 10 11 -4 1 8 x Out (y) 6.5 17 -19 -16 -25 -28 3.5 2 5 -3x+5 RULE: Multiply the x by -3 and then add 5

What is wrong with the Graph?
The graph needs to have numeric labels on the axes. We can not determine a coordinate without them. Does the graph stop or go on forever? If it stops, there should be closed dots, if it continues there should be arrows. The graph needs to have variable labels on the axes. We can not determine a coordinate without them.

Qualities of a Complete Graph
Every complete graph MUST have: y Graph Paper Axes Variable Labels for the Axes 5 Scale the Axes Accurately Plot Points Accurately Plot Key Points x 5 5 If necessary, connect the points 5 If necessary, draw arrows on the curve

Day 15: September 27th Objective: Use graphs and rules to analyze a contextual situation with a limited domain. Identifying common errors in scaling and plotting points. THEN Review and practice equation-solving skills. Also, learn how to check answers and recognize that a solution is a value that makes an equation true. Homework Check 3-60 to 3-62 (pgs , RscrcPg) Wells Time 3-69 to 3-72 (pgs 118 to 119) Conclusion Homework: 3-64 to 3-68 (pgs ) AND 3-73 to 3-77 (pg 120)

Solving for x and Checking the Answer
+ – + – Explntn Original Balance Divide = The left side must equal the right side. Check:

Day 16: September 28th Objective: Understanding what makes an equation have 1, infinite, or no solutions. And start to solve equations without manipulatives. THEN Continue to practice solving equations. Homework Check 3-78 to 3-80 (pg 121, RscrcPg) Wells Time 3-87 to 3-91 (pgs 123 to 124) Conclusion Homework: 3-82 to 3-86 (pgs ) AND 3-92 to 3-96 (pg 125)

Guess my Number Ten Two Three Infinite Answers No Solutions
I’m thinking of a number that… When I… I get… My number is… Triple my number AND Add four Ten Double my number Add Four My Number plus Seven Add three Subtract my number Subtract one My Number plus Two Subtract three Two Three Infinite Answers No Solutions

Using an Equation to Solve and then Checking the Answer
When I double my number and add four, I get my number plus seven. What is my number? Express the question as an equation with a variable. Check: The left side must equal the right side. Your number is 3 Don’t forget to answer the question

3-90: Solutions (c) Any Number TRUE! (a) 4; (b) 8; (d) 0.15

Day 17: September 30th Objective: Continue to practice solving equations that cannot be solved using algebra tiles. These equations will come from real-world contexts. THEN Discover connections between all of the representations of a pattern: a graph, a table, a geometric presentation, and an equation. Homework Check 3-97 to 3-99 (pgs 126 to 127) Wells Time 4-1 (pg 139) Conclusion Homework: to (pg 128) AND 4-2 to 4-7 (pgs )

Describing a Variable in Words
John invests $30 into a government bond that increases in value $1.50 every year. Assuming the bond continues to grow at a constant rate, find a rule for the total amount of money of the bond using x and y. In your rule, what real-world quantity does x stand for? In your rule, what real-world quantity does y stand for? x is the number of years after investing y is the total amount of dollars in the bond

Tile Pattern Team Challenge
DRAW figures 0, 4, and 5 DESCRIBE Figure 100 DESCRIBE how the figures grow FIND the number of tiles in each figure and record your information in a TABLE and GRAPH. Find a RULE for the number of tiles in terms of the figure number COMPARE the graph, figures, and x-> table

3-90: Solutions c = 10 x = 12 No Solution t = 0.2

Day 18: October 3rd Objective: Write linear algebraic rules relating the figure number of a geometric pattern and its numbers of tiles. Identify connections between the growth of a pattern and its linear equation. THEN Discover connections between all of the representations of a pattern: a graph, a table, a geometric presentation, and an equation. Homework Check 4-8 to 4-12 (pgs , RscrPg) Wells Time 4-18 to 4-20 (pgs , RscrPg) Conclusion Homework: 4-13 to 4-17 (pg 145) AND 4-21 to 4-25 (pg 148)

Exponential Function Web
Table Non-Algebraic Rule or Equation Graph Algebraic Pattern

Tile Patterns + 4 tiles + 4 tiles + 4 tiles 101 Pattern Figure 0
2 tiles initially Figure 1 100 Figure 2 Figure 3 Figure 100 Growth Triangle 4 Growth Initial Graph 1 y-intercept (0,2) Rule

Day 19: October 4rd Objective: Develop connections between multiple representations of patterns and identify rules for these patterns using the y=mx+b form of a linear equation. THEN Apply your understanding of growth, Figure 0, and connections between multiple representations to generate a complete pattern. Homework Check 4-26 to 4-30 (pgs ) Wells Time 4-37 (pgs ) Conclusion Homework: 4-32 to 4-36 (pg 151) AND 4-39 to 4-48 (pgs )

Equation of a Line Variable: The Input Variable: The Output Parameter:
Growth Parameter: Starting Value Parameter = Constant value Variable = The value can vary

Day 20: October 5th Objective: Assess Chapters 1, 2, and 3 in an individual setting. THEN Apply m as growth factor and b as Figure 0 or the starting value of a pattern to create graphs quickly without an x->y table. Homework Check Chapters 1-3 Individual Test Wells Time 4-49 to 4-53 (pgs ) Conclusion Homework: 4-54 to 4-58 (pg 158)

Graphing a Line without a Table
Graph y = 4x + 3 without making a table. y = 4x + 3 1 4 1. Plot the starting value on the y-axis 1 4 2. Use the change to find at least 2 more points 1 4 3. Don’t forget to connect the points 1 4

Graphing a Line without a Table
Graph y = -3x + 8 without making a table. y = -3x + 8 1 -3 1 -3 1. Plot the starting value on the y-axis 1 -3 2. Use the change to find at least 2 more points 1 -3 3. Don’t forget to connect the points 1 -3 1 -3

Day 21: October 6th Objective: Practice moving directly from one representation to another in the representation web. THEN Focus on systems of equations and examine the meaning of points of intersection. Homework Check 4-59 to 4-60 (pgs ) Wells Time 4-67 to 4-69 (pgs , RscrcPg) Conclusion Homework: 4-62 to 4-66 (pgs ) AND 4-71 to 4-75 (pgs )

Race Scatter Plot

System of Equations Point of Intersection
Where two curves cross. Can be written as a coordinate point or (x,y). This point is on BOTH curves. System of Equations A collection of two or more curves with the same variables. For example:

Contextual Systems of Equations

Day 22: October 7th Objective: Develop an understanding of solving systems of equations through multiple representations. Continue to write rules and find intersections from contexts. THEN How to solve systems of equations algebraically when both equations are in y=mx+b form. Homework Check 4-76 to 4-79 (pgs ) Wells Time 4-85 to 4-88 (pgs ) Conclusion Homework: 4-80 to 4-84 (pgs ) AND 4-90 to 4-94 (pg 172)

Buying Bicycles Latanya and George are saving up money to buy new bicycles. Latanya opened a savings account with $50. She is determined to save an additional $30 a week. George started a savings account with $75. He is able to save 25 a week. When will they have the same amount in their savings accounts? Solution Method 2: Create one Graph for both Money (y) depends on the weeks (x) it has been saved Solution Method 1: Create tables Latanya George Weeks Dollars Weeks Dollars Dollars 50 75 1 80 1 100 5 weeks 2 (5, 200) The solution is where the two curves intersect 2 110 125 3 140 3 150 4 170 4 175 The answer is where the input AND the output are identical 5 200 5 200 6 230 6 225 Weeks 7 260 7 250 Use the tables to set up a good window

Both equations SHOULD give you the same answer.
Chubby Bunny Barbara has a bunny that weighs 5 lbs and gains 3 lbs per year. Her cat weighs 19 lbs and 1 lbs per year. (a) When will the bunny and cat weigh the same amount? Write rules where x represents the number of years and y represents the weight of the animal. Since we want to know when the weights (y) are equal, the right sides need to be equal too. Both equations SHOULD give you the same answer. 7 years (b) How much do the cat and bunny weigh at this time? pounds Substitute the x from (a) into an equation:

Day 23: October 10th Objective: Identify dimensions of rectangles formed with algebra tiles and will identify factors of quadratics. Also write the area as a sum and a product while learning not all expressions are factorable. THEN Assess Chapter 4 in a team setting. Homework Check 5-1 to 5-3 (pg 191) Wells Time Chapter 4 Team Test Conclusion Homework: 4-96 to (pgs ) AND 5-4 to 5-9 (pg 192)

Example: Equal Values Method
Solve the following system of equation algebraically: Both equations equal y. Set them equal to each other.

Exploring an Area Model
Arrange the tiles into one rectangle. Area as a Product: Area as a Sum: Dimensions:

Arrange the tiles into one rectangle. Rearrange. Put the x2 in the bottom left corner and the units in the top right. Area as a Product: Area as a Sum: Dimensions:

Arrange the tiles into one rectangle. Don’t forget parentheses Rearrange. Put the x2 in the bottom left corner and the units in the top right. Area as a Product: These represent the same area. They must be equal. Area as a Sum: Make your own corner piece Therefore: x by x + 2 Dimensions:

Day 24: October 11th Objective: Multiply expressions using algebra tiles. Identify, use, and describe the distributive property. THEN Assess Chapter 4 in a team setting. Homework Check 5-10 to 5-14 (pgs ) Wells Time 5-21 to 5-26 (pgs ) Conclusion Homework: 5-15 to 5-20 (pgs ) AND 5-27 to 5-32 (pg 199)

Product v Sum Product Sum a (2x)(4x) 8x2 b (x+3)(2x+1) 2x2+7x+3 c
e x(2x+y) 2x2+xy f (2x+5)(x+y+2) 2x2+2xy+9x+5y+10 g 2(3x+5) 6x+10 h y(2x+y+3) y2+2xy+3y

The Distributive Property: Multiply a Binomial by a Monomial
The product of a and (b+c) is given by: a( b + c ) = ab + ac Example: Simplify 2x(x – 9) Every term inside the parentheses is multiplied by a. x -9 Area Method: “Arrow” Method: 2x 2x2 -18x Do NOT forget to answer the question.

The Distributive Property: Multiply with the Area Model
3 terms times 2 terms Distribute: ( x2 - x + 3 )( x + 5) x x A 3x2 box: x +5 x3 -x2 +3x +5x2 -5x +15 x3 – x2 + 3x + 5x2 – 5x + 15 = x3 + 4x2 – 2x + 15

The Distributive Property: FOIL
Write the following as a sum: ( 3x – 2 )( 2x + 7) Firsts Outers Inners Lasts Simplify Multiply the… 6x2 + 21x + -4x + -14 = 6x2 + 17x – 14 This only works for a binomial multiplied by a binomial.

Day 25: October 12th Objective: Solve linear equations that involve multiplication. Solve quadratic equations that simplify to linear equations. THEN Solve two-variable linear equations for one variable. Homework Check 5-33 to 5-36, 5-37 (a,b,d), 3-38 (pgs ) Wells Time 5-45 to 5-48 (pgs ) Conclusion Homework: 5-39 to 5-44 (pg 202) AND 5-49 to 5-54 (pgs )

The Distributive Property and Solving Equations
Solve: x +3 +1 x 5 -x -x2 -3x x x2 5x x +5

Solutions 3-37 3-38 x = 9 y = 6 x = 2 x = 0 x = -3.5 x = -10/3 y = -1

Solving for y in terms of x
+ – + – Make sure to divide every term by 2. = Solving for will allow us to easily find the change and starting point for a linear equation. Change: 1 Start: 2

Solving for y in terms of x
+ – + – = Change: -3 Start: -4

Day 26: October 13th Objective: Solve single- and multi-variable linear equations. THEN Through the use of a table, learn how to write and solve a proportional equation based on a proportional relationship. Homework Check 5-55 (pgs 207) Wells Time 5-63 to 5-66 (pgs ) Conclusion Homework: 5-57 to 5-62 (pg 208) AND 5-67 to 5-71 (pgs )

In the Hot Seat? Bring something to write on.
CLOSE YOUR TEXTBOOK! Hot Seat In the Hot Seat? Bring something to write on. One chair/desk per team is set up in the front of the room. Using Numbered Heads, Person #1 from each team comes to the front of the room and sits. Teacher gives everyone a problem to work on in a specified amount of time. Teams can talk, but not the individuals in front. Check individual and team answers; two points for correct individual answers and 1 point for correct team answers. Person #2 from each team is up next and repeat.

Solving a Proportion Solve: Solve: Cancel the divide by 5
Cancel the divide by X Cancel the divide by 2 Cancel the divide by 3

Day 27: October 14th Objective: Practice setting up and solving proportions involving quantities taken from a variety of contexts. THEN Apply proportional understanding to solve an application problem. Homework Check 5-72 to 5-76 (pgs ) Wells Time 5-83 to 5-84 (pgs ) Conclusion Homework: 5-77 to 5-82 (pgs ) AND 5-85 to (pgs )

Cross Multiplication can be used to solve a proportion.
Solving a Proportion Solve: Solve: Cross Multiplication can be used to solve a proportion.

Multiply each numerator by the opposite denominator.
Solving a Proportion Solve: Solve: Multiply each numerator by the opposite denominator.

Estimating the Fish Population
Team Actual Population Estimated Population Cost SCORE

Day 28: October 17th Objective: Learn how to write and interpret mathematical sentences and begin to write equations from word problems. THEN Continue to learn how to define variables and how to write and solve equations to solve word problems. Homework Check 6-1 to 6-5, 6-7 (pgs ) Wells Time 6-13 to 6-15 (pgs ) Conclusion Homework: 6-8 to 6-12 (pgs ) AND 6-16 to (pg 238)

Guess and Check to Algebraic
The perimeter of a triangle is 31 cm. Sides #1 and #2 have equal length, while Side #3 is one centimeter shorter than twice the length of side #1. How long is each side? Length of Side #1 Length of Side #2 Length of Side #3 Perimeter of Triangle Check 5 9 Too Low Too High 31 Side One: cm Side Two: cm Side Three: cm

Day 29: October 18th Objective: Learn how to write equations from word problems. Also, compare writing a single equation with one variable to writing a system of equations with two variables. THEN Understand how to use AND the benefits of using substitution to solve systems of linear equations. Homework Check 6-22 to 6-25 (pgs ) Wells Time 6-32 to 6-36 (pgs ) Conclusion Homework: 6-26 to 6-31 (pgs ) AND 6-37 to 6-42 (pgs )

Guess and Check to Algebraic
Elise took all of her cans and bottles from home to the recycling plant. The number of cans was one more than four times the number of bottles. She earned 10¢ for each can and 12¢ for each bottle, and ended up earning $2.18 in all. How many cans and bottles did she recycle? Guess # of bottles # of cans Total Earnings Check 10 2 Too High Too Low $2.18 Bottles: bottles Cans: cans

Writing a system of Equations
Elise took all of her cans and bottles from home to the recycling plant. The number of cans was one more than four times the number of bottles. She earned 10¢ for each can and 12¢ for each bottle, and ended up earning $2.18 in all. How many cans and bottles did she recycle? b: Number of bottles Elise took to the recycling plant c: Number of cans Elise took to the recycling plant Equal Values Method Solve the other equation for c too Bottles: bottles Cans: cans

Substitution Method Solve: We can solve an equation with one Variable:
Don’t forget to solve for y: Answer the question:

6-34: Solutions x=4, y=12 No Solution x=3, y=-1 b=-3, c=-8

Substitution: No Solution
Solve the following system of equation algebraically: The two lines are parallel. They never intersect. FALSE No Solution.

Day 30: October 19th Objective: Examine how a solution to a system of equations relates to those equations and to a graph of those equations. THEN Develop the Elimination Method for solving systems of equations. Homework Check 6-43 to 6-48 (pgs ) Wells Time 6-56 to 6-60 (pgs ) Conclusion Homework: 6-50 to 6-55 (pgs ) AND 6-61 to 6-66 (pg 253)

6-44: The Hills are Alive Focus: The conductor charges $2 for each yodeler and $1 for each xylophone. It costs $40 for the entire club, with instruments, to ride the gondola. x: Number of xylophones from the club to ride the gondola y: Number of yodelers from the club to ride the gondola x y

6-45: The Hills are Alive Focus: The number of yodelers is twice the number of xylophones. x: Number of xylophones from the club to ride the gondola y: Number of yodelers from the club to ride the gondola x y

6-45: The Hills are Alive x:
A gondola conductor charges $2 for each yodeler and $1 for each xylophone. It costs $40 for an entire club, with instruments, to ride the gondola. Two yodelers can share a xylophone, so the number of yodelers on the gondola is twice the number of xylophones. How many yodelers and how many xylophones are on the gondola? x: Number of xylophones from the club to ride the gondola y: Number of yodelers from the club to ride the gondola Check in BOTH equations good The solution can be written as a coordinate point good

6-46: The Hills are Alive Graph: (8,16) x = 8 and y = 16 (8,16)
This is the ONLY point that makes both equations true. (8,16) x = 8 and y = 16 (8,16) The club had 16 yodelers and 8 xylophones. x

The Elimination Method
+ – + – + – + – = =

The Elimination Method
+ – + – = CHECKS:

Elimination Method Solve the following system of equation:
Add the equations to eliminate a variable: Solve the other variable: Answer the question: Check in both Equations:

In order to add, there must be opposites to eliminate. Add the equations to eliminate a variable: Solve the other variable: Answer the question: Check in both Equations:

Day 31: October 20th Objective: Assess Chapters 4-5 in an individual setting. THEN Study more complex applications of the Elimination Method. Learn that multiplying both sides of an equation by a number creates an equivalent equation. Also, there are different approaches to setting up elimination that yield the same result. Homework Check Chapters 4-5 Individual Test Wells Time 6-67 to 6-70 (pgs ) Conclusion Homework: 6-71 to 6-76 (pg 256)

One Solution Solve the following system of equation algebraically and graphically: The lines only intersect once since there is one solution. Both equations equal y. Set them equal to each other.

No Solution No Solution.
Solve the following system of equation algebraically and graphically: The two lines are parallel. They never intersect. Add the equations to eliminate a variable: No Solution.

Every point that satisfies:
Infinite Solutions Solve the following system of equation algebraically and graphically: The two equations are equivalent. They lie on top of each other. They intersect everywhere. True Infinite Solutions. Every point that satisfies:

Day 32: October 21st Objective: Review each strategy for solving systems of linear equations and choose the best strategy. Also, all methods will produce the same results but some are more efficient. Homework Check 6-77 to 6-78 (pg 257) Group Hot Potato So Many Tools Worksheet Conclusion Homework: Finish Worksheet AND 6-81 to 6-86 (pg 259)

Adding and Subtracting Fractions
Addition: Subtraction: Least Common Denominator (if you can find it) Common Denominator Subtract the Numerators Add the Numerators

Elimination Method x y Solve the following system of equation:
Pick a variable to eliminate: x y The Elimination Method is similar to adding/subtracting fractions, except that you want opposites. The goal is to multiply equations, if needed, so the coefficients (the number before a variable) for one of the variables is opposite of the other.

Sometimes you need to multiply BOTH equations to have opposite coefficients on the same variable Add the equations to eliminate a variable Solve for the other variable Answer the question Check in both Equations: BACK

When each Method is Most Effective
When BOTH equations have the same variable isolated Equal Values: Substitution: Elimination: When ONE equation has a variable isolated When BOTH equations have the both variables on the same side

Honors Algebra 1 Mr. Wells.

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