honors algebra 1 mr. wells. day one: september 6 th objective: discuss the syllabus and classroom...

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)

http://www.cpm.org/pdfs/stuRes/AC/chapter_01/1.1.1A.pdf

Support• www.cpm.org

– Homework help and answers– Resources (including worksheets from class)– Extra support/practice– Parent Guide

• www.hotmath.com– Pay site– All the problems from the book– Homework help and answers

• My Webpage on the HHS website– Classwork and Homework Assignments– Worksheets– Extra Resources

http://www.cpm.org/

http://www.hotmath.com/

http://www.haverford.k12.pa.us/hhs/site/default.asp

Getting To Know You, Part 1

1. Find the other students who have the missing pieces of your graph. Every graph will have sections 1, 2, 3, and 4.

2. Locate a group of desks to sit in (Not permanent).3. Choose a scenario for your graph from the list below.

Make sure to discuss how the graph fits the scenario.

1. A Runner in a timed race2. Temperature changing over time3. Babysitting earnings over time

4. 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

Perimeter: The distance around the edge of a figure

Area: The number of square units the figure covers

40 units

75 square units

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

810

10a b 5 3

111

ab

a+b

Coordinate Plane

y-ax

isx-axis

+

+–

–

y-axis goes up and down just like the tail in the letter

Quadrant

I

Quadrant

II

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 )

The first number tells how far left (-) or right (+)

The second number tells far down (-) or up (+)

Alphabetical

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.

4.1 5.3 4.3 13.7=

33=4.56 Feet

1-31: Growing, Growing, Growing

Fig. 2 Fig. 3 Fig. 4Fig. 1 Fig. 5

Fig # 0 1 2 3 4 5 100

Tiles 8 15 24

Generalize Pattern/Find a Rule:

1-31: Find a Convenient Shape


Fig # 0 1 2 3 4 5 100

Tiles 8 15 240 3 35 10200


1-31: Make a Convenient Shape


Fig # 0 1 2 3 4 5 100

Tiles 8 15 240 3 35


10200

1-32: New Tile Patern


Fig # 0 1 2 3 4 5

Tiles 11 15 19 793 7 2419


Fig. 2 Fig. 3 Fig. 4

Fig #

2 3 4

Tiles

How is the pattern changing?

Rule?

01

13 5 7 9

511

613

The growth rate is consistent. From one figure to the next, 2 tiles are always added.

LINEAR

# OF TILES = Fig # *2, +1

+2 +2 +2 +2 +2 +2

Fig. 2 Fig. 3 Fig. 4

Fig #

2 3 4

TilesHow is the pattern changing?

Rule?

01

14 7 1

013

516

619

The growth rate is consistent. From one figure to the next, 3 tiles are always added.

LINEAR

# OF TILES = Fig # *3, +1

+3 +3 +3 +3 +3 +3

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

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)

Algebra Tiles*Make sure all tiles are positive side up (negative [red] side down)*

1

1

Area = 15

1

Area = 5

x

1

Area = x

x

x

Area = x2

y

1

Area = y

y

y

Area = y2

x

y Area = xy

Unit Tile

5 Piece

x Tile

x2

Tile

y Tile

y2

Tilexy

Tile

Algebra Tiles: Perimeter

*Make sure all tiles are positive side up

(negative [red] side down)*

1

1

45

1

12

x

1

2x + 2

x

x

4x

y

1

2y + 2

y

y

y + y + y + y

x

y 2x +2y

P =

P =

y

y

= 4y

1

5

P =

P = P =

P =

P =

1

x

x

x

1

y

y

x

1

1

Answers to 2-13

a. 4x 2y 6

b. 2x 4

c. 2x 4y 2

d. 4x 2y 6

Commutative PropertiesAre two the expressions equivalent?

Commutative Property of Addition: When adding two or more numbers together, order is not important

5 1 7 3

1 35 7

a b b aCommutative Property of Multiplication: When multiplying

two or more numbers together, order is not important

ab baAre there Commutative Properties for Subtraction and Division?

5173

1357

Variable

A symbol which represents an unknown.

Examples:

xy

zm

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


Combining like TermsTerms: 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.

6x2 + 4x + 5 + 2x2 + 3x + 6

The x TileThe x2 Tile

Unit Tiles8x2 + 7x + 11

x2 x 6x2x 5

5+66+2 4+3

Ex: Simplify the expression below:

Substitution and EvaluationSubstitution: 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.

PEMDAS

22 2 3 5 3 2

22 5 5 3 2

2 25 5 3 2 50 15 2

22 5 2y x x

63

Legal Mat Move: Flipping

+

–

To move a tile between the positive and opposite regions, it must be placed on the opposite side.

Algebra

1

x

x 1

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

11

0

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

y y

0

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

1 ? 1

0 ? 0

+

–

?

x ? x

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


2-65: Recording Your Work

+

–

+

–

?

Left Right Explntn

2x 1 3 x 3

2 3 x 2

2x 1 3 x 3

2 3 x 2 Flip

x 5

x 1 Remove 0’s

5

1 Balance

Right Side is Greater

Original

2-75: Solving for x

+

–

+

–

=

Explntn

x 1 2 2x 1 5 x 1

x 1 2 2x 1 5 x 1 Flip

x 2 2x 4 x Remove 0’s

3x 2 4 x CLT

x = 3

Original

2x 2 4 Balance

2

2

2x 6 Balance

2

2

x 3 Divide

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), 2-109 (pg 81), 2-101 (pg 77)• Wells Time• Chapter 2 Team Test• Conclusion


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

60 ? x6 x6

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

100? x14.286 x14.286

142.86

142.86 Months

Using a Diagram to solve a Proportion Question

One more way to organize your work for 2-99

0x

20

6

15

10.8

36

14.1

y

x 1.8

x 1.8÷ 1.8

= 27

7.83 =

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


3-2: Finding Rules from Tables

A

D

S

Hard

Dark

Right

Heptagon

Quadrilateral

Decagon

3-2: Finding Rules from Tables

-34

3

60

3

144

36

Silent Board Game

In (x) -6 2 ½ 10 -2 1 5 0 -1.5 x

Out (y) 2 26 -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.

-22 -2.5 -10 -1 11 -8.5 3x-4

RULE:Multiply the x by 3 and then subtract 4

Silent Board Game

In (x)

9 -1 0 4 0.5 20 -5 7 3 x

Out (y) 24 7 12


4 6 14 46 -4 20 2x+6

RULE:Multiply the x by 2 and then add 6

Silent Board Game

In (x)

2 11 -3 -½ 6 100 -8 5 0 x

Out (y) -17 11 -5


1 -76 -195 21 5 -2x+5

RULE:Multiply the x by -2 and then add 5

Silent Board Game

In (x)

-4 0 1.5 8 0 50 -2 6 12 x

Out (y) 16 64 36


0 02.25 2500 4 144 x2

RULE:Multiply the x by itself (square x)

Silent Board Game

In (x)

7 -0.5 10 11 -4 ½ 1 0 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:

Years (x)

0 1 2 3 4 5

Height (y) 17 21 255 9 13

y = 4x+5RULE:

+4 +4-4 -4-4

Initial Height before planting

The change in height after one year

4 5

Graph:

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 100-101, RsrcPg)• Wells Time• 3-32 to 3-35 (pgs 105 to 106)• Conclusion


http://www.cpm.org/pdfs/stuRes/AC/chapter_03/3.1.3.pdf

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 108-109)• Wells Time• 3-51 to 3-54 (pgs 112 to 113)• Conclusion


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 2-29 assigned on September 15th

• Classwork: The answers to 1-51 (b) assigned on September 12th

Silent Board Game

In (x) -6 2 ½ 10 -2 1 5 0 -1.5 x

Out (y) -3 -19 4


13 0 5 -1 -9 1 -2x+1


Silent Board Game

In (x)

2 11 -3 -½ 6 100 -8 5 0 x

Out (y) 2.5 -4.5 -0.5


-2 0-3.25 47 -7 -3 0.5x-3

RULE:Multiply the x by 0.5 and then subtract 3

Silent Board Game

In (x)

7 -0.5 10 11 -4 ½ 1 0 8 x

Out (y) 6.5 17 -19


-16 -25 -28 3.5 2 5 -3x+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

3 2y x Every complete graph MUST have:

• Graph Paper• Axes

x

y

• Variable Labels for the Axes

55

5

5

• Scale the Axes• Accurately Plot Points• Accurately Plot Key Points• If necessary, connect the points• If necessary, draw arrows on the curve


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 114-116, RscrcPg)• Wells Time• 3-69 to 3-72 (pgs 118 to 119)• Conclusion



Solving for x and Checking the Answer

+

–

+

–

=

Explntn

3 2 8x Original

Balance

2

23 10x

3 3103x

Divide

1033 2 8 10 2 8

8 8

Check:

103x

The left side must equal the right side.


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



Guess my NumberI’m thinking of a number that…

When I… I get… My number is…

• Triple my numberAND

• Add fourTen

• Double my numberAND

• Add Four

My Number plus Seven

• Double my number• Add three• Subtract my number

AND• Subtract one

My Number plus Two

• Double my number• Subtract three• Subtract my number

AND• Add four

My Number plus Two

Two

Three

Infinite Answers

No Solutions

Using an Equation to Solve and then Checking the Answer

2 4 7x x x x

4 7x 4 4

3x

2 3 4 3 7 6 4 3 7

10 10

Check:

The left side must equal the right side.

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.

Your number is 3 Don’t forget to answer

the question

3-90: Solutions

0.5 2 0.5 2x x 0.5x 0.5x

2 2TRUE!

(c)

Any Number

2 0.5 1 0.5 1x x x

(a) 4; (b) 8; (d) 0.15


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


Describing a Variable in Words

John invests $30 into a government bond that increases in value $1.50 every year.

1. 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.

2. In your rule, what real-world quantity does x stand for?

3. In your rule, what real-world quantity does y stand for?

1.5 30y x

x is the number of years after investing

y is the total amount of dollars in the bond

Tile Pattern Team Challenge

1. DRAW figures 0, 4, and 5

2. DESCRIBE Figure 100

3. DESCRIBE how the figures grow

4. FIND the number of tiles in each figure and record your information in a TABLE and GRAPH.

5. Find a RULE for the number of tiles in terms of the figure number

6. COMPARE the graph, figures, and x-> table

3-90: Solutions

a)c = 10

c)x = 12

b)No Solution

d)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 142-144, RscrPg)• Wells Time• 4-18 to 4-20 (pgs 146-147, RscrPg)• Conclusion

Homework: 4-13 to 4-17 (pg 145) AND 4-21 to 4-25 (pg 148)



Exponential Function Web

Table

GraphRule or

Equation

PatternAlgebraic

Non-Algebraic

Tile PatternsP

atte

rn

Figure 1

Figure 2

Figure 3 Figure 100

101

100

Figure 0

Gra

ph

Rule

y 4x 2

Growth

+ 4 tiles + 4 tiles + 4 tiles

Initial

2 tiles initially

Growth Triangle4

1

y-intercept(0,2)


Table

GraphRule or

Equation

PatternAlgebraic

Non-Algebraic

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 149-150)• Wells Time• 4-37 (pgs 152-153)• Conclusion


Equation of a Line

y m bx Variable:

Variable:

Parameter:

Parameter:

Parameter = Constant value Variable = The value can vary

The Output

The Input

Growth

Starting Value


Table

GraphRule or

Equation

PatternAlgebraic

Non-Algebraic

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 156-157)• Conclusion

Homework: 4-54 to 4-58 (pg 158)

Graphing a Line without a TableGraph y = 4x + 3 without making a table.

1. Plot the starting value on the y-axis

2. Use the change to find at least 2 more points

y = 4x + 31

4

1

4

1

4

1

4

3. Don’t forget to connect the points

Graphing a Line without a TableGraph y = -3x + 8 without making a table.

1. Plot the starting value on the y-axis

2. Use the change to find at least 2 more points

y = -3x + 81

-3

3. Don’t forget to connect the points

1

-3

1

-3

1

-3

1

-3

1

-3


Table

GraphRule or

Equation

PatternAlgebraic

Non-Algebraic

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 159-160)• Wells Time• 4-67 to 4-69 (pgs 162-164, RscrcPg)• Conclusion




Table

GraphRule or

Equation

PatternAlgebraic

Non-Algebraic

Race Scatter Plot

System of Equations

Point of IntersectionWhere two curves cross. Can

be written as a coordinate point or (x,y). This point is on

BOTH curves.

3 4y x

2 6y x

System of EquationsA collection of two or more

curves with the same variables. For example:

3 4

2 6

y x

y x

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 167-168)• Wells Time• 4-85 to 4-88 (pgs 169-171)• Conclusion


Buying BicyclesLatanya 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?

Latanya George

Weeks WeeksDollars Dollars0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

50

80

110

140

170

200

230

260

75

100

125

150

175

200

225

250

Solution Method 1: Create tablesMoney (y)

depends on the weeks (x) it has

been saved

The answer is where the input AND the output

are identical

Solution Method 2: Create one Graph for both

Use the tables to set up a good window

(5, 200)The solution is where

the two curves intersect

5 weeks

WeeksD

olla

rs

Since we want to know when the weights (y) are equal, the

right sides need to be equal too.

Chubby BunnyBarbara 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.

3 5y x 19y x 3 5x 3 5x 3 5x

3 5x x x2 5 19x

5 52 14x

7x 2 27 years

(b) How much do the cat and bunny weigh at this time?Substitute the x from (a) into an equation: 3 7 5y 26 pounds19 7y

Both equations SHOULD give you the same answer.

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


Example: Equal Values Method

Solve the following system of equation algebraically:

2 22

3 28

y x

y x

22 3 822 xx 22 5 28x

50 5x10 x

3 10 28y 30 28y 2y

10,2

y

2 22x Both equations equal y. Set them equal to

each other.

Exploring an Area ModelArrange the tiles into one rectangle.

Dimensions:

Area as a Product:

Area as a Sum:


Dimensions:

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:

Area as a Product:

Area as a Sum:

Rearrange. Put the x2 in the bottom left corner and the units in

the top right.

Mak

e yo

ur o

wn

corn

er p

iece

x + 4 by x + 2

4 2x x 4 2x x

2 6 8x x

These represent the same area.

They must be equal.

24 2 6 8x x x x Therefore:

Don’t forget parentheses


Objective: Multiply expressions using algebra tiles. Identify, use, and describe the distributive property. THEN Assess Chapter 4 in a team setting.



Product v Sum

Product Sum

a (2x)(4x) 8x2

b (x+3)(2x+1) 2x2+7x+3

c 2x(x+5) 2x2+10x

d (2x+1)(2x+1) 4x2+4x+1

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)

2x

x -9

2x2 -18x

Every term inside the parentheses is multiplied by a.

2 9x x 22x

22 18x x

18x

Area Method: “Arrow” Method:

Do NOT forget to answer the question.

The Distributive Property: Multiply with the Area Model

Distribute: ( x2 - x + 3 )( x + 5)

x2 -x +3

x

+5

x3

x3 – x2 + 3x + 5x2 – 5x + 15 = x3 + 4x2 – 2x + 15

-x2

+5x2 -5x

+3x

+15

3 terms times 2 terms

A 3x2 box:

The Distributive Property: FOIL

Write the following as a sum:

( 3x – 2 )( 2x + 7)• Firsts• Outers• Inners • Lasts• Simplify

+ -4x

= 6x2 + 17x – 14

+ 21x + -14 6x2

Multiply the…

This only works for a binomial multiplied by a binomial.


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 200-201)• Wells Time• 5-45 to 5-48 (pgs 203-204)• Conclusion


The Distributive Property and Solving Equations

5 3 5 1x x x x Solve:

-x

x +3

-x2 -3x25 3x x

x

x +5

x2 5x

x 5+1

2 6 5x x 2 25 3 6 5x x x x 5 3 6 5x x 5 3 5x

3 10x 10 3x

Solutions

3-37

a) x = 9

c) y = 6

e) x = 2

b) x = 0

d) x = -3.5

f) x = -10/3

3-38

a) y = -1

c) x = -2.5

b) x = 5

d) x = 8

Solving for y in terms of x

+

–

+

–

=

2 3 4x y x

2 2 4y x 2 2

2y x

x x

Change: Start: 1 2

Make sure to divide

every term by 2.

2

Solving for will allow us to easily find the change and starting point for a linear

equation.

Solving for y in terms of x

+

–

+

–

=

2 2 2 1x y x

2 2 2 1x y x 2 4 2x y x

2 3 2y x

2

2

3 4y x 1

3 4y x

x x

Change: Start: -3 -4


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 209-210)• Conclusion


Hot Seat• 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.

CLOSE YOUR TEXTBOOK!

In the Hot Seat? Bring something

to write on.

Hot Seat

• 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




to write on.

Solve for : 5 4 3 75x x

Hot Seat







to write on.

Solve for : 2 4y x y

Hot Seat







to write on.

Solve for : 6 6 3 8x x

Hot Seat







to write on.

Solve for : 3 6 24y x y

Hot Seat







to write on.

Solve for : 2 3 2 1 17x x

Hot Seat







to write on.

Solve for : 5 2 11y x y

Hot Seat







to write on.

Solve for : 3 4x y x

Hot Seat







to write on.

2Solve for : 2 1 2 5 12x x x x x

Hot Seat







to write on.

Solve for : 2 3 1 4w v w

Hot Seat







to write on.

Solve for : 4 1 2 3 2 5x x x x x

Solving a Proportion

Solve:

5

15 2 3x 15 2 6x

9 2x

5152 3x 2 2

4.5 x

3 32 5

xCancel

the divide by 5

Cancel the

divide by 2

Solve:

x

7 12x 127x

x73 4x 3 3

7 43 x

Cancel the

divide by X

Cancel the

divide by 3


Objective: Practice setting up and solving proportions involving quantities taken from a variety of contexts. THEN Apply proportional understanding to solve an application problem.




Solve:

5

15 2 3x 15 2 6x

9 2x

5152 3x 2 2

4.5 x

3 32 5

x Solve:

x

7 12x 127x

x73 4x 3 3

7 43 x

Cross Multiplication can be used to

solve a proportion.


Solve:

843 12 84x

3 96x

3 4x

32x

4 712 3x Solve:

12 12

3 3

120300x

0.4x

100 430 3x

300 300

Multiply each numerator by the opposite denominator.

Estimating the Fish Population

TeamActual

PopulationEstimated Population

Cost SCORE


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 231-234)• Wells Time• 6-13 to 6-15 (pgs 236-237)• Conclusion


3

Guess and Check to AlgebraicThe 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

5 2 5 1 9 5 5 9 19 Too Low

9 2 9 1 17 9 9 17 35 Too High

x x 2 1x 2 1x x x 31

4 1 31x

4 32x

2 1 31x x x

1 1

8x

Side One:

Side Two:

Side Three: 2 8 1

8

15

cm

8 cm

cm


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.



Guess and Check to AlgebraicElise 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

4 10 1 41 10 0.12 41 0.1 $5.30 Too High

4 2 1 9 2 0.12 9 0.1 $1.14 Too Low

x 4 1x 0.12 0.1 4 1x x $2.18

0.12 0.1 4 1 2.18x x

0.52

0.52 0.1 2.18x

0.52 2.08x

0.12 0.4 0.1 2.18x x

0.1 0.1

4x

Bottles:

Cans: 4 4 1 174bottles

cans

Writing a system of EquationsElise 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?

21.8 1.2 4 1b b

5.220.8 5.2b

21.8 5.2 1b 1 1

4 bBottles:

Cans: 4 4 1 174bottles

cans

b:Number of bottles Elise took to the recycling plant c: Number of cans Elise took to the recycling plant

4 1c b 0.12 0.1 2.18b c

0.12 0.1 2.18b c

0.1 2.18 .12c b 0.12b 0.12b

0.121.8 1.2c b

1.2b 1.2b

Solve the other equation for c too

Equal Values Method

Substitution Method

Solve: 5 3 13

7x y

xy 7x y7x

y

7x

yWe can solve an equation

with one Variable:

5 7 3 13x x

2

2 35 13x

2 22x

5 35 3 13x x

35 35

11x

Don’t forget to solve for y:

11 7y 4

Answer the question:

11

4

x

y

6-34: Solutions

a)x=4, y=12

c)No Solution

b)x=3, y=-1

d)b=-3, c=-8

Substitution: No Solution

2 2 18

3

x y

x y

Solve the following system of equation algebraically:

2 2 83 1y y 6 2 2 18y y

6 18

No Solution.

3 yx

FALSE

The two lines are parallel. They

never intersect.


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 245-247)

• Wells Time

• 6-56 to 6-60 (pgs 250-252)

• Conclusion


6-44: The Hills are AliveFocus: 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

2 40x y

x y

6-45: The Hills are AliveFocus: The number of yodelers is twice the number of

xylophones.


2y x

x y

6-45: The Hills are AliveA 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?


2 40

2

x y

y x

2x

y

2 402x x 4 40x x 5 40x

8x 5 5

2 8y 16

8,16The solution can be written as a

coordinate point

Check in BOTH equations

8 2 16 40 40 40

good

16 2 816 16

good

6-46: The Hills are Alive

x

y

Graph:

2 40x y 2y x

2 40x y 2y x

(8,16)This is the

ONLY point that makes both

equations true.

x = 8 and y = 16

(8,16)

The club had 16 yodelers and 8

xylophones.

The Elimination Method

+

–

+

–

=

5 3 16x y 2 3 2x y +

–

+

–

=

The Elimination Method

+

–

=

5 3 16x y 2 3 2x y +

–

2x

7 14x 7 7

2 2 3 2y 4 3 2y

3 6y 4 4

2y 3 3

CHECKS: 3 2 2 2 2 3 2 5 2 16 2, 2

Elimination MethodSolve the following system of equation:

2 2

2 3 10

x y

x y

2 2

2 3 10

x y

x y

_____________

2 8y

2 4 2x 2 2x

1,44y 1x

2 2

4 4

2 2

Add the equations to eliminate a variable:

Solve the other variable:

Check in both Equations: 2 1 4 2 2 1 3 4 12



3 4 1

2 4 2

x y

x y

3 4 1x y _____________

1x

3 1 4 1y

4 4y

1,1 1y

3 3

4 4


Solve the other variable:

Check in both Equations: 3 1 4 1 1 2 1 4 1 2


1

2 4 2x y 3 4 1y

In order to add, there must be opposites to eliminate.


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 254-255)• Conclusion

Homework: 6-71 to 6-76 (pg 256)

The lines only intersect once since there is one

solution.

One SolutionSolve the following system of equation algebraically and

graphically:2 22

3 28

y x

y x

22 3 822 xx 22 5 28x 50 5x10 x

3 10 28y 30 28 2

10,2

y

2 22x Both equations equal y. Set them equal to

each other.

No Solution.

The two lines are parallel. They

never intersect.

No Solution

2 2 18

2 2 6

x y

x y

2 2 18

2 2 6

x y

x y

_____________

0 12


Solve the following system of equation algebraically and graphically:

Infinite Solutions

2 5

2 4 10

y x

y x

2 02 4 15 xx 4 10 4 10x x

10 10

2 5x y

True

The two equations are equivalent. They lie on top of each other. They intersect everywhere.

Solve the following system of equation algebraically and graphically:

Infinite Solutions.Every point that satisfies:

2 5y x

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

2 13 5 7 3

4 105 32 1

3 5 5 3 7 5 3 24 5 10 2

35 620 20

Add the Numerators

Least Common

Denominator (if you can

find it)Common

Denominator

Addition: Subtraction:

10 315 15

1315

2920

Subtract the Numerators

Elimination Method

4 3 10

9 4 1

x y

x y

Solve the following system of equation:

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.

Pick a variable to eliminate:

x y

9


4 3 10

9 4 1

x y

x y

36 27 90x y ______________

43 86y

4 3 2 10x 4 6 10x

4 4x

1,22y

4

1x

36 16 4x y

43 434 4

6 6


Sometimes you need to multiply BOTH equations to have

opposite coefficients on the same variableAdd the equations to

eliminate a variable

Solve for the other variable

Answer the question

BACK

4


4 3 10

9 4 1

x y

x y

16 12 40x y ______________

43 43x

4 1 3 10y 4 3 10y

3 6y

1,21x

3

2y

27 12 3x y

43 433 3

4 4


Sometimes you need to multiply BOTH equations to have

opposite coefficients on the same variableAdd the equations to

eliminate a variable

Solve for the other variable

Answer the question

BACK

When each Method is Most Effective

Equal Values:

Substitution:

Elimination:

35

10

2

1x

y x

y

0.5 4

8 3 31

x y

x y

4 5 11

6 2 10

x y

x y

When BOTH equations have the same variable

isolated

When ONE equation has a variable isolated

When BOTH equations have the both variables

on the same side

honors algebra 1 mr. wells. day one: september 6 th objective: discuss the syllabus and classroom...

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