Reasoning with Equations and Inequatlitiesstaceybarnesresources.weebly.com/.../5/1/0/9510230/sa… · Web viewAnalyze & interpret data. ... When given a word problem, ... What events

DAY-1

Subject: Algebra I Grade

9

Topic: Creating 1-variable EquationsStage 1: Desired Results

Established Goals:MAFS.912.A-‐CED.1.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

Understanding(s) & Misconceptions:

Essential Questions:

Students may not understand the function of a variable. Students may think variables are a distinct number, when they are really an unknown quantity.

What is the purpose of letters in math? Why can’t I add 4s to 5 to make 9s?

Knowledge: Skills: Variable: unknown

quantity written as a letter

Term: separate quantities within an equation

Critical thinking Analyze & interpret data

Stage 2: Assessment EvidenceWhat authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:

#HomeGoal:

Create equations with one unknown

Product/Performance: Standards:When given a word problem, students will be able to create an equation that reflects the known quantities as well as the unknown.

MAFS.912.A-‐CED.1.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

Stage 3: Learning PlanWhat learning experiences and instruction will enable students to

achieve the desired results?Where are your students headed?Where have they been?How will you make sure the students know where they are going?

Objectives will be on the board.

How will you hook students at the beginning of the unit?

Bell chimer: Jason and Miguel were riding their bikes. Jason fell 12 more times than Miguel. The boys fell a total of 24 times. Write an equation that reflects the amount of times Miguel and Jason fell.

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?

PowerPoint presentation: at least 3 examples: 1 for me to solve, 1 for us all to solve, 1 for students to solve)

Textbook homework

#HomeHow will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?

Journal entry: what did you learn today? (ex: key terms, skills, etc)

How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?

Exit ticket: Match equations with statements—survey on PowerPoint slide.

Homework check

How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?

Students will have opportunities to ask questions when they don’t understand. I will also have written notes available for those who need extra time to write (ELL students or exceptional learners). PowerPoint will be infused with large text and pictures for those with needs. Extra help and time will be given to those with special needs, as well.

Adjustments. What did/did not work? How will you change next year’s plan?

#HomeDAY-2


9

Topic: Solving 1-variable EquationsStage 1: Desired Results

Established Goals:MAFS.912.A--‐REI.1.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.



I want the students to know how to solve a simple 1 variable equation. Students should remember the order of operations and use them to solve an equation (that has a solution). I also want students to understand the reasoning of solving equations, and how it relates to their life outside of the classroom.

What is an equation? How do you solve a 1-variable equation? How do you apply this skill in the real world?

Knowledge: Skills: Simple equations can

be solved by isolating the variable.

To isolate the variable, do the opposite

Problem-solving Analyzing data & applying

knowledge

#Homeoperation to both sides. Example: if the variable is added by 7, the subtract 7.

Justify the means of finding a solution.

Stage 2: Assessment EvidenceWhat authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

Solve simple equations

Product/Performance: Standards:Students will be able to correctly solve simple equations given a worksheet and prove their understanding by explaining in 3 sentences their rationale for solving an equation. Students will also be able to create their own equation with one variable that pertains to their lives (such as if I have $20, how many $2.99 games can I buy?).

MAFS.912.A--‐REI.1.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.


achieve the desired results?Where are your students headed?

On the board, the objective for this lesson will be written.

#HomeWhere have they been?How will you make sure the students know where they are going?How will you hook students at the beginning of the unit?

The chimer (displayed on the projector screen at beginning of class):Jose has four more followers on Twitter than Nike. Abri has twelve more than Jose. If all three have a total of 31 followers together, how many followers do each person have?

First, write the expression using a variable.Second, ask the class how to figure out the answer. (self-knowledge activity)

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?

PowerPoint presentation: at least 3 examples: 1 for me to solve, 1 for us all to solve, 1 for students to solve) .

Justly Justifying worksheet:Equations are to be solved in steps, and each step is to be justified and explained. (explanation activity)

Students are to journal their thoughts of today’s lesson. (interpretation activity)

#HomeHow will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?

Students will complete an exit ticket (Did You Get It?) to show them their comprehension of the material.

Homework checkHow will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?



#Home

Name:________________________________ Period:_______ Date:__________

Justly Justified?Did the following students truly justify each step? Did they solve the equations correctly? Find and correct any errors in the following examples. Make sure to continue correcting the equation all the way through each example.

1. 7 ( x – 3) = 4 ( 2x – 1)

Step Reason

7 ( x – 3) = 4 ( 2x – 1) Given

7x – 3 = 8x – 1 Distributive Property

-2 = x Addition/Subtraction Property of Equality

X = -2 Reflexive Property of Equality

2. 2x−47 =6x−7

Step Reason

2x−47

=6x−7 Given

2x – 4 = 7 (6x – 7) Multiplication Property of Equality

2x – 4 = 42 x – 49 Multiplication Property of Equality

45 = 40x Addition/Subtraction Property of Equality

4540

=x Division/Multiplication Property of Equality

98=x Division Property of Equality

#HomeExit Ticket

Did you get it?Solve each equation, justifying each step.

1. 5x – 3 = 4x 2. 3(2x – 9) = 4x + 5

Step Reason Step Reason

#HomeDAY-3


9

Topic: Solving 1-variable Rational and Radical EquationsStage 1: Desired Results

Established Goals:MAFS.912.A--‐REI.1.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.



I want the students to understand the system for solving radical equations. Students should remember how to solve equations, and just add on that knowledge that when a radical is involved, there is more than 1 answer, however there may be solutions that don’t satisfy the original equation, making it extraneous

How do you isolate a variable when there’s a radical over it? Why are there 2 answers after radical is gone? How do you know a solution is extraneous? What happens when my solutions do not work in the original equation? What do you do with the solution that does not work?

Knowledge: Skills: Solve equations with

radicals Radicals are fractional

exponents

Problem-solving Analyze and apply

knowledge

Stage 2: Assessment EvidenceWhat authentic performance tasks will students demonstrate the

#Homedesired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

Solve simple equations w/ radicals

Product/Performance: Standards:Students will be able to correctly solve radical equations on a worksheet. By showing their work, students will show a comprehension of the steps to solving equations, and will prove their solutions true or false by using them in the original equation. Students will show proficiency by knowing what do to with the solution that does not satisfy the original equation.

MAFS.912.A--‐REI.1.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.



On the board, the objective for this lesson will be written.

How will you hook students at the beginning of the

Yesterday’s work will be in today’s chimer, along with 1

#Homeunit? question regarding a radical.

Tell students to take yesterday’s lesson and apply it today. (application activity)


Students will apply yesterday’s knowledge to todays. We will change the radicals in exponential form and vice versa. (perspective activity)


Rad video

Radical Mathematical worksheet



Exit slip: Jasmine is afraid of heights. Her friend, Daisy, finally talked Jasmine into riding the Ferris wheel. At first, Jasmine is not scared. However, the higher up the Ferris wheel climbed, the more scared she became. When the Ferris wheel hit a certain height, Jasmine had to close her eyes.

#HomeOn a clear day, the distance a person can see is given by the formula v=1.225√a, where v is the distance in miles and a is the altitude in feet.

When Jasmine could see 49 miles in the horizon, that’s when she had to close her eyes. How far above the ground was she?




#HomeSummative assessment is the exit slip and worksheet.

#Home

#HomeDAY-4


9

Topic: Solving 1-variable inequalitiesStage 1: Desired Results

Established Goals: MAFS.912.A--‐REI.2.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters



Students will be able to isolate the variable, use the correct inequality sign, and have the correct answer. Students may have incorrect signs, especially if the variable was negative when it was isolated. Students may also trip up over closed or open circles while graphing.

How is an inequality different than an equation? What does the inequality represent? What happens when we have an isolated variable that’s negative? What is the difference in “<” and “≤?”

Knowledge: Skills: To solve inequalities is

to isolate the variable When

dividing/multiplying by a negative number, flip the sign.

Graph the answer on the number line—equal to is a closed

Critical thinking Graphing Analyze and apply

#Homecircle, greater/less than is an open circle, and shade the values that the variable could represent


Solve inequalities with 1 variable.

Product/Performance: Standards:After given a worksheet, students will be able to isolate the variable on one side of the inequality, and have the correct sign (less than, greater than, equal to) with the correct answer. Then, students will be able to graph on a number line the values of the variable.

MAFS.912.A--‐REI.2.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters



Objective will be listed on the board.

#HomeHow will you hook students at the beginning of the unit?

At the beginning, the chimer will include solving equations to build on prior knowledge. The last question will contain an inequality to hook the students, make them question their methods, and think of how to solve.



Worksheet

Exit ticket: Erin has found 3 pairs of boots that she wants to buy for the winter months, costing $150, $152, and $190. She already has $58 saved, and works a job that pays her $8.25/hour. How many hours will she have to work in order to have enough money to buy any of these boots? How many hours would she have to work for the most expensive?

Journal entry: What did you learn today? (ex: key terms, skills, etc)

How will you help students to exhibit and self-evaluate their growing skills, knowledge, and

In groups, students will work together to figure out the answers.

#Homeunderstanding throughout the unit?

Homework check

An exit ticket will be given at the end.

Summative assessment will also be given that covers skills from the beginning of unit.




#Home

SOLVING EQUATIONS AND INEQUALITIES

Solve. Show your work to receive credit.

1. 2 x−5=7 2. 9u+12=5u 3. 4u5 =8

4. √9=x 5. √s+5=√3+√s 6. √ t+4=8

7. −2g≤−16 8. (x−4)6>9 9. −8≤ 4c6 <6

#Home

DAY-5


9

Topic: Creating 2+ variable equationsStage 1: Desired Results

Established Goals:.MAFS.912.A-‐CED.1.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.



Students may think only 1 variable can be in an equation. Students may try to represent unknowns with the same variable. Students may also thing that variables stand for objects, not quantities.

What happens when there are two unknowns in a problem? How do we represent this?

Knowledge: Skills: More than 1 variable

can exist in a single problem

Critical thinking Analyze and interpret

data Application of skills

Stage 2: Assessment EvidenceWhat authentic performance tasks will students demonstrate the

#Homedesired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

Create an equation with two unknown quantities.

Product/Performance: Standards:Given a word problem, students can decipher important information and form an equation based on the information, including correct terms, and using two or more variables.

MAFS.912.A-‐CED.1.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.



Objectives will be on the board.


Chimer: A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. Rewrite this algebraically to determine how many multiple choice questions are on the test.

What events will help students experience and

PowerPoint presentation: at least 3 examples: 1 for me to

#Homeexplore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?

solve, 1 for us all to solve, 1 for students to solve)

Textbook homework



Exit ticket: Mary runs a computer repair business. She charges a flat rate of $50 plus $25 per hour of service. Write an equation to represent the cost, C, of h hours of service.



#HomeAdjustments. What did/did not work? How will you change next year’s plan?

#HomeDAY-6


9

Topic: Highlight Quantity of InterestStage 1: Desired Results

Established Goals:MAFS.912.A-‐CED.1.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.



I want the students to understand that formulas can be rearranged to find a quantity. For instance, if I know the hypotenuse and side b of a right triangle, I can find side a by rearranging the formula.

A formula is a set formula, why would I rearrange it?

Knowledge: Skills: Rearranging formulas

will benefit when some quanties are known while others aren’t.

Critical thinking

Stage 2: Assessment EvidenceWhat authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:

#HomeGoal:

Rearrange formulas and highlight specific quantites.

Product/Performance: Standards:When given a formula, studets will be able to correctly reposition each term to solve for a specific variable.

MAFS.912.A-‐CED.1.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.



Objectives will be placed on the board.


Chimer will be 5-questions regarding solving an equation. The last question will not have any numbers, but will ask to solve for a specific variable.

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?How will you cause students to reflect and rethink? How will you


Do the Formula Shuffle: have big numbers, operation signs, and letter to hang on students. Have one team of students stand in a certain formula (like

#Homeguide them in rehearsing, revising, and refining their work?

a2+b2=c2). The other teams rearrange the formula students to highlight a specific term.



Exit ticket: Gravity




#HomeExit Ticket:

http://formulas.tutorvista.com/physics/gravity-formula.html

Rewrite the formula to find mass of body 1 (m1).If a spaceship with a mass of 9x1016 Kg is moving around the planet with a mass of 2000 Kg, how can we determine the distance between the spaceship and the planet?

#HomeDAY-7


9

Topic: Solving Systems of Equations-EliminationStage 1: Desired Results

Established Goals:MAFS.912.A--‐REI.3.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.



First, I want the students to understand what a system of equations represents. I want the students to learn how to eliminate a variable to solve a systems of equations that contain 2 or more variables. Students should realize that an ordered pair (x,y) is the solution to a system of equations.

What do systems of equations represent? How can I solve the system when the equation contains more than 1 variable?

Knowledge: Skills: System of equations:

collection of two or more equations with a same set of unknowns

Eliminating a variable will help solve any system.

Critical thinking Analyzing and interpreting

data Application of previous

knowledge

#HomeStage 2: Assessment Evidence

What authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

Eliminate a variable to solve a system of equations.

Product/Performance: Standards:From the textbook problems, students will successfully eliminate a variable in one equation to solve the other variable in a system of equations. The ordered pair students find will satisfy both equations.

MAFS.912.A--‐REI.3.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.



Objectives will be placed on the board


Chimer will review previously learned material on how to create equations with two variables.

What events will help students experience and explore the big idea and questions in the unit?


#HomeHow will you equip them with needed skills and knowledge?How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?

Textbook homework



Exit ticket: Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said, “I wonder whether the dollar belongs inside the cash box or not.” The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?

Homework checkHow will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without

Students will have opportunities to ask questions when they don’t understand. I will also have written notes available for those who need extra time to write (ELL

#Homecompromising the goals of the unit?

students or exceptional learners). PowerPoint will be infused with large text and pictures for those with needs. Extra help and time will be given to those with special needs, as well.


#HomeDAY-8


9

Topic: Solving Systems of Equations-SubstitutionStage 1: Desired Results




Students should know how rearrange one equations to focus on one variable, and then substitute that answer into the other equation.

What do systems of equations represent? How can I solve the system when the equation contains more than 1 variable?

Knowledge: Skills: Rearranging equations

to substitute variables Cognitive development Critical thinking Application of previous

knowledgeStage 2: Assessment Evidence

What authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

Solve system of equations by substituting

#HomeProduct/Performance: Standards:When given a problem from the textbook, students will successfully use the substitution method for solving systems of equations, finding the correct solution and using the method properly.




Objectives will be placed on the board.


Chimer: 5 problems that have students rearranging formulas to find a specific variable.

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their


Textbook homework


#Homework?How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?

Exit ticket

Homework check




#HomeExit ticket:

#HomeDAY-9


9

Topic: Solving Systems of Equations-GraphingStage 1: Desired Results




Students may not graph points correctly

How can I solve a system of equations with a graph? What does the graph represent?

Knowledge: Skills: How to plot points

given an equation. Finding the intercepts

of the lines to determine solution.

Critical thinking Graphing Analyze and interpret

data


To find solutions for systems of equations by graphing.

Product/Performance: Standards:When given a word problem, students will

MAFS.912.A--‐REI.3.6Solve systems of linear

#Homesuccessfully create a system of equations that represents the data from the problem. Then, students will find a solution by graphing the equations.

equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.



Objectives will be listed on the board.


Chimer: have students plot ordered pairs of numbers on a graph.



Graphing video

Textbook homework


How will you help students to exhibit and self-evaluate their growing skills,

Exit slip: If 4 apples and 2 oranges cost $1 and 2 apples and 3 orange cost

#Homeknowledge, and understanding throughout the unit?

$0.70, how much does each apple and each orange cost? There are no quantity discounts.

Summative assessment: Seasonal Systems of Equations




Seasonal System of Equations

#HomeSolve each problem using a system of equations and write your answer as an ordered pair. Solve each system using any algebraic method: substitution, elimination, or graphically.

1. It takes Jack Frost 5 minutes to fly 35 miles with the wind. It takes him 7 minutes to go 35 miles against the wind. Determine his speed in still air (x) and the speed of the wind (y).

Ordered Pair M:_______________

2. The Easter bunny made 13 eggs one day. Some were yellow and the rest were purple. The number of purple eggs he made was one more than twice the number of yellow eggs. How many yellow eggs (x) and purple eggs (y) did the Easter bunny make?

Ordered Pair E:_______________

3. After a big snow storm, Tim and Tom decided to shovel driveways for money. Tom shoveled 3 less than twice as many driveways as Tim. They shoveled a total of 15 driveways. How many driveways did Tim (x) and Tom (y) each shovel?

Ordered Pair I:_______________

4. Your high school is having a competition where students have to guess how many jelly beans are in a jar. The tens digit is 4 more than twice the ones digit. The sum of the digits is 4. How many jelly beans are in the jar? Find the tens digit (x) and the ones digit (y).

Ordered Pair O:______________

5. Cathy and Vicky go shopping for gift wrap one day. Cathy buys 3 rolls of wrapping paper and 5 bows for a total of $32. Vicky gets 1 roll of wrapping paper and 2 bows for $11. How much does each roll of wrapping paper (x) and each bow (y) cost?

Ordered Pair L:______________

6. Scarves and socks are on sale at the store! One woman was able to buy 5 scarves and 4 pairs of socks for $30. Another woman purchased 3 pairs of socks and 2 scarves for $19. Find the price of one scarf (x) and one pair of socks (y).

#HomeOrdered Pair D:________________

7. Cassie got 3 times as many gifts as Oscar. Together Cassie and Oscar got a total of 12 gifts. How many gifts did Cassie (x) and Oscar (y) each get?

Ordered Pair F:_________________

8. Mallory and Alex each drank a cup of hot chocolate after playing in the snow. Mallory put 6 more marshmallows in her cup than Alex. Together Mallory and Alex had a total of 6 marshmallows. How many marshmallows did Mallory (x) and Alex (y) each have in their hot chocolate?

Ordered Pair N:_______________

9. Bobby’s grocery list had 3 more than twice as many items on it than Emily’s list. Emily has 8 fewer items on her list than Bobby. How many items were on Emily’s (x) and Bobby’s (y) grocery lists?

Ordered Pair G:_______________

10. Adrienne has two different bookshelves in her apartment. The taller bookshelf is 1 foot shorter than 5 times the height of the smaller bookshelf. If she stacked the shorter bookshelf on top of the taller bookshelf, they would be a total of 60 inches tall. Find the heights in feet of the taller bookshelf (x) and the shorter bookshelf (y).

Ordered Pair A:_______________

11. Ballard got 2 feet less than twice the amount of snow Bellevue got. Ballard got 3 feet more snow than Bellevue. How many feet of snow did Ballard (x) and Bellevue (y) each get?

Ordered Pair J:________________ 12. A 32 year old mother realized that her age is twice the sum of

her two children’s ages. Her son, Miles is two years older than her daughter, Amelia. How old are Amelia (x) and Miles (y)?

#HomeOrdered Pair H:________________

13. Two families go ice skating one day. The first family spends $25 on skate rentals for 5 kids and 2 adults. The second family spends $14 on skate rentals for 3 kids and 1 adult. How much does each child’s skate rental (x) and each adult’s skate rental (y) cost?

Ordered Pair C:______________

14. At Fred’s house, George ate the same number of sugar cookies and chocolate chip cookies. Twice the number of sugar cookies he ate decreased by one equals the number of chocolate chip cookies he ate. How many sugar cookies (x) and chocolate chip cookies (y) did George eat at Fred’s house?

Ordered Pair B:_____________

15. Mike built a rectangular snow fort with a perimeter of 24 feet. The length of the fort was 8 feet less than 3 times the width. What was the length (x) and width (y) of the fort?

Ordered Pair K:_____________

#HomeDAY-10


9

Topic: Solving Systems of Equations- The MatrixStage 1: Desired Results




Matrices can be used to solve systems of equations. Students may confuse which row or column belongs to which equation or variable. Students also need to recognize that a coefficient of a variable with no number is one.

What do systems of equations represent? How can a matrix help determine the solution of a system of equations?

Knowledge: Skills: Matrix representation

of data Rearrange data from

an equation to numbers

Complex thinking Analyze and interpret

data Reordering representation

of dataStage 2: Assessment Evidence

What authentic performance tasks will students demonstrate the desired understandings? By what criteria will performances be judged? Through what evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals…) will students

#Homedemonstrate achievement of the desired results? How will students reflect upon and self-assess their learning:Goal:

To solve a system of equations with a matrix

Product/Performance: Standards:When given systems of equations that bear 3 variables, students will successfully use matrices to find the solution.




Objectives will be listed on the board.


Chimer: Have students solve a system of equations in all the ways they have learned thus far. Then, introduce a new set with three variables, and set it in a matrix.

What events will help students experience and explore the big idea and questions in the unit?How will you equip them with needed skills and knowledge?How will you cause


Matrix video

Worksheet-collaborative effort

#Homestudents to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?

if finished before bell. After bell, it’s homework



Exit ticket:

Worksheet check




#HomeTHE MATRIX SOLUTION

Solve using a matrix.

#HomeName:__________________________ Period:________ Date:______________

REASONING WITH EQUATIONS AND INEQUALITIES

UNIT EXAM

Create equation and solve. If it’s an inequality, be sure to reflect it on the number graph. Give your answers in complete sentences. Each question is worth 5 points.Problem Solution Problem SolutionKeith received 60 dollars for his birthday. He went to a sporting goods store and bought a baseball glove, baseball, and bat. He had 29 dollars left over, how much did he spent on the baseball gear?

On Monday, 210 students went on a trip to the zoo. All 4 buses were filled and 6 students had to travel in cars. How many students were in each bus?

Sara spent half of her allowance going to the movies. She washed the family car and earned eight dollars. What is her total weekly allowance if she ended with thirteen dollars?

Your quiz grades are 78, 72, 87, and 90. What score on the fifth quiz will make your average quiz grade at least 82?

You rent a car and are offered 2 payment

The Frosty Ice-Cream Shop sells sundaes for

#Homeoptions. You can pay $25 a day plus 15¢ a mile (option A) or you can pay $10 a day plus 40¢ a mile (option B). For what amount of daily miles will option A be the cheaper plan? Explain.

$2 and banana splits for $3. On a hotsummer day, the shop sold 8 more sundaes than banana splits and made $156.

You have just been given a new job in sales. You have two salary options. You can receive a straight salary of $500 per week (no commission option) or you can receive a salary of $200 per week plus 5% of your weekly sales (commission option). What dollar amount of product must you sell each week in order for the commission option to be the better deal? Select the correct equation and solve.

500<200 s

500≥200 s

500<200+( s )5%

500≥200 s+5%

Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number ofCDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week? Use the substitution method to find the number of CDs she sold last week and this week.

{l=6−3 t110=l+ t

{ t=6+3 ll=110−t

{l=6+3tt=6−3l

{6+3 t=ll+ t=110

#HomeThe price, e, of an entertainment system at Extreme Electronics is $220 less than twice theprice, u, of the same system at Ultra Electronics. The difference in price between thesystem at Extreme Electronics and Ultra Electronics is $175. Which system of linearequations can be used to determine the price of the system at each store?Use the substitution method to solve.

Marcos had 8 coins in nickels and quarters. He had 3 more quarters than nickels. Hewrote a system of equations to represent this situation, letting x represent the number ofnickels and y represent the number of quarters. Then he solved the system by graphing.What is the solution by graphing?

The sum of three numbers is 24. Twice the smallest number is 2 less than the largest number, and the largest number is equal to the sum of the other two. Which are the three numbers? Explain

a. 5, 12, 15b. -2, 7, 12c. 5, 7, 12d. -12, 2, 7

Two complementary angles have measures of s and t. If t is 8 less than twice s, which system of linear equations can be used to determine the measure of each angle?

{s+t=90t=2 s−8

{2 s+t=180t=2 s+8

{s+t=1808=2 s−t

{90+s=t8−2 s=t

A theater has tickets at $6 for

Rearrange the following

#Homeadults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing?Solve using your own method.

formulas to show r:

A=π r2

V= 43π r3

C=2πr

True/False:This graph shows the system of inequalities:

{ x+ y≥22x− y>1

True/False:This shows the correct way to solve using elimination.

In your own words, describe the steps to solve this system of equations by elimination.

{ 8 s+t=148 s−2 t=−4

Is this the correct number-line graph for this inequality?

3 x+6≤18

Mary babysits for $4 per hour, and she also

Solve the system of equations by

#Hometutors at $7 per hour. She is only allowed 13 hours per week, but she wants to make at least $63. Write a system of inequalities to represent this situation.

your preferred method.

{ √x−z= yx2+ y2=125z=x−2 y

#HomeName:__________________________ Period:________ Date:______________

REASONING WITH EQUATIONS AND INEQUALITIES

UNIT EXAM

Create equation and solve. If it’s an inequality, be sure to reflect it on the number graph. Give your answers in complete sentences. Each question is worth 5 points.Problem Solution Problem SolutionKeith received 60 dollars for his birthday. He went to a sporting goods store and bought a baseball glove, baseball, and bat. He had 29 dollars left over, how much did he spent on the baseball gear?

60 = 29 + g

He spent $31 on the gear.

On Monday, 210 students went on a trip to the zoo. All 4 buses were filled and 6 students had to travel in cars. How many students were in each bus?

210 = 4(k) + 6

There were 51 students on each

bus.

Sara spent half of her allowance going to the movies. She washed the family car and earned eight dollars. What is her total weekly

½(x)=13

She spent a total of $26, therefore her

total allowance was $26

Your quiz grades are 78, 72, 87, and 90. What score on the fifth quiz will make your average quiz grade at least 82?

78+72+87+90+x5

≥82

I need at least an 83 for my

average to be 82.

#Homeallowance if she ended with thirteen dollars?You rent a car and are offered 2 payment options. You can pay $25 a day plus 15¢ a mile (option A) or you can pay $10 a day plus 40¢ a mile (option B). For what amount of daily miles will option A be the cheaper plan? Explain.

25+0.15m<10+0.40m

Option A will be cheaper at below 60

miles. At 60 miles, the two plans are the same, and at 61 miles, plan B is

cheaper.

The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.

2 s+3b=156s=8+b

The ice cream shop sold 28

banana splits and 36 sundaes.

You have just been given a new job in sales. You have two salary options. You can receive a straight salary of $500 per week (no commission option) or you can receive a salary of $200 per week plus 5% of your weekly sales

500<200 s

500≥200 s

500<200+(s )5%

500≥200 s+5%

I would need to sell more than $6,000 worth of products in order for commission to be the better deal.

Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number ofCDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and

{l=6−3 t110=l+ t

{ t=6+3 ll=110−t

{l=6+3tt=6−3l

{6+3 t=ll+ t=110

(6+3t )+ t=110Kitts sold 26 CDs this week and 84 CDs last week.

#Home(commission option). What dollar amount of product must you sell each week in order for the commission option to be the better deal? Select the correct equation and solve.

t, the number of CDs she sold this week? Use the substitution method to find the number of CDs she sold last week and this week.

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Find a system of linear equations to determine the price of the system at each store?Use the elimination

{ e−u=175e=2u−220

e−u=175−e+2u=220u=395

e=2 (395 )−220e=570

The price at Extreme Electronics is 570, whereas the price at Ultra Electronics is 395.

Marcos had 8 coins in nickels and quarters. He had 4 more quarters than nickels. Hewrote a system of equations to represent this situation, letting x represent the number ofnickels and y represent the number of quarters. Then he solved the system by graphing.What is the solution by graphing?

{8=x+ yx+4= y

x y x y-1 9 -4 00 8 -1 32 6 0 44 4 1 58 0 2 6He had 2 nickels and 6 quarters.

#Homemethod to solve.The sum of three numbers is 24. Twice the smallest number is 2 less than the largest number, and the largest number is equal to the sum of the other two. Which are the three numbers? Explain

e. 5, 12, 15f. -2, 7, 12g. 5, 7, 12h. -12, 2, 7

{x+ y+z=242x=z−2z=x+ y

When the smallest number is 5, which is 2 less than 12, the largest number. The middle number, 7, add with the smallest, 5, to equal 12.

Two complementary angles have measures of s and t. If t is 8 less than twice s, which system of linear equations can be used to determine the measure of each angle?

{s+t=90t=2 s−8

{2 s+t=180t=2 s+8

{s+t=1808=2 s−t

{90+s=t8−2 s=t

A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for

{6a+3.5 s+2.5c=1,300a+s+c=278a=2 s−10

On this night, 150 adults, 80 students,

and 48 children bought tickets.

Rearrange the following formulas to show r:

A=π r2

V= 43π r3

C=2πr

√ Aπ =r

3√ 3V4π =r

C2π

=r

#Homethe showing?Solve using your own method.True/False: this graph shows the system of inequalities:

{ x+ y≥22x− y>1

True

True/False:This shows the correct way to solve using elimination.

False

In your own words, describe the steps to solve this system of equations by elimination.

{ 8 s+t=148 s−2 t=−4

First, you want to eliminate 1 variable. The easiest one to

eliminate would be s. So,

multiply one of the equations by -1. Add the new equation and the other equation (not the old one)

together. Once you eliminate the s, you can

find t. Once you find t, then plug it into one of the

original equations to

find s.

Is this the correct number-line graph for this inequality?

3 x+6≤18

No

#HomeMary babysits for $4 per hour, and she also tutors at $7 per hour. She is only allowed 13 hours per week, but she wants to make at least $63. Write a system of inequalities to represent this situation.

{4b+7 t ≥63b+ t ≤13

Solve the system of equations by your preferred method.

{ √x−z= yx2+ y2=125z=x−2 y

x=11y=2z=7

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