English Language Arts 10 – 2 Web viewGive students a system of equations and have them write contextual word ... This leads nicely into more examples for solving systems of linear

MATHEMATICS 10C:Systems of Linear Equations

Eastglen, J. Percy Page, M.E. LaZerte, Strathcona, W.P. Wagner

Teacher Team: Eastglen High School: Chris Hammond, Mark DobkoJ. Percy Page High School: Rebecca Lyons, Deanna MatthewsM.E. LaZerte High School: Lori Lepatsky, Phuong Nguyen, Victoria WisheuStrathcona Composite High School: Darlene Scammell, Maureen SelkW.P. Wagner High School: Kim Burnham

Facilitator: John Scammell (Consulting Services)Editor: Rita Feutl

Textbook Resources: McAskill, Bruce, Wayne Watt, Eric Balzarini, Scott Carlson, Blaise Johnson, Ron Kennedy, Terry Melnyk, Harold Wardrop. Mathematics 10. Toronto: McGraw Hill Ryerson, 2010. Print.Van Bergeyk, Chris, Dave Van Bergeyk, Garry Davis, Jack Hope, Delcy Rolheiser, David Sufrin, David Zimmer, David Ellis. Foundations and Pre-Calculus Mathematics 10. Pearson Canada Inc., 2010. Print.

The use of Understanding by Design: MATHEMTICS 10C: Systems of Linear Equations content is expressly and solely for Edmonton Public School Board teachers on a non-profit, non-commercial,

internal basis.

2010

Mathematics 10C Systems of Linear Equations 2

TABLE OF CONTENTS

STAGE 1 DESIRED RESULTS

Big Idea 4

Enduring Understanding 4

Essential Questions 4

Knowledge 5

Skills 5

Stage 2 ASSESSMENT EVIDENCE

General Teacher Notes 6

Transfer Task #1 My Cellphone is my Life 6

Transfer Task #2 Money Matters 11

Rubric for Transfer Task 15

Stage 3 LEARNING PLANS

Lesson #1 Modelling Real Life Situations 16

Lesson #2 Solving Systems Graphically with and without Technology 20

Lesson #3 Determining the Number of Solutions 24

Lesson #4 Solving Systems Algebraically 27

APPENDIX

1. Balance Problems 32

2. Foxtrot Cartoon 33

3. Modelling Systems 34


Unit: Systems of Linear Equations

STAGE 1 Desired Results

Big Idea

Real world applications can be modeled and analyzed using more than one linear equation to find solution(s).

Enduring Understandings

Students will understand:

that there are connections between the real world and systems of equations. that there are multiple ways to solve problems involving systems of linear

equations. the relationship between the graph of a system of equations and the meaning

of the solution. that solutions can be communicated in a variety of ways.

Essential Questions

Which method of solving systems of equations is best in a given situation? When is the solution to the system not the answer to the problem? In what ways will technology help or hinder our understanding of systems? When is it possible for “no solution” to be the solution to the problem? What real life situations modelled by systems of equations have one solution,

no solution or an infinite number of solutions?

Knowledge


Implementation note: Post the BIG IDEA in a prominent place in your classroom and refer to it often

Implementation note: At least every second lesson, pause & ask students to consider one of the essential questions. Has their thinking changed, evolved?

Students will know: what a system of equations is and what comprises its solution. that there are 0, 1 or infinitely many solutions to a linear system and what

conditions lead to each. that solutions can be verified. that the solution to a linear system can be found graphically or algebraically. that systems of equations can be used to model real world situations.

Skills

Students will be able to: solve a system of equations algebraically and graphically with and without

technology. explain their strategy for solving a system of equations. verify solutions. interpret and communicate a solution within a context. determine the number of solutions to a system from a graph or equations. model a situation requiring a system of equations algebraically and/or

graphically.


Implementation note: Teachers need to continually ask themselves: what knowledge and skill(s) will the students leave with at the end of the unit?

STAGE 2 Assessment Evidence

1 Desired Result

General Teacher Notes:

You may choose from two transfer tasks. Only one transfer task is needed to evaluate student understanding of the concepts relating to systems of linear equations. The rubric will evaluate either completed task.

Transfer Task #1: MY CELLPHONE IS MY LIFE

Criteria:

Each student will:

recognize what the rate and initial value in a real-life situation represent in an equation.

graph two or more equations representing the situation. potentially describe the slope of horizontal lines. write equations for application problems. use the intersection of the graphs and solution to the equation to solve the

problem. use a graphing calculator or graphing software to graph linear equations.

o change the view window to see the part of the graph that is useful for solving a problem.

*When work is judged to be limited or insufficient, the teacher makes decisions about appropriate intervention to help the student improve.


Implementation note: Students must be given the transfer task & rubric* at the beginning of the unit. They need to know how they will be assessed and what they are working towards.

Teacher Notes for Transfer Task #1: My Cellphone is my Life

This is a list of some cell phone providers that students may research: Telus, Bell, Fido, Koodo, Shaw, Rogers, Virgin, Solo, Speakout, etc.

Students could be given tasks over the course of the unit. For instance, count the number of texts they receive and send in a day or week. Research cell phone plans available in their community.

Going Beyondo speak to the meaning of the lines below and above the point of intersectiono research the average texts per month for teenagers in North America and

adjust your plan if necessary


Implementation note: Teachers need to constantly ask, what performances & products will reveal evidence of understanding?What other evidence will be collected to reflect the desired results?

MY CELLPHONE IS MY LIFEStudent Assessment Task

Your parents are currently paying for your cellphone. But this month, your parents received a HUGE cellphone bill and freaked out about your charges. They’ve taken away your cell phone and cancelled your plan. You need a phone! You decide to find your own plan.

You have a part-time job and your parents will only let you work six hours a week at most. Your job pays minimum wage. Assume you get paid every two weeks.Your parents found this plan for you at $20 per month and $0.20 per text after the first thousand texts (incoming and outgoing).

Goal:Find a better plan than your parents’ plan for your needs and budget.

Role:You are to research two different plans to compare with your parents’ plan.

Product/Performance:Decide what your texting needs are. Then present the following information on a poster:

the maximum you want to pay for your plan within your budget the two plans and your parents’ plan the fixed cost of the plans and any cost per text over the fixed cost the equations of the plans, one of which is your parents’ plan comparison and solution of three plans, represented graphically and

algebraically, as a system of equations the slope and y-intercepts and what they mean the point of intersection and what it means a defence of the plan that most suit your needs that will not go over budget


Teacher Key

(This sample is based on research done on February 2010)

Maximum desired cost is $50 per month

Parent Plan $20 plan with 1000 free textsTelus Plan $30 plan with 1000 free textsTelus Fixed Plan flat rate of $40 including unlimited texts

Slope of parents’ plan is the price per text after 1000 texts.Slope of the Telus plan is 15¢ per text.Slope of the fixed plan is 0 as texts are included in the plan.The y intercept for Telus is $30 per month.The y intercept of the parents’ choice is $20 per month.The y intercept of the flat rate is $40 per month.

The intersection of these two lines represents where the cost and number of texts is the same for both plans. This intersection occurs at (100, 40).

Monthly Cost of Cell Phone Plans


Parents Plan

Best

Plan B

NUMBER OF TEXTS OVER 1000

This is where they are equalC

OST

PE

R M

ON

TH

($)

Algebraic Solutions texts (over 1000)

-

texts

This means for $40 per month I would get an additional 100 texts for a total of 1100 texts. Therefore, I would choose the fix plan for $40 because I send and receive more than 1100 text messages combined.

Alternate Project: http://www.remc11.k12.mi.us/bstpract/bpIII/066/066.PDF


http://www.remc11.k12.mi.us/bstpract/bpIII/066/066.PDF

Transfer Task #2: MONEY MATTERS

Criteria:

Each student will:

recognize what the rate and initial value in a real-life situation represent in an equation.

graph two or more equations representing the situation. potentially describe the slope of horizontal lines. write equations for application problems. use the intersection of the graphs and solution to the equation to solve the

problem. use a graphing calculator or graphing software to graph linear equations.

o change the view window to see the part of the graph that is useful for solving a problem.

Teacher Notes for Transfer Task #2: Money Matters

Prior to transfer task have students define the following vocabulary:


Implementation note: Students must be given the transfer task & rubric* at the beginning of the unit. They need to know how they will be assessed and what they are working towards.

being on call contract work domain hourly wage hourly wage plus commission graduated commission

piece work range salary straight commission

*When work is judged to be limited or insufficient, the teacher makes decisions about appropriate intervention to help the student improve.


Going Beyond

Working at Tec Wizard, your sales are $11490. What would be your rate of commission at In Fashion in order to earn the same income? Also, express the equation that represents the new rate of commission with the same base pay.

What would be the equation, in slope y-intercept form, that would represent the base salary for In Fashion in order to earn the same income of $600 at Tec Wizard?

If you cannot change the base salary, what would be the equation, in general form, that would represent the same income earned for In Fashion as Tec Wizard?

Implementation note: Teachers need to constantly ask: what performances & products will reveal evidence of understanding?What other evidence will be collected to reflect the desired results?

MONEY MATTERSStudent Assessment Task

You are looking for a job and you have applied to many different places. Your uncle is offering $400 a month to be on call working for the family

business. Tec Wizard is offering 5% straight commission on total sales. In Fashion is offering $200 a month salary plus 3% commission on total

sales.

Goal:Compare the three job offers.

Role:Evaluate the pros and cons of each job for you as an individual and choose the job that best fits your needs.

Product/Performance:For your poster:

Identify the variables and determine the three equations that represent the situations.

Give graphical representations of the equations. Determine the three intersection points on the graph and interpret their

meaning. Interpret the y-intercepts and slopes for all three equations Discuss which job you would choose and why. What are the advantages

and disadvantages of each? Algebraically solve for the three points of intersection. Define the domain and range in each equation. Identify the dependent and independent variables.

Teacher KeyAnalysis of Different Jobs (1)

If the base stays the same the new equation is y = 0.033x +200If the commission stays the same the new equation is y = 0.03x + 240 in general form is y = 3x -100y+24000

Going Beyond:Analysis of Different Jobs (2)

MO

NT

HLY

PAY

($)

SALES ($)

SALES ($)

MO

NT

HLY

PAY

($)

Systems of Linear Equations Unit Rubric

Assessment

Level

CriteriaExcellent

4Proficient

3Adequate

2Limited*

1Insufficient /

Blank*

Performs Calculations

Performs precise and explicitcalculations.

Performs focused and accuratecalculations.

Performs appropriate and generally accuratecalculations.

Performs superficial and irrelevant calculations.

No score is awarded because there is no evidence of student performance.

Presents Data Presentation of data is insightful and astute.

Presentation of data is logical and credible.

Presentation of data is simplistic and plausible.

Presentation of data is vague and inaccurate.

No data is presented.

Explains Choice

Shows a solution for the problem; provides an insightful explanation.

Shows a solution for the problem; provides a logical explanation.

Shows a solution for the problem; provides explanations that are complete but vague.

Shows a solution for the problem; provides explanations that are incomplete or confusing.

No explanation is provided.

Communicates findings

Develops a compelling and precise presentation that fully considers purpose and audience; uses appropriate mathematical vocabulary, notation and symbolism.

Develops a convincing and logical presentation that mostly considers purpose and audience; uses appropriate mathematical vocabulary, notation and symbolism.

Develops a predictable presentation that partially considers purpose and audience; uses some appropriate mathematical vocabulary, notation and symbolism.

Develops an unclear presentation with little consideration of purpose and audience; uses inappropriate mathematical vocabulary, notation and symbolism.

No findings are communicated.

STAGE 3 Learning Plans

Lesson 1

Modelling Real Life Situations

STAGE 1

BIG IDEA


ENDURING UNDERSTANDINGS


that there are connections between the real world and systems of equations.

that there are multiple ways to solve problems involving systems of linear equations.

ESSENTIAL QUESTIONS

When is it possible for “no solution” to be the solution to the problem?

What real life situations modelled by systems of equations have one solution, no solution or an infinite number of solutions?

KNOWLEDGE

Students will know that systems of equations can be used to model real world situations.

SKILLS

Students will be able to model a situation requiring a system of equations algebraically and/or graphically.

Lesson Summary

This lesson will teach students to go from concrete to pictorial to symbolic when modelling real life situations.

Lesson Plan

Hook: Finding solutions to pictorial problems that model systems of equations with two and/or three variables.

Have students look at Balance Problems document (see Appendix). Note: The weights for each question are different.

Have students find solutions to the problems and discuss the way they solved the problems. Strategy is more important than the solution. Students can work in small groups, then put their answers on the board or make posters/flip chart paper that outlines how they came up with their answers. Ask them: How do you know you’re right?

Now move the strategies towards a more mathematical discussion. Turn the pictures into equations (modelling) with variables.

Have a teacher-guided discussion on what just occurred. Talk about what a system is, and that the x and the y have a meaning, etc. At this point, define solution.

Have the students create their own modelling situation on an index card and have their elbow partner turn the question into symbols. Limit them to two objects. Note: they must have a system that works. Have them put their answers on the back.

Show students Foxtrot cartoon (see Appendix) and discuss. Or go to: http://www.gocomics.com/foxtrot/2009/01/25/

Put up a word problem on the board. Have students draw a pictorial representation, and then change the pictures into equations with two variables.

Example: Three shirts and two pairs of jeans cost $230 and two shirts and four pairs of jeans cost $340. How much is a shirt and how much is a pair of jeans?

Now use a larger sample so that students will not want to draw a picture and will go right from words to symbols.

Example: Omar and his brother Mohammed go to the local candy shop to buy some treats. Omar has $5 and buys 40 sours and 18 licorice. Mohammed has $8 and buys 50 sours and 40 licorice. How much does each type of candy cost?

http://www.gocomics.com/foxtrot/2009/01/25/

Going Beyond Have students write systems with more than two equations and/or more

than two variables. They can try problems on these sites:

Smiles: http://www.figurethis.org/challenges/c30/challenge.htm

Gone Fishing: http://www.figurethis.org/challenges/c58/challenge.htm

Give students pictorial examples and have them write contextual word problems to go with them.

Give students a system of equations and have them write contextual word problems to go with them.

Let students work on Level-3 questions at: http://www.mathplayground.com/algebraic_reasoning.html

For strong students, you may put up a question with infinite solutionsE.g.: 2 burgers + 3 gingerbread men = $5.50

4 burgers + 6 gingerbread men = $11.00And ask the question: How many solutions can you find?

For extra practice, similar to worksheets: http://www.amblesideprimary.com/ambleweb/mentalmaths/buttons.html

Supporting Provide manipulatives for students who are working at the concrete level.

Examples: Cube-a-Links, pattern blocks, pencils, erasers, rulers, markers, coins, or whatever is available

Let students work on Level-1 or -2 questions at: http://www.mathplayground.com/algebraic_reasoning.html

AssessmentModelling Systems document (see Appendix)

Resources

http://www.mathplayground.com/algebraic_reasoning.html

http://www.amblesideprimary.com/ambleweb/mentalmaths/buttons.html


http://www.figurethis.org/challenges/c58/challenge.htm


Websites: Smiles: http://www.figurethis.org/challenges/c30/challenge.htm

Gone Fishing: http://www.figurethis.org/challenges/c58/challenge.htm

Additional source of pictorial questions: http://www.learner.org/courses/learningmath/algebra/session6/part_e/

homework.htmlhttp://www.mathplayground.com/algebraic_reasoning.html

Balance Problems: Teaching Student-Centred Mathematics Grades 5-8 by John Van de Walle, Lou Ann H Lovin Publisher: Allyn & Bacon, Copyright: 2006, Published: 06/17/2005


http://www.learner.org/courses/learningmath/algebra/session6/part_e/homework.html

http://www.learner.org/courses/learningmath/algebra/session6/part_e/homework.html



Lesson 2

Solving Systems of Equations Graphically with and without Technology

STAGE 1

BIG IDEA






the relationship between the graph of a system of equations and the meaning of the solution.

that solutions can be communicated in a variety of ways.

ESSENTIAL QUESTIONS

When is the solution to the system not the answer to the problem?

In what ways will technology help or hinder our understanding of systems?


KNOWLEDGE

Students will know: that solutions can be verified that the solution to a linear system can be found

graphically or algebraically

SKILLS

Students will be able to: solve a system of equations algebraically and

graphically with and without technology verify solutions

Lesson Summary

Students will solve systems of equations graphically with and without technology.

Lesson Plan

Hook: Tortoise and Hare Demo

Put a line of masking tape on the floor with one-foot increments marked along it for at least 12 feet (or use a measuring tape). Have one student be the hare and the other the tortoise. Have the hare stand on the 0 mark of the tape and the tortoise stand on the four-foot mark (the hare is giving a head start to the tortoise). At each clap of the hands the hare will move two feet and the tortoise will move one foot along the line. Have the students predict when the hare will catch the tortoise. Then run the demo by clapping slowly as the students move. Have the students note where the hare catches up.

On the board draw a graph of what just happened – this is another way to draw a picture (tying it to previous lesson). Put claps on the x-axis and position on the y-axis. Draw a dot for the tortoise and the hare for each clap. Circle the place where the hare passed the tortoise. The dots will form lines; have the students come up with the equations of the lines.

Have the students notice that this is a system of equations and the “solution” is the intersection point of the lines. Graphing and finding the intersection point is another way to solve systems. Also ask some questions about the graph such as who is ahead at a certain point, how you can tell, etc. This leads nicely into more examples for solving systems of linear equations by graphing.

Practise working through a couple of graphing examples – non-contextual and contextual.

Suggestion: Use third example from Balance Problems (see Appendix) to show another way to solve this.

In classroom discussions, teachers should be sure to cover the following topics: What is a solution? How do you know if you are correct? (verify solution) What does it mean to satisfy the system?

Give each pair of students a system of equations and a grid on 11x17 paper. Have them graph the solution on the graph paper and swap with another group. They should check each other’s work.

Do examples of graphing using the graphing calculator – non-contextual and contextual. Choose questions that fit in the standard window settings and ones where the window settings need to be adjusted. You should discuss what window settings make sense in the context of the question (that is, domain and range).

Check for understanding:

Essential Question: In what ways will technology help or hinder our understanding of the system?

Do a contextual example where the answer to the question is not the point of intersection. For example:

Compare pay schemes. Which job should you choose if…..?

Essential Question: When is the solution to the system not the answer to the problem?

Going Beyond Check “Extend” questions in Mathematics 10, textbook, p.431. Give students graphs of nonlinear systems and have them determine the

solutions. Give questions where the intersection point is not in the domain of the

context of the question.

Supporting Give students graphs of linear systems and their equations and have them

find the solutions and verify.

Assessment

Foundations and Pre-calculus Mathematics 10, textbook, pp. 403-415Mathematics 10, textbook, pp. 416-431 Exit slips

ResourcesGraphing calculatorMaterials for Tortoise and Hare Demo: measuring tape, masking tape

Lesson 3

Determining the Number of Solutions

STAGE 1

BIG IDEA






the relationship between the graph of a system of equations and the meaning of the solution.

that solutions can be communicated in a variety of ways.

ESSENTIAL QUESTIONS

In what ways will technology help or hinder our understanding of systems?



KNOWLEDGE

Students will know: what a system of equations is and what

comprises its solution. that there are 0, 1 or infinitely many solutions to a

linear system and what conditions lead to each that solutions can be verified. that systems of equations can be used to model

real world situations.

SKILLS

Students will be able to: verify solutions. interpret and communicate a solution within a

context. determine the number of solutions to a system

from a graph or equations.

Lesson Summary

Students will determine the number of solutions to a system in a variety of ways.

Lesson Plan

Choose a student’s example from the first lesson (choose one that has a simple solution) to demonstrate an equation with one solution. Have students work in pairs on a pictorial example of a system with infinitely many solutions (example below). Discuss the results, challenges, patterns, and different processes used. Write these as a system of equations, rearrange in terms of y and graph them. Then do the same with a system with no solutions (example shown below).

1. Infinitely many solutions: How much does a goldfish or a seahorse cost?

=$132

=$662. No solutions: How many minutes does it take to bake a pie or a gingerbread man?

=90 minutes

=150 min

Lead the discussion back to graphing from the last lesson. Change the questions into equations and have students graph them, discussing the slope and y-intercept of each line and what situation creates the number of solutions in each system.

Individually or in groups, students will create three systems (one solution, no solution, infinitely many solutions) and represent them three ways: graphically, algebraically and pictorially. Introduce the word coincident.

Discussion may occur about how to recognize the number of solutions without having to rearrange the equations. This would lead into the game of Last Man Standing.

Last Man Standing Game:Have all the students stand up. Put a system of equations up on the board. Much like the paper/rock/scissors game, have students simultaneously show the number of solutions by holding up a fist (no solutions), one finger (one solution) or all five fingers (infinitely many solutions). If students get the answer wrong they sit down and become judges. Put up a new question and continue the game until one student remains. Have several systems ready to go for this game.

Going Beyond

Leading questions: Can we think of an example with two (or more than one) solutions? Can we think of a real-world situation that has no solution or infinitely

many solutions?

Assessment

Informal assessment: Last Man Standing Game (above)

Resources

Foundations and Pre-calculus Mathematics 10, textbook, pp. 442-449.

Number of Solutions for Systems of Linear Equations, Mathematics 10, textbook, pp. 446-459

Vocabulary

coincident lines intersecting lines

infinite parallel

Lesson 4

Solving Systems Algebraically

STAGE 1

BIG IDEA



Students will understand: that there are connections between the real

world and systems of equations. that there are multiple ways to solve problems

involving systems of linear equations. that solutions can be communicated in a variety

of ways.

ESSENTIAL QUESTIONS

Which method of solving systems of equations is best in a given situation?


When is the solution to the system not the answer to the problem?

KNOWLEDGE

Students will know: that solutions can be verified. that the solution to a linear system can be found

graphically or algebraically. that systems of equations can be used to model

real world situations.

SKILLS

Students will be able to: solve a system of equations algebraically and

graphically with and without technology. explain their strategy for solving a system of

equations. verify solutions. interpret and communicate a solution within a

context.

Lesson Summary

Students will be able to solve a system of equations algebraically.

Lesson Plan

Part 1Introduce the first pictorial example on the board, without writing the matching equations. Have the students discuss how to solve these without graphing and write in words the steps that they used to come up with a solution. Does their answer work? Pick out the steps that are more like the elimination method and focus on them. Let the students know that the other steps (substitution method) will be studied in Part 2 of this lesson.

At this point, write the equations on the board and work through the steps that the students suggested.

+ = 20 2x + y = 20

+ = 15 x + y = 15

Take up another example and work through the same process to solve this system:

+ = 100 3x + 2y = 100

+ = 80 x + 2y = 80

Let the students know that this process is called elimination and demonstrate more traditional questions with subtraction, different coefficients for both variables, fractions and word problems.

Give students practice time with more questions.

Part 2Introduce the first pictorial example on the board, without writing the matching equations. Pull out the student work from Lesson 1 that was more like substitution and go over them. Write the equations on the board and work through the steps that the students suggested.

= x = 2y

+ = 30 x + 3y = 30

Take up another example and work through the same process to solve this system:

= + 3 x = 2y + 3

+ = 11 2y + x = 11

Let the students know that this process is called substitution and demonstrate more traditional questions with subtraction, different coefficients for both variables, fractions and word problems.

Give students practice time with more questions.

Part 3: Wrap Up

Spend a few minutes reviewing the different ways that we have solved equations. Split the students into groups and give them three different systems of equations. Have them discuss how to solve them and answer the questions “Which method of solving systems is best for each equation?” Results can be shared in a number of different ways such as group presentation, expert-based sharing, etc.

1. Six pencils and four crayons cost $3.40. Three similar pencils and ten similar crayons cost $4.90. How much would you expect to pay for a set of eight pencils and twelve crayons?

2. You have been offered two jobs. Job A pays you $300 per month and 2% commission of sales. Job B pays a straight commission of 10% of sales. Under what circumstances would you choose A? B?

3. A ring costs three times as much as a necklace. Two rings and one necklace cost $140. How much does each item cost?

As a follow-up to the second question, discuss the essential question “When is the solution to the system not the answer to the problem?”

Going Beyond

Provide the students with questions in three variables, pictorial and symbolic. Some examples of these can be found in the worksheets from Lesson 1.

Supporting

Some students will benefit from having manipulatives to solve systems and may need more practice with simpler questions.

Assessment

The practice time and the closing presentation will give a chance for the teacher to do a formative assessment.

ResourcesFoundations and Pre-calculus Mathematics 10, textbook, pp. 416 – 439.Mathematics 10, textbook , pp. 468 – 501

Vocabulary

substitution elimination

Math 10 Unit CSystems of Linear Equations

APPENDIX

Lesson 1 Balance Problems

Source: Van de Walle, John, Lou Ann H. Lovin. Teaching Student-Centred Mathematics Grades 5-8 . Allyn & Bacon, 2006. Print.

1.

2.

5.

4.

3.

Lesson 1

Lesson 2Modelling Systems

A. Solve the following picture problems.

1. Find the value of one ladybug.

2. Find the value of one guitar.

3. Find the value of one umbrella.

4. Find the value of one gear.

5. Find the value of one pear.

6. Find the value of three gears.

Source: http://www.mathplayground.com/algebraic_reasoning.html

B. For each picture above, write a system of equations.

1.

2.

3.

4.

5.

6.


C. Read the following word problems, draw pictures for the systems, and then write them as equations.

1. Two hoodies and three T-shirts cost $140. Four hoodies and one t-shirt costs $180.

2. For $15, Murphy downloaded five songs and two music videos. Sania downloaded three songs and three music videos for $18.

3. John and his sister went to the pet store to buy some fish. He bought six Nemo fish and two goldfish for $94. She only paid $50 to buy two Nemo fish and ten goldfish.

4. Homer and Marge decided that they need to get out more and buy tickets to Oilers games and Eskimo games. Mr. Winter bought two Eskimos tickets and one Oilers ticket for $130. For $260 Ms. Burnham bought four Eskimos tickets and two Oilers tickets.

5. Doughboy and Mr. Tim meet every day to buy snacks for lunch and they each spend $6.50. Doughboy always buys four doughnuts and one cinnamon bun. Mr. Tim gets two doughnuts and three cinnamon buns.

D. Write each system of equations in words.

1. How much money is each item worth?

=$250 =$220

2. How much money is each item worth?

=$132

=$66

3. How much does each item weigh?

=32200 lbs

=64300 lbs

http://www.clipart.com/en/close-up?o=3793308&memlevel=A&a=a&q=clothes&k_mode=all&s=1&e=18&show=&c=&cid=&findincat=&g=&cc=&page=&k_exc=&pubid=





4. How much baking time for each item?

=88 min =132 min

5. How many points is each item worth?

=32=28

6. How many calories in each item?

=3080 cal

=3160 cal

Modelling Systems Answer Key

A. Solve

1. ladybug = 92. guitar = 63. umbrella = 8

4. gear = 65. pear = 56. three gears = 36

B. Systems of Equations

1.

2.

3.

4.

5.

6.

C. Word Problems

1.

2.

3.

4.

5.

D. Write equations in words. Answers are not intended, but provided for reference for high-end kids.

1. jacket: $70, shoe: $202. infinite solutions3. scooter: 100lbs, truck: 32000 lbs4. pancake: 40 min, gingerbread man: 12 min

5. square: ; smiley face:

6. hamburger: 540 cal; fries: 500 cal

Unit 43

Documents

English Language Arts 10 – 2 Web viewGive students a system of equations and have them write contextual word ... This leads nicely into more examples for solving systems of linear