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DRAFT/Algebra I Unit 2/MSDE Mathematics Lesson Plan/Systems of Equations through the Lens of Art Integration

Background InformationContent/Course Algebra I

Unit Unit 2: Linear and Exponential Relationships

Essential Questions/Enduring Understandings Addressed in the Lesson

Essential Questions When and how is mathematics used in solving real world problems?

o How can systems of equations and inequalities model and be used to solve real-world problems?

What characteristics of problems would determine how to model the situation and develop a problem solving strategy?

o How can multiple representations of functions be used to reason and make sense of relationships and model change?

o What characteristics of a problem help determine if a linear or exponential model could serve as an appropriate function to represent the situation?

What is the most appropriate structure to represent mathematical situations?o How are the symbolic, numeric, graphic, and verbal representations of functions

and equations related?

Enduring Understandings Mathematics can be used to solve real world problems and can be used to

communicate solutions to stakeholders.o Systems of equations and inequalities can be used to solve real world problems.

Multiple representations may be used to model a given real world relationship.

Standard Addressed in This Lesson

A.RE1.6 Solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables.

Lesson Title Systems of Equations Through the Lens of Art Integration

DRAFT Maryland Common Core State Curriculum Lesson Plan for Algebra I May 2012 Page 1 of 28


Background InformationRelevance/Connections This lesson connects with students’ ability to define appropriate quantities (N.Q.2) for the

purpose of modeling as studied in Unit I. This lesson will also build on student experiences with graphing and solving systems of linear equations from middle school. Consider making connections with art teachers in your school to infuse vocabulary used in descriptive analysis of a piece of art work.

Student Outcomes The student will: understand that the point of intersection of a system of equations satisfies both equations. translate a real world problem to a system of equations. solve systems of linear equations algebraically, graphically and numerically. select the most efficient method to solve a system of equations. verify that the coordinates of the point of two graphs makes both equations in the system

true.Summative Assessment(Assessment of Learning)

What evidence of student learning would a student be expected to produce to demonstrate attainment of this outcome? Students will create a scenario inspired by their art piece that can be modeled by a system of linear equations. Students will produce and present this display to the class. Students will be able to describe the solution in the context of the scenario.

Prior Knowledge Needed to Support This Learning(Vertical Alignment)

Students have solved systems of linear equations in two variables in 8 th grade. Standard 8.EE.8a, 8b and 8c deal with solving pairs of simultaneous linear equations. The treatment of solving systems of 2 linear equations should be treated as a review. This review will prepare students for solving systems that consist of combinations of linear and quadratic equations as well as other combinations of equations.

Method for determining student readiness for the lesson

How will evidence of student prior knowledge be determined?The Warm Up included in this lesson provides a means of determining which students possess the prior knowledge needed to ready for this lesson.

What will be done for students who are not ready for the lesson? Pair students who demonstrate, during the Warm Up, that they do not possess the needed prior with students who demonstrate that they are ready for the lesson.



Background InformationCommon Misconceptions

(See Algebra I Unit 2, unit plan for strategies for dealing with Common Misconceptions)

Students may have trouble understanding the differences between systems that have one solution, no solutions, and infinitely many solutions in the context of the problem. Students may also have trouble understanding what the intersection truly means in the context of the problem.

Students may have trouble grasping conceptual understanding of what a solution to a system of equations represents in all representations ( graphic, numeric and algebraic).



Learning ExperienceStandards for Mathematical

Practice(SMP)

Component Details

SMP #4 Model with Mathematics

The first problem in the Warm-Up requires students to create linear models for given scenarios.

Warm Up/Drill Materials Needed Warm Up handout (attached)

Implementation Students will complete the warm up individually. The warm up serves as a means of activating prior knowledge of:

o writing linear equations in slope-intercept form from verbal representations.

o completing a table of values given a linear equation in slope intercept form.

o graphing linear equations While students are working, monitor students and help where necessary. Use the results of observations to determine the readiness of the class. While students are working on the Warm Up circulate and distribute one

puzzle piece to each student. Distribute the pieces strategically so students who seem to possess the needed prior knowledge are paired with students who do not seem to possess the needed prior knowledge.

Review the Warm Up

For ELLs: highlight key words such as “each, per, rate” etc as having to do with the

slope and terms such as “fees, starting amount, already” etc as having to do with the y intercept.

have bilingual dictionaries available for use.

UDL ConnectionsUDL Principle II: Provide Multiple Means of Action and Expression,Checkpoint 5.3 Build fluencies with graduated levels of support for practice and performance, discusses that learners must develop fluencies and that fluency is built through many opportunities for performance. This activity is providing




Practice(SMP)

Component Details

students an opportunity for the distributed practice over time that the brain needs for long term retention of a skill.

Activity 1 Materials Needed Guided Notes handout

Implementation Work through the problem on the “Guided Notes” handout. As you work

through the problem provide opportunities for students to “Turn and Talk” to their neighbor and then share their thoughts whole class for each step of the problem.

Tell students that in the next activity they will take this process one step further in that they will be creating their own scenario and then setting up and solving a system of equations to model the scenario.

Motivation Materials Needed Pictures of famous works of art (attached) “I See, I Think, I Feel, I Wonder” template (attached)

Preparation Make one copy of each famous work of art Create puzzle pieces by cutting each famous work of art into three pieces

for groups of three or four pieces for groups of 4.Implementation

After Activity1, project the image of a work of art that is not used for one of the puzzles.

Instruct students to examine the projected image and record their thoughts about the image on a copy of the “I see, I think, I feel, I wonder” handout.

To prepare students for Activity 2, model how to come up with a scenario inspired by the projected image that could be represented by a system of




Practice(SMP)

Component Details

linear equations. Model how to create, solve and interpret the system of equations.

Note: This process will motivate students to look at the artwork and begin to wonder about their own art “puzzle piece.” This activity will develop students’ abilities to analyze artwork if they have not done so in the past. It also serves a hook and will engage visual learners.

UDL ConnectionsUsing Art as the motivation is a novel way to begin a lesson. The brain responds to novelty and this will hopefully recruit student interest. UDL Principle III: Provide Multiple Means of Engagement; Guideline 7: Provide options for recruiting interest, discusses this topic.

http://www.udlcenter.org/aboutudl/udlguidelines/principle3

SMP #4 Model with Mathematics Students must create, solve and analyze the solution to a system of linear equations, inspired by a famous work of art.

Activity 2 Materials Needed “Exploring Art” handout (attached) Poster board or chart paper Markers Grid paper Glue Copy of “Poster Format” handout (attached) Graphing calculator (optional)

Implementation Instruct students to find others in the class who have pieces that come

from the same piece of art. Note: This is a grouping strategy for this activity.

Distribute a copy of the “Exploring Art” handout to each student. Instruct the members of each group to put their puzzle pieces together and





Practice(SMP)

Component Details

to analyze the resulting image. Group members should work together to complete the “Exploring Art”

activity in preparation for group presentations. Display a copy of the “Poster Format” handout to provide guidance to the

students as to how to create their displays.

Closure Implementation Groups presentations

Note: Grade presentations with a rubric of your choosing. Ideas for presentation techniques

gallery walk whole class presentation

Evidence of student attainment will be determined by the presentation, mathematical accuracy, and analysis of the scenarios.

UDL ConnectionsThis segment of the lesson provides a different way for students to communicate what they know. This adheres to UDL Principle II: Provide Multiple Means of Action and Expression which discusses the need to provide various ways for students to express themselves. http://www.udlcenter.org/aboutudl/udlguidelines/principle2

Supporting InformationDetails




Supporting InformationInterventions/Enrichments

Students with Disabilities /Struggling Learners

ELL Gifted and Talented

Students with Disabilities/Struggling Learners: Students may need help coming up with a scenario from their artwork. Be prepared to

help struggling students as they attempt to develop a scenario. Instruct students to create a scenario involving simpler numbers to work with (i.e no

decimals, fractions, negative numbers). Allow students to use a graphing calculator to solve the system of linear equations.

ELL students: ELL students may have trouble writing the scenario and analyzing it in complete

sentences. Bilingual dictionaries should be made available. Provide ELL students with “fill in the blank” sentences depending on their English

proficiency level. For a class with a large ELL population, consider working with ELLs as a pullout

group to help them create a poster.

Gifted and Talented students: Challenge accelerated students to come up with a scenario that would involve three

linear equations Accelerated students might be asked to analyze the graph further by answering

questions such as:o What would happen if you changed …?o How can you change your scenario so that the intersection is now in the IV

quadrant?o What would that intersection represent?o Is that intersection possible in the real world?



Warm Up

1. Write a linear equation, in slope intercept form ( ), to model the following scenarios.

a. You are driving a car at a speed of 55 miles per hour. Write an equation to model the distance in miles. (Remember, Distance = (Rate)(Time))

b. You are buying a bouquet of roses for your girlfriend. Each rose costs $3 and there is a bouquet assembly fee of $4.

c. It is finally snowing. Snowflakes are falling at a rate of 500 snowflakes per minute.

d. You are emptying your swimming pool. The pool has 5,000 gallons of water and you are emptying it at a rate of 10 gallons per minute.

2. Fill in the table of values for each of the given the linear functions. For the third table select your own values of x.


x y-10123

x y-2024

x y


3. Graph the following systems of linear equations and circle the point of intersection.

a. b.

c. d.



The Dancing Class by Edgar Degas



Bar at the Folies Bergere by Manet



Mother About to Wash Her Sleepy Child by Mary Cassatt



Mona Lisa by Leonardo da Vinci



Paul Gauguin – Bouquet of flowers 1896


http://www.famousartistsgallery.com/gallery.html


Henri Matisse- Seville Still Life 1911


http://www.famousartistsgallery.com/gallery/frame/matisse-gr.html


Henri Matisse- View of Collioure 1906


http://www.famousartistsgallery.com/gallery/frame/matisse-gr.html


Joan Miró- The Tilled Field 1923-1924


http://www.famousartistsgallery.com/gallery/miro-fh.html


Joan Miró- The Village of Prades 1917


http://www.famousartistsgallery.com/gallery/miro-fh.html


Claude Monet- Wild Poppies 1873


http://www.famousartistsgallery.com/gallery/monet-w9.html


Claude Monet- Water Lilies 1916


http://www.famousartistsgallery.com/gallery/monet-wd.html


Pablo Picasso – Landscape with Dead Tree 1919


http://www.famousartistsgallery.com/gallery/picasso-bw.html


Pablo Picasso- La Arene de Barcelona 1900


http://www.famousartistsgallery.com/gallery/picasso-bw.html


I See, I Think, I Feel, I Wonder

I see _____________________________ Something you notice or observe with your eyes.

I think ____________________________ What you think about what you see.

I feel _____________________________ An emotion you experience because of what you see or think.

I wonder __________________________

Something you’re curious about or a question you have.



GUIDED NOTES

Imagine that your friends are planning a wonderful vacation trip to the beach. You will need to rent a car and are comparing different prices.

Enterprise charges a flat fee of $50 and an additional $2 per mile driven. Hertz charges a flat fee of $70 and an additional $1 per mile driven.

a) Write equations to model the cost of renting a car from:

Enterprise

Hertz

b) Complete a table of values for each equation.

ENTERPRISE HERTZ

X Y

0

10

20

30


X Y

0

10

20

30

http://www.google.com/imgres?hl=en&biw=1024&bih=596&tbm=isch&tbnid=sXRZy-BupTWs5M:&imgrefurl=http://www.cartoon-clipart.com/cartoon_clipart_images/cartoon_man_relaxing_while_on_vacation_at_the_beach_0515-1011-1516-2024.html&docid=ZJVIpG3ayqqKQM&imgurl=http://www.cartoon-clipart.com/cartoon_clipart_images/cartoon_man_relaxing_while_on_vacation_at_the_beach_0515-1011-1516-2024_SMU.jpg&w=300&h=252&ei=D3sQT8bYBafn0QH03eiJAw&zoom=1


c) Graph the equations on the same graph. Use 2 different colors.

d) Estimate the intersection by looking at the graph.

e) What does the intersection represent? Use a complete sentence.

f) Verify the solution algebraically. Does it make sense?

g) For how many miles would it be better to rent from Hertz? For Enterprise?



Exploring Art

As a group, you will be creating a poster to present to the class. You will be creating a scenario inspired by your group’s art piece that can be modeled with linear equations. You may want to look at the teacher sample or the notes to get started. You must answer the following questions in complete sentences and be prepared to answer questions from your classmates.

On your poster, be sure to include all of the following items:

title of your artwork

artist’s name

date when the artwork was created (if available)

written description of the scenario

2 linear equations which model the scenario

table of values for each equation

graph of the equations on the same coordinate plane label the x and y axis with units and give your graph a title write the intersection as an ordered pair and clearly mark it on your graph

Your poster must display the answers to the applicable questions for your scenario.

Do the lines that model your scenario intersect? a. If so, what does the intersection mean in the context of the problem? Does this make

sense in the context of your scenario? Why or Why not?

b. If not, what kind of lines could they be and why?



Poster Format

Artwork

Scenario

Equations

Table of Values

Graph


TitleArtistDate

Answers to questions

Documents

DRAFT/Algebra I Unit 2/MSDE Mathematics Lesson Plan/Systems …mdk12.msde.maryland.gov/.../A1_U2_LP_SystesmofLine… · Web viewDRAFT/Algebra I Unit 2/MSDE Mathematics Lesson Plan/Systems