EMS Math Department / Unit 4: Systems of Equations / Dates: November 30th – December 17th
Math Florida Standard(s)
Benchmarks, Descriptions
and DOK levels / MAFS.912.A-CED.1.2 (DOK 2): Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Identify quantities in a mathematical problem or real world situation that should be represented by distinct variables and describe what quantities the variables represent. Create at least two equations in two or more variables to represent relationships between quantities. MAFS.912.A-CED.1.3 (DOK 3): Represent constraints by systems of equations and interpret solutions as viable or nonviable options in a modeling context. MAFS.912.A.REI.3.5 (DOK3): Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Recognize and use properties of equality to maintain equivalent systems of equations. Justify that replacing one equation in a two-equation system with the sum of that equation and a multiple of the other will yield the same solutions as the original system. MAFS.912.A.REI.3.6 (DOK 1): Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Solve systems of linear equations by any method. Justify the method used to solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. MAFS.912.A-REI.4.11 (DOK 2): Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. MAFS.912.A.REI.4.12 (DOK 2): Graph the solutions to a linear inequality in two variables as a half-plane and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Identify characteristics of a linear inequality and a system of linear inequalities, such as: boundary line, shading, and determine the appropriate points to test and derive a solution set form. Explain the meaning of the intersection of the shaded regions in a system of linear inequalities.
Learning Goal / Students will be able to solve systems of linear and non-linear equations and/or inequalities through various methods, and interpret solutions as they relate to real-world problems.
Essential Question(s) / How would you decide which method to use to solve and justify systems of equations? How could you apply systems of equations to problem solving in the real world? How do you explain how a system of equations will help a business man determine the break-even point and help to analyze future trends?
Assessments / Pre-Assessments / Bell ringer- What is a system
Formative Assessments / Quizzes and independent practice
Summative Assessments / Linear system test/ final project.
Progress Monitoring/ Feedback Loop / Homework will give immediate feedback as to progress as they will be graded whole class and students will be able to ask questions immediately.If the student has a 70 or below on a quiz he can study more and retake it within a 7 day period for full credit. If the student has below a 70, the instructor will provide real time remediation.
Higher Order Question(s) / What do you notice about…? What is the relationship of the quantities? How do the important quantities in your problem relate to each other? How do you know your answer is correct/reasonable?
Key Vocabulary / Equivalent Systems, Elimination, Substitution, Graphing of System, No Solution, Infinitely Many, Half Plane, Viable, Non-Viable.
Monday, November 30th, 2015 / Intro to Systems of Equations / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will unpack the standards and familiarize themselves with vocabulary associated with systems of equations through thinking maps, reflections, and learning scales.
BELL RINGER
( 5 minutes) /
- What is a system? Think about different systems what characteristics do they have in common?
I DO: /
- Introduce systems
WE DO: /
- Research and com put with a good definition for a system.
- Unpack the standards.
- Define Vocabulary
- Review graphing test.
- What is my grade?
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish vocabulary if you have not already done so
EXIT TICKET:
(5 minutes) /
- What do you know about systems?
Tuesday, December 1st, 2015 / Graphing Systems of Equations / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will approximate solutions to systems of equations by graphing two lines and finding the point of intersection through guided Cornell Notes and practice problems.
BELL RINGER
( 5 minutes) /
- Graph these lines. Y= 2x+5. 3x-4y= 5, and y-3=-2(x-1)
I DO: /
- Assess and monitor
WE DO: /
- Cornell Notes for graphing systems.
- Guided Practice
- Independent work - must be on graph paper Page442-444 (4, 12,14,18,22,32,33
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish independent work – Must be on graph paper
EXIT TICKET:
(5 minutes) /
- How do you graph a system?
Wednesday, December 2nd, 2015 / Solving Systems by Substitution / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of equations algebraically using the substitution method by taking Cornell Notes and completing practice problems.
BELL RINGER
( 5 minutes) /
- What could make graphing a system difficult?
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Cornell Notes – Substitution
- Guided Practice
- Independent Practice Page 451(4,6,8,10,12, 17,22,31,32)
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish independent work
EXIT TICKET:
(5 minutes) /
- How do you solve a system with substitution?
Thursday, December 3rd, 2015 / Solving Systems by Substitution / Rigor Level: DOK 2 & 3
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of equations algebraically using the substitution method by taking Cornell Notes and completing practice problems.
BELL RINGER
( 5 minutes) /
- 2 systems Graph one and solve one with substitution.
I DO: /
- Assess & Monitor
- Check homework
WE DO /
- Review Homework
- Rally Robin – Substitution & graphing systems. Evens
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Substitution and graphing evens
EXIT TICKET:
(5 minutes) /
- When is ti better to use substitution instead of graphing? .
Friday, December 4th, 2015 / Solving Systems by Elimination (Addition and Subtraction) / Rigor Level: 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of equations algebraically using the elimination method with addition and subtraction by taking Cornell Notes and completing practice problems.
BELL RINGER
( 5 minutes) /
- 2 systems Graph one and solve one with substitution.
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Cornell Notes – Elimination
- Guided Practice
- Independent Practice Page 459 (4,6,10,14,18,2026,30 , 39,40,41)
- Five question quiz
YOU DO: /
- Monitor yourself on the learning scale
Homework /
- Finish independent practice
EXIT TICKET:
(5 minutes) /
- How are you doing on the system unit?
Monday, December 7th, 2015 / Solving Systems by Elimination (Multiplication) / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of equations algebraically using the elimination method with multiplication by taking Cornell Notes and completing practice problems.
BELL RINGER
( 5 minutes) /
- What are the three ways to solve systems?
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Cornell Notes – Elimination with multiplication
- Guided Practice
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish independent practice
EXIT TICKET:
(5 minutes) /
- How do you use elimination to create equivalent equations?
Tuesday, December 8th, 2015 / Solving Systems by Elimination Real-World Problems / Rigor Level: DOK 2 & 3
Algebra Daily Agenda
Daily Objective /
- Students will apply what they know about solving systems of equations by elimination to real-world problems through application practice.
BELL RINGER
( 5 minutes) /
- 3 systems solve one with graphing, one with substitution,& solve one with elimination
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Scribe & Squire word problems worksheet
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Word problem worksheet
EXIT TICKET:
(5 minutes) /
- Create the system word problem and solve it.
Wednesday, December 9th, 2015 / Review Solving Systems by Elimination / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve special types of systems including those with no solution and infinitely many solutions.
BELL RINGER
( 5 minutes) /
- 3 systems solve one with graphing, one with substitution,& solve one with elimination
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Cornell Notes – Special Systems
- Guided Practice
- Independent Practice
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish Independent Practice – worksheet
EXIT TICKET:
(5 minutes) /
- What makes a system special?
Thursday, December 10th, 2015 / Solving Special Types of Systems / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will review solving systems in the various ways using think pair share.
We BELL RINGER
( 5 minutes) /
- 3 systems solve one with graphing, one with substitution,& solve one with elimination
I DO: /
- Assess & Monitor
- Check homework
WE DO /
- Review homework
- Think Pair Share worksheet
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish think pair share worksheet
EXIT TICKET:
(5 minutes) /
- What is your favorite ways to solve systems? Why?
Friday, December 11th, 2015 / Assessment on Solving Systems of Equations / Rigor Level: 2 & 3
Algebra Daily Agenda
Daily Objective /
- Students will demonstrate knowledge of solving systems of linear equations both graphically and algebraically through a paper and pencil Test
BELL RINGER
( 5 minutes) /
- 3 Systems
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Discuss systems
YOU DO: /
- Take linear system test.
Homework /
- None
EXIT TICKET:
(5 minutes) /
- How did you do on this linear part of the unit?
Monday, December 14th, 2015 / Systems of Inequalities / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of inequalities by determining the shaded area of the graph that satisfies two or more inequalities.
BELL RINGER
( 5 minutes) /
- Graph an equation
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review test for linear systems
- Cornell Notes Systems of inequalities
- Guided Practice
- Independent Practice
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Page 417 (12,14,26,34,38,40,42,44,54,56) Get colored pencils
E2XIT TICKET:
(5 minutes) /
- What is your solution in a linear inequality?
Tuesday, December 15th, 2015 / More Systems of Inequalities / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of inequalities by determining the shaded area of the graph that satisfies two or more inequalities using Cornell Notes
BELL RINGER
( 5 minutes) /
- Graph a linear inequality
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Cornell Notes – system of inequalities
- Guided Practice
- Independent practice
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Page 481 (4,10,12,14,16,18,24,28,,29,40)
10,12,14,18,24,27,28,EXIT TICKET:
(5 minutes) /
- How does the solution of a system of linear inequalities differ from a system of linear equations? Can a system of linaer inequalities be special?
Wednesday, December 16th, 2015 / Algebra Nation Non-Linear Systems / Rigor Level: DOK 2
Algebra Daily Agenda
Daily Objective /
- Students will solve systems of inequalities by determining the shaded area of the graph that satisfies two or more inequalities using scribe and Squire
BELL RINGER
( 5 minutes) /
- Graph a linear inequality
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Think Pair Share worksheet
YOU DO /
- Monitor yourself on the learning scale
Homework /
- Finish think pair share worksheet
EXIT TICKET:
(5 minutes) /
- Explain how to solve a system of inequalities
Thursday, December 17th, 2015 / Springboard Non-Linear Systems / Rigor Level: DOK 2 & 3
Algebra Daily Agenda
Daily Objective /
- Students will use tables to approximate the solutions of systems that include both linear and non-linear equations through Algebra Nation Video Program and Note-Taking Guide.
BELL RINGER
( 5 minutes) /
- 3 systems – 2 linear and one inequality
I DO: /
- Assess & Monitor
- Check homework
WE DO /
- Review homework
- Algebra Nation – non linear systems
- Guided Practice
- Independent practice
YOU DO /
- Monitor yourself on the learning scale
Homework /
- 2 problems
EXIT TICKET:
(5 minutes) /
- How do you solve a non linear system?
Friday, December 18th, 2015 / Springboard Non-Linear Systems / Rigor Level: 2 & 3
Algebra Daily Agenda
Daily Objective /
- Students will use graphs to approximate the solutions of systems that include both linear and non-linear equations through completion of a Springboard Activity.
BELL RINGER
( 5 minutes) /
- Mini Task for non linear system
I DO: /
- Assess & Monitor
- Check homework
WE DO: /
- Review homework
- Springboard – Non Linear Systems
- Guided Practice
- Independent practice
YOU DO: /
- Monitor yourself on the learning scale
Homework /
- Finish independent practice
EXIT TICKET:
(5 minutes)
Note: Learning Scales, Accommodations, and Math Practice Standards are below.
Learning Goal Scale
Level / Date / Skill4 / I can apply all these skills to the real world.
3 / Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically
I can analyze the solutions when given a linear and nonlinear system.
Solve systems of linear equations (focusing on pairs of linear equations in two variables) exactly and approximately
2 / Given a system including linear and nonlinear functions, I can approximate the solutions.
I can determine if an ordered pair is a solution to a system of inequalities.
I can solve linear equations accurately using 2 or more methods.
1 / Given a graphic system I can tell the solution of the system.
Given an ordered pair, I can see it is a viable solution to the system.
Given a system of graphs I can tell if it is no solution or infinitely many solutions
WICR Strategies used during each unit.
Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process Writing
• using a rubric as evaluation
On-Demand/Timed-Writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective Writing
• students write about what they have learned and what they still need / Higher-Level Questioningin Classes
• Costa’s Level 1: Studentsfind the answers right therein the text.
• Costa’s Level 2: Studentsmust figure out the answerfrom information in thetext.
• Costa’s Level 3: Studentsapply what they havelearned or use what theyhave learned to evaluate orcreate. / Think Pair Share
Sharing Ideas With a Partner or in a Group
Carousel or Gallery Walk
Problem Solving in Groups
Projects in Groups / Before Reading Activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During Reading Activities
• marking the text
• Cornell notes
• graphic organizers
After Reading Strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
- Read directions for the student
- Check for understanding
- Allow to leave class for assistance
- Extra time for exams
- Daily agenda
- Allow student time to step out to de-escalate
- Testing in small groups
- Use of a planner/binder for organization
- English Language Dictionary
- Extended time on assignments =1 day
- Preferential seating
- Written direction given
- Break directions into chunks
- Read Aloud to Students
- Visual manipulatives
- Cooperative Learning,
- Vocabulary, Description, Introduction,
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make Sense of Problems and Persevere in Solving Them
• Make a plan! • Try different approaches when your problem is hard. • Solve your problem in more than one way. • Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason Abstractly and Quantitatively
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.
MAFS.K12.MP.3.1 Construct Viable Arguments and Critique the Reasoning of Others.
• Explain both what to do and why it works. • Work to make sense of others’ mathematical thinking.
MAFS.K12.MP.4.1 Model with Mathematics
• Apply math to real-world situations. • Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate Tools Strategically
• Choose appropriate tools for your problem. • Use mathematical tools correctly and efficiently. • Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to Precision
• Communicate your mathematical thinking clearly and precisely. • Use the level of precision you need for your problem. • Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and Make Use of Structure
• Find, extend, analyze, and create patterns. • Use patterns and structures to solve problems.
MAFS.K23.MP.8.1 Look for and Express Regularity in Repeated Reasoning
• Use patterns and structures to create and explain rules and shortcuts. • Use properties, rules, and shortcuts to solve problems. • Reflect on your thinking before, during, and after you solve a problem.