Unit Title - Web viewPrior to taking the unit pre-test to ... the students will struggle if I...

EDU 6524 – Curriculum DesignSummer 2015 Unit Plan Mary Ewart

Unit TitleModule 1 Topic C: Solving Equations and InequalitiesGrade/Subject9th – 12th grade - Algebra 1Author(s)Mary EwartUnit FocusOverall Big Ideas/Understandings:

Unknown quantities can be represented by a variable(s) and solved for. Inverse operations are used to find an unknown quantity. Equations can be considered simultaneously. Inequalties have an infinite number of solutions.

Connection to the Student Profile:Academic Thinking Skills & Strategies Questions Critically and Thinks Creatively

o Engages in active inquiry Solves Problems Effectively

o Develops and applies multiple strategies to solve complex problemso Synthesizes informationo Reaches accurate conclusions with clarity, accuracy, and precision

Communication & Collaboration Skills Offers Ideas and Makes Contributions

o Offers ideas; dialogues effectivelyo Assumes personal responsibility in group settingso Shares work openly

Personal Attributes Exhbits a Strong Work Ethic

o Stives for excellence and works to the highest potentialo Persists in difficult taskso Shows pride in work

Literacy & Language Writes clearly and effectively in English for a variety of audiences and purposesMathematical & Scientific Reasoning Understands and applies mathematical principles and concepts Solves problems, reasons and communicates mathematically

Guiding Questions: How many solutions exist to an equation? How do you know? How many solutions exist to an inequality? How do you know? Can more than one equation be considered at the same time? What would that

mean for the solution set?

Standards and Levels of ProficiencyCCSS Taught in This Unit:

A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.★

A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s lawV=IR to highlight resistance R.

A-REI.A.1 Explain 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.

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-REI.C.5 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.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.D.10

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A-REI.D.12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Interdisciplinary Skills & Attributes: Writes clearly and effectively in English for a variety of audiences and purposes Communication and Collaboration: offers ideas, accepts responsibility in a group

setting, shares work openly Persists in difficult tasks, attends to precision

Proficiency Scales: The LWSD Proficiency Scales for high school level mathematics are undergoing a revision and the new scales are not yet available. Rather than align this unit to old scales, I will go back and put this information in when it becomes available.

Unit Learning Target, Activity & Assessment

Target: By the end of this unit, students will be able to determine an unknown quantity or quantities by solving an equation, inequality or system of linear euqations or inequalities.

Activity: Prior to taking the unit pre-test to assess prior knowledge, students will record the Unit Target in their Cornell Notes. Then students will work in groups to discuss vocabulary and prior knowledge about the target. Each group will be responsible for identifying 2 knowns and 2 unknowns (“knowns” can just be familiar words/concepts). Students will share out to the whole class, and teacher will lead a whole class discussion on how the target fits with prior knowledge, current place in curriculum, and future learning.

Lake Washington School District | Unit and Lesson Planning 2

Assessment of Understanding: Students will complete a Haiku discussion board post where they restate or explain the Unit LT in their own words, and post.Determing Baseline Knowledge

In order to determine my student’s baseline knowledge, I am going to admister a pre-test using Haiku. This pre-test is multiple choice, intentionally. It is a skills-based test; I am looking to determine if students can solve an equation, inequality, or system of equations. Once I understand how much skill knowledge my students have, I will be able to make decisions on the conceptual development and how much time I need to spend on each topic in unit. The pretest is at the bottom of this document. It is not formatted nicely because it will be given by Haiku, and Haiku does not format as nicely.VocabularyNumerical symbolVariable symbolNumerical expressionAlgebraic expressionEquivalent numerical expressionsEquivalent algebraic expressionsSolutionSolution SetGraph of an Equation in Two VariablesEquationInequalityProperties of EqualityProperties of InequalitySolveLinear Function

Pre-Test1. Simplify:

3x+3y-8x-2y

A. 11x+5y B. -5x+yC. 11x+y D. -5x+5y

2. Simplify:

5x + 5(x + 4) – 2(x+3)

A. 8x + 14 B. 12x + 26C. 8x + 7 D. 8x + 263. Solve

x – 2 = 8


A. -6 B. -10C. 6 D. 104. Solve

A. x = 2 B. x = 50C. x = -2 D. x = -505. Solve

A.-3 B. -8C. 3 D. -56. Solve

A. B.

C. D.7. Solve

A. B.

C. D.8. Solve and graph

A. B.

C. D.

9. An office manager needs to replace at least 7 chairs. Chairs with armrests cost $209 each, and chairs without armrests cost $139 each. She can spend at most $1000. If x represents the number of chairs with armrests and y represents the number of chairs without armrests, Lake Washington School District | Unit and Lesson Planning 4

which system of inequalities has a solution that includes all the possible choices she can make?

A. B.

C. D.

10. Match the graph with the number of solutions of graph has.


11. Solve the system of equations using substitution.

A. (2, -27) B. (-1, 0)C. (-2, 9) D. (1, -18)12. Solve the system of equations using elimination.

A. (13, 0) B. (-9, 4)C. (-9, -4) D. (13, 8)13. Tickets for a high school talent show were $3 for students and $10 for adults. A total of 264 people attended the show. The school collected $1639 in ticket sales. Which system of linear equations can be used to find how many student tickets were sold?

A. B.

C. D.

Connecting to the LearnerWhat do you THINK might be student preconceptions related to this unit?

Variables can only stand for one value. Two variables cannot equal the same value (for example, x=6 , y=6 at the same

time. Solutions to a system have to exist. Solutions to equations have to exist. Inequalities only have one solution.

How will you determine/what strategies will you use at the beginning of the school year or prior to the unit that will help you learn the students’ life experiences, interests, and biases? How will you use that information to develop your lessons and activities for the unit?

I am going to revamp my beginning of the year questionnaire that I give my students. In the past it has had short answer questions, mostly related to getting to know the students. I always ask what grade they would like to earn and how they are going to earn it, and I also ask for their favoriate pasttimes, activites, and at least one item that is on their bucket list. I am going to add a more “essay” type section where I ask the students to tell me the following:

1. What would you like me to know about you?2. What are your inner feelings about mathematics?3. Have you had any unusual positive or negative experiences that affected

your attitude toward mathematics? If so, what were they?4. What are your reasons for taking this class?


5. What area of mathematics have you had the most success in the past? What about the biggest area of struggle?

I am going to use results of this survey to determine what types of problems I need to focus on in math, as well as to gleam insight on what will be most helpful for students. For instance, I have learned that organizing my notes in a standard manner that remains the same is important for all students. The type of format was not as important in the past, so I chose Cornell Notes and I have continued to teach in this format for years. I always get a lot of positive feedback about this, and I learned about a need for organization from conversations with students. I will ask students what ways they learn best, and try to incorporate common areas of strength (for example, group work?).

What might students struggle with in the unit (based on your prior experiences)? What might be common student errors in reasoning?

Students struggle with graphing inequalities on a coordinate plane. They often forget that values on the line itself might not be included and that a half plane needs to be shaded as part of the solution. They also struggle with confusing the slope and y-intercept when graphing any two-varibale equation or inequality. Lastly, the students will struggle if I present the problems as word problems rather than just the equation(s) or inequality(ies).Students often struggle with the reasoning behind not including or including the points on a line when graphing an inequality or system of inequalities. This comes from a lack of conceptual understanding of what, exactly, an inequality is and why there are an infinite number of solutions to an inequality.

Instructional Plan –Progression of Learning What is it we expect our

students to learn?

Assessment Plan How will pre-

assessment, formative assessment, and leveled summative assessment, including district assessments, be used?

Differentiation Plan How will we respond when some

students do not learn it? How will we respond when some

students already know it?

1. Please see section below. 1. Pre-Assessment prior to start of unit.

1.

2. 2. Entrance Ticket for first box on learning progression below.

2.

3. 3. Second box on learning progression after Lesson 1&2 of unit as exit ticket.

3.


4. 4. Exit ticket for third box on learning progression after Lesson 3&4 of unit.

4.

5. 5. Quiz after Lesson 1-4

5.


6.


7.

8. 8. Padlet exit ticket for fourth learning progression box after lesson 12 &13

8.

9. 9. Fifth box of LP to determine students’ readiness for summative assessment.

9.

10. 10. Summative Assessment after Lesson 1-14.

10.

Assessment Plan Questions:1. How will you pre-assess the students’ knowledge in order to gather baseline information

for your starting point? Will you use a curriculum generated pre-assessment or one your create yourself? Be sure to explain how this is aligned to the learning target for the unit. How will you share the results of this with your students?

Students will be pre-assessed using Haiku and a multiple choice assessment. This is an assessment that I have created myself based on the learning targets for the unit. I created it by focusing on the skills only that students would need to be successful on the learning target for the unit. Since the learning target for the unit is “By the end of this unit, students will be able to determine an unknown quantity or quantities by solving an equation, inequality or system of linear euqations or inequalities.”, I started the pre-test with questions about simplying expressions, and then moved into the very basic skill of solving one-step equaitons or inequalities. Then I moved in to more complicated equations and inequalities, and finally, to writing equations and inequalities from word problems, graphing equations and inequalities, and solving systems. This focuses on all the skills that will be required for the students to successfully complete the end of unit assessment, which will have more application type problems on it, but will require mastery of all the skills on the pre-test. Students will receive their results instantly on Haiku and will be asked to reflect on their current level of knowledge before we move in to the unit.

2. What types of formative assessments will you use during the unit to check for ongoing understanding of concepts and skills? How will these assessments be directly tied to your learning targets for the unit? What will each measure? How will students know


their scores and track their progress through the use of formative assessments to know they are making progress toward the Learning Target for the unit.

Here is a document that outlines the main concepts required for students to be able to successfully complete the unit learning target. I created 5 main checkpoints for me to assess student understanding towards to ultimate goal. These questions will be asked of

students throughout the unit, mainly as entrance of exit ticket activities. I will provide written feedback on each activity and return it to students so they can monitor their own progress towards the unit target. Additionally, students will take a quiz once a week based on the lessons from that week that build towards being able to master the unit target. The quizzes will be graded and returned with written feedback so the students can reflect and monitor their own progress.

3. How will you incorporate student self-assessment through the use of a scoring rubric? How do you anticipate that this will impact student learning? How will you use technology for assessment purposes?

Here is the scoring rubric that I created for the final unit target:Level Target Assessment

Question/Technique

Differentiated Task

Level 4 Write an equation, inequality, or

system of linear equations or

inequalities to model a situation,

then determine the unknown quantity

1:1 conversation

Explain and show the steps to solve the following situation:

On one trip, a traveling salesperson was

reimbursed $732 for 4 Lake Washington School District | Unit and Lesson Planning 10

or quantities by solving.

nights in a hotel and18 meals with clients. On the next trip, he

was reimbursed $366 for 2 nights in a hotel

and 9 meals with clients. Let x equal the amount the company

pays per night for lodging and let y equal

the amount the company pays per

meal. How much does the company

reimburses the salesperson for lodging

and meals?

Level 3 Determine an unknown quantity or quantities by

solving an equation,

inequality or system of linear

equations or inequalities.

Assessment Task /Test Question– Solve the following inequality:

x+ y>5200 x+140 y ≥900

PowerPoint Activity – Students take a handout with a situation that is

modeled algebraically with a

system and then solved, and use it

to create a PowerPoint to teach other

students how to solve those types

of problemsLevel 2 Determine an

unknown quantity or quantities by

solving an equation or inequality.

Whiteboard/Padlet Response Work – Solve the equations/inequalities below:

7 x+20=413 ( x−9 )=8114>2 y+4

3 x+8−2 x<213

Pick one equation and explain each step

Scaffolded prompt for a system of equations/inequalities; guides students step-by-step through the algebraic process

Graphing practice of two lines or two inequalities on the same coordinate plane

Level 1 With help, determine an

unknown quantity or quantities by

solving an equation or inequality.

1:1 conversation

Describe the steps necessary to solve one

of the equations/inequalities

below:

7 x+20=413 ( x−9 )=8114>2 y+4

3 x+8−2 x<213

Sorting Activity – rearrange the steps

to solve an equation/inequality

in the correct order, or identify

steps that are already in the correct order


Level 0 Unable to solve for an unknown quantity or quantities.

Entrance Ticket

Solve the following equations/inequalities:

b+8=14−x9≥2

Leveled 1:1 work with teacher or high performing student on this target that start with ordering the steps to solve an equation, then

moves to one-step equations/inequalities and works into more complicated

equations/inequalities

I intend to provide it, without the column on differentiation, to my students at the start of the unit, witht the unit handout. This will allow students to see the progression of understanding in this unit, as well as see sample types of problems that would qualify as Level 0, 1, 2, 3, and 4. I believe having this knowledge ahead of time will take the guesswork out of what students need to do and learn in order to receive a score the would be happy with. When students clearly understand the expectations of a course, as well as the requirements to show particular levels of understanding, it increases confidence and provides students with a goal to work towards.I will use Haiku, padlet.com, and kahoot.com to administer various assessments during this unit. Haiku will be used for the pre-assessment so that students are given instant feedback on their beginning level of knowledge. Padlet.com and kahoot.com will be used throughout the unit as exit or entrance tickets, and will provide (as well as Haiku) a forum for discussion and reflection on understanding.

4. What will you use as your leveled summative assessment?

For my leveled summative assessment, I will be using the assessment generated by EngageNY.org, but with modifications made due to the fact that students can access the assessments on the website, with the answers. The modifications to the assessment will be made with the other members of the Algebra 1 collaborative team, but the original assessment questions are included below. This summative assessment is actually at the end of two units, so I am only including the problems related to this unit learning target.

1. Solve the following equations for x. Write your answer in set notation.

a. 3 x−5=16b. 3 ( x+3 )−5=16c. 3 (2x−3 )−5=16d. 6 ( x+3 )−10=32e. Which two equations above have the same solution set? Write a sentence

explaining how the properties of equality can be used to determine the pair without having to find the solution set for each.

2. Let c and d be real numbers.

a. If c=42+d is true, then which is greater: c or d , or are you not able to tell? Explain how you know your choice is correct.


b. If c=42−d is true, then which is greater: c or d , or are you not able to tell? Explain how you know your choice is correct.

3. If a<0 and c>b, circle the expression that is greater:

a (b−c) or a (c−b)

Use the properties of inequalities to explain your choice.

4. Solve for

x in each of the equations or inequalities below, and name the property and/or properties used:

a. 34x=9

b. 10+3 x=5 x

c. a+x=b

d. cx=d

e. 12x−g<m

f. q+5x=7 x−r

g. 34

( x+2 )=6( x+12)

h. 3(5−5 x)>5 x

5. The equation 3 x+4=5 x−4 has the solution set {4 }.

a. Explain why the equation (3 x+4 )+4=(5 x−4 )+4 also has the solution set {4 }.

b. In part (a), the expression (3 x+4)+4 is equivalent to the expression 3 x+8. What is the definition of equivalent expressions? Why does changing an expression on one side of an equation to an equivalent expression leave the solution set unchanged?

c. When we square both sides of the original equation, we get the following new equation:

(3 x+4 )2=(5 x−4 )2.

Show that 4 is still a solution to the new equation. Show that 0 is also a solution to the new equation but is not a solution to the original equation. Write a sentence that describes how the solution set to an equation may change when both sides of the equation are squared.


d. When we replace x by x2 in the original equation, we get the following new equation:

3 x2+4=5 x2−4.

Use the fact that the solution set to the original equation is {4 } to find the solution set to this new equation.

6. Students and adults purchased tickets for a recent basketball playoff game. All tickets were sold at the ticket booth—season passes, discounts, etc. were not allowed.

Student tickets cost $5 each, and adult tickets cost $10 each. A total of $4,500 was collected. 700 tickets were sold.

a. Write a system of equations that can be used to find the number of student tickets, s, and the number of adult tickets, a, that were sold at the playoff game.

b. Assuming that the number of students and adults attending would not change, how much more money could have been collected at the playoff game if the ticket booth charged students and adults the same price of $10 per ticket?

7. Assuming that the number of students and adults attending would not change, how much more money could have been collected at the playoff game if the student price was kept at$5 per ticket and adults were charged $15 per ticket instead of $10? The local theater in Jamie’s home town has a maximum capacity of 160 people. Jamie shared with Venus the following graph and said that the shaded region represented all the possible combinations of adult and child tickets that could be sold for one show.

a. Venus objected and said there was more than one reason that Jamie’s thinking was flawed. What reasons could Venus be thinking of?

b. Use equations, inequalities, graphs, and/or words to describe for Jamie the set of all possible combinations of adult and child tickets that could be sold for one show.


Differentiation Plan Questions:1. Please provide examples what types of lessons, strategies and activities you will use to

both extend and enrich and/or to modify/adapt your curriculum.

Please see the rubric for examples of differentiation strategies at each level of understanding for students related to the final learning target of the unit. Additionally, all homework assignments have “bonus” or “challenge” problems that students who are already mastering the daily targets can attempt. These problems connect the day’s learning to a new concept, new application, or present the problem in a different way. It does not speed up the curriculum, but instead forces students to think deeper and harder about what they have learned. In the same way, daily assignments can be shortened so that struggling students only have to work on a few problems that address the target and can focus on understanding without being overwhelmed by the amount of work.

2. How will you address the needs of IEP and 504 students?

All notes will be provided in a Cornell Note format and placed on Haiku for further reference. Students will receive handouts to guide their following along with the class during instruction and group work. Additionally, homework and classwork assignments will be shortened/modified with more simple numbers that don’t change the concept for students who require this type of modification/accommodations.

3. How will you address the needs of ELL students?

Please refer to ways IEP/504 students are helped. Additionally, visual representations of all concepts are provided in notes, as well as definitions of terms – both academic and related to the math, and terms that are necessary to understand a word problem but aren’t mathematical (for example, when computing the area of a deck, I will show a picture of a deck so students understand what a deck is.) A word wall will be maintained, and students will be encouraged to talk to each other in groups throughout activities almost daily in the unit.

4. How will you building in problem solving and/ or critical thinking for all of your students?

Problem solving and critical thinking are primary components of this curriculum, so I will not have to reinvent the wheel. There will be many opportunities for students to think criticially and develop a conceptual understanding of the topics. Daily students will be given questions to think about/discuss/work collaboratively to solve. The teacher will guide them through these, but encourage students to come to conclusions on their own before simply providing students with the answer.

5. How are your differentiated lessons, activities, and strategies linked to the achievement of the learning targets?

Again, this is covered in the rubric above.


Instructional Plan Section:

Here is the information given to studnts at the beginning of this unit of instruction. The handout actually coveres 2 sections, and this unit plan focuses on one, so I have highlighted the information the pertains to this unit. This covers the structure of this lesson and provides guidance for what topics are going to be covered and in which order. Each lesson is one class period, which is why you will see some “Day 2” lesson titles.

Module 1 Topics C & DSolving Equation and Inequalities

Creating Equations to Solve Problems

Topic OutlineM.1 Lesson 10 – True and False EquationsM.1 Lesson 11 – Solution Sets for Equations & InequalitiesM.1 Lesson 12 – Solve EquationsM.1 Lesson 13 – Some Potential Dangers When Solving EquationsM.1 Lesson 14 – Solving InequalitiesM.1 Lesson 15 – Solution Sets of Two or More Equations (or Inequalities) Joined by “and” or “or”.M.1 Lesson 16 – Solving and Graphing Inequalities Joined by “and” or “or”.M.1 Lesson 17 – Equations Involving Factored ExpressionsM.1 Lesson 18 – Equations Involving a Variable Expression in the DenominatorM.1 Lesson 19 – Rearranging FormulasM.1 Lesson 20 – Solution Sets to Equations with Two VariablesM. 1 Lesson 21 – Solution Sets to Inequalities with Two VariablesM.1 Lesson 22 – Solution Sets to Simultaneous EquationsM.1 Lesson 23 – Solutions Sets to Simultaneous Equations Day 2M. 1 Lesson 24 – Applications of Systems of Equations and InequalitiesM. 1 Lesson 25 – Solving Problems in Two Ways – Rates and AlgebraM. 1 Lesson 26 – Recursive Challenge Problem – The Double and Add 5 GameM. 1 Lesson 27 - Recursive Challenge Problem – The Double and Add 5 Game Day 2M. 1 Lesson 28 – Federal Income Tax

Module 1 Topics C & D Content StandardsA-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities,

and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.★

A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s lawV=IR to highlight resistance R.

A-REI.A.1 Explain 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.

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-REI.C.5 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.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A-REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.


A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.★

A-SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients.A-SSE.A.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example,

interpret P(1+r)n as the product of P and a factor not depending on P.A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations

arising from linear and quadratic functions, and simple rational and exponential functions.A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.

Module 1 Topics C & D Learning TargetsLearning Targets Not Yet Emerging Mastery1. Understand that an equation is a statement of equality between two expressions.2. Find values to assign to the variables in equations that make the equations true statements.3. Sort all values in the domain into two disjoint sets: the solution set and the set of numbers for which the equation is false.4. Understand the commutative, associative and distributive properties as identities.5. Justify the steps of solving an equation using the properties of equality.6. Identify equations that have the same solution set.7. Identify operations that may result in the equation having more solutions than the original equation.8. Use addition and multiplication properties of inequality to solve inequalities.9. Graph the solution sets of inequalities on a number line.10. Describe the solution set of two equations (or inequalities) joined by either “and” or “or”.11. Graph the solution set of an “and” or “or” equations or inequalities on the number line.12. Solve two inequalities joined by “and” or “or” and graph the solution set.13. Know and use the zero product property.

14. Interpret equations such as 1x=3 as two equations and find

the solution set.15. Solve a formula for a specified variable.16. Recognize and identify solutions to two variable equations.17. Represent the solution set for two variable equations graphically.18. Create two variable equations to represent a situation.19. Recognize and identify solutions to two variable inequalities.20. Represent the solution set for two variable inequalities graphically.21. Create two variable inequalities to represent a situation.22. Graph a two variable inequality.23. Identify solutions to simultaneous equations or inequalities.24. Solve systems of linear equations and inequalities: a. algebraically b. graphically25. Create equivalent systems of equations.26. Solve systems by elimination.27. Use systems to solve contextual problems.28. Know the meaning and notation of recursive sequences.29. Use recursive sequences to model and answer problems.


1. Introduction to the Unit How will you introduce the unit to your students? What strategies will you use?

Students will be introduced to the unit in a few ways. Primarily, there is a pre-test, which will show the students the types of skills necessary in this unit. Additionally, there will be a class discussion that will start with a culminating word problem. Students will start by brainstorming individually on the problem, move into groups, and then to a whole class discussion. They will be focused on trying to identify what the problem is asking for, and what skills they know they have that would help them solve the problem. They also need to focus on areas they may not know what to do to solve, as this should lead them into the Learning Target for the unit.

How will you teach the Learning Target(s) for the unit to your students? (Textbox 322)

Students will receive the handout above, and the Learning Target for the unit will be displayed on the ActivBoard. I will ask students to preassess their level of understanding on each individual target, and then I will lead a class discussion about how the different targets form the larger unit target.

How will you determine if the students if the students had a clear understanding of the learning targets for the unit? What evidence will you gather to show student understanding?

Students will complete a Haiku discussion board post where they restate or explain the Unit LT in their own words, and post.

If your students do NOT understand the learning target(s) for the unit, what will you do to help them understand the targets? (Textbox 322)

I will pull any student who struggled to restate the LT on the Haiku discussion board during the

beginning warm up activity of the next day. I will pair each of them with someone who had a strong

response, and have the students discuss the difference in the summaries. Then I will ask the student

who struggled to restate the LT again to me verbally.

2. Body of the Unit What lessons will you teach to develop students’ understanding of vocabulary, concepts, and skills?

Lessons 11, 12, 14, 15, 16, 19, 20-23 are all primary skill and concept development lessons. The remaining lessons are used to introduce the topics, or to extend and apply the skills and concepts learned.

What will be the scaffolded sequence of the lessons?

This unit starts simply, and then builds on each additional skill. Students start by learning about whether values are true or false in an equation, and then move on to learning what that means for being a part of a solution set. Then students learn how to generate answers that are in the solution set, and the difficulty of a single variable equation or inequality increases throughout the lesson. Then studnets learn how to apply the strategies to factored and rational equations, and then to abstract formulas. Once students master single variable situations, the unit moves to systems of equations with more than one variable and then to systesm of inequalities.


What strategies will you use to teach the lessons?

These lessons are all a combinations of group work/inquiry/discovery, direct instruction, and guided and independent practice. Many start with a real world application or question that students work to solve, and then move in to the academic vocabularly, definition of properties, and algorithms necessary to apply what they discovered to multiple scenarios, and to understand why what they discovered worked. There are multiple points where students use non-verbal strategies and whole body movement, as well as graphic organizers. Students take notes every day at some point during a new lesson.

What instruction will you provide regarding how to create/read/use a rubric? (Textbox 325) and (Textbox 331)

Students will be given access to the sample test for this unit at the beginning of the unit, as well as the rubric used to grade it. As the unit is introduced, I will take time to explain to students how to read the rubric, and how to grade a solution based on the rubric. This will be done by taking an example problem and solution and using the rubric to grade it. Students can then use it to continue to study throughout the unit.

What instruction will you provide to help students effectively complete self and/or peer assessments? (Textbox 325) and (Textbox 331)

Students will often be asked to peer assess exit tickets/discussion board responses/padlet responses during class. There will be a rubric that we develop together at the start of the year for this process, and students will be asked to use it as they asses both their own work according to the rubric and their peers.

How will you use student work or self-assessment to make instructional decisions? (Textbox 325)

Entrance tickets, homework responess, and exit tickets/discussion board posts/ padlet posts will be used to evaluate how students are learning on a daily basis (as well as informal observation and monitoring of class discussions and questioning). Using this will allow me to determine if we need to spend more time on a topic. Additionally, students will take a small skills based quiz each week that will also allow me to dicuss with my content team how students are doing, and whether adjustments in pacing need to be made.

When and how will you teach your students how to track their progress (toward learning target)? (Textbox 326)

Students receive the LT for each lesson and the unit at the beginning of the unit Students will be asked to preassess their understanding on all LTs, and then asked to re-evaluate as they go into each weekly quiz.

How will build critical thinking and/or problem solving into your lessons? (Textbox 327)

Every lesson is focused on developing the skills and concepts needed to be able to problem solve and think critically. From the beginning questions to activate prior knowledge, skills and interest, to the final homework problems that have students applying the new information, the lessons are focused on driving students to be able to think critically and solve problems.

How will you help students see the value in using critical thinking and/or problem solving to increase their comprehension of concepts or to develop strong skill levels? (Textbox 327)


Again, in a math classroom, this is the fundamental goal of all instruction. Throughout each lesson, I will continually refer back to the unit and lessons LTs, and ask students to consider how what we are doing is going to help them achieve the LT, and then from there, where the LT will help them in solving problems.

How will you help students see that the use of critical thinking and/or problem solving is moving them toward mastery of the unit learning target(s)? (Textbox 327)

See above.

How will you provide ongoing feedback to your students regarding their progress throughout the unit?

Students will receive feedback in the following ways: verbal response to questions or discussion, sticky notes on assignments, responses on discussion board posts, questions and padlet responses, audio recordings of my thoughts on longer assignments or projects, 1:1 conferencing with student notetaking and traditional comments and questions on assessments and homework.

How will you teach your students the ethical use of technology prior to the unit? (Textbox 329)

Students will spend one homework assignment the first week of class reviewing the infographic available at http://www.knowthenet.org.uk/infographic/be-careful-trolling-can-happen-anyone. Then they will write a discussion board post on what it means to them, and we will hold a whole class discussion on this topic as well.

How will you use technology effectively in your lesson instruction and assessment? (Textbox 328)

I use PowerPoint and the ActivBoard for all instruction to the class. Haiku will be used for compiling a copy of all notes and instructional materials, as well as discussion boards, calendaring, and some assessments. Students will use their netbooks to access online graphing calculator tools like desmos.com/calculator, and padlet for discussion boards, as well as videos of real life situations that can be modeled and then solved using Algbera.

How will the students use technology during the lessons and in assessment? (Textbox 328)

See above.

3. Closure to the Unit How will you wrap up the unit prior to the summative assessment?

The final lesson is designed to tie together all the information from the unit and provide students with a complete picture of how all the learning fits into the unit LT. Students will also be asked to review prior to the final assessment.

Will you do any type(s) of review activities? If so, what strategies will you be using?

Students will be using the provided sample assessment and rubric to create 1-2 test problems per standard in their groups. They will post the problems on Haiku and attempt to solve at least one other group’s problems as part of their own review.How will students reflect on their learning and determine if they have met the unit learning target(s)? (Textbox 331)


http://www.knowthenet.org.uk/infographic/be-careful-trolling-can-happen-anyone

http://www.knowthenet.org.uk/infographic/be-careful-trolling-can-happen-anyone

Prior to the summative assessment, students will use the handout with the lesson and unit LTs, as well as the sample assessment and rubric to evaluate their own learning on the LTs in the unit. Students can complete the sample assessment, use the rubric to evaluate their own understanding, and link the problems with the unit and lesson LTs and CCSS to determine which ones they need to work on prior to the assessment.

After the summative assessment how will you provide feedback to the students?

Students will receive their assessment back, with the rubric used to grade it. There will be a reflection activity after – wehther students can earn additional points back will have to be determined in collaboration with my content team.

Learning Environment ResourcesWhat lesson-specific considerations are needed for the Framework for Teaching (learning environment- Domain 2) components related to: Respect and Rapport, Culture for Learning, Classroom Procedures, Managing Student Behavior, and classroom Physical Space?

Students need to be instructed on basic procedures for group work and classroom procedures. All this will occur prior to this unit. Students will learn cues and prompts on when they should be listening, turning/talking, working in groups, sharing out, replying as a whole class, etc. There are multiple opportunities where students will be working with their table groups, on their netbooks, and moving around the room, but all this will be pre-taught prior to this unit.

What resources, technologies, materials, adopted curriculum, equipment, and/or tools will be needed to teach this unit? (Textbox 328)

The resoureces needed are: EngageNY curriculum, ActivBoard/ActivSlate, student netbooks, Haiku, digital projector, chart paper and pens, handouts developed to supplement notes, PowerPoint, DI lessons developed from EngageNY materials, internet access.

How will students use the resources, materials, and technologies during the unit ?

Students will take notes, access Haiku, graph using desmos.com/calculator, respond in discussion boards, use padlet.com to post information, complete handouts/homework, and work in groups using the chart paper and pens.

How and when will you ensure that students use technology appropriately for their age level and build digital citizenship? (Textbox 329)

Students will start the year with an introduction to digital citizenship that will carry in to their work during this unit. Students will be monitored during their computer usage time using the district monitoring software. See above for examples of other technologies that students will be using throughout the unit. There are times in every lesson


where students will be asked use technology in various ways.

Parent/Family Connection Local and/or Global ConnectionsWhat opportunities might this unit present for communicating and collaborating with parents/families?

There are multiple ways that students will see connections to the real world in this unit. Students can then bring that information home to their families and reflect on other places this content is present. During the systems work, I will be asking students to come up wth examples of real world situations that can be modeling with linear systems, and this is something I am going to ask their parents to sign off on having a conversation about.

What opportunities might this unit present for communicating and collaborating with the extended community?

I would like students to reach out to the internet community and see if they can find examples of linear systems that are present in other disciplines or real life professions. I will also provide extra credit if students can recruit a local member of the community to talk about how equations, inequalities or systems are used in their current profession.

How will the lesson’s learning activities engage students with problem solving and real world connections?

As mentioned previously, all lessons tied into real world examples, and bring the learning back to a word problem or circumstance that is based in the real world. This allows students to continually monitor how their learning appears in real world settings.


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