roswell independent school district maps/2014.2015/grade 8...101 roswell independent school district...

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Roswell Independent School District Unit 5 Lesson Plan– Graphing Systems of Equations (Quarter 2)

Subject(s): PreAlgebra – Mathematics Grade:

8th

Teacher(s): School:

LESSON ELEMENT STUDENT-FRIENDLY TRANSLATION

(# 2,3,4 only)

1. Standards Addressed: 8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y= 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

2. Learning Target(s): 1) Students can explain that the solution to a system of

linear equations is the point of intersection on the graph of the two linear equations. Students can look at a graph of a system of linear equations and

determine if there is one, infinitely many or no solution. 2) Students can

estimate the solution to a system of linear equations by using a graph. 3) Given

a real-world problem that results in a system of linear equations, students can estimate the solution by graphing.

1) I can create a system of equations to solve a problem.

2) I can analyze a graph of a system of equations to determine the number of solutions to the system.

3) I can solve a system of equations by graphing.

3. Relevance/Rationale: (Why are the outcomes of this lesson important in

the real world? Why are these outcomes essential for future learning?) Being able to connect a real-world situation to an algebraic equation is essential in simplifying calculations. All major technological and analytical careers include linear equations to represent cause/effect relationships. Architects, surveyors, and cartographers are some of the professions that require the application of writing and solving linear equations. Solving systems of linear equations allows students to relate two situations to find useful information about the way the situations interact or might be similar or different. Essential Question: What are some ways in which we could find one set of answers for many variations of the same situation?

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` Assessment/Progress Monitoring: (How will you and your students know

if they have successfully met the outcomes? What specific criteria will be met in a successful product/process? What does success on this lesson’s outcome look like?)

The summative assessment will have the students complete the two types of real world problems that we concentrated on in this unit. The hope is that the students will be able to prove that they understand how to translate Real World situations into Systems of Linear Equations, and then know how to solve those Systems to determine the answer to the situation.

5. Activities/Tasks: (What learning experiences will students engage in? How will you use these learning experiences or their student products as formative assessment opportunities?) – Duration:

DAYs 1, 2, 3, & 4 DAYs 5, 6, & 7 DAYs 8, 9, & 10 Preassessment – Students will complete the Concentric Circles with Systems of Linear Equations Activity. Directions and resources are located with this activity. This activity will determine whether the students know the different solutions that can be present for Systems of Linear Equations and activates their prior knowledge of solving the systems. See website under artifacts for activity sheets. Launch – Teacher and students will briefly review how a single slope-intercept equation could be used to model a real world problem. Particular emphasis will be given to the real world meanings of slope as a rate of change and y –intercept as the initial condition or starting value of y. Questions are asked on the “Slope-Intercept Linear System Real World Problems” worksheet. Students will be asked to consider if a real world situation could be modeled using two slope intercept form equations. See website under artifacts for activity sheets. Teacher Facilitation – Teacher will review basic verbal problem solving skills. Students will be asked to read aloud the problems on the “Slope-Intercept Linear System Real World Problems” worksheet. The teacher will elicit oral responses from the students on variable definitions, equation set ups, what the problem asks for, and techniques for solving systems of

Preassessment – Students will complete the “Where’s the Money” worksheet to refresh the previous lesson’s skills. See website under artifacts for activity sheets. Launch – Student’s will complete the “Candy is Coming Activity!!!” In this activity, the students will complete a chart to determine combinations of two different items that can be purchased given a specific number of M&M Bags; they are to determine the number of Hershey Bars that fits the scenario. The activity seeks to guide students into considering real world linear equations in standard form. Teacher Facilitation - Teacher will review basic verbal problem solving skills. Students will be asked to read aloud the problems on the “Standard Form Real World Model Problems” worksheet. The teacher will elicit oral responses from the students on variable definitions, equation set ups, what the problem asks for, and techniques for system and equation solving. All exercises come from the worksheet. Student Application - Following completion of the first problem, students will complete a second similar problem on their own. The teacher will circulate through the class looking for students who need assistance and take questions. Formative Assessment – Teachers assess student learning through

Preassessment – Students will complete the “Warm Up Activity” worksheet about the characteristics of real world slope intercept and standard form linear systems. Students will seek to develop a way to distinguish between the two types systems in a verbal problem. See website under artifacts for activity sheets. Launch – Students will complete the “Mix-and-Match Real World Systems of Equations Activity.” Directions and resources are located with this activity. This activity will determine whether the students know how to match real world scenarios with an appropriate System of Linear Equations. See website under artifacts for activity sheets. Teacher Facilitation - Teacher will check to see that students matched the systems and real world scenario correctly and then direct students to solve the problem with their partner. Student Application – Each pair of students will solve their systems problem and prepare a presentation to be delivered to the rest of the class. As the presentations take place, the other students should be taking notes, asking questions, and offering suggestion for improvement. If you have a larger class, select certain groups to give their presentations. Or you may want to do a Group Merry-Go-Round Activity in which each group prepares a poster, places the poster on the wall, and the students walk around the room placing their ideas and/or concerns on the poster. Formative Assessment – Teacher assesses student learning through visual observation of student performance in matching the systems and real world scenario correctly and their ability to present their problem to the class. Students write their solutions to the system on the promethean board and present them to the class. Presentation should include definition of variables, steps to solutions and explanation of how the systems were identified. Students will observe and critique each other’s work for clarity and correctness.

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equations. See website under artifacts for activity sheets. Student Application – Following completion of the first problem, students will complete a second similar problem on their own using the “Slope-Intercept Linear System Real World Problems” worksheet. The teacher will circulate through the class looking for students who need assistance and take questions. See website under artifacts for activity sheets. Formative Assessment – Teachers assess student learning through responses to verbal questions and visual observations of student work. Assessment emphasis will be placed on each student’s second problem performance.

responses to verbal questions and visual observations of student work. Assessment emphasis will be placed on each student’s second problem performance.

Suggested CMP 3 Investigations: 8

th Grade Module- It’s in the System

Investigation 1.3 questions A-C

6. Artifacts/Materials: (What texts, digital resources & materials will be used in

this lesson?) Prentice Hall Mathematics Course 3 (Red Book) print and digital resources, Promethean, ActivExpressions, individual whiteboards, Ramp Up to Algebra, graphic organizers, ExamView, Holt Course 3 Problem Solving, commoncoresheets.org, Connected Mathematics 3(Pearson) http://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/real_world_systems_of_linear_equations.pdf

7. Access for All: (How will you ensure that all students have access to and are

able to engage appropriately in this lesson? Consider all aspects of student diversity.)

Structured stationery for note taking, immediate feedback through use of instant response boards or technology, flipcharts that incorporate video and sound, instructional strategies/activities that appeal to visual, auditory, and kinesthetic learners, cooperative learning opportunities for group learners, manipulatives

8. Modifications/Accommodations: (What curriculum modifications

and/or classroom accommodations will you make for Students with Disabilities in your class? Be as specific as possible.) – ELL, SPED, Gifted

SPED: Preferred seating near the teacher, reduced assignments, copies of the notes, and extended time as indicated by IEP’s ELL: visual aids, graphic organizers, small group and one-one one instruction Gifted: Increase rigor, escalate objectives, and propose interest-based extension activities.

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Roswell Independent School District Unit 6 Lesson Plan – Solving Systems of Equations Using Algebra (Quarter 2)


8th

Teacher(s): School:


(# 2,3,4 only)

1. Standards Addressed: 8.EE.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y= 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

2. Learning Target(s): 1) Students can solve a system of linear equations by applying the substitution

and elimination methods.

1) I can create a system of equations to solve a problem.

2) I can solve a system of equations using algebraic methods, including elimination, substitution, and by inspection.

3. Relevance/Rationale: (Why are the outcomes of this lesson important in the

real world? Why are these outcomes essential for future learning?) Being able to connect a real-world situation to an algebraic equation is essential in simplifying calculations. All major technological and analytical careers include linear equations to represent cause/effect relationships. Architects, surveyors, and cartographers are some of the professions that require the application of writing and solving linear equations. Solving systems of linear equations allows students to relate two situations to find useful information about the way the situations interact or might be similar or different. Essential Question: Why do we model certain situations by graphing the linear equation?

4. Assessment/Progress Monitoring: (How will you and your students know if

they have successfully met the outcomes? What specific criteria will be met in a successful product/process? What does success on this lesson’s outcome look like?)

Individual Cumulative Assessment, LES lessons, homework, teacher created worksheets, exit slips, admit slips, study guide, individual white boards, observations

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DAYs 1, 2, & 3 DAYs 4 DAYs 5, 6, & 7 DAYs 8 & 9 DAY 10

Day 1- Launch: The students will work interactively with a teacher created flipchart. The students will work in small groups. Students will begin by reviewing and using the graphing strategy to solving a system of linear equation. After the students review solving by graphing, they will begin their exploration with solving the system algebraically. The system should have both equations already in slope intercept form. Explore: The students will explore the concept of solving the system of linear equations through substitution by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of substituting equivalent values for a specific variable. Summary/Formative Assessment: Students will complete a teacher created assignment to ensure their understanding solving systems of linear equations through substitution. The system should have both equations in y=mx+b form already.

Day 2- Launch: The students will work interactively with a teacher created

Application of Systems by Substitution- Students will work in small groups to write systems of linear equations that represent real-world problem situations and solve by substitution.

Summary/Formative Assessment: Students will work in small groups on the CMP 3 8

th Grade

Module It’s in the System Investigation 2.1 questions A-C.

Day 5- Launch: The students will work interactively with a teacher created flipchart. The students will work in small groups. Students will begin by reviewing and using the substitution strategy to solving a system of linear equations. After the students review solving by substitution, they will begin their exploration with solving the system through elimination. The system should have a variable that can already cancel, where student only need to add to eliminate the variable. Explore: The students will explore the concept of solving the system of linear equations through elimination by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of eliminating variables so they can solve for a specific variable. Summary/Formative Assessment: Students will complete a teacher created assignment to ensure their understanding solving systems of linear equations through elimination. The systems should have equations where a variable can already be eliminated.

Day 8- Students will generalize that some systems can be solved by inspection, noticing the traits that result in one solution, no solution, or infinite solutions. Summary/Formative Assessment: Students will complete the following assignment to ensure their understanding of solving systems by inspection: Day 9- Students will engage in review of all concepts for the learning cycle. Students will complete a teacher created study guide task.

-Assessment: Students will complete an individual cumulative assessment containing multiple choice, short answer, and extended response questions.

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flipchart. The students will work in small groups. Students will begin by reviewing the substitution method. The system that launches the lesson should have only one equation with an isolated variable. Explore: The students will explore the concept of solving the system of linear equations through substitution by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of substituting equivalent values for a specific variable. Summary/Formative Assessment: Students will complete a teacher created assignment to ensure their understanding solving systems of linear equations through substitution. The system should have only one equation with an isolated variable.

Day 3- Launch: The students will work interactively with a teacher created flipchart. The students will work in small groups. Students will begin by reviewing the substitution method. The system that launches the lesson should have no equation with an isolated variable. Therefore, an equation needs to be transformed to isolate the variable.

Day 6- Launch: The students will work interactively with a teacher created flipchart. The students will work in small groups. Students will begin by reviewing the elimination method. The system that launches the lesson should have no variables that can cancel. However, it should have one coefficient that is a factor of another coefficient of the same variable. For example, 2x and 4x. Explore: The students will explore the concept of solving the system of linear equations through elimination by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of eliminating one variable to solve for another. Summary/Formative Assessment: Students will complete a teacher created assignment to ensure their understanding solving systems of linear equations through elimination. The system should have no equation where the variables will already cancel. For this assignment, only one equation needs to be transformed through multiplication to eliminate a variable. Example 1:

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Explore: The students will explore the concept of solving the system of linear equations through substitution by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of substituting equivalent values for a specific variable. Summary/Formative Assessment: Students will complete a teacher created assignment to ensure their understanding solving systems of linear equations through substitution. The system should have no equation with an isolated variable.

Example 2:

Example 3:

Day 7- Launch: The students will work interactively with a teacher created flipchart. The students will work in small groups. Students will begin by reviewing the elimination method. The system that launches the lesson should have no variables that can already cancel. Both equations must be transformed through multiplication in order for a variable to eliminate. Explore: The students will explore the concept of solving the system of linear equations through elimination by interacting with the teacher created flipchart. The flipchart should help students grasp the concept of eliminating a variable to solve for another. Summary/Formative Assessment: Students will work in small groups on the CMP 3 8

th Grade Module It’s in the

System Investigations 2.2 questions A-D and 2.3 questions A-D.

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this lesson?) Prentice Hall Mathematics Course 3 (Red Book) print and digital resources, Promethean, ActivExpressions, individual whiteboards, Ramp Up to Algebra, graphic organizers, ExamView, Holt Course 3 Problem Solving, commoncoresheets.org, Connected Mathematics 3(Pearson)




8. Modifications/Accommodations: (What curriculum modifications and/or

classroom accommodations will you make for Students with Disabilities in your class? Be as specific as possible.) – ELL, SPED, Gifted


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Roswell Independent School District Unit 7 Lesson Plan – Pythagorean Theorem (Quarter 2)


8th

Teacher(s): School:


(# 2,3,4 only)

1. Standards Addressed: 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

2. Learning Target(s): 4) Students can apply the Pythagorean Theorem to determine unknown

side lengths in right triangles in real-world.

5) Students can apply the Pythagorean Theorem to find the distance between two points un a coordinate system

6) Students can determine if numbers are rational or irrational

1) I can apply the Pythagorean Theorem to solve for unknown side lengths of a right triangle

2) I can find the distance between two points on a coordinate plane using Pythagorean Theorem

3) I can determine if numbers are rational or irrational

3. Relevance/Rationale: (Why are the outcomes of this lesson important in

the real world? Why are these outcomes essential for future learning?) The Pythagorean Theorem is used in a number of fields today. It is important because it is a universal law that allows you to always find the hypotenuse of a right triangle. This is essential when building anything. It is a foundational and essential theorem in Geometry, which can help determine the slope of an inclined plane or the length of a ladder. It is also used in drawing geometrical patterns. Essential Question: Why does the Pythagorean Theorem only work on right triangles?

4. Assessment/Progress Monitoring: (How will you and your students know



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DAY 1 & 2 DAY 3 & 4 DAY 5 DAY 6 DAY 7

Day 1 -Pythagorean Theorem and the Hypotenuse: Students will learn what the Pythagorean Theorem is and why it only works on right triangles. They will learn of the many uses of this theorem, and apply these skills to solve for the hypotenuse of a right triangle with a PowerPoint on Pythagorean Theorem from https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&es_th=1&ie=UTF-8#q=pythagorean+theorem+presentation+intranet (Scroll down to the presentation from intranet). Teacher will present students with additional practice problems on the Promethean Board. Students will participate throughout the presentation by solving problems in their notes. By the end of the lesson students will be able to answer the following questions on an exit slip:

You know the sum of the two shortest side lengths of a triangle must be greater than the third side. Is there a similar relationship among the squares on the sides of a triangle?

Is the relationship the same

Day 3 -Rational or Irrational? This lesson comes from the CMP3 Grade 8 book, Looking for Pythagoras. It is lesson 4.4, Getting Real: Irrational Numbers. Students need to be able to determine if numbers are rational or irrational, in order to solve for triangles that have radicals for measurements. Students may work in groups of two-four for this problem. Launch: Students will be presented with this number 0.12122122212222… They will be asked questions to open a math discussion such as: Why does this pattern go on forever

without repeating? How is this kind of decimal the same as

or different from the repeating decimal 0.6666 . . . or 0.121212 . . . ?

How is 0.12122122212222 . . . the same as or different from the decimal 1.414213562?

Students will discuss with their group peers and share ideas with the class. The teacher will tell students that the number is an example of an irrational number because it goes on forever without repeating any fixed set of digits. Irrational numbers cannot be represented as a nonrepeating, nonterminating decimal or fraction. A rational number on the other hand can be represented as a terminating decimal or fraction. These are numbers that have a pattern of some sort. Students will then be asked to give other examples of irrational and rational numbers and square roots. By the

-Pythagorean Theorem and the Coordinate Plane: This lesson comes from the CMP3 book, Looking for Pythagoras. It is lesson 3.3, Finding Distances. Students will review the components of a coordinate plane and how they can be used with the Pythagorean Theorem to find the distance between two points of a line segment. Students may work in groups of 3-4. Launch: Teacher will lead students in a discussion on finding the distance between two points through these questions: How can you find the

distance between these two points?

How can you use the Pythagorean Theorem to find the length of this line segment?

The teacher will show the following image and ask:

-Is it a right triangle?: This lesson comes from the CMP3 book, Looking for Pythagoras. It is lesson 3.4, Measuring the Egyptian Way. Students will investigate this focus question: If a triangle with sides a, b, and c, satisfies the relationship , is the triangle a right triangle? Students may work in groups of 2-4 for this problem. Launch: Students will watch the Launch video. This video demonstrates how Egyptians used right triangles made out of rope to measure their land. The students will then be given a 12 inch ruler and 12 inch piece of yard. They will have to divide the yard into 12 equal segments and mark them off with a marker. Students will need to tape the ends together and form a right triangle with the side lengths that are whole numbers of segments. They will have to answer: What are the side

lengths of the triangle

-Assessment: Students will complete an individual cumulative assessment containing multiple choice, short answer, and extended response questions.

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for all triangles?

Formative Assessment: Teacher will observe throughout the lesson looking correct usage of the formula and process. Teacher will also evaluate the exit slip.

Day 2 Finding the missing leg of a right triangle w/Pythagorean Theorem This lesson will begin with a problem like this:

Students will be using Thinking Protocol from MC2 to solve the problem. Students will be given three color pens or pencils. The first color is for them to fill in anything they know about the problem by themselves. They will be given two sentence starters to complete: “I know…” and “I need to find…” After they have worked by themselves, they will use the second color to work with a partner. Making conjectures from yesterday’s lesson students will work together to try to solve for the side. The students should notice that they are not solving for the

end of this section students should be able to easily identify a rational or irrational number given a square root. Explore: Students will then begin to work on Problem 4.4 (A-E). This section will guide them through a series of questions meant to deepen their understanding of rational and irrational numbers. They will have to discuss with their peers questions like these: Write an example of a rational or

irrational number greater than 0.5 but less than 0.6.

Students will make the connections that there an infinite number of irrational numbers. They will see the connection between rational/irrational numbers and Pythagorean Theorem with problems like these:

Summary: Students will have to present their findings to the class. They should have evidence to support their ideas. Some of the questions they should be able to answer are: Do rational numbers occur in real-world

settings? Do irrational numbers occur in real-world settings?

Can you identify every number as either rational or irrational?

Can you put any real number on a number line? If you choose any two real numbers, can you always find another real number between these?

How do rational and irrational numbers pertain to the Pythagorean Theorem.

What right triangle has this hypotenuse?

What are the lengths of the legs?

How can you use this information to find the length of the hypotenuse?

So, what is the distance between points K and L?

Explore: Students will work on Problem 3.3, questions A-E. Students will make conjectures, by finding the distance between two coordinates on a grid. Some of the answers will contain square roots, so students will have to estimate the distance using Pythagorean theorem.

you formed? What are some of the

ways you could check that this is a right triangle?

How do you think Egyptians used the knotted rope?

Explore: Students will work with their group on questions (A-D). They will make conjectures on how to determine if a triangle is a right triangle. Summary: Students should be able to summarize their results to the class. They should be able to answer: If a triangle with sides

a, b, and c, satisfies the relationship is the triangle a right triangle?

How do you know? Can you rearrange the

sides of a right triangle to form

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hypotenuse(c), but for the leg of the triangle (a or b). After about 10 minutes, the teacher will choose a couple of students to share some of their ideas with the class. They will use this last color to write what they learned as a class. The teacher will then show a video from https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem-2 . This will be followed by students solving problems on individual white boards. Formative Assessment: Students will be assessed during the Thinking Protocol Activity. Teacher will look for understanding through student conversations and white board activity. A teacher created assignment will be sent home.

Formative Assessment: Teacher will observe each group during the Explore and Summary part of the lesson. Making sure that each student understands the difference between all real numbers. Student summaries will be the main indicators of comprehension.

Day 4 -Pythagorean Theorem with radicals: Students will use their knowledge on rational and irrational numbers to solve Pythagorean Theorem problems like this: Students will practice these type of problems through a teacher created presentation. Since students have already solved for missing sides on a right triangle and know how to simplify square roots, they just have to put both skills together. Students will participate during the presentation by solving problems on individual white boards. Formative Assessment: Students will take home a teacher created worksheet to practice. Teacher will check this homework for accuracy.

Summary: Students will show the class their findings. They will share the conjectures they made and the process they went through. They should be able to answer the following questions: How do you find the legs

of the right triangle you need?

Can you always find a right triangle where the hypotenuse is the distance between any two points?

Formative Assessment: Students should be able to answer the questions in the summary section. Teacher will observe as students work in their groups.

another triangle that is not a right triangle?

Formative Assessment: Students should be able to answer the questions in the summary section. The teacher will evaluate student responses to check for understanding and clear up any misconceptions. Review/Practice for Pythagorean Theorem: Students will engage in a review of all concepts for the learning cycle. Students will complete a study guide task at home, and be given to chance to ask questions the following day.



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Roswell Independent School District Unit 8 Lesson Plan – Working with Exponents (Quarter 2)


8th

Teacher(s): J. Busby, C. Busby, K. Diaz, A. Foster School: MVS


(# 2,3,4 only)

1. Standards Addressed: 8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.A.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 8.EE.A.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities

2. Learning Target(s): 7) Students can apply properties of exponents to simplify expressions

involving exponents. This includes zero and negative exponents, and multiplication and division properties of exponents.

8) Students can simplify and solve problem situations involving scientific notation and decimals that can be better represented by scientific notation.

4) I can use the properties of exponents such as the zero, negative, product, and quotient rule, to simplify expressions that involve exponents.

5) I can compare expression to see which quantities are larger or smaller.

6) I can simplify and solve problems that involve scientific notation

3. Relevance/Rationale: (Why are the outcomes of this lesson important in the

real world? Why are these outcomes essential for future learning?) Exponents are used in a variety of ways in our everyday lives. The most common way that students use them is when they are talking about measurements of area and volume. Exponents are also used in many careers such as: -Bankers: to calculate interest earned on investments -Scientists: to measure the growth of bacteria -Builders: to design projects, estimate how much material they will need and prepare the material as needed. -Engineers: to help them design and build machinery, structures and equipment.

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4. Assessment/Progress Monitoring: (How will you and your students know




DAY 1 DAY 2 DAY 3 & 4 DAY 5 DAY 6 & 7

What is an Exponent?: This lesson comes from the 8

th grade

CMP3 book Growing, Growing, Growing. It is section 1.1, Making Ballots: Introducing Exponential Functions. Students should work in groups of two to four. Students will be investigating the growth in the number of ballots created by repeatedly cutting a piece of paper in half. Launch: Students will watch the launch video on Chen’s ballot-making task. Students will predict the number of ballots that would result in three, four, or even ten cuts before the video. Teacher should also review what expanded and exponential form looks like. The teacher should present the challenge by posing the following questions: How can you predict the number

of ballots after 8 cuts? How can you predict how many

cuts to make if we need 128 ballots?

Negative and Zero Exponents: Students will be given an admit slip to review yesterday’s lesson. They will have to write numbers in expanded and exponential form. Some of the admit slips will be shown on the board. Students will then be presented with a PowerPoint on Zero and Negative Exponents from https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&es_th=1&ie=UTF-8#q=zero%20exponents%20powerpoint (Scroll down to the PPT from VCSD) . This presentation will guide students through zero and negative exponents. They will participate throughout the lesson by writing down notes and working out problems on the Promethean Board. The teacher should deepen student comprehension on zero exponents by referring to yesterday’s lesson. They

Day 3 Multiplying Exponents: This lesson comes from the 8

th grade

CMP3 book Growing, Growing, Growing. It is section 5.2 on Rules of Exponents. Students will use patterns among exponents to formulate several important properties for the finding the product of exponents. Students should work in groups of three to four. Launch: Teacher will show a problem like

this then expand the exponents, and combine the exponents to create 3n^7. Students will work with their group to try and figure out how the teacher got the answer. Once students have a general idea that the exponents are combined when multiplying they will begin explore. Explore: To reinforce this skill students will work on A-E. These questions will guide students by asking them to write the exponents in expanded form to solve for the product of two numbers. They will begin with problems that result in a single base and power and to multiple bases and

Scientific Notation: This lesson comes from the 8

th grade CMP3 book,

Growing, Growing, Growing. It is section 5.4, Operations with Scientific Notation. Students should work in groups of two to four. Students will learn how scientific notation helps solve problems. Launch: Students will watch the launch video that talk about water usage. This will introduce the students to large numbers and how they can be simplified using scientific notation. To start a discussion students should discuss the following questions using the data from problem 5.4: Which is greater—the

amount of water used by irrigation or the amount used by livestock?

How might you carry out this calculation?

How much water is

Review/Practice for Exponents: Students will engage in a review of all concepts for the learning cycle. Students will complete a study guide task at home, and be given to chance to ask questions the following day. -Assessment: Students will complete an individual cumulative assessment containing multiple choice, short answer, and extended response questions.

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Explore: Students will cut and stack paper for the first two or three cuts. This will help them see and understand the relationship between the number of cuts and the number of ballots created. Students will create a table for their data. They should see a pattern emerge as they count the ballots they’ve made.

Summarize: Students will share their findings to the class. They should have made conjectures about the relationship between the number of cuts and the number of ballots, and how exponents explain this relationship. They should be able to answer the following questions: How did you find each of the

entries in your table? What is the relationship between

this number of ballots and the previous number of ballots?

Explain that relationship in terms of the number of cuts.

Formative Assessment:

should make the connection that a paper cut zero times is just one all the time. When students finish they should work on an assignment to reinforce the skills they just learned. The following website contains some worksheets directly related to zero and negative exponents: http://www.teacherweb.com/ny/arlington/algebraproject/U6L2ZeroandNegativeExponents.pdf .

Formative Assessment: Teacher will assess students through observation during the lesson. Teacher should observe if students can simplify exponents containing negative and zero exponents.

powers. Summary: Students will summarize their results and ideas to the class. Students should make the conjecture that if the bases are the same, the base stays the same but the powers combine. They should also be able to work on problems with multiple bases and powers. Formative Assessment: The teacher will check for student understanding throughout the Explore and Summary section. It should be clear that students understand that the powers get added when multiplying exponents.

Day 4 Dividing Exponents: On this day students will be asked to further their skills by solving a problem such as:

The students will be using the Thinking Protocol from MC2 to solve the problem. Students will be given three color pens or pencils. The first color is for them to fill in anything they know about the problem by themselves. They will be given two sentence starters to complete: “I know…” and “I need to find…” After they have worked by themselves, they will use the second color to work with a partner. Together students will write the base in expanded to try and solve the problem.

used per person each day?

Explore: Students will use strategies to work their way from A-D. Some of the tasks include comparing two different methods and performing complex calculations.

Summary: The teacher should go over the questions in the problem. The main purpose of the summary is to have students explore a variety of strategies for solving these problems. In some cases they may see why one strategy might work better than another. Students should be able to present their findings on scientific notation. Formative Assessment: Teacher will assess

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Students should be able to answers the questions in the summary section as well as share any interesting strategies. Students may summarize their results on a poster, which can also be used as a formative assessment.

The last color will be used when students summarize their results to the class. Students will then be presented with a teacher created flipchart. This should guide students into making the conjecture that when dividing exponents, they are actually subtracting. Formative Assessment: Students will complete a teacher created worksheet on the quotient rule for exponents.

throughout the lesson, checking for accuracy and comprehension. An exit slip can be given as an additional formative assessment.









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Roswell Independent School District Unit 9 Lesson Plan-Measurement of Geometry (Quarter 3)


8th

Teacher(s): School:


(# 2,3,4 only)

1. Standards Addressed: 8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. 8.EE.A.2 : Use square root and cube root symbols to represent solutions to equations of the form =p and =p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that of √2 is irrational. 8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions

2. Learning Target(s): 1) Students will be able to classify and describe basic geometric shapes by their

characteristics 2) Students will be able to discover symmetry with any object or shape. 3) Students will be able to find the area of two-dimensional geometric figures. Students will

be able to find the nets and surface area of three-dimensional geometric shapes. 4) Students will be able to apply formulas and find the volume of prisms and pyramids in

real world situations. 5) Students know the formulas for finding the volume of cones, cylinders, and spheres and

use them to solve real-world problems involving volume. 6) Students can solve equations in the form =p by using cube roots. Students can use the

cube root symbol appropriately to represent solutions to these types of equations. Students can apply these skills to problems involving volume.

7) Students can explain the difference between rational and irrational numbers, both on their own and in relation to pi and other measurements connected to volume.

8) Students can use a rational approximation to represent an irrational number. Students use varying approximations to describe the location of an irrational number

1) I can classify and describe basic geometric shapes by their

characteristics 2) I can see symmetry in objects and shapes. 3) I can find the area of two-dimensional geometric figures, the

nets, and surface area of three-dimensional geometric shapes.

4) I can use formulas to find the volume of prisms and pyramids in real-world situations.

5) I will use formulas to find the volume of cones, cylinders, and spheres and use them to solve real-world problems

6) I can solve equations and use cube root to represent solutions to problems involving volume.

7) I can explain the difference between rational and irrational numbers on their own and in relation to pi and volume.

8) I can use an approximation to represent an irrational number and describe its location

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3. Relevance/Rationale: (Why are the outcomes of this lesson important in the real world? Why

are these outcomes essential for future learning?) Surface area and volume are relevant concepts in everyday life. We use them to make coffee, wrap gifts, load bookshelves, and pave roads. Essential Question: Why do we need to find volume?

4. Assessment/Progress Monitoring: (How will you and your students know if they have

successfully met the outcomes? What specific criteria will be met in a successful product/process? What does success on this lesson’s outcome look like?)



DAYs 1-2 DAYs 3-7 Day 8 DAYs 9-11 DAYs 12-15

Day 1- Students will work in small groups on the CMP 3 7

th

Grade Module Shapes and Designs Investigation 1.1. Launch: Students will review their knowledge of 2-D shapes by using the “popcorn out” strategy with the whole class. Students should recall general classification terms such as triangles, quadrilaterals, circles, pentagons, etc. Explore: Students will complete investigation 1.1 to discover different classifications by looking at characteristics of the

Day 3- Launch: Students will individually contrast 2-D and 3-D shapes by writing down any differences between the two that they can think of. Explore: After seeing the differences between 2-D and 3-D shapes, students will interact with a teacher made flipchart. The flipchart will include the following 3-D Shapes: Cube, Rectangular Prism, Trapezoidal Prism, Triangular Prism, Pentagonal Prism, Hexagonal Prism, Octagonal Prism, Decagonal Prism, Square Pyramid, Rectangular Pyramid, Trapezoidal Pyramid, Triangular Pyramid, Pentagonal Pyramid, Hexagonal Pyramid, Octagonal Pyramid, Decagonal Pyramid, Cylinder, Cone, and Sphere. The students will fill out a notes page as they move through the flipchart on the Promethean Board. To complete the notes page, the students will draw the net for each shape, and identify the number of faces, edges, and vertices each shape has.


th

Grade Module Filling and Wrapping Investigations 3.1, 3.2, and 3.3. Launch: Students will review key components of circles and their vocabulary. Components to be included are: radius, diameter, circumference, area, center, and chord. Explore: After reviewing vocabulary, students will work on questions A and B in investigation 3.1. Students will find the relationship between the circumference, radius, and diameter


th Grade

Module Filling and Wrapping Investigation 4.1 Launch: Students will begin by answering two questions. “How is the net useful to finding the surface area of a prism?” “Will a net be useful in finding the surface area of a cylinder?” The students will be given a cardboard cylinder, such as a paper towel roll. The students will look at the cylinder, and design the net to match. The students will keep the following questions in mind as they design the net: “What would a net for this particular cylinder look like?”; “What information do you need to make a net for this cylinder? How would you use that information?”; “How is the perimeter of the base related to the rectangular part of your net?” Students will be told that they will now work in the reverse direction and create a cylinder from a net.

Day 12- Ping Pong Ball Project (3 Days): Students will work on the Ping Pong Ball Project that was provided by MC². Students work in small groups. Students will complete Part I of the project. Students design 3 different packages to contain ping pong balls. Using centimeter grid paper, students draw the nets of their designs. Summary/Formative Assessment: Teacher Observation: Look for correct nets of 3-D figures. Some students might have misconceptions when visualizing how nets will fold to make a specific shape. Day 13- Students will work in small groups on Part II of the ping pong ball project. Students find the surface area of the nets. The students multiply the dimensions of the nets by a student chosen scale factor. The students create the new nets with the new dimensions on centimeter grid paper. The students find the surface area of the new nets. Students explore the difference between the surface

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shapes. For example, quadrilateral isn’t the most specific name for some four sided shapes. Students will continue to create more specific groups. Students will sort the shapes by their characteristics, such as sides, angles, and types of symmetry. Summary/Formative Assessment: Students will complete the following assignment to ensure their understanding of classifying shapes: http://cdn.kutasoftware.com/Worksheets/PreAlg/Classifying%20Triangles%20and%20Quadrilaterals.pdf Day 2- Students will work in small groups. The students will recall the concept of finding the area of 2-D shapes (with the exception of circles). Summary/Formative

Summary/Formative Assessment: Students will complete the following assignments to show their understanding of Classifying 3-D Shapes and their Nets. Classifying Solids: http://cdn.kutasoftware.com/Worksheets/PreAlg/Classifying%20Solids.pdf More Nets of Solids: http://cdn.kutasoftware.com/Worksheets/Geo/10-More%20Nets%20of%20Solids.pdf Day 4- Students will work in small groups on the CMP 3 7

th Grade Module Filling

and Wrapping Investigation 2.1. Launch: Students will begin the lesson by making 3-D prisms. The students will use sheets of computer paper. Each prism will have the same lateral area. For a rectangular prism, students will fold the paper into four equal rectangles. A pentagonal prism will be made by folding

of a circle. Since this concept was covered in 7

th grade, this

should be a quick review. After completing 3.1, students will complete questions A-D in investigation 3.2, and questions A-B in investigation 3.3. These investigations will help students find the connection between the area, circumference, radius, and diameter of a circle. Summary/Formative Assessment: Students will individually answer the following questions on an exit ticket: “What is the relationship between the diameter or radius of a circle and its circumference? How does the area of a circle increase as the circle’s radius and diameter increase? What is the relationship between the area of a circle and its radius?”

Explore: Students will work on Questions A-D in Investigation 4.1. This investigation helps students derive the formula for the surface area of a cylinder. Summary/Formative Assessment: Students will individually answer the following questions on an exit ticket: “How can you calculate the Surface Area of a cylinder? Why does that strategy work?” Day 10- Students will work in small groups on the CMP 3 7

th Grade

Module Filling and Wrapping Investigation 4.2. Launch: Students will create two cylinders from sheets of computer paper. The students will use one sheet of paper to make a wide and short cylinder by making the shorter side of the paper the height. The paper will be rolled into a cylinder, and will not have bases. The students will use one sheet of paper to make a long and narrow cylinder by making the long side the height. The paper will be rolled into a cylinder, and will not have bases. Students will answer the following questions before beginning the exploration: “Is there a way to find the volume of a cylinder without filling it with cubes or something else? If you fill this container with centimeter cubes, will that help you

areas of the original nets and the new nets. Finally, students calculate the price to make each package. The price is $0.005 for each square centimeter.

Summary/Formative Assessment: Teacher Observation: Look for student understanding of the concept of surface area. The students should know the connection between the nets of 3-D shapes and surface area. Day 14- Students will work in small groups on Part III of the ping pong ball project. Students find the volume of all six figures. Students explore the connection between the volume of the original nets and the new nets. Students find the price to ship each package if the price to ship a package is $.005 for each cubic centimeter. Finally,

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