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GATEWAY REGIONAL HIGH SCHOOL

MATHEMATICS GRADE 8

PACING GUIDE

PURPOSE STATEMENT/PHILOSOPHY

The Math 8 curriculum is comprised of the following major concepts or ‘Big Ideas’:  (1) tools of algebra; (2) equations and inequalities; (3) rational and irrational numbers;  (4) polynomials;  (5) functional and relations; and (6) linear systems. While knowledge of content is being developed students are engaged in hands-on and cooperative activities that encourage mathematical reasoning, problem solving, communicating and making connections. Through these activities students utilize technology such as graphing calculators, computers, and calculator-based lab equipment. In addition they are encouraged to think more critically through activities that involve investigations, explorations, and discovery. Finally, evaluation appears in several formats: tests, performance tasks, and long- and short-term projects using EdConnect and Desmos.  

PACING GUIDE

Month

# Days

Standards

Skills

Activities

Assessments

September

20

8.NS.1

8.NS.2

8.EE.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.

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 (e.g., π2).

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

Collaborative discussions – Laws of Exponents

Creative option:

- Students should be arranged into 4 groups (multiplying, dividing, power to a power, and power of 0)

- Watch the video on the laws of exponents “Super Base (WSHS Math Rap Song)

https://www.youtube.com/watch?v=QIZTruxt2rQ

- Give each group a poster board and ask them to make a creative, catchy poster including the following information

        - Their group’s exponent rule

        - A sample problem

        - Explanation

        - Catchy hint to help them remember the rule

        - Any additional decorations

CRP12

A Penny for Your Thoughts:  Exploring Squares and Square Roots

- Students should be arranged individually or in pairs

- Give each group about 30 pennies (other items with the same size and shape can be substituted)

- Give each student the “A Penny for Your Thoughts” worksheet to complete

CRP12

Bingo

Spinner Activity –

Root Race

- Students should be arranged in groups of 2-4 people.

- Each group should be given a deck of cards with all of the face cards and jokers removed.

- Deal out four cards to everyone within the group.

- Each student must find the product of all four numbers.  Then they need to find the square root (to the nearest tenth).

- Students should record their numbers, products, and roots.

- First group to get all of their problems correct wins!

- Adaptation ideas:

- Require that two students need to get the same answers before being checked.

- Do not tell the group which problems are incorrect once they have been checked.

- Activity can be done using a pair of dice to create a 2 digit number.

Analyzing questions

8.1.8.A.2, CRP11

Interactive Whiteboard Lessons based on student need

Quiz- In EdConnect:Rational Numbers

Quick Checks-Rational and Irrational Numbers

Test- evaluate squares and radicals to solve real world problems.  

Performance Assessment:

8.NS.A.1 Converting Decimal Representations of Rational Numbers to Fraction Representations

8.NS.A.2 Irrational Numbers on the Number Line

 

 

October

25

8.GA.1

8.GA.2

8.GA.3

8.GA.4

8.G.5

Verify experimentally the properties of rotations, reflections, and translations:

  1. Lines are taken to lines, and line segments to line segments of the same length.
  2. Angles are taken to angles of the same measure.
  3. Parallel lines are taken to parallel lines.

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Use formal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Collaborative discussions CRP12

Cooperative group work (eg. Placemat Activity)/ Differentiated group work – Translalation Lab.  

https://njctl.org/courses/math/8th-grade-math/2d-geometry/attachments/translations-lab/8.1.8.A.2, CRP11, CRP4

Analyzing questions with Dilations.  https://njctl.org/courses/math/8th-grade-math/2d-geometry/attachments/dilations-lab/8.1.8.A.2, CRP11

Interactive Whiteboard Lessons based on student need

Three Act Videos:  http://threeacts.mrmeyer.com/tacocart/

Quiz- Rotations, Reflections, and Translations.

Quick Checks-Two- Dimensional Congruence

Test- Proportionality in tables and Graphs

Problem Solving, Similar Figures and Scale Drawings

https://njctl.org/courses/math/8th-grade-math/2d-geometry/attachments/2d-geometry-chapter-test-retest/

Project – Scale Drawing Project.  

Performance Assessment - 8.G.A.1 Reflections, Rotations, and Translations

8.G.A.2 Congruent Triangles

8.G.A.3 Effects of Dilations on Length, Area, and Angles

8.G.A.4 Are They Similar

8.G.A.5 Street Intersections

8.G.A.5 Similar Triangles II

8.G.A.5 Triangle's Interior Angles

November/December

20

8.GA.6

8.GA.7

8.GA.8

Explain a proof of the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

 

Building a bridge project 8.1.8.A.2, CRP2

Collaborative discussions

Cooperative group work (eg. Placemat Activity)/ Differentiated group work8.1.8.A.2, CRP11

Analyzing questions

Interactive Whiteboard Lessons based on student need

Quiz- Pythagorean Theorem,

Quick Checks-Distance and Mid-point.  

4

8.GA

Benchmark

Cooperative group work/ Differentiated group work

Analyzing questions

Benchmark Assessment-2-D Geometry

December/ January

28

8.EE.7

7.         Solve linear equations in one variable.

a.         Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b.         Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Collaborative discussions – Khan Academy linear equations.  

Analyzing questions

Interactive Whiteboard Lessons based on student need

Three Act Videos:  

http://threeacts.mrmeyer.com/ditchdiggers/

Radical Makeover Lab

https://njctl.org/courses/math/8th-grade-math/equations-with-roots-and-radicals/attachments/radical-make-over-lab/

Labs: Select one of the following fro Desmos

Connect Three

Slippery Slopes!

Marble Masters

RAFT – Occasions for an Equation.  

Quiz – Multistep Equations

Performance Assessments:

8.EE.C.7 The Sign of Solutions

8.EE.C.7 Coupon versus discount

Feb/March

26

  • 8.EE.5

8.EE.6

8.F.3

8.F.4

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships

represented in different ways.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation

y = mx + b for a line intercepting the vertical axis at b.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Construct a function to model a linear relationship between two quantities

Evaluating expressions

Collaborative discussions

Cooperative group work (eg. Placemat Activity)/ Differentiated group work

Analyzing questions – Three Act Videos.

http://threeacts.mrmeyer.com/25billionapps/

Interactive Whiteboard Lessons based on student need

Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Three Act Videos:  http://mrmeyer.com/threeacts/joulies/

Quiz- Proportional Relationships

Quick Checks-Solve Linear Equations.

Performance Assessments:

8.F.A.1 Function Rules        

8.F.A.2 Battery Charging

8.F.A.3 Introduction to Linear Functions

8.F.B.4 Chicken and Steak, Variation 1

8.F.B.4 Baseball Cards

8.EE.C.7 The Sign of Solutions

8.EE.C.7 Coupon versus discount

12

8.EE.8

Analyze and solve pairs of simultaneous linear equations

Collaborative discussions

Writing Systems to Model Situations 

Analyzing questions

Interactive Whiteboard Lessons based on student need

Assessment – Solving system of Equations.  

Benchmark Assessment-Linear Functions.  

May

23

  • 8.F.1
  • 8.F.2
  • 8.F.3

8.F.4

8.F.5

The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Compare properties of two functions each represented in a different way

Interpret the equation y = mx + b as defining a linear function

Construct a function to model a linear relationship between two quantities.

Describe qualitatively the functional relationship between two quantities by analyzing a graph

Collaborative discussions

Comparing Different Representations of Functions  (CRP11)

Analyzing a Graph – Three Act Videos.  http://threeacts.mrmeyer.com/25billionapps/ CRP8

Interactive Whiteboard Lessons based on student need

Quick Checks- describe the relationship using that graph.

 

Test- construct graphs from two quantities that form a linear relationship

Lab - compare properties of two functions and represent functions in multiple ways

June

12

8.G.9

Use formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Collaborative discussions  - Kahn Academy Volume.  

Cooperative group work (eg. Placemat Activity)/ Differentiated group work

Analyzing questions – Using the Smart Responders.  

Lab: RAFT – Volume Verification

Interactive Whiteboard Lessons based on student need

Quiz- identify what a 3-dimensional figure.

 

Quick Checks- use a formula to find the volume of a prism and cylinder.

Performance Assessment:  

https://njctl.org/courses/math/8th-grade-math/3d-geometry/attachments/volume-activity/

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Numbers and Operations

Timeframe: 20 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to find the squares and square roots of both rational and irrational numbers.

Students will know the perfect squares. They will also be able to simplify perfect square radical expressions as well as non-perfect square radicands.

Students will use the perfect squares to approximate square roots.

Students will understand the properties of exponents and will use them to solve equations with perfect square and cube roots.

LEARNING TARGETS

ESSENTIAL QUESTIONS

What is the difference between rational and irrational numbers?

ENDURING UNDERSTANDINGS

Squares and Radicals can help solve real world problems.

Squares and Radicals affect the numbers that are being used within an operation.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Assessment-Rational and Irrational Numbers
  • Evaluate squares and radicals

8.NS.A.1 Converting Decimal Representations of Rational Numbers to Fraction Representations

8.NS.A.2 Irrational Numbers on the Number Line

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.


 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: 2-D Geometry

Timeframe: 25 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

  • Students will be able to transform figures on a coordinate plane.
  • Students will be able to use their understanding of angle relationships to find unknown angles.
  • Students will be able to describe a sequence of transformations that will result in congruent figures.
  • Students will be able to describe a sequence of transformations and dilations that will result in similar figures.

LEARNING TARGETS

ESSENTIAL QUESTIONS

  • How can you use models of one and two-dimensional figures to show congruent figures?
  • How can you use models of one and two-dimensional figures to show similar figures?

ENDURING UNDERSTANDINGS

  • Congruent figures can be formed by a series of transformations.
  • Similar figures can be formed by a series of transformations.
  • Understand angle relationships in one and two-dimensional figures.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Benchmark Assessment- use models to show their understanding of congruent and similar one and two-dimensional figures.

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

8.G.A.1 Reflections, Rotations, and Translations

8.G.A.2 Congruent Triangles

8.G.A.3 Effects of Dilations on Length, Area, and Angles

8.G.A.4 Are They Similar

8.G.A.5 Street Intersections

8.G.A.5 Similar Triangles II

8.G.A.5 Triangle's Interior Angles


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Pythagorean Theorem

Timeframe: 20 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to explain the proof of the Pythagorean Theorem.

Students will find unknown side lengths using the Pythagorean Theorem.

Students will use the Pythagorean Theorem to solve problems involving distance and midpoints.

Students will solve real world application problems using the Pythagorean Theorem.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How does the Pythagorean Theorem help solve real world problems?

How do we compute the distance and midpoint within problems?

ENDURING UNDERSTANDINGS

The Pythagorean Theorem can be used to solve real world problems.

The Pythagorean Theorem aids in solving problems involving right triangles. 

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Apply the theorem to problems involving right triangles that model real world problems.
  • Find distances and midpoints between two points.

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

8.G.B.6 Converse of the Pythagorean Theorem

8.G.B.7 Running on the Football Field

8.G.B.8 Finding isosceles triangles


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Solving Equations

Timeframe: 28 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to solve two-step equations.

Students will be able to solve multiple-step equations.

Students will be able to solve equations that contain fractions.

Students will be able to solve equations that contain the same variable on both sides of the equation.

Students will be able to simplify and compare algebraic expressions that contain the same variable.

Students will be able to and translate word problems into equations and solve them.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How can the value of an unknown variable be found?

ENDURING UNDERSTANDINGS

How to solve an equation in one variable for that variable.

How to translate word problems into an equation

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Assessment- solve equations starting with a review of inverse operations and two-step equations and progressing to more complex equations and using the skills to solve word problems.

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper

8.EE.C.7 The Sign of Solutions

8.EE.C.7 Coupon versus discount


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Graphing Equations

Timeframe: 26 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to identify point on a line given its equation.

Students will be able to graph a line given different forms of the equation.

Students will be able to describe how slope relates to horizontal and vertical lines.

Students will be able to relate similar triangles to slope.

Students will be able to identify a linear function from a table.

Students will be able to use proportional relationships to solve real world problems.

Students will be able to solve linear equations for desired variables and values.

LEARNING TARGETS

ESSENTIAL QUESTIONS

  • What is meant by the slope of a line, and how can knowing a line’s slope help to graph a line and find parallel and perpendicular lines?
  • How can real world situations be modeled by proportional relationships?
  • How can solutions be found within an equation?

ENDURING UNDERSTANDINGS

  • Various methods can be used to solve equations and the solution to an equation can be checked by substituting into the original equation.
  • Linear relationships can be graphed to help solve real world problems and make predictions.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

Labs: Select one of the following

  • Connect Three
  • Slippery Slopes!
  • Marble Masters 

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

8.F.A.1 Function Rules        

8.F.A.2 Battery Charging

8.F.A.3 Introduction to Linear Functions

8.F.B.4 Chicken and Steak, Variation 1

8.F.B.4 Baseball Cards

8.EE.C.7 The Sign of Solutions

8.EE.C.7 Coupon versus discount


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Systems of Equations

Timeframe: 12 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will be able to graph systems of linear equations to find a solution.

Students will be able to solve a system of equations by using substitution and elimination.

Students will be able to translate real world problem into a system.

LEARNING TARGETS

ESSENTIAL QUESTIONS

How can real world situations be modeled by systems?  How can solutions be found to a system?

ENDURING UNDERSTANDINGS

The point at which lines intersect is the solution to the system with those lines.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Benchmark Assessment-Linear Functions and Systems of Equations

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

8.EE.C.8a Intersection of Two Lines

8.EE.C.8 How Many Solutions


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Functions

Timeframe: 23 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will understand what a function is and its corresponding graph.

Students will compare properties of different functions and relate the information to real world situations.

Students will graph slope-intercept form of a line.

Students will construct a function and determine the rate of change and initial value.

Students will describe a functional relationship by examining a graph.

LEARNING TARGETS

ESSENTIAL QUESTIONS

What is a function?

How are functions represented?

What can a relationship between numbers tell about a problem?

Are properties of functions and graphs the same for all functions?

ENDURING UNDERSTANDINGS

Properties of functions and their graphs are similar but not identical.

Slope-intercept form is an easy way of graphing functions.

The definition of a function and what it’s graph represents.

The ability to graph a function and write a function from a graph.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

Relationships and Functions

Lab – Intro to Functions (either group or individual)

Domain and Range

Vertical Line Test

Comparing Different Representations of Functions  

8.F.A.1 Function Rules        

8.F.A.2 Battery Charging

8.F.A.3 Introduction to Linear Functions

8.F.B.4 Chicken and Steak, Variation 1

8.F.B.4 Baseball Cards


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area:  Mathematics

Unit Title: Geometry

Timeframe: 12 Days

Lesson Components

UNIT SUMMARY

A summary of what the unit will contain and the learning students will be engaged in.

Students will identify what a 3-dimensional figure is.

Students will use a formula to find the volume of a prism and cylinder.

Students will use a formula to find the volume of pyramids, cones & spheres. square and cube roots.

LEARNING TARGETS

ESSENTIAL QUESTIONS

What is a 3-dimensional figure?

How can I find the volume of a 3-dimensional figure?

How can the volume of a 3-dimensional figure help me solve real world problems?

ENDURING UNDERSTANDINGS

There are different formulas that can be used when solving for the volume of a 3-dimensional figure.

21st Century Themes/Career Readiness Practices

Global Awareness:  Students will analyze and synthesize information from multiple news sources relating to current events/global issues.  Students will explore stereotypes and understand other cultures through class readings and writing prompts.

Creativity and Innovation: Students will brainstorm and produce original narratives/arguments inspired from the texts read.  Students will analyze texts for discussion and for developing a written response.  Students will be open and responsive to new and diverse perspectives and develop arguments relating to the risks and rewards of undertaking bold actions.  

Critical Thinking and Problem Solving:  Students will use various types of reasoning as appropriate to the situation.  Students will analyze how parts of a text interact to produce the overall theme or purpose.  Students will effectively analyze and evaluate evidence, arguments, claims, beliefs, and alternate points of view.  Students will synthesize and make connections between information and arguments.  Students will interpret information and draw conclusions based on analysis.

Communication and Collaboration: Students will articulate thoughts and ideas effectively using oral, written, and nonverbal communication skills in a variety of contexts. Students will use various media to communicate.  Students will demonstrate ability to work effectively and respectfully with diverse teams and work to accomplish a common goal.

Information Literacy: Students will critically evaluate information from the internet in short research projects to assess its credibility for research purposes and use the information to accomplish a task. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information.

Media Literacy: Students will interpret and analyze a variety of media sources to better understand the unit theme.  This includes how media can influence beliefs and behaviors.  Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of media. Students will create media products.

ICT Literacy-Information, Communications and Technology:  Students will use technology as a tool to research, organize, evaluate, and communicate information. Students will apply a fundamental understanding of the ethical/legal issues surrounding the access and use of information technologies.

Life and Career Skills/Standards/Practices: Students will interact with others through listening and speaking in a respectable and professional manner, manage goals, work independently and be self-directed.

EVIDENCE OF LEARNING

 Assessment (attach benchmarks/unit tests)

  • Assessment-Rational and Irrational Numbers
  • Evaluate squares and radicals

8.NS.A.1 Converting Decimal Representations of Rational Numbers to Fraction Representations

8.NS.A.2 Irrational Numbers on the Number Line

Materials/Equipment:

Calculator, Interactive White Board, graph paper, ChromeBooks 

Differentiation/Adaptations/Modifications:

The curriculum has a strong foundation of differentiated instruction. Differentiated instruction or modifications for all students, special education, ELL, and gifted & talented students include but not limited to learning environment, scheduling of learning tasks, materials and procedures. The classroom teacher often makes these modifications as appropriate to each child’s developmental and academic needs and/or directed by a child’s IEP or 504 plans. Gifted & talented students as well as all students are given choice of learning activities, assessments and projects as appropriate to the unit of study or lesson to meet their intellectual and academic differences.

  • Projects are designed so teacher may add or omit criteria based on student needs.
  • Extended time is allotted for students when directed by IEP’s or 504 plans.
  • Modification of project dimensions or materials for students with special needs.
  • Small groups/Flexible groupings
  • Shortened assignments
  • Assignment notebooks
  • Study sheets/summary sheets/outlines of most important facts
  • Supplemental aids (vocabulary, summary cards, modern translation of original work, etc.)
  • Visual demonstrations
  • Presentation of material in small steps
  • Read or paraphrase subject matter
  • Instructions/directions given in different channels (written, spoken, demonstration)
  • Visual or multisensory materials
  • Functional level materials
  • Mnemonic aids/devices
  • Additional time for test preparation
  • Review/testing matched to student pace
  • Test directions read/explained thoroughly
  • Oral, short-answer, modified tests
  • Emphasis on successes
  • Graphic Organizers
  • Student choice of texts, projects, writing prompts, etc.

Resources Provided:

Textbook, Internet resources, graph paper


Technology Standards:
(See Pacing Guide for Specific Integration)

Career Ready Practices:

(See Pacing Guide for Specific Integration)

Standard 8.1 Educational Technology:  All students will use digital tools to access manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

A. Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems and operations.

  • 8.1.8.A.2  Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or more digital applications to be critiqued by professionals for usability.

B. Creativity and Innovation: Students demonstrate creative thinking, construct knowledge and develop innovative products and process using technology.

  • 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. telecollaborative project, blog, school web).

D. Digital Citizenship: Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

  • 8.1.8.D.1 Understand and model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics including appropriate use of social media.
  • 8.1.8.D.2 Demonstrate the application of appropriate citations to digital content.
  • 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property.
  • 8.1.8.D.4 Assess the credibility and accuracy of digital content.
  • 8.1.8.D.5 Understand appropriate uses for social media and the negative consequences of misuse.

E: Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information.

  • 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP6. Demonstrate creativity and innovation.

CRP7. Employ valid and reliable research strategies.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.