DE ALB COUNTY SCHOOL DISTRICT RIGOROUS CURRICULUM …...Course Grade 8 Unit of Study Unit 2:...

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DEKALB COUNTY SCHOOL DISTRICT

RIGOROUS CURRICULUM DESIGN

UNIT PLANNING ORGANIZER

Subject(s) Mathematics

Grade and Course

Grade 8

Unit of Study Unit 2: Exponents and Equations

Pacing 5 Weeks

“Unwrapped” Priority Georgia Standards of Excellence

Skills and Concepts

Work with radicals and integer exponents MGSE8.EE.1 - KNOW and APPLY the properties of integer exponents to GENERATE equivalent numerical expressions. Analyze and solve linear equations and pairs of simultaneous linear equations MGSE8.EE.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, TRANSFORM 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 COLLECT like terms.

Know that there are numbers that are not rational, and approximate them by rational numbers. MGSE8.NS.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.



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“Unwrapped” Priority Standards

“Unwrapped” Skills (Students Need to Be Able to Do)

“Unwrapped” Concepts (Students Need to Know)

Bloom’s Taxonomy Levels

DOK (For Overall Standard)

MGSE8.EE.1

• KNOW

• APPLY

• GENERATE

• properties of integer exponents

• properties of integer exponents

• equivalent numerical expressions

• 1 (Remember)

• 2 (Understand)

• 3 (Apply)

• 3 (Strategic Thinking)

MGSE8.EE.7

• SOLVE

• linear equations in one variable

• 3 (Apply)


MGSE8.EE.7a

• GIVE

• TRANSFORM

• Examples of linear equations in one variable with

o One solution

o Infinitely Many

o Solutions o No

Solutions

• Given equations

into simpler

equivalent forms

(where a and b are

different numbers)

• 3 (Apply)

• 3 (Apply)




3

o x= a

o a = a

o a= b

MGSE8.EE.7b

• SOLVE

• USE

• COLLECT

• linear equations with rational number coefficients, including equations whose solutions require expanding expressions

• the distributive property

• like terms

• 3 (Apply)

• 3 (Apply)

• 3 (Apply)


MGSE8.NS.1

• KNOW

• UNDERSTAND

• SHOW

• CONVERT

• numbers that are not rational are called irrational

• informally that every number has a decimal expansion

• for rational numbers: decimal expansion repeats eventually

• decimal expansion, which repeats eventually, into a rational number

• 1 (Remember)

• 2 (Understand)

• 3 (Apply)

• 3 (Apply)

• 2 (Skills and Concepts)



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Supporting Standards

Work with radicals and integer exponents MGSE8.EE.2 - Use square root and cube root symbols to represent solutions to equations. Recognize that 𝑥2 = p (where p is a positive rational number and lxl < 25) has 2 solutions and 𝑥 3 = p

(where p is a negative or positive rational number and lxl < 10) has one solution. Evaluate square roots of perfect squares < 625 and cube roots of perfect cubes > -1000 and < 1000. MGSE8.EE.3 - Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3×108 and the population of the world as 7×109, and determine that the world population is more than 20 times larger.

MGSE8.EE.4 - Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g. use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g. calculators). Analyze and solve linear equations and pairs of simultaneous linear equations.

Know that there are numbers that are not rational, and approximate them by rational numbers. MGSE8.NS.2 - Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate √2 to the nearest tenth). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.



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CCSS for Mathematical Practice

1. Make sense of problems and persevere in solving them. (Daily) 2. Reason abstractly and quantitatively. (Daily) 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. (Daily) 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Essential Questions Corresponding Big Ideas

1. How can I apply the properties of integer exponents to generate equivalent numerical expressions?

2. What is the difference between rational and irrational numbers?

3. What strategies can I use to create and solve linear equations with one solution, infinitely many solutions, or no solutions?

1. Exponents are useful for representing very large or very small numbers. Properties of integer exponents can be used to generate equivalent numerical expressions.

2. a. All real numbers, rational and irrational, can be plotted on a number line. Rational approximations of irrationals can be used to compare sizes, estimate locations on a number line and estimate values of expressions. b. Every number has a decimal expansion. Decimal expansions of some rational numbers repeat. Decimal expansions of irrational numbers do not repeat.

3. Linear equations in one variable can have one solution, infinitely many solutions, or no solutions.



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Unit Assessments Pre-Assessment Post-Assessment

Student Version:

Gr8_Mathematics_Unit2_Preassessment_Student

Teacher Version:

Gr8_Mathematics_Unit2_Preassessment_Teacher

Student Version:

DeKalb County Benchmark

Teacher Version:



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Performance Assessment

Engaging Scenario

Current Situation: Students at your school have been struggling with Math. You know that it is because sometimes math is not always fun and engaging. You want to create interactive games that can help students learn about exponents, equations and real numbers. Your goal is to create interactive math games that are fun and interesting that all 8th grade teachers will be able to use to help their students learn. Your goal is to present your product to a group of teachers so that your games will be chosen and used all the 8th grade teachers in the county. You want to be the top math game designer in your school district.

Student Challenge: Designing interesting and interactive games to teach the standards relating to exponents, equations and real numbers.

Student Role: Game Designer

Intended Audience: Eighth Grade Teachers and Department Chairs

Product or Performance: Presentation of Collection of Interactive Games that target identified standards and construct a viable argument.

Performance Task Synopses

Task 1: MGSE8.NS.1. The students will demonstrate their understanding of real numbers as rational or irrational by creating a game. Also, they will demonstrate if a real number is rational, the equivalence of the number in decimal expansion as a terminating decimal or a repeating decimal. They will convert a repeating decimal into a rational number. Task 2: MGSE8.EE.1, MGSE8.EE.3, MGSE8.EE.4. In Part A of this task he students will design a matching game teaching the properties and characteristics of integer exponents (Product of Power Property, Power of a Power Property, Power of a Product Property, Zero Exponent Rule, and Negative Exponent Rule). In Part B of this task students will use the properties of exponents and scientific notation.

Task 3: MGSE8.EE.7, MGSE8.EE.7a, MGSE8.EE.7b In this task, students will create an equations card sort with various solution types, step-by-step solutions with justifications.

Task 4: MGSE8.NS.1, MGSE8.EE.1, MGSE8.EE.3, MGSE8.EE.4, MGSE8.EE.7, MGSE8.EE.7a, MGSE8.EE.7b. Students create a presentation for 8th grade math teachers and department chairs demonstrating how their interactive games target the intended standard. They will include a written example of how each game aligns with each standard and provide additional examples to support the use of their games.



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Performance Task 1 In Detail

Know that there are numbers that are not rational, and approximate them by rational numbers. MGSE8.NS.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. Circumstances of Performance: In-Class (Approximate Time 40 – 50 minutes) Task 1 Student Directions: Students are All Mixed Up!!! You will use the statements below to create a card game (Ex. Concentration).

o You will create a set of cards with each statement. o You will create a set of cards which justify why the statement may be correct or ALL Mixed

Up!!! o Include the rules of the game and how to win.

Eighth grade students are sharing what they know about real numbers. Several students gave the following statements: Mario: A square root is always an irrational number. Jessica: A fraction is never an irrational number. Antonio: A decimal is sometimes an irrational number. Carol: A repeating decimal is an irrational number. John: A mixed number is not a rational number. Jada: Fractions can only change to terminating decimals when written as decimal expansion. Mohamed: To change a repeating decimal to a fraction, first write an equation by setting the decimal equal to a variable that will represent the fraction. Next, write another equation by multiplying both sides of the equation by 10 only. Then, subtract the first equation from the second equation. Finally, solve the equation by dividing both sides. Decide which student(s) is demonstrating an understanding of real numbers from his/her given statement. If a student is all “mixed up”, justify why you think the student is all mixed up with supporting evidence.

Task 1 Teacher Notes: The purpose of this task is for students to demonstrate their understanding of real number and the subsets of real numbers. Mario: A square root is always an irrational number. (Mario’s statement is incorrect because some square roots of perfect squares like 4 and 9 are natural numbers, which are also rational numbers.) Jessica: A fraction is never an irrational number. (Jessica’s statement is correct because any number that can be written as a fraction that consists of two integers is by definition a rational number.) Antonio: A decimal is sometimes an irrational number. (Antonio’s statement is correct because a non-repeating, non-terminating decimal is an irrational number.) Carol: A repeating decimal is an irrational number. (Carol’s statement is incorrect because a repeating decimal can be converted to a rational number written in the form of two integers a/b.) John: A mixed number is not a rational number. (John’s statement is incorrect because a mixed can be written in the form of two integers a/b). Jada: Fractions can only change to terminating decimals when written as decimal expansion. (Jada’s statement is incorrect because a fraction can convert to terminating and repeating decimals.)



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Mohamed: To change a repeating decimal to a fraction, first write an equation by setting the decimal equal to a variable that will represent the fraction. Next, write another equation by multiplying both sides of the equation by 10 only. Then, subtract the first equation from the second equation. Finally, solve the equation by dividing both sides. (Mohamed’s statement is incorrect because you multiply both sides of the equation by a power of 10.)

Performance Task 1 Scoring Guide

4 Distinguished 3 Proficient 2 Developing 1 Beginning

All proficient criteria plus:

o Provide several examples to support their answers.

o Created web-based game.

o Creates card game which provides detailed justification of if a statement is correct or if it is all mixed up.

o Creates card game with errors in explanations.

o Provided explanations and/or mathematical representations that could not be clearly understood or interpreted.


Work with radicals and integer exponents MGSE8.EE.1 - KNOW and APPLY the properties of integer exponents to GENERATE equivalent

numerical expressions. MGSE8.EE.3 - Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3×108 and the population of the world as 7×109, and determine that the world population is more than 20 times larger.

MGSE8.EE.4 - Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g. use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g. calculators). Analyze and solve linear equations and pairs of simultaneous linear equations.

Circumstances of Performance: In-Class (Approximate Time 75-90 minutes)

Task 2 Student Directions: Radicals, Exponents and Scientific Notation Part A Matching the Rule to the Property Eighth grade students are confused when using the properties of integer exponents. They do not know when to add, subtract, or multiply the exponents. They are puzzled as to why any number (except zero) raised to the zero power is 1. They don’t know what to do when the negative exponent is in the numerator or the denominator. They need your help. Your job is to:



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o Create an interactive game which compares and explains the different properties of integer exponents so they know when to apply the appropriate property.

o In the game students should be able to match the rule to the property o Provide at least 2 examples for each property (Product of Power Property, Power of a Power

Property, Power of a Product Property, Zero Exponent Rule, and Negative Exponent Rule).

Part B GiantBurger! You have done a fabulous job of creating a game that explains the properties of integer exponents to the eighth grade students. Omar was interested in figuring out how learning about the integer properties relates to real-life. He came across the newspaper ad below: “Every day, 7% of Americans eat at GiantBurger restaurants”. Omar was curious if this was a true statement. Help Omar decide whether this headline is true using the following information. • There are about 8 x 103 GiantBurger restaurants in America. • Each restaurant serves about 2.5 x 103 people every day. • There are about 3 x 108 Americans.

o Explain your reasons and show clearly how you figured it out. o Explain to Omar how the properties of exponents and knowledge of working with scientific

notation can help interpret the ad? Task 2 Teacher Notes: In Part A students will create a game which teaches the properties and characteristics of integer exponents: Product of Power Property, Power of a Power Property, Power of a Product Property, Zero Exponent Rule, and Negative Exponent Rule. Task 2 B Teacher Notes: In Part B, students will use properties of exponents and scientific notation to evaluate a newspaper headline. This task can be very engaging and may be adapted to fast food chains nearby. Through the mathematics exploration of this task, students evaluate whether a fast food chain’s claims are reasonable. This task is found at http://www.map.mathshell.org/tasks.php?collection=9&unit=HA18. Extension of the task(Part B): The percentage estimate you discovered should not be exactly 7%, but it should be close. Your job is to investigate what looks like a small percentage difference and determine if the difference is significant. Using the percentage, you calculated, determine about how many people eat at GiantBurger each day. If 7% of Americans eat at GiantBurger each day, how many people would that be? What is the difference in the two? Is GiantBurger overestimating based on your answer or underestimating? How many people would they be overestimating/underestimating by in a week? In a month? If you originally stated that their headline using 7% is true, do you still feel this way? Why or why not? Can a small difference in a percentage make a big difference in actual values? Explain. If you originally stated that their headline using 7% was not true, do you still feel that way? Do you now have additional data to back up your claims? Explain.



http://www.map.mathshell.org/tasks.php?collection=9&unit=HA18



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All Proficient criteria plus: o Created game cards

with complex expressions applying and combining more than one property in their explanation.

o Provided 3 or more game cards for each property.

o Provided a detailed explanation with mathematical language and examples for the extension task.

o Provided an

interactive matching game which compared the Product, Power to Power, and Quotient Rule for exponents.

o Attended to

precision with mathematical justifications which explained the Zero Exponent Rule and the Negative Exponent Rule.

o Calculated the

number of people who ate at GiantBurger restaurants 8 x 103 x 2.5 x 103= 20.0 x 106

= 2x107 o Attends to precision

in finding 7% of 3 x 108 = 2.1 x 107

o Attends to precision in finding 2 x 107 as a percentage of 3 x 108 . = 6.7%

o Provided a viable argument for the following statement is true since: 6.7% is approximately equal to 7%.

o Provided an interactive matching game which compared the Product, Power to Power, and Quotient Rule for exponents with errors and/or misunderstandings of the property.

o Provided viable argument about the claims of GiantBurger but errors exist in the number of restaurants that exist or the servings of people.




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Analyze and solve linear equations and pairs of simultaneous linear equations MGSE8.EE.7 - SOLVE linear equations in one variable.



Circumstances of Performance: In-Class (Approximate Time 45 - 60 minutes) Task 3 Student Directions: Create a card sort that will help the 8th graders understand solving linear equations and their solutions. Card Descriptions (See sample):

o Equations (Minimum of 5) -one solution -no solution -infinitely many solutions

o Detailed procedures showing solutions step by step o Each problem must also meet one of the specs of the standard as listed: 1) linear equation in

one variable 2) include rational number coefficients 3) require use of the distributive property 4) variables on both sides of the equation 5) require collecting like terms.

Solution Type Equation Step by Step

One Solution

2y + 1 - 17 = -2y + 32 2y - 16 = -2y + 32 2y + 2y- 16 = 32

4y -16 = 32 4y + 1 + 16 = 32 + 16

4y = 48 4y = 48

4 4 y = 12

Task 3 Teacher Notes: Students will create a card sort designing mathematical problems that meet the specs of the standards. They design equations and provide step-by-step solutions with justifications as part of a community service project for the school. Students should follow the directions in the task, working with a partner or small group. Have students pair up to discuss the steps used to solve the equations. Teachers should end the lesson by using discussion questions like those that follow in order to help students make the mathematics more explicit. Teacher Questions for facilitating student discussion: Which categories of problems were the easiest to create? What strategy did you use to create the problems with infinitely many solutions? What challenges did your group encounter while completing this task? Did you notice any patterns? If so, describe the pattern(s). Source: Georgia Framework Unit 2



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All “3” criteria plus: o Created word

problems for 2 equations that were in real-world contexts.

o Provided additional examples with solutions.

o Created card sort with all criteria.

o Attended to precision when solving all equations

o Created card sort but all criteria were not include and/or errors existed in solutions to the problems.

o Created card sort but errors existed in calculations of solutions and context of problems were not clear.


Task 4 Student Directions:

Work with radicals and integer exponents

MGSE8.EE.1 - KNOW and APPLY the properties of integer exponents to GENERATE equivalent numerical expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations MGSE8.EE.7 - SOLVE linear equations in one variable.



Know that there are numbers that are not rational, and approximate them by rational numbers. MGSE8.NS.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. It’s Game Day It is time for you to present your interactive games to a group of 8th grade math teachers and department chairs. You are convinced that by using your games students will have a better understanding of the targeted standards and will enjoy learning. If you convince this group, the entire district will use your games. Items to include in your presentation:

o Marketing your product (Why use your games? How would you advertise it?) o Provide written examples of how each game aligns the standard (Include Tasks 1 – 3)



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o Provide additional examples to support the use of your games. .

Task 4 Teacher Notes: Students have become designers of interactive math games. They now have the task of packaging their materials and convincing a group of teachers and department chairs to use their materials. Have standards available for student use. Encourage students to use technology for their presentations (PowerPoint, Prezi, Google Slides etc. What challenges did your group encounter while completing this task?



All proficient criteria plus: o Provided additional

mathematical examples and counter-examples to support viable arguments.

o Attended to precision with mathematical language with written examples of how each game aligns to the standards.

o Constructs viable argument in presentation to justify how each game targets the skills and concepts of the standard.

o Provided a viable argument and presentation that addresses some aspects of the standard with misunderstandings of how each game targeted the skills and concepts.




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Instructional Strategies Instructional Strategies

Research-Based Effective Teaching Strategies

21st Century Learning Skills

Learning Objectives (posted and referenced)

Identifying Similarities and Differences

Summarizing and Note Taking

Reinforcing Effort, Providing Recognition

Homework and Practice

Nonlinguistic Representations

Cooperative Learning

Purposeful small group instruction

Increased think time

Setting Objectives, Providing Feedback

Check for Understanding

Generating and Testing Hypotheses

Cues, Questions, and Advance Organizers

Interdisciplinary Non-Fiction Writing

Teamwork and Collaboration

Initiative and Leadership

Curiosity and Imagination

Innovation and Creativity

Critical thinking and Problem Solving

Flexibility and Adaptability

Effective Oral and Written Communication

Accessing and Analyzing Information

Other



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Intervention Strategies Intervention Strategies

(Tiers 1, 2, 3) Additional Supports in

Classroom

Specially Designed Instruction for Special

Education Students

Strategies for English Language Learners

Re-voicing

Explaining

Prompting for participation

Challenging or countering

Asking “Why?” “How?”

Reread

Practice new academic vocab.

Assistive technology

Pre-teach & re-teach in a different way

Repetition

Use of manipulatives

Collaborative work

Direct/explicit instruction

“Chunking”

Accommodating different learning styles

Create differentiated text

sets

Providing additional guided practice

Conferencing

Additional time

Small group collaboration

Modify quantity of work

Take student’s dictation

Scaffold information

Differentiated content process or product

Consistent reward system

Refer to students’ IEP or 504 plan

Assistive technology

Visuals/Realia

Front-loading

Echoing/Choral response

Color-coding

Multiple exposures in different media

Pair-share

Modeling

Language scaffolds: eg, sentence frames

Deconstruct complex sentences and texts

L1 support

increased opportunities for

student-student talk

Strategic vocabulary instruction

Additional think time



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Strategies for Gifted Learners

Tier 1: Low Preparation Tier 2: Medium Preparation

Flexible-Learning Groups by Readiness, Interest,

Learning Profiles

Gifted Education Cluster Classes

Choice of Books Gifted Education Collaboration Classes

Homework Options Tiered Activities and Products

Use of Reading Buddies Use of Literature Clubs

Various Journal Prompts Multiple Testing Options

Student/Teacher Goal Setting Multiple Texts

Varied Pacing with Anchor Options Alternative Assessments

Work Alone or Together Subject Advancement within class

Flexible Seating Curriculum Compacting

Varied Scaffolding Tiered Centers

Varied Computer Programs Spelling by Readiness

Design-A-DAY Varying Organizers

Varied Supplemental Materials Community Mentorships

Computer Mentors Stations

Think-Pair-Share by Readiness, Interest, Learning Profiles

Group Investigations

Open-ended Activities Students are Assessed in Multiple Ways

Explorations by Interest Student choice in selecting learning activities.

Options for Competition Simulations

Tier 3: High Tier 4: Advanced/Autonomous

Advanced Content English/language arts, mathematics, science and/or social studies courses

Above grade level accelerated English/language arts, mathematics, science and/or social studies courses

Resource Classes Advanced Placement Classes

Independent/Directed Study International Baccalaureate Classes

Socratic Seminars Internship/Mentorships

Whole Grade Acceleration



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Instructional Resources and Materials Suggested Resources Suggested Technology Resources

Math Tools: o Number Line o Calculator o Grid Paper

Explanation of Standards:

o GADOE Grade Level Curriculum Overview -Grade 8

o GADOE Grade 8 Framework Unit 2

Graphic Organizer Properties of Exponents Graphic Organizer

Solving Equations Song

Technology Resources: o GADOE Grade Level Curriculum

Overview -Grade 8

o GADOE Grade 8 Framework Unit 2 Carnegie Learning Grade 8 Text

Exponent Rules: http://www.onlinemathlearning.com/exponent-rules.html

Properties of Integer Exponents: http://www.mathworksheetsland.com/8/3intexpo.html

Exponent Jeopardy https://jeopardylabs.com/play/exponent-rules5

Scientific Notation https://www.mathsisfun.com/numbers/scientific-notation.html

Rational and Irrational Numbers http://www.openmiddle.com/rational-and-irrational-numbers-2/

Activities for Solving Equations https://lzlomek.wordpress.com/2012/10/10/activities-for-solving-equations/

https://hbgsdmath.wikispaces.com/Graphic+Organizers

http://www.onlinemathlearning.com/exponent-rules.html

http://www.onlinemathlearning.com/exponent-rules.html

http://www.mathworksheetsland.com/8/3intexpo.html

http://www.mathworksheetsland.com/8/3intexpo.html

https://jeopardylabs.com/play/exponent-rules5

https://www.mathsisfun.com/numbers/scientific-notation.html

https://www.mathsisfun.com/numbers/scientific-notation.html

http://www.openmiddle.com/rational-and-irrational-numbers-2/


https://lzlomek.wordpress.com/2012/10/10/activities-for-solving-equations/

https://lzlomek.wordpress.com/2012/10/10/activities-for-solving-equations/



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Unit Vocabulary Unit Vocabulary Terms Interdisciplinary Connections

Academic / Tier 2 Unit-Specific / Domain / Tier 3

Base Cube Irrational Like Terms Non-perfect squares Non-perfect cubes Significant digits Perfect squares Perfect cubes Radical Rational Solution Square Variable

Addition Property of Equality Additive Inverses Algebraic Expression Cube root Decimal expansion Denominator Exponent Equation Equivalent Estimate Expression Exponential notation Inverse Operation Multiplication Property of Equality Multiplicative Inverse Negative exponents Negative integers Non-repeating decimals Non-terminating decimals Numerical expressions Numerator Positive exponents Positive integers Product of Powers Rule Integer Properties of integer exponents Powers Powers of 10 Quotient of Powers Rule Rational numbers Reciprocal Real number system Repeating decimal Standard notation Significant digits Scientific notation Terminating decimal

Physical Science Standard SCSh5. Students will demonstrate the computation and estimation skills necessary for analyzing data and developing reasonable scientific explanations. Arts, AV Technology and Communications Career Cluster Introduction to Digital Media Standard AAVTC-IDM-1 Standard: Demonstrate employability skills required by business and industry. AAVTC-IDM-6 Find and solve problems of the production process through open-ended inquiry, the consideration of multiple options, weighing consequences, and assessing results.



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Weekly Planner Course: __Math 8_________________________ Unit 2: ___Exponents and Equations__________

Pacing Priority (in bold) and Supporting Standards

Engaging Learning Experiences

Core Instruction (in bold) and additional resources

Formative Assessments

Mathematical Literacy: The ability to read, listen, think creatively, and communicate about problem situations, mathematical representations, and the validation of solutions will help students to develop and deepen their understanding of mathematics. (National Council of Teachers of Mathematics, 2000)

5 weeks Make modifications to the pacing based upon student pre-assessment results and the daily analysis of student work.

See CAAG for a listing of all standards. Instruction should be supported with the implementation of the Standards for Mathematical Practice (SMP).

Students should complete the listed experiences to support understanding and mastery of the math standards. Students are expected to exhibit the SMP.

Teachers should implement the listed experiences to support core instruction on the math standards. Teachers should model the SMP during the 3-Part Lesson Structure.

Teachers should use the assessments to support student learning at all levels. The unit pre-assessment should be administered prior to unit instruction for diagnostic purposes.

o Differentiate instruction based upon the pre-assessment results. o Make modifications to the pacing based upon student pre-assessment results and the daily analysis of student work. o Implement the Formative Assessment Lesson (FAL) to monitor the progress of students during the instructional unit. o Introduce the learning targets on a daily basis in kid friendly language using “I Can” statements. o Provide instruction using the Concrete-Representational-Abstract (CRA) sequence of instruction. o Utilize the Gradual Release Model of Responsibility (I do, We do, You do) during instruction to support student learning of

concepts/skills. o Use UPS Check and the 3 Read Protocol for the Problem Solving Process. o Use Newman’s Prompt to diagnose the hurdles students face while problem solving. o Incorporate Mathematical Visualization to model math concepts, skills, and problem solving.

o Remind students that mistakes are respected, expected, and inspected in the mathematics classroom.

Unit Expectations o Performance Assessment (4 Tasks and Scoring Guide) o Formative Assessment Lessons

GADOE Instructional Tasks

Weekly core instruction should include the implementation of instructional tasks from the Georgia Department of Education (GADOE) located at www.georgiastandards.org along with other district and supplemental instructional resources. Included in the planner are possible suggestions for GADOE tasks.

http://www.georgiastandards.org/



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Week 1

MGSE8.NS.1 MGSE8.NS.2 MGSE8.EE.2

Engaging Scenario Task 1: All Mixed Up GADOE Gr. 8 Unit 2: Rational or Irrational Reasoning?

o Are you Rational or Irrational Gallery

o Distinguish between rational and irrational numbers – LearnZillion Video

o Really, I’m Rational

Pre-Assessment (Unit Pre-Assessment) Task 1 scoring guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Rational and Irrational

Week 2 MGSE8.EE.1

GADOE Gr. 8 Unit 2: Alien Attack Task 2: Radicals, Exponents and Scientific Notation. Giant Burgers

o Introduction to Exponent properties involving products video by Khan Academy

o FAL: Applying Properties of Exponents

o Show What You Know Graphic Organizer– Carnegie Learning Lesson 7.6, Problem 1 pages 282-287 (Note: Do not include Scientific Notation)

o Justify the Steps – Carnegie, Lesson 7.6, Problem 2

Task 2 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Who’s Correct – Carnegie Lesson 7.6, Problem 3

https://www.georgiastandards.org/Georgia-Standards/Frameworks/8th-Math-Unit-2.pdf


http://mdk12.msde.maryland.gov/share/ccsc/uos/resources/math/gr8_irrational_numbers/LP_8_NS_A_1_Are_you_Rational_or_Irrational_Final.docx

http://mdk12.msde.maryland.gov/share/ccsc/uos/resources/math/gr8_irrational_numbers/LP_8_NS_A_1_Are_you_Rational_or_Irrational_Final.docx

https://learnzillion.com/lesson_plans/4774-distinguish-between-rational-and-irrational-numbers



http://www.cpalms.org/Public/PreviewResourceLesson/Preview/51183



http://www.map.mathshell.org/download.php?fileid=784

https://www.opened.com/video/exponent-properties-involving-products/183386

https://www.opened.com/video/exponent-properties-involving-products/183386

http://map.mathshell.org/download.php?fileid=1668




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Week 3 MGSE8.EE.1 MGSE8.EE.3 MGSE8.EE.4

GADOE Gr. 8 Unit 2 FAL: Estimating Length Using Scientific Notation

o Introduction to Scientific Notation Classroom Activity Math Shorts Video for Scientific Notation Classroom Activity

o Scientific Notation Space Chart o Operations with

Numbers in Scientific Notation

o Space Math II- Applications of Scientific Notation

Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Exit Tickets

Week 4

MGSE8.EE.7 MGSE8.EE.7a MGSE8.EE.7b

GADOE Gr. 8 Unit 2: Solving a Linear Equation Teacher Version Task 3:Linear Equation Card Sort

Solving a Linear Equation Student Handout Unique Solution, No Solution, and Infinite Solution Classification of Solutions Teacher Version Classification of Solutions Student Handouts Twin’s Inheritance Task

Task 3 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Illustrative Mathematics: Solving Equations

Week 5 MGSE8.NS.1 MGSE8.EE.1 MGSE8.EE.7

Task 4; It’s Game Day GADOE Gr. 8 Unit 2: Writing a Math Website – Culminating Task

Task 4 Scoring Guide Suggested informal progress monitoring checks: Ticket Out the Door Hot Seat Discussion of the Essential Questions Post-Assessment (District Benchmark)



http://www.uen.org/mathshorts/downloads/scientific_notation_classroom_activity.pdf

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

http://betterlesson.com/lesson/resource/2519198/scientific-notation-space-chart-docx

http://betterlesson.com/lesson/resource/2519198/scientific-notation-space-chart-docx

https://www.nasa.gov/pdf/371727main_SMII_Problem9.pdf



http://www.d11.org/Instruction/Mathematics/6-8/Documents/BigIdeasMath_Public/Tasks_Gr08/8.EE.7.a-b_Twins_Inheritence_Task.pdf

https://www.illustrativemathematics.org/content-standards/8/EE/C/7/tasks/392

DE ALB COUNTY SCHOOL DISTRICT RIGOROUS CURRICULUM …...Course Grade 8 Unit of Study Unit 2:...

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