8th grade Algebra Curriculum Guide

2015 – 2016

Unit 2: Equations and Inequalities Time Frame: Quarter 1 Connections to Previous Learning: Students use the properties of arithmetic learned in middle school to build and transform algebraic expressions and equations of continued complexity. Students use fluency in solving linear equations in one variable, to solve linear equations, inequalities, and literal equations. Focus within the Grade Level: Students understand that solving linear equations and inequalities in one variable is a process of reasoning, using steps that are reversible. Students will give precise attention to units when applying these skills to real world situations. Connections to Subsequent Learning: Students apply the properties of operations to algebraic expressions and extend these properties to functions such as square root, exponential, and trigonometric.

Unit 1

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8th grade Algebra Curriculum Guide

2015 – 2016

Common Core Standards in this unit: Solve equations and inequalities in one variable. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Understand solving equations as a process of reasoning and explain the reasoning. A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equation with coefficients represented by letters.

Estimated Days on the Unit 15 – 20 days

Mathematical Practices 1. 2. 3. 4. 5. 6. 7. 8.

Unit 1

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make sure of structure. Look for and express regularity in repeated reasoning.

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8th grade Algebra Curriculum Guide

2015 – 2016

Common Core 8th grade Standards connected to Algebra Unit th

 taught in 7 grade Analyze and solve linear equations and inequalities. 

Unit 1

8.EE.7 Solve linear equations in one variable.

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8th grade Algebra Curriculum Guide

2015 – 2016 8th Grade ALDs

11th Grade ALDs

Unit 1

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8th grade Algebra Curriculum Guide

2015 – 2016 Stage 1 Desired Results Transfer Goals

Students will be able to independently use their learning to… • • • •

Apply concepts and procedures involving expressions, equations, and inequalities to solve to real world examples. Solve equations and inequalities in one variable. Understand solving equations as a process of reasoning and explain the reasoning. Analyze and solve linear equations.

Meaning Goals UNDERSTANDINGS Students will understand that… • Linear equations can have one solution, infinitely many solutions, or no solution. • A solution to an equation makes the mathematical sentence true. • Linear inequalities have a range of solutions or no solution. • A solution to an inequality makes the mathematical sentence true.

ESSENTIAL QUESTIONS • • • • •

What is a solution? How are equations and inequalities used to solve real world problems? When is it advantageous to represent relationships between quantities symbolically? numerically? graphically? Why are procedures and properties necessary when manipulating numeric or algebraic expressions? How can the structure of expressions/equations/inequalities help determine a solution strategy?

Acquisition Goals Students will know… • The inverse operations.

Unit 1

Students will be skilled at… • Solve linear equations in one variable, including literal equations. • Solve linear inequalities in one variable, including literal inequalities. Clover Park School District 6/2/15

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8th grade Algebra Curriculum Guide

2015 – 2016

Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning to Work with radical and integer exponents. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (This occur again with Pythagorean Theorem and Volume)

Analyze and solve linear equations and inequalities. 8.EE.7 Solve linear equations in one variable.

Solve equations and inequalities in one variable. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Understand solving equations as a process of reasoning and explain the reasoning. A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Explanations, Examples, Comments, and Pre-requisite Material Explanation: -

th

Solving equations is a review from 8 grade along with one and two step inequalities.

Vocabulary Cards Cards -

Equation Inequality Solution Identity

Pre-requisite skills: Cards -

1 & 2 step solving Translate words into expressions or equations

Pre-requisite Material: Holt Algebra 1 Lesson 2-1 Solving Equations by Adding or Subtracting Holt Algebra 1 Lesson 2-2 Solving Equations by Multiplying or Dividing

Unit 1

Stage 3 MATERIALS BY STANDARD(S):

Teacher should use assessment data to determine which of the materials below best meet student instructional needs. All materials listed may not be needed.

Book resources Holt Algebra 1 Lesson 2-3 Solving Two-Step and Multi-Step Equations Prentice Hall Algebra 2-2: Solving Two Step equations Holt Algebra 1 Lesson 2-4 Solving Equations with Variables on Both Sides Prentice Hall Algebra 2-3: Solving Multi-Step equations Holt Algebra 1 Lesson 3-4 Solving Two-Step and Multi-Step Inequalities Prentice Hall 3-4: Solving Multi-Step Inequalities Holt Algebra 1 Lesson 3-5 Solving Inequalities with Variables

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8th grade Algebra Curriculum Guide -

2015 – 2016

Holt Algebra 1 Lesson 3-1 Graphing and Writing Inequalities Holt Algebra 1 Lesson 3-2 Solving Inequalities by Adding or Subtracting Holt Algebra 1 Lesson 3-3 Solving Inequalities by Multiplying or Dividing

A.CED.1

Equations can represent real world and mathematical problems. Include equations and inequalities that arise when comparing the values of two different functions, such as one describing linear growth and one describing exponential growth. Examples: 1. Given that the following trapezoid has area 54 cm2, set up an equation to find the length of the base, and solve the equation. 2. Lava coming from the eruption of a volcano follows a parabolic path. The height h in feet of a piece of lava t seconds after it is ejected from the volcano is given by ℎ(𝑡) = −𝑡 2 + 16𝑡 + 936. After how many seconds does the lava reach its maximum height of 1000 feet? 3. A government buys 𝑥 fighter plans at 𝑧 dollars each, and 𝑦 tons of wheat at 𝑤 dollars each. It spends a total of 𝐵 dollars, where 𝐵 = 𝑥𝑥 + 𝑦𝑦. Find the number of tons of wheat the government can afford to buy if it spends a total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each.

A.REI.1

Properties of operations can be used to change expressions on either side of the equation to equivalent expressions. In addition, adding the same term to both sides of an equation or multiplying both sides by a non‐zero constant produces an equation with the same solutions. Other operations, such as squaring both sides, may produce equations that have extraneous solutions. Examples: 1. Explain why the equation x/2 + 7/3 = 5 has the same solutions as the equation 3x + 14 = 30. Does this mean that x/2 + 7/3 is equal to 3x + 14? 2. Show that x = 2 and x = ‐3 are solutions to the equation 𝑥 2 + 𝑥 = 6. Write the equation in a form that shows these are the only solutions, explaining each step in your reasoning. 3.

Unit 1

on Both Sides Holt Algebra 1 Lesson 3-6 Solving Compound Inequalities Holt Algebra 1 Ch. 2 Extension Absolute Value Prentice Hall 3-7: Absolute Value Equations and Inequalities Additional resources Helpful Hint Sheets for a Study Aid Solving Linear Equations: Stations Activity Pass the Paper DI Activity Sorting Equations and Solving Complex Equations: Lessons, PowerPoint On Balance (Noyce Foundation) Puzzle Solving Equations One-Variable Inequalities: Stations Activity Puzzle Solving Inequalities The Shoe Problem (Georgia Task) Linear Equations and Inequalities (Georgia Task) Jaden’s Phone Plan (Georgia Task) Acting Out (Georgia Task) Absolute Value worksheets additional Cafeteria Actions and Reactions: Develop Understanding Task page 20 Greater Than?: Soldify Understanding Task page 34 Taking Sides: Practice Understanding Task page 38

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8th grade Algebra Curriculum Guide

Unit 1

2015 – 2016

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8th grade Algebra Curriculum Guide

2015 – 2016

Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning to Solve equations and inequalities in one variable. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Understand solving equations as a process of reasoning and explain the reasoning A.REI.3 Solve linear equations and inequalities in one variable, including equation with coefficients represented by letters. Explanations, Examples, and Comments

Stage 3 MATERIALS BY STANDARD(S):

Teacher should use assessment data to determine which of the materials below best meet student instructional needs. All materials listed may not be needed.

Vocabulary -

Equation Inequality Solution Identity Formula Literal Equations

Book Resources Holt Algebra 1: 2-5 Solving for a Variable Prentice Hall Algebra2-5: Literal Equations and Formulas

Pre-requisite skills: -

1 & 2 step solving Translate words into expressions or equations

Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents.

Additional Resources Serving Up Symbols: Develop Understanding Task page 12 Examining Units: Solidify Understanding Task page 16 Elivira’s Equations: Solidify Understanding Task page 24 Solving Equations, Literally: Practice Understanding Task page 27 Cafeteria conundrums: Develop Understanding Task page 30

A.CED. 4 Limit to formulas which are linear in the variable of interest. Examples: 1. The Pythagorean Theorem expresses the relation between the legs a and b of a right triangle and its hypotenuse c with the equation 𝑎2 + 𝑏 2 = 𝑐 2 Why might the theorem need to be solved for c? 2. Solve the equation for c and write a problem situation where this form of the equation might be useful. 4 3. Solve 𝑣 = 𝜋𝑟 2 for radius r. 3 4. Motion can be described by the formula below, where t = time elapsed, u=initial velocity, a = acceleration, and s = distance traveled s = ut+½at2. Why might the equation need to

Unit 1

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8th grade Algebra Curriculum Guide be rewritten?

2015 – 2016 Stage 2 - Evidence SAMPLE Assessment Evidence PERFORMANCE TASK(S): The Twins’ Inheritance

Evaluative Criteria:

SBAC Sample Items F-BF.2 (N.276) A-REI.3 (I.088)

Formative assessments

SBAC Sample Items from 8th 8.EE.7 (D.201) 8.EE.7 (D.204) 8.EE.7 (D.137)

A.CED.1, 4 and A.REI.1, 3 Equations: #1, #2, #3, #4, MC 1, MC 2

SBA Review by Target Target C review 1 Target C review 2 Target C review 3

A.REI.BE Absolute Value Inequalities: #1, #2, #3, #4

A.CED.1,4 and A.REI.3 Inequalities: #1, #2, #3, #4, MC 1, MC 2 A.REI.B3 Absolute Value Equations: #1, #2, #3, #4

OTHER ASSESSMENT EVIDENCE: Washington State Common Core State Mathematics Standards Transition Document: https://www.k12.wa.us/CoreStandards/pubdocs/Transition8th.pdf Washington State: Materials to help districts and others understand the

organization and content of the standards and the content and evidence base used to support the standards: http://achieve.org/achieving-common-core

For the vertical progression, see the University of Arizona progression documents. Stage 3 – Learning Plan Sample Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning Unit 1

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8th grade Algebra Curriculum Guide LEARNING ACTIVITIES: A suggested guide to layout of unit by days

2015 – 2016 Stage 3 – Learning Plan Sample

NOTES:

CED.1 and REI.1 Day 1: Solving Multi-Step Equations -

Holt Algebra 1 Lesson 2-3 Solving Two-Step and Multi-Step Equations Prentice Hall Algebra 2-2: Solving Two Step equations

Day 2: Solving Multi-Step Equations - Pass the Paper DI Activity Day 3: Solving Variables on Both Sides - Holt Algebra 1 Lesson 2-4 Solving Equations with Variables on Both Sides - Prentice Hall Algebra 2-3: Solving Multi-Step equations Day 4: Solving Equations - Solving Linear Equations: Stations Activity - Puzzle Solving Equations Day 5: Solving Equations - Sorting Equations and Solving Complex Equations Day 6: Solving Multi-Step Inequalities - Greater Than ? - Holt Algebra 1 Lesson 3-4 Solving Two-Step and Multi-Step Inequalities - Prentice Hall 3-4: Solving Multi-Step Inequalities Day 7: Solving Inequalities - Taking Sides - Holt Algebra 1 Lesson 3-5 Solving Inequalities with Variables on Both Sides - One-Variable Inequalities: Stations Activity Day 8: Solving Inequalities Unit 1

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8th grade Algebra Curriculum Guide -

2015 – 2016

Stage 3 – Learning Plan Sample Holt Algebra 1 Lesson 3-6 Solving Compound Inequalities

Day 9: Solving Absolute Value Equations (Can wait until More Functions unit) - Holt Algebra 1 Ch. 2 Extension Absolute Value Day 10: Solving Absolute Value Inequalities (Can wait until More Functions unit) - Prentice Hall 3-7: Absolute Value Equations and Inequalities Day 11: Solving Absolute Value (Can wait until More Functions unit) -

More practice

CED.1 and REI.1 Day 1: Literal Equations - Examining Units - Holt Algebra 1: 2-5 Solving for a Variable - Prentice Hall Algebra2-5: Literal Equations and Formulas Day 2: Literal Equations - Elvira’s Equations - Literal Equations: Stations Activity Day 3: Literal Equations - Solving Equations, Literally - Cafeteria conundrums

Unit 1

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