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.
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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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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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2015 – 2016
8th Grade ALDs
11th Grade ALDs
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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.
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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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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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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
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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
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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
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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
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