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Goddard: Eighth Grade Common Core State Standards (CCSS) Mathematics

Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.1Cluster: Work with radicals and integer exponents.Standard: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3–5 = 3–3 =1/33 = 1/27.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐

Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Properties of Integer Exponents Integer: A number with no fractional part Exponents: Shows how many times you multiply a number by itself Expression: Numbers, symbols and operations grouped together to show the value of something Equivalent: Having the same value

Be Able to Do (Verbs) Level I Level II Level III Level IV Level V

List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square:

Knowledge/ Remembering

Memorize facts, definitions, &

formulas

Comprehension/ Understanding

Perform Procedures

ApplicationDemonstrate

understanding of math

AnalysisConjecture,

Generalize, Prove

Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Know ☒ ☐ ☐ ☐ ☐ Apply ☐ ☐ ☒ ☐ ☐ Generate ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Bases must be the same before exponents can be added, subtracted or multiplied. • Exponents are subtracted when like bases are being divided• A number raised to the zero (0) power is equal to one.• Negative exponents occur when there are more factors in the denominator. These exponents can be expressed as a positive if left in the denominator.• Exponents are added when like bases are being multiplied• Exponents are multiplied when an exponents is raised to an exponent• Several properties may be used to simplify an expressionEssential Questions:

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?1

Can I determine the properties of integer exponents by exploring patters and applying my understanding of properties of whole number exponents? Can I use the properties of integer exponents to simplify expressions?What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge)

1. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐2. Work with exponential rules I ☐ II ☐ III ☒ IV ☐ V ☐3. Mathematical notation I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)

Instructional Resources/Tools:

Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:

Example 1: Example 2: Example 3:

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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.2Cluster: Work with radicals and integer exponents.Standard: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Square Root: A value that when multiplied by itself, gives the number. Cube Root: A number that must be multiplied times itself three times to equal a given number. Rational: Perfect Square: A number made by squaring a whole number Irrational: Solution: Any and all values that make the equation or expression true.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Represent ☐ ☐ ☒ ☐ ☐ Evaluate ☐ ☐ ☐ ☐ ☒ Know ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students recognize perfect squares and cubes, understanding that non-perfect squares and non-perfect cubes are irrational. Students recognize that squaring a number and taking the square root √ of a number are inverse operations; likewise, cubing a number and taking the cube

root 3√❑ are inverse operations.

Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I recognize taking a square root as the inverse of squaring a number? Can I recognize taking a cube root as the inverse of cubing a number? Can I evaluate the square root of a perfect square?

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Can I evaluate the cube root of a perfect cube? Can I justify that the square root of a non-perfect square will be irrational?What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge

1. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐2. Work with exponential rules I ☐ II ☐ III ☒ IV ☐ V ☐3. Mathematical notation I ☒ II ☐ III ☐ IV ☐ V ☐4. Pattern recognition I ☐ II ☒ III ☐ IV ☐ V ☐5. Knowledge of rational and irrational numbers I ☒ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.3Cluster: Work with radicals and integer exponents.Standard: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as

much one is than the other. For example, estimate the population of the United States as 3 x 108 and the population of the world as 7 x 109, and determine that the world population is more than 20 times larger.

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐

Know (nouns) DefinitionList the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Integer: A number with no fractional part Power of Ten: Product of multiplying ten by itself, one or more times Scientific Notation: A single digit times an integer power of ten Estimate: An approximation for a real value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Estimate ☐ ☒ ☐ ☐ ☐ Express ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students use scientific notation to express very large or very small numbers. Students compare and interpret scientific notation quantities in the context of the situation, recognizing that if the exponent increases by one, the value increases 10 times. Likewise, if the exponent decreases by one, the value decreases 10 times.

Students solve problems using addition, subtraction or multiplication, expressing the answer in scientific notation.Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I write an estimation of a large quanitity by expressing it as the product of a single digit number and a positive power of ten? Can I write an estimation of a very small quanitity by expressing it as the product of a single digit number and a negative power of ten? Can I compare quanitites written as the product of a single digit number and a power of ten by stating their multiplicative relationships?

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What learning progressions are needed to master this standard? Give specific, measurable skill statements.


1. Integer as exponents: Rules I ☐ II ☐ III ☒ IV ☐ V ☐2. Pattern recognition I ☐ II ☒ III ☐ IV ☐ V ☐3. Knowledge of rational and irrational numbers I ☒ II ☐ III ☐ IV ☐ V ☐4. Scientific Notation I ☐ II ☒ III ☐ IV ☐ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.4Cluster: Work with radicals and integer exponents.Standard: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation

and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.



Scientific Notation: A single digit times an integer power of ten Operations: Mathematical process; most common: add, subtract, multiply and divide





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Perform ☐ ☒ ☐ ☐ ☐ Choose ☐ ☐ ☐ ☐ ☒ Interpret ☐ ☐ ☐ ☐ ☒ Use ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students understand scientific notation as generated on various calculators or other technology. Students enter scientific notation using E or EE (scientific notation), * (multiplication), and ^ (exponent) symbols.

Students add and subtract with scientific notation. Students use laws of exponents to multiply or divide numbers written in scientific notation, writing the product or quotient in proper scientific notation. Students understand the magnitude of the number being expressed in scientific notation and choose an appropriate corresponding unit.Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I add and subtract two numbers written in scientific notation? Can I multiply and divide two numbers written in scientific notation?

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Can I select the appropriate units for measuring derived measurments when comparing quantities written in scientific notation? Can I indenfity and interpret the various ways scientific notation is displayed on calculators and through computer software?What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge)

1. Integer as exponents: Rules I ☐ II ☐ III ☒ IV ☐ V ☐2. Pattern recognition I ☐ II ☒ III ☐ IV ☐ V ☐3. Knowledge of rational and irrational numbers I ☒ II ☐ III ☐ IV ☐ V ☐4. Scientific Notation I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.5Cluster: Understand the connections between proportional relationships, lines, and linear equations.Standard: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different

ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒

Level 3: Strategic Thinking ☒ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Proportion: An equation that conveys a proportional relationship Unit Rate: The ratio of two measurements in which the second term is one Slope: Steepness of a straight line Proportional Relationship: Two quantities having the same ratio





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Graph ☐ ☐ ☒ ☐ ☐ Interpret ☐ ☐ ☐ ☐ ☒ Compare ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students identify the unit rate (or slope) in graphs, tables and equations to compare two proportional relationships represented in different ways. Given an equation of a proportional relationship, students draw a graph of the relationship. Students recognize that the unit rate is the coefficient of x and

that this value is also the slope of the line.Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I graph a proportional relationship in the coordinate plane? Can I interpret the unit rate of a proportiaonal relationship as the slope of the graph? Can I justify that the graph of a proportional relationship will always intersect the origin (0,0) of the graph. Can I use a graph, a table, or an equation to determine the unit rate of a proportional relationship and use the unit rate to make comparisons between

various proportional relationships?

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1. Construct a graph/table. I ☐ II ☐ III ☒ IV ☐ V ☐2. Interpret a graph/table. I ☐ II ☐ III ☐ IV ☒ V ☐3. Understand proportions. I ☐ II ☒ III ☐ IV ☐ V ☐4. Understand unit rate. I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.6Cluster: Understand the connections between proportional relationships, lines, and linear equations.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Similar Triangles: Triangles with the same size, but not necessarily the same shape Slope: Steepness of a straight line Non-Vertical Line: Not in an up/down position (a line with slope) Coordinate Plane: A flat surface that contains the x and y-axis that extends forever Origin: On a coordinate plane, the point (0,0) Y-intercept: Where a straight line crosses the y-axis of a graph





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Explain ☐ ☐ ☒ ☐ ☐ Derive ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Using a graph, students construct triangles between two points on a line and compare the sides to understand that the slope (ratio of rise to run) is the same between any two points on a line.

Given an equation in slope-intercept form, students graph the line represented. Students write equations in the form y = mx for lines going through the origin, recognizing that m represents the slope of the line. Students write equations in the form y = mx + b for lines not passing through the origin, recognizing that m represents the slope and b represents the y-

intercept.Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathmatical situations? Can I create right triangles by drawing a horizontal line segment and a vertical line segment from any two points on a non-vertical line in the coordinate

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plane? Can I justify that these right triangles are similar by comparing the ratios of the lengths of the corresponding legs? Can I justify that sense the triangles are similar, the ratios of all corresponding hypontenuses, representing the slope of the line, will be equivalent? Can I justify that an equation in the form y=mx will represent the graph of a proportional relationship with a solve of m and a y-intercept of zero? Can I justify that an equation in the form y=mx+b represents the graph of a linear relationship with a slope of m and a y-intercept of b.What learning progressions are needed to master this standard? Give specific, measurable skill statements.


1. Construct a graph. I ☐ II ☐ III ☒ IV ☐ V ☐2. Interpret a graph. I ☐ II ☐ III ☐ IV ☒ V ☐3. Understand proportions. I ☐ II ☒ III ☐ IV ☐ V ☐4. Find and Interpret: Slope Intercept Form of a linear equation I ☐ II ☐ III ☐ IV ☒ V ☐5. Find the slope of line. I ☐ II ☒ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.7Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Solve linear equations in one variable.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear equation: An equation that makes a straight line when graphed Variable: Letters or other symbols that represent unknown values





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students recognize that the solution to the equation is the value(s) of the variable, which make a true equality when substituted back into the equation. Equations shall include rational numbers, distributive property and combining like terms.

If each side of the equation were treated as a linear equation and graphed, the lines would be parallel. Students write equations from verbal descriptions and solve.Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I use the properties of real numbers to determine the solution of the linear equation? Can I simplify a linear equation by using the distributive property and/or combining like terms? Can I give examples of linear equations with one solution, infinitely many solutions, or no solution?

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1. Properties of real numbers I ☐ II ☐ III ☐ IV ☐ V ☐2. Integer Rules I ☐ II ☐ III ☐ IV ☐ V ☐3. Know the meaning of the word variable I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.7aCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: 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 equations 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).



Linear Equations: An equation that makes a straight line when graphed Variable: Letters or other symbols that represent unknown values Solution: Any and all values that make the equation or expression true.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Transform ☐ ☐ ☐ ☐ ☒ Give Examples ☐ ☒ ☐ ☐ ☐ Show ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathmatical situations? Can I use the properties of real numbers to determine the solution of the linear equation? Can I simplify a linear equation by using the distributive property and/or combining like terms? Can I give examples of linear equations with one solution, infinitely many solutions, or no solution? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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1. Properties of real numbers I ☐ II ☒ III ☐ IV ☐ V ☐2. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐3. Know the meaning of the word variable I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.7bCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and

collecting like terms.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear Equations: An equation that makes a straight line when graphed Rational Number: Solution: Any and all values that make the equation or expression true. Coefficients: Number portion of a variable term Distributive Property: The product of a number and a sum is equal to the sum of the individual products. For example, a(b+c)=ab+ac Like terms: Terms with the same variable part





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove



FORMTEXT Essential Questions:

How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I use the properties of real numbers to determine the solution of the linear equation? Can I simplify a linear equation by using the distributive property and/or combining like terms? Can I give examples of linear equations with one solution, infinatly many solutions, or no solution? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

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1. Properties of real numbers I ☐ II ☒ III ☐ IV ☐ V ☐2. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐3. Knowledge of rational numbers I ☒ II ☐ III ☐ IV ☐ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.8Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Analyze and solve pairs of simultaneous linear equations.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Simultaneous linear equations: Two or more linear equations solved at the same time





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve ☐ ☐ ☒ ☐ ☐ Analyze ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Students graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations. Students recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions.

Given two equations in slope-intercept form (Example 1) or one equation in standard form and one equation in slope-intercept form, students use substitution to solve the system.


How can algebraic expressions and equations be used to model, analyze and solve mathmatical situations? Can I explain how a line represents the infinite number of solutions to a linear equation with two variables? Can I explain how the point(s) of intersection of two graphs will represent the solution to the system of two linear equations because that/those point(s) are

solutions to both equations? Can I use algebraic reasoning (simple substitution) and the properties of real numbers to solve a system of linear equations?

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Can I use the graphs of two linear equations to estimate the solution of a system? Can I use mathematical reasoning to solve simple systems of linear equations? Can I solve real-world problems and mathematical problems dealing with systems of linear equations and interpret the solution in the context of the

problem?What learning progressions are needed to master this standard? Give specific, measurable skill statements.


1. Graph linear equations I ☐ II ☐ III ☒ IV ☐ V ☐2. Mathematical vocabulary: simultaneously, intersection, point of intersection, ordered pair,

solution, parallel linesI ☒ II ☐ III ☐ IV ☐ V ☐

3. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐4. Properties of real numbers I ☐ II ☒ III ☐ IV ☐ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.8aCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection

satisfy both equations simultaneously.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Solution: Any and all values that make the equation or expression true. Variable: Letters or other symbols that represent unknown values Intersection: Lines that meet or cross on a single plane





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Understand ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




How can algebraic expressions and equations be used to model, analyze and solve mathematical situations? Can I explain how a line represents the infinite number of solutions to a linear equation with two variables? Can I explain how the point(s) of intersection of two graphs will represent the solution to the system of two linear equations because that/those point(s) are

solutions to both equations?

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Can I use algebraic reasoning (simple substitution) and the properties of real numbers to solve a system of linear equations? Can I use the graphs of two linear equations to estimate the solution of a system? Can I use mathematical reasoning to solve simple systems of linear equations? Can I solve real-world problems and mathematical problems dealing with systems of linear equations and interpret the solution in the context of the



1. Mathematical vocabulary: simultaneously, intersection, point of intersection, ordered pair, solution, parallel lines

I ☒ II ☐ III ☐ IV ☐ V ☐

2. Integer Rules I ☐ II ☐ III ☒ IV ☐ V ☐3. Interpret a graph/table. I ☐ II ☐ III ☐ IV ☒ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐I ☐ II ☐ III ☐ IV ☐ V ☐

Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.8bCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example,

3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear Equation: An equation that makes a straight line when graphed Variable: Letters or other symbols that represent unknown values Estimation: An approximation for a real value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve ☐ ☐ ☒ ☐ ☐ Estimate ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)






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I ☒ II ☐ III ☐ IV ☐ V ☐

2. What a linear equation looks like. I ☐ II ☒ III ☐ IV ☐ V ☐I ☐ II ☐ III ☐ IV ☐ V ☐I ☐ II ☐ III ☐ IV ☐ V ☐I ☐ II ☐ III ☐ IV ☐ V ☐

Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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Quarter Taught: Quarter 1 Quarter 2 Quarter 3 Quarter 4 Domain: Expressions and Equations Code: 8.EE.8cCluster: Analyze and solve linear equations and pairs of simultaneous linear equations.Standard: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine

whether the line through the first pair of points intersects the line through the second pair.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear Equation: An equation that makes a straight line when graphed Variable: Letters or other symbols that represent unknown values





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove








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I ☒ II ☐ III ☐ IV ☐ V ☐

2. What a linear equation looks like. I ☐ II ☒ III ☐ IV ☐ V ☐3. Interpret a graph. I ☐ II ☐ III ☐ IV ☒ V ☐4. Slope/Intercept Form. I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




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