1: Square Roots and Surface Area

1.9N: Number

1.9N5: Determine the square root of positive rational numbers that are perfect squares.

1.9N5.1: Determine whether or not a given rational number is a square number and explain the reasoning.

Square Roots

1.9N5.2: Determine the square root of a given positive rational number that is a perfect square.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

1.9N5.4: Determine a positive rational number given the square root of that positive rational number.

Operations with Radical Expressions
Square Roots

1.9N6: Determine an approximate square root of positive rational numbers that are non-perfect squares.

1.9N6.1: Estimate the square root of a given rational number that is not a perfect square using the roots of perfect squares as benchmarks.

Square Roots

1.9N6.2: Determine an approximate square root of a given rational number that is not a perfect square using technology, e.g, calculator, computer.

Square Roots

1.9N6.3: Explain why the square root of a given rational number as shown on a calculator may be an approximation.

Square Roots

1.9SS: Shape and Space (3-D Objects and 2-D Shapes)

1.9SS2: Determine the surface area of composite 3-D objects to solve problems.

1.9SS2.1: Determine the overlap in a given concrete composite 3-D object, and explain its effect on determining the surface area (limited to right cylinders, right rectangular prisms and right triangular prisms).

Surface and Lateral Areas of Prisms and Cylinders

1.9SS2.2: Determine the surface area of a given concrete composite 3-D object (limited to right cylinders, right rectangular prisms and right triangular prisms).

Surface and Lateral Areas of Prisms and Cylinders

1.9SS2.3: Solve a given problem involving surface area.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

2: Powers and Exponent Laws

2.9N: Number

2.9N1: Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by:

2.9N1.a: representing repeated multiplication using powers

Exponents and Power Rules

2.9N1.2: Explain, using repeated multiplication, the difference between two given powers in which the exponent and base are interchanged, e.g., 10³ and 3 to the tenth power.

Exponents and Power Rules

2.9N1.3: Express a given power as a repeated multiplication.

Exponents and Power Rules

2.9N1.4: Express a given repeated multiplication as a power.

Exponents and Power Rules

2.9N2: Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents:

2.9N2.a: (a to the m power)(a to the n power) = a to the (m+n) power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.b: a to the m power ÷ a to the n power = a to the (m-n) power, m > n

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.c: (a to the m power) to the n power = a to the mn power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.d: (ab) to the m power = a to the m power x b to the m power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.e: (a/b) to the n power = a to the n power/b to the n power, b ≠ 0.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.1: Explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents:

2.9N2.1.a: (a to the m power)(a to the n power) = a to the (m+n) power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.1.b: a to the m power ÷ a to the n power = a to the (m-n) power, m > n

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.1.c: (a to the m power) to the n power = a to the mn power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.1.d: (ab) to the m power = a to the m power x b to the m power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

2.9N2.1.e: (a/b) to the n power = a to the n power/b to the n power, b ≠ 0.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

3: Rational Numbers

3.9N: Number

3.9N3: Demonstrate an understanding of rational numbers by:

3.9N3.a: comparing and ordering rational numbers

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

3.9N3.b: solving problems that involve arithmetic operations on rational numbers.

Estimating Population Size

3.9N3.1: Order a given set of rational numbers, in fraction and decimal form, by placing them on a number line, e.g., 3/5, - 0.666..., 0.5, - 5/8.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

3.9N3.2: Identify a rational number that is between two given rational numbers.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

3.9N3.3: Solve a given problem involving operations on rational numbers in fraction form and decimal form.

Fractions with Unlike Denominators

4: Linear Relations

4.1PR: Patterns and Relations (Patterns)

4.9PR1: Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution.

4.9PR1.2: Write a linear equation to represent a given context.

Linear Inequalities in Two Variables
Modeling One-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

4.9PR1.3: Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table.

Direct and Inverse Variation
Points, Lines, and Equations

4.9PR1.5: Describe a context for a given linear equation.

Absolute Value with Linear Functions

4.9PR2: Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.

4.9PR2.2: Graph a given linear relation, including horizontal and vertical lines.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

4.9PR2.3: Match given equations of linear relations with their corresponding graphs.

Absolute Value with Linear Functions
Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

4.9PR2.6: Solve a given problem by graphing a linear relation and analyzing the graph.

Absolute Value with Linear Functions
Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

5: Polynomials

5.1PR: Patterns and Relations (Variables and Equations)

5.9PR5: Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).

5.9PR5.1: Identify the variables, degree, number of terms and coefficients, including the constant term, of a given simplified polynomial expression.

Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Graphs of Polynomial Functions

5.9PR5.4: Match equivalent polynomial expressions given in simplified form.

Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

5.9PR6: Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2).

5.9PR6.1: Identify equivalent polynomial expressions from a given set of polynomial expressions, including pictorial and symbolic representations.

Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

5.9PR6.4: Apply a personal strategy for addition and subtraction of given polynomial expressions, and record the process symbolically.

Addition and Subtraction of Functions
Addition of Polynomials

5.9PR7: Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially and symbolically.

5.9PR7.3: Apply a personal strategy for multiplication and division of a given polynomial expression by a given monomial.

Dividing Polynomials Using Synthetic Division

5.9PR7.4: Provide examples of equivalent polynomial expressions.

Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6: Linear Equations and Inequalities

6.1PR: Patterns and Relations (Variables and Equations)

6.9PR3: Model and solve problems using linear equations of the form:

6.9PR3.a: ax = b

Solving Algebraic Equations II
Solving Equations on the Number Line

6.9PR3.b: x/a = b, a ≠ 0

Solving Algebraic Equations II
Solving Equations on the Number Line

6.9PR3.c: ax + b = c

Solving Algebraic Equations II

6.9PR3.d: x/a + b= c, a ≠ 0

Solving Algebraic Equations II

6.9PR3.f: a(x + b) = c

Solving Algebraic Equations II

6.9PR3.i: a/x = b, x ≠ 0 where a, b, c, d, e and f are rational numbers.

Solving Algebraic Equations II
Solving Equations on the Number Line

6.9PR3.3: Solve a given linear equation symbolically.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

6.9PR3.5: Represent a given problem using a linear equation.

Solving Equations by Graphing Each Side

6.9PR3.6: Solve a given problem using a linear equation and record the process.

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

6.9PR4: Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

6.9PR4.1: Translate a given problem into a single variable linear inequality using the symbols ≥, >, < or ≤.

Systems of Linear Inequalities (Slope-intercept form)

6.9PR4.2: Determine if a given rational number is a possible solution of a given linear inequality.

Solving Linear Inequalities in One Variable

6.9PR4.3: Graph the solution of a given linear inequality on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

6.9PR4.6: Solve a given linear inequality algebraically and explain the process orally or in written form.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

6.9PR4.7: Compare and explain the process for solving a given linear equation to the process for solving a given linear inequality.

Linear Inequalities in Two Variables

6.9PR4.8: Compare and explain the solution of a given linear equation to the solution of a given linear inequality.

Linear Inequalities in Two Variables

6.9PR4.10: Solve a given problem involving a single variable linear inequality and graph the solution.

Exploring Linear Inequalities in One Variable
Rational Numbers, Opposites, and Absolute Values

7: Similarity and Transformations

7.9SS: Shape and Space (3-D Objects and 2-D Shapes)

7.9SS3: Demonstrate an understanding of similarity of polygons.

7.9SS3.1: Determine if the polygons in a given set are similar and explain the reasoning.

Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

7.9SS3.2: Draw a polygon similar to a given polygon and explain why the two are similar.

Similar Figures

7.9SS3.3: Solve a given problem using the properties of similar polygons.

Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

7.9SS4.5: Solve a given problem that involves a scale diagram by applying the properties of similar triangles.

Perimeters and Areas of Similar Figures
Similar Figures

7.9SS: Shape and Space (Transformations)

7.9SS4: Draw and interpret scale diagrams of 2-D shapes.

7.9SS4.1: Identify an example in print and electronic media, e.g., newspapers, the Internet, of a scale diagram and interpret the scale factor.

Similar Figures

7.9SS4.2: Draw a diagram to scale that represents an enlargement or reduction of a given 2-D shape.

Dilations
Similar Figures

7.9SS4.3: Determine the scale factor for a given diagram drawn to scale.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

7.9SS4.4: Determine if a given diagram is proportional to the original 2-D shape and, if it is, state the scale factor.

Dilations
Perimeters and Areas of Similar Figures
Similar Figures

7.9SS5: Demonstrate an understanding of line and rotation symmetry.

7.9SS5.2: Complete a 2-D shape or design given one half of the shape or design and a line of symmetry.

Holiday Snowflake Designer

8: Circle Geometry

8.9SS: Shape and Space (Measurement)

8.9SS1: Solve problems and justify the solution strategy using the following circle properties:

8.9SS1.b: the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc

Chords and Arcs
Inscribed Angles

8.9SS1.2: Solve a given problem involving application of one or more of the circle properties.

Chords and Arcs
Circles
Inscribed Angles

8.9SS1.4: Explain the relationship between the measure of the central angle and the inscribed angle subtended by the same arc.

Chords and Arcs
Inscribed Angles

8.9SS1.5: Determine the measure of a given angle inscribed in a semicircle using the circle properties.

Inscribed Angles

8.9SS1.6: Explain the relationship between inscribed angles subtended by the same arc.

Chords and Arcs
Inscribed Angles

9: Probability and Statistics

9.9SP: Statistics and Probability (Data Analysis)

9.9SP1: Describe the effect of:

9.9SP1.c: ethics

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP1.d: cost

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP1.e: time and timing

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP1.f: privacy

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP1.g: cultural sensitivity on the collection of data.

Stem-and-Leaf Plots

9.9SP1.1: Analyze a given case study of data collection, and identify potential problems related to bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity.

Real-Time Histogram

9.9SP1.2: Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity may infl uence the data.

Polling: Neighborhood
Populations and Samples

9.9SP2: Select and defend the choice of using either a population or a sample of a population to answer a question.

9.9SP2.1: Identify whether a given situation represents the use of a sample or a population.

Polling: City
Polling: Neighborhood
Populations and Samples

9.9SP2.2: Provide an example of a situation in which a population may be used to answer a question and justify the choice.

Polling: Neighborhood

9.9SP2.3: Provide an example of a question where a limitation precludes the use of a population and describe the limitation, e.g., too costly, not enough time, limited resources.

Polling: Neighborhood

9.9SP3: Develop and implement a project plan for the collection, display and analysis of data by:

9.9SP3.a: formulating a question for investigation

Correlation
Describing Data Using Statistics
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP3.b: choosing a data collection method that includes social considerations

Box-and-Whisker Plots
Describing Data Using Statistics

9.9SP3.c: selecting a population or a sample

Polling: City
Polling: Neighborhood

9.9SP3.d: collecting the data

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP3.e: displaying the collected data in an appropriate manner

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

9.9SP3.f: drawing conclusions to answer the question.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Stem-and-Leaf Plots

9.9SP3.1: Create a rubric to assess a project that includes the assessment of:

9.9SP3.1.a: a question for investigation

Correlation
Describing Data Using Statistics
Real-Time Histogram

9.9SP3.1.b: the choice of a data collection method that includes social considerations

Describing Data Using Statistics

9.9SP3.1.c: the selection of a population or a sample and justifying the choice

Polling: City
Polling: Neighborhood
Populations and Samples

9.9SP3.1.d: the display of the collected data

Correlation
Describing Data Using Statistics
Stem-and-Leaf Plots

9.9SP3.1.e: the conclusions to answer the question.

Conditional Statements

9.9SP3.2: Develop a project plan that describes:

9.9SP3.2.a: a question for investigation

Correlation
Describing Data Using Statistics
Real-Time Histogram

9.9SP3.2.b: the method of data collection that includes social considerations

Describing Data Using Statistics

9.9SP3.2.c: the method for selecting a population or a sample

Polling: City
Polling: Neighborhood
Populations and Samples

9.9SP3.2.d: the method to be used for collection of the data

Describing Data Using Statistics

9.9SP3.2.e: the methods for analysis and display of the data.

Polling: City
Real-Time Histogram

9.9SP: Statistics and Probability (Chance and Uncertainty)

9.9SP4: Demonstrate an understanding of the role of probability in society.

9.9SP4.1: Provide an example from print and electronic media, e.g., newspapers, the Internet, where probability is used.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability

Correlation last revised: 9/24/2019

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