1: Number

1.A: Number Concepts

1.A.1: Demonstrate a knowledge of the interrelationship of the sets of numbers within the real number system.

1.A.1.1: Compare and order integers.

Rational Numbers, Opposites, and Absolute Values

1.A.1.2: Find and be able to model an understanding of common multiples, common factors, lowest common multiple and greatest common factor as they apply to whole numbers.

Finding Factors with Area Models
Operations with Radical Expressions

1.A.1.4: Distinguish between exact values and decimal approximations of square roots and cube roots.

Square Roots

1.A.2: Develop a number sense of powers with integral exponents and rational bases.

1.A.2.7: Explain and apply the exponent laws for powers with integral exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

1.B: Number Operations

1.B.1: Use a scientific calculator to solve problems involving real numbers.

1.B.1.8: Document and explain the calculator keying sequences used to perform:

1.B.1.8.a: square roots, cube roots

Square Roots

1.B.1.8.d: sine, cosine, tangent

Sine, Cosine, and Tangent Ratios

1.B.2: Decide which arithmetic operations can be used to solve a problem and then solve the problem.

1.B.2.9: Perform arithmetic operations with integers concretely, pictorially and symbolically.

Addition of Polynomials

1.B.2.11: Add, subtract, multiply and divide fractions concretely, pictorially and symbolically.

Fractions with Unlike Denominators

1.B.2.15: Use a variety of methods to solve problems, such as drawing a diagram, making a table, guessing and testing, using objects to model, making it simpler, looking for a pattern, using logical reasoning and working backward.

Biconditional Statements
Conditional Statements
Estimating Population Size

1.B.3: Illustrate and apply the concepts of rates, ratios, percentages and proportions to solve problems.

1.B.3.16: Understand the meaning of rate, ratio, percentage and proportion; and apply these concepts to solve problems.

Beam to Moon (Ratios and Proportions) - Metric
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Independent and Dependent Events
Part-to-part and Part-to-whole Ratios
Percent of Change
Real-Time Histogram

1.B.3.17: Express rates and ratios in equivalent forms.

Part-to-part and Part-to-whole Ratios

2: Patterns and Relations

2.A: Patterns

2.A.1: Generalize, design and justify mathematical procedures, using appropriate patterns and technology.

2.A.1.2: Given a first-degree equation, substitute numbers for variables and graph and analyze the relation.

Direct and Inverse Variation
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

2.A.1.3: Translate between an oral or written expression and an equivalent algebraic expression.

Using Algebraic Expressions

2.A.1.4: Write equivalent forms of algebraic expressions, or equations, with integral coefficients.

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

2.B: Variables and Equations

2.B.1: Generalize arithmetic operations from the set of rational numbers to the set of polynomials.

2.B.1.5: Identify constant terms, coefficients and variables in polynomial expressions.

Addition of Polynomials

2.B.1.8: Perform the operations of addition and subtraction on polynomial expressions.

Addition and Subtraction of Functions
Addition of Polynomials

2.B.1.10: Find the product of:

2.B.1.10.a: two monomials

Multiplying Exponential Expressions

2.B.1.10.c: two binomials.

Modeling the Factorization of x2+bx+c

2.B.1.11: Determine equivalent forms of algebraic expressions by identifying common factors.

Simplifying Algebraic Expressions II

2.B.1.12: Factor trinomials of the form ax² + bx + c, where a = 1, or of the form ax² + abx + ac.

Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

2.B.1.13: Factor polynomials of the form A² ? B², where A and B are both monomial expressions.

Factoring Special Products

2.B.1.14: Find the quotient when a polynomial is divided by a monomial.

Dividing Polynomials Using Synthetic Division

2.B.2: Solve and verify linear equations and inequalities in one variable.

2.B.2.15: Illustrate the solution process for a one-step, single variable, first-degree equation, using concrete materials or diagrams.

2.B.2.15.a: x + a = b

Solving Equations on the Number Line

2.B.2.15.b: x ? a = b

Solving Equations on the Number Line

2.B.2.15.c: ax = b

Solving Equations on the Number Line

2.B.2.15.d: x/a = b

Solving Equations on the Number Line

2.B.2.16: Solve and verify, using a variety of techniques, one-step linear equations of the form:

2.B.2.16.a: x + a = b

Solving Equations on the Number Line

2.B.2.16.b: x/a = b

Solving Equations on the Number Line

2.B.2.16.c: ax = b

Solving Equations on the Number Line

2.B.2.18: Solve and verify one- and two-step first-degree equations of the form:

2.B.2.18.a: x/a + b = c

Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

2.B.2.18.b: ax + b = c

Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

2.B.2.19: Solve and verify first-degree, single variable equations of the form:

2.B.2.19.a: ax = b + cx

Solving Algebraic Equations II

2.B.2.19.b: a(x + b) = c

Solving Algebraic Equations II

2.B.2.19.d: a(bx + c) = d(ex + f)

Solving Algebraic Equations II

3: Shape and Space

3.A: Measurement

3.A.1: Solve problems involving perimeter, area, surface area and volume.

3.A.1.1: Estimate, measure and calculate the surface area and volume of any right prism, cylinder, cone or pyramid.

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

3.A.1.2: Demonstrate concretely, pictorially and symbolically that many rectangles are possible for a given perimeter or a given area.

Area of Triangles

3.A.2: Solve problems, using right triangles.

3.A.2.3: Use the Pythagorean relationship to calculate the measure of the third side of a right triangle, given the other two sides, in 2-D applications.

Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

3.A.2.5: Explain the meaning of sine, cosine and tangent ratios in right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3.A.2.6: Calculate an unknown side or an unknown angle in a right triangle, using trigonometric ratios.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3.A.3: Specify conditions under which triangles may be similar, and use these conditions to solve problems.

3.A.3.8: Recognize when, and explain why, two triangles are similar; and use the properties of similar triangles to solve problems.

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

3.B: Transformations

3.B.1: Create and analyze patterns and designs, using symmetry, translation, rotation and reflection.

3.B.1.9: Draw designs, using ordered pairs, in all four quadrants of the coordinate grid.

Points in the Coordinate Plane

3.B.1.10: Draw and interpret scale diagrams, including:

3.B.1.10.a: enlargements

Dilations
Similar Figures

3.B.1.10.b: reductions.

Dilations
Similar Figures

4: Statistics and Probability

4.A: Data Analysis

4.A.1: Develop and implement a plan for the display and analysis of data.

4.A.1.1: Read and interpret graphs that are provided.

Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

4.A.2: Analyze experimental results expressed in two variables.

4.A.2.3: Interpret a scatterplot to determine if there is an apparent relationship.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

4.A.2.4: Determine, by inspection, the line of best fit from a scatterplot for an apparent linear relationship.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

4.A.2.5: Draw and justify conclusions from the line of best fit, by:

4.A.2.5.a: interpolation

Trends in Scatter Plots

4.A.2.5.b: extrapolation.

Trends in Scatter Plots

Correlation last revised: 9/24/2019

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