Program of Studies

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.

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.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

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.

1.B.2.10: Illustrate and explain the order of operations.

Equivalent Algebraic Expressions I

Order of Operations

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

Fractions with Unlike Denominators

1.B.2.13: Estimate and calculate operations on rational numbers.

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

Proportions and Common Multipliers

Real-Time Histogram

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

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

1.B.4: Apply exponent laws to solve problems.

1.B.4.18: Use exponent laws to evaluate expressions with numerical bases.

Dividing Exponential Expressions

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.

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 *ax*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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.

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

Addition and Subtraction of Functions

Addition of Polynomials

2.B.1.9: Represent multiplication, division and factoring of monomials, binomials and trinomials of the form x² + bx + c, using concrete materials and diagrams.

Modeling the Factorization of *x*^{2}+*bx*+*c*

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 *x*^{2}+*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 *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

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

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

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

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

Modeling and Solving Two-Step Equations

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.1.17: Illustrate the solution process for a two-step, single variable, first-degree equation, using concrete materials or diagrams.

Modeling and Solving Two-Step Equations

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

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

2.B.2.18.c: where a, b and c are integers.

Modeling and 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.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.

Pyramids and Cones

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.

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.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Similar Figures

Similarity in Right Triangles

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

3.B.1.10.b: reductions.

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.

Correlation

Histograms

Polling: City

Real-Time Histogram

Stem-and-Leaf Plots

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

4.A.2.2: Create scatterplots for discrete and continuous 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

Trends in Scatter Plots

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

4.A.2.5.a: interpolation

4.A.2.5.b: extrapolation.

Correlation last revised: 9/16/2020

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