FP10.1: Demonstrate understanding of factors of whole numbers by determining the: prime factors, greatest common factor, least common multiple, principal square root, and cube root.

FP10.1.a: Develop, generalize, explain, and apply strategies for determining the greatest common factors or least common multiples.

Finding Factors with Area Models

FP10.1.c: Determine the prime factors of a whole number and explain the strategies used.

Finding Factors with Area Models

FP10.1.d: Analyze concretely, pictorially, or numerically and explain whether a whole number is a perfect square or a perfect cube.

Operations with Radical Expressions
Square Roots

FP10.1.e: Develop, generalize, explain, and apply strategies for determining the square root of a perfect square and the cube root of a perfect cube.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

FP10.1.g: Solve problems that involve prime factors, greatest common factors, least common multiples, square roots, or cube roots.

Finding Factors with Area Models
Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

FP10.2: Demonstrate understanding of irrational numbers in both radical (including mixed radical) and exponent forms through representing, identifying, simplifying, ordering, relating to rational numbers, and applying exponent laws.

FP10.2.d: Order a set of Real numbers, including rational and irrational numbers, on a number line and explain the strategies used.

Comparing and Ordering Decimals

FP10.2.e: Express a radical as a mixed radical in simplest form (limited to numerical radicands).

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

FP10.2.f: Express a mixed radical as an entire radical (limited to numerical radicands).

Square Roots

FP10.2.g: Explain, using examples, how changing the value of the index of a radical impacts the value of the radical.

Simplifying Radical Expressions

FP10.2.k: Extend and apply the exponent laws to powers with rational exponents (limited to expressions with rational and variable bases and integral and rational exponents):

FP10.2.k.1: a to the m power times a to the n power = a to the (m+n) power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

FP10.2.k.2: a to the m power/ a to the n power = a to the (m-n) power, where a is not to equal 0

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

FP10.2.k.3: a to the m power to the n power = a to the mn power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

FP10.2.k.4: ab to the m power = a to the m power times b to the n power

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

FP10.2.k.5: a/b to the n power = a to the n power/b to the n power, where b is not equal to 0

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

FP10.2.l: Analyze simplifications of expressions involving radicals and/or powers for errors.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions

FP10.3: Demonstrate understanding of SI and imperial units of measurement including: linear measurement; surface are of sphers, right cones, cylinders, prisms, and pyramids; volume of spheres, right cones, cylinders, prisms, and pyramids; relationships between and within measurement systems.

FP10.3.i: Analyze 3-D objects, their nets, and labelled diagrams to develop and generalize strategies and/or formulas for determining the surface area and volume of right cones, cylinders, prisms, and pyramids and composite objects.

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

FP10.3.j: Solve, using personal strategies and/or formulas, situational questions related to surface area, volume, and dimensions of right cones, cylinders, prisms, and pyramids, and composite 3-D objects.

Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

FP10.4: Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

FP10.4.a: Develop, generalize, explain, and apply relationships between the ratios of side lengths and angle sizes in similar right triangles.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

FP10.4.c: Solve problems, with or without the use of technology, involving one or more right triangles by applying primary trigonometric ratios and/or the Pythagorean Theorem.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

FP10.4.d: Create and solve problems that involve indirect and direct linear measurements by using the primary trigonometric ratios, the Pythagorean Theorem, and measurement instruments such as a clinometer or metre stick.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

FP10.5: Demonstrate understanding of the multiplication and factoring of polynomial expressions (concretely, pictorially, and symbolically) including: multiplying of monomials, binomials, and polynomials; common factors; trinomial factoring; and relating multiplication and factoring of polynomials.

FP10.5.d: Develop, generalize, explain, and apply a strategy for multiplying polynomials.

Modeling the Factorization of x²+bx+c

FP10.5.g: Explain, using concrete or visual models, how the processes of factoring and multiplication are related.

Factoring Special Products

FP10.5.h: Develop (using concrete materials, pictures, or visualization), generalize, explain, and apply strategies for factoring and verifying the factors of binomials, including numerical binomial expressions (e.g., 32+20=4(8+5)).

Factoring Special Products

FP10.5.i: Sort a set of polynomials according to the type(s) of factoring that could be applied to them.

Modeling the Factorization of x²+bx+c

FP10.5.j: Explain and apply strategies for determining whether given factors are those of a given polynomial.

Polynomials and Linear Factors
Quadratics in Factored Form

FP10.5.k: Develop, generalize, explain, and apply strategies for factoring a trinomial.

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

FP10.5.m: Explain how differences of squares can be factored using trinomial factoring strategies.

Factoring Special Products

FP10.6: Expand and apply understanding of relations and functions including: relating data, graphs, and situations; analyzing and interpreting; and distinguishing between relations and functions.

FP10.6.a: Provide and discuss examples of different types of relations relevant to one?s life, family, or community (e.g., person A is the mother of person B, or person A is a brother of person B.).

Linear Functions

FP10.6.b: Explain, by providing situational and graphical examples, the relationship between the categories of ?relations? and ?functions?.

Introduction to Functions
Linear Functions

FP10.6.e: Explain why data points should or should not be connected on the graph for a situation.

Absolute Value with Linear Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Slope

FP10.6.f: Provide and explain examples of situations that could be represented by a given graph.

Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form

FP10.6.g: Sketch a graph to represent a situation presented orally or in writing.

Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form

FP10.6.h: Determine, and express in a variety of ways, the domain and range of a graph, a set of ordered pairs, or a table of values.

Introduction to Functions
Logarithmic Functions
Radical Functions

FP10.6.i: Generalize, explain, and apply strategies for determining whether a set of ordered pairs or a graph represents a function.

Introduction to Functions
Linear Functions

FP10.7: Demonstrate, with and without the use of technology, understanding of slope (concretely, pictorially, and symbolically) with respect to: line segments and lines; rate of change; ratio of rise to run; parallel lines; and perpendicular lines.

FP10.7.a: Provide examples, relevant to self, family, or community, to explain the importance of slope.

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope-Intercept Form of a Line

FP10.7.b: Illustrate and explain, using examples relevant to self, family, or community, how slope is rate of change.

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope-Intercept Form of a Line

FP10.7.d: Classify lines in a given set as having positive or negative slopes, and explain how the sign of the slope affects the interpretation or meaning of the slope.

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

FP10.7.e: Explain the meaning of zero or slopes with no Real value.

Slope-Intercept Form of a Line

FP10.7.f: Explain why the slope of a straight line can be determined by using any two distinct points on that line.

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

FP10.7.g: Draw a line given its slope and a point on the line.

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.7.h: Determine another point on a line, given the slope and a point on the line.

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

FP10.7.i: Generalize, explain, and apply strategies for determining whether two lines are parallel or perpendicular.

Cat and Mouse (Modeling with Linear Systems) - Metric

FP10.7.j: Apply knowledge and skills related to slope to solve situational questions relevant to self, family, and community (e.g., determine the slopes of the poles in a tepee and the impact of changing the slopes on the dimensions and strength of the tepee).

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope-Intercept Form of a Line

FP10.8: Demonstrate understanding of linear relations including: representing in words, ordered pairs, trables of values, graphs, funciton notation, and equations; determining characteristics including intercepts, slope, domain and range; relating different equation forms to each other and to graphs.

FP10.8.b: Explain, using examples, the impact of the domain of a linear function on the graph of the function (e.g., if the domain is not all Real numbers, then the graph will not show a solid line).

Exponential Functions

FP10.8.d: Analyze situations, graphs, tables of values, equations, or sets of ordered pairs to determine if the relationship described is linear.

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side

FP10.8.e: Match corresponding types of representations of linear relations (e.g., situations, graphs, tables of values, equations, and sets of ordered pairs).

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side

FP10.8.f: Develop, generalize, explain, and apply strategies for determining the intercepts (as values and ordered pairs) of a linear relation from its graph.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.8.g: Determine the slope, domain, and range of the graph of a linear relation.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Compound Interest
Exponential Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

FP10.8.h: Sketch examples of linear relations to demonstrate the number of x or y intercepts possible for any line.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.8.i: Match, with explanation, slopes and y-intercepts to graphs of linear relations.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Compound Interest
Exponential Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side

FP10.8.j: Solve a situational question that involves the intercepts, slope, domain, or range of a linear relation.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems) - Metric
Compound Interest
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

FP10.8.k: Express the equation of a linear relation in different forms (including the slope-intercept or general form) and compare the graphs of the linear relations.

Absolute Value with Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

FP10.8.l: Generalize, explain, and apply strategies for drawing or sketching the graph of a linear relation in slope-intercept, general, or slope-point form, or function notation.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.8.m: Graph, with and without technology, a linear relation given in slope-intercept, general, or slope-point form, and explain the strategy used to create the graph.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.9: Demonstrate understanding of the writing and application of equations of linear relations, given a graph of a relation; a point that satisfies a relation and the slope of the relation; two distinct points that satisfy a relation; and a point that satisfies the relation and the equation of a line parallel or perpendicular to the relation.

FP10.9.a: Develop, generalize, explain, and apply strategies for writing an equation for a linear relation using data obtained from a graph.

Absolute Value with Linear Functions
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

FP10.9.b: Develop, generalize, explain, and apply strategies for writing an equation for a linear relation when given:

FP10.9.b.1: a point that satisfies the relation and the slope of the relation

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.9.b.2: two points that satisfy the relation

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.9.c: Compare and critique the structure and purposes of different forms of linear relations, including y=mx+b, Ax+By=C, and y-y1=m(x-x1) (e.g., there is no way to write a vertical linear relation in the form y = mx+b).

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

FP10.9.d: Graph and write equations for linear data generated within an experiment or collected from a situation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

FP10.9.e: Apply knowledge and skills of linear relations and their equations to solve situational questions.

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

FP10.10: Solve problems that involve systems of linear equations in two variables, graphically and algebraically.

FP10.10.a: Match, with justification, situations and systems of linear equations.

Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

FP10.10.b: Sketch, describe, provide and explain situational examples of the different ways that the graphs of two linear equations (two variables) can intersect and explain the meaning of the points of intersection.

Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

FP10.10.c: Develop, generalize, explain, and apply strategies for solving systems of equations graphically, with and without the use of technology and verify the solutions.

Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

FP10.10.d: Develop, generalize, explain, and apply strategies, including verification of solutions, for solving systems of equations algebraically.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

FP10.10.f: Apply knowledge and skills with systems of linear equations to solve situational questions.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)