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.

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

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

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.

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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

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)).

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

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

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

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

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.).

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

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

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

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

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.

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

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.

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

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.

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

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

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

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

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

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).

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).

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

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

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.

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

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

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

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

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.

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.

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.

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.

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

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

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).

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

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

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.

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.

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.

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

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

Correlation last revised: 9/16/2020

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