10.FP10.2.b Create and explain a pattern that describes the decimal form of an irrational number (e.g., write the digits from 0 to 9 in order, then put two of each digit – 0011223344 … – followed by three of each digit and so on).
10.FP10.2.c Approximate the value of a given irrational number and explain the strategy used.
10.FP10.3.c Explain the selection of measurement instruments (e.g., rulers, callipers, or tape measures) and the strategies used to determine linear measurements (e.g., circumference of a bottle, length of a curve, or perimeter of the base of an irregular 3-D object).
10.FP10.3.d Critique the statement "the length of the wall is greater in yards than it is in metres".
10.FP10.3.e Compare the size of SI and imperial units of measurement (linear, surface area, and volume) using referents.
10.FP10.3.f Develop, generalize, explain, and apply strategies and/or formulas for converting between units within the imperial or SI system of measurements, limited to linear, surface area, and volume units. (e.g., converting square feet to square yards or m³ to cm³).
10.FP10.3.h Verify, with explanation (such as unit analysis and/or mental mathematics and estimation), a conversion of units (within the SI or imperial systems of measurement or between them).
10.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.
10.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.
10.FP10.3.l Explain the relationship between the volumes of:
10.FP10.3.l.1 right cones and right cylinders with the same base and height
10.FP10.3.l.2 right pyramids and right prisms with the same base and height.
10.FP10.3.m Analyze a treaty for its inclusion of measurements, such as in the surveying for land entitlement, and create and solve situational questions that are relevant to self, family, and community.
10.FP10.4 Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
10.FP10.4.a Develop, generalize, explain, and apply relationships between the ratios of side lengths and angle sizes in similar right triangles.
10.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.
10.FP10.5 Demonstrate understanding of the multiplication and factoring of polynomial expressions (concretely, pictorially, and symbolically) including:
10 multiplying of monomials, binomials, and trinomials
10 common factors
10 trinomial factoring
10 relating multiplication and factoring of polynomials.
10.FP10.5.a Develop, generalize, explain, and apply a strategy of symbolic manipulation to determine the product of two binomials by analyzing concrete and pictorial models.
10.FP10.5.c Develop (concretely, pictorially, or symbolically), explain, and apply understanding of how multiplication of binomials is related to the multiplication of two-digit numbers (e.g., use algebra tiles and base ten blocks to compare and relate the products of (x+1)(3x+2) and (11)(32)).
10.FP10.5.d Develop, generalize, explain, and apply a strategy for multiplying polynomials.
10.FP10.5.e Analyze the multiplication of two polynomials for errors and explain the strategy used.
10.FP10.5.f Explain why evaluating at a value for the variable in a product of polynomials in factored form should give the same solution as evaluating the expanded and simplified form of the polynomial product at the same value (e.g., explain why x²+5x+6 should have the same value as (x+3)(x+2) when evaluated at x = -4).
10.FP10.5.g Explain, using concrete or visual models, how the processes of factoring and multiplication are related.
10.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)).
10.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).
10.FP10.8 Demonstrate understanding of linear relations including:
10 representing in words, ordered pairs, tables of values, graphs, function notation, and equations
10 determining characteristics including intercepts, slope, domain, and range
10 relating different equation forms to each other and to graphs.
10.FP10.8.a Critique the statement "any straight line is the graph of a linear function".
10.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).
10.FP10.8.c Analyze situations to identify, with justification, the independent and a dependent variable.
10.FP10.8.q Determine the related range value, given a domain value for a linear function (e.g., if f(x) = 3x – 2, determine f(–1)) and explain what the resulting value tells about the linear function.
10.FP10.8.r Determine the related domain value, given a range value for a linear function (e.g., if g(t) = 7 + t, determine t so that g(t) = 15) and explain what the resulting value tells about the linear function.
10.FP10.8.s Explain why a linear function would never have a term of x2 when in simplified form.
10.FP10.9 Demonstrate understanding of the writing and application of equations of linear relations, given:
10 a graph of a relation
10 a point that satisfies a relation and the slope of the relation
10 two distinct points that satisfy a relation
10 a point that satisfies the relation and the equation of a line parallel or perpendicular to the relation.
10.FP10.9.a Develop, generalize, explain, and apply strategies for writing an equation for a linear relation using data obtained from a graph.
10.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).
10.FP10.9.d Graph and write equations for linear data generated within an experiment or collected from a situation.
10.FP10.10 Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
10.FP10.10.a Match, with justification, situations and systems of linear equations.
10.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.