Unit A: Mathematical Reasoning

Comments

Generalize, design, and justify mathematical procedures, using appropriate patterns, models, and technology

The intention is to integrate this unit throughout the course. Unit A provides time to encourage students to reason mathematically using a variety of activities and tasks.

- use logic and divergent thinking to present mathematical arguments in solving problems (A-1)

Use a scientific calculator or a computer to solve problems involving rational numbers

- document and explain calculator keying sequences used to perform calculations involving rational numbers (A-2)

Outcome A-2 has been designated in red and as such remains part of the course. All students are to be exposed to this outcome but mastery is not required of all students. Teachers should be guided by the time available in dealing with explanations of calculator keying sequences.

Outcome J-4 is boxed in blue and has been moved from Unit J. Emphasis is to be on solving problems in context. Problems should require the use of integers and decimal fractions more than common fractions.

Unit B: Statistics

Comments

Collect and analyze experimental results expressed in two variables, using technology, as required

No changes in this unit.

- assess the strengths, weaknesses, and biases of samples and data collection methods (B-1)

- critique ways in which statistical information and conclusions are presented by the media and other sources (B-2)

- create scatterplots for discrete and continuous variables (B-3)

- interpret a scatterplot to determine if there is an apparent relationship (B-4)

- determine the line of best fit from a scatterplot for an apparent linear relationship, by

• inspection
• using technology (equations are not expected) (B-5)

- draw and justify conclusions from the line of best fit (B-6)

- design, conduct, and report on an experiment to investigate a relationship between two variables (B-7)

Unit C: Polynomials

Comments

Explain and illustrate the structure and the interrelationship of the sets of numbers within the rational number system

- give examples of numbers that satisfy the conditions of natural, whole, integral, and rational numbers, and show that these numbers comprise the rational number system (C-1)

- describe, orally and in writing, whether or not a number is rational (C-2)

Generalize arithmetic operations from the set of rational numbers to the set of polynomial numbers

This part of Unit C is intended to emphasize a conceptual understanding of algebraic operations using simple expressions. More complex expressions, involving powers with exponents other than one, are dealt with in Unit H.

- identify constant terms, coefficients, and variables in polynomial expressions (C-3)

- represent and justify the addition and subtraction of polynomial expressions, using concrete materials and diagrams (C-5)

Outcomes C-5 and C-7 are shown in green. These outcomes deal with the use of concrete materials or manipulatives. They will be identified under "Suggestions for Instruction" rather than "Prescribed Learning Outcomes" in future revisions of Senior 1 Mathematics (10F) documents. Teachers are encouraged to use concrete materials as part of their methodology but are not expected to have all students master the use of concrete materials for testing purposes. Students should be permitted to use concrete materials on all tests and exams in Senior 1 Mathematics (10F).

- perform the operations of addition and subtraction on polynomial expressions (C-6)

- represent multiplication of two monomials, and of a monomial and a polynomial, using concrete materials and diagrams (C-7)

- find the product of two monomials, and of a monomial and a polynomial (C-8)

- evaluate polynomial expressions, given the value(s) of the variable(s) (C-10)

Generalize, design, and justify mathematical procedures, using appropriate patterns, models, and technology

- model situations that can be represented by first-degree equations (C-4)

- write equivalent forms of algebraic expressions, or equations with integral/rational coefficients (C-9)

Unit D: Spatial Geometry

Comments

Use spatial problem solving in building, describing and analyzing geometric shapes

Unit D is in purple and provides students/teachers with a choice. All students are required to complete one unit emphasizing spatial reasoning. The choice is between Unit D: Spatial Geometry and Unit K: Transformational Geometry.

- recognize and draw the locus (set of points) in solving practical problems (D-1)

- draw the plan and elevations of a 3-D object from sketches and models (D-2)

- sketch or build a 3-D object, given its plan and elevation views (D-3)

Unit E: Linear Relations

Comments

Solve and verify linear equations and inequalities in one variable

- illustrate the solution process for a first-degree, single-variable equation, using concrete materials or diagrams (E-1)

Outcome E-1 is shown in green. This outcome deals with the use of concrete materials or manipulatives. It will be identified under "Suggestions for Instruction" rather than "Prescribed Learning Outcomes" in future revisions of Senior 1 Mathematics (10F) documents. Teachers are encouraged to use concrete materials as part of their methodology but are not expected to have all students master the use of concrete materials for testing purposes. Students should be permitted to use concrete materials on all tests and exams in Senior 1 Mathematics (10F).

- solve and verify first-degree, single-variable equations of forms such as:

where a, b, c, d, e, and f are all rational numbers (with a focus on integers), and use equations of this type to model and solve problem situations (E-2)

- solve, algebraically, first-degree inequalities with one variable, display the solutions on a number line, and test the solutions (E-3)

Unit F: Similarity and Congruence

Comments

- recognize when, and explain why, two triangles are congruent, and use the properties of congruent triangles to solve problems (F-1)

- relate congruence to similarity in the context of triangles (F-3)

- determine equivalent forms of algebraic expressions by identifying common factors and by factoring trinomials of the form x²+bx+c (H-4)

- represent multiplication, division, and factoring of monomials, binomials and trinomials of the form x²+bx+c, using concrete materials and diagrams (H-5)

Unit J: Measurement

Comments

Describe the effects of dimension changes in related 2-D shapes and 3-D objects in solving problems involving area, perimeter, surface area, and volume

- calculate area and perimeter to solve design problems in two dimensions (J-1)

Outcomes J-1, J-2, and J-3 are to be deleted. The geometric concepts of perimeter, area, and volume are dealt with in previous grades. Substitution into area and volume formulas should be dealt with in H-10.

Unit K: Transformational Geometry

Apply coordinate geometry and pattern recognition to predict the effects of translations, rotations, reflections, and dilations on 1-D lines and 2-D shapes