### 1: Number

#### 1.A: Number Concepts

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.

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.

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.

#### 1.B: Number Operations

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

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.

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

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

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.

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.

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

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

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

### 2: Patterns and Relations

#### 2.A: Patterns

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.

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.

#### 2.B: Variables and Equations

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.

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.

2.B.1.10: Find the product of:

2.B.1.10.a: two monomials

2.B.1.10.c: two binomials.

2.B.1.11: Determine equivalent forms of algebraic expressions by identifying common factors.

2.B.1.12: Factor trinomials of the form ax² + bx + c, where a = 1, or of the form ax² + abx + ac.

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.

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

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

2.B.2.15.c: ax = b

2.B.2.15.d: x/a = b

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

2.B.2.16.b: x/a = b

2.B.2.16.c: ax = b

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

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

2.B.2.18.b: ax + b = c

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

2.B.2.19: Solve and verify first-degree, single variable equations of the form:

2.B.2.19.a: ax = b + cx

2.B.2.19.b: a(x + b) = c

2.B.2.19.d: a(bx + c) = d(ex + f)

### 3: Shape and Space

#### 3.A: Measurement

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.

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.

3.A.2.5: Explain the meaning of sine, cosine and tangent ratios in right triangles.

3.A.2.6: Calculate an unknown side or an unknown angle in a right triangle, using trigonometric ratios.

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.

#### 3.B: Transformations

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.

3.B.1.10: Draw and interpret scale diagrams, including:

3.B.1.10.a: enlargements

3.B.1.10.b: reductions.

### 4: Statistics and Probability

#### 4.A: Data Analysis

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.

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.

4.A.2.4: Determine, by inspection, the line of best fit from a scatterplot for an apparent linear relationship.

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

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.