### 1: Square Roots and Surface Area

#### 1.9N: Number

1.9N5: Determine the square root of positive rational numbers that are perfect squares.

1.9N5.1: Determine whether or not a given rational number is a square number and explain the reasoning.

1.9N5.2: Determine the square root of a given positive rational number that is a perfect square.

1.9N5.4: Determine a positive rational number given the square root of that positive rational number.

1.9N6: Determine an approximate square root of positive rational numbers that are non-perfect squares.

1.9N6.1: Estimate the square root of a given rational number that is not a perfect square using the roots of perfect squares as benchmarks.

1.9N6.2: Determine an approximate square root of a given rational number that is not a perfect square using technology, e.g, calculator, computer.

1.9N6.3: Explain why the square root of a given rational number as shown on a calculator may be an approximation.

#### 1.9SS: Shape and Space (3-D Objects and 2-D Shapes)

1.9SS2: Determine the surface area of composite 3-D objects to solve problems.

1.9SS2.1: Determine the overlap in a given concrete composite 3-D object, and explain its effect on determining the surface area (limited to right cylinders, right rectangular prisms and right triangular prisms).

1.9SS2.2: Determine the surface area of a given concrete composite 3-D object (limited to right cylinders, right rectangular prisms and right triangular prisms).

1.9SS2.3: Solve a given problem involving surface area.

### 2: Powers and Exponent Laws

#### 2.9N: Number

2.9N1: Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by:

2.9N1.a: representing repeated multiplication using powers

2.9N1.2: Explain, using repeated multiplication, the difference between two given powers in which the exponent and base are interchanged, e.g., 10³ and 3 to the tenth power.

2.9N1.3: Express a given power as a repeated multiplication.

2.9N1.4: Express a given repeated multiplication as a power.

2.9N2: Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents:

2.9N2.a: (a to the m power)(a to the n power) = a to the (m+n) power

2.9N2.b: a to the m power ÷ a to the n power = a to the (m-n) power, m > n

2.9N2.c: (a to the m power) to the n power = a to the mn power

2.9N2.d: (ab) to the m power = a to the m power x b to the m power

2.9N2.e: (a/b) to the n power = a to the n power/b to the n power, b ≠ 0.

2.9N2.1: Explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents:

2.9N2.1.a: (a to the m power)(a to the n power) = a to the (m+n) power

2.9N2.1.b: a to the m power ÷ a to the n power = a to the (m-n) power, m > n

2.9N2.1.c: (a to the m power) to the n power = a to the mn power

2.9N2.1.d: (ab) to the m power = a to the m power x b to the m power

2.9N2.1.e: (a/b) to the n power = a to the n power/b to the n power, b ≠ 0.

### 3: Rational Numbers

#### 3.9N: Number

3.9N3: Demonstrate an understanding of rational numbers by:

3.9N3.a: comparing and ordering rational numbers

3.9N3.b: solving problems that involve arithmetic operations on rational numbers.

3.9N3.1: Order a given set of rational numbers, in fraction and decimal form, by placing them on a number line, e.g., 3/5, - 0.666..., 0.5, - 5/8.

3.9N3.2: Identify a rational number that is between two given rational numbers.

3.9N3.3: Solve a given problem involving operations on rational numbers in fraction form and decimal form.

### 4: Linear Relations

#### 4.1PR: Patterns and Relations (Patterns)

4.9PR1: Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution.

4.9PR1.2: Write a linear equation to represent a given context.

4.9PR1.3: Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table.

4.9PR1.5: Describe a context for a given linear equation.

4.9PR2: Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.

4.9PR2.2: Graph a given linear relation, including horizontal and vertical lines.

4.9PR2.3: Match given equations of linear relations with their corresponding graphs.

4.9PR2.6: Solve a given problem by graphing a linear relation and analyzing the graph.

### 5: Polynomials

#### 5.1PR: Patterns and Relations (Variables and Equations)

5.9PR5: Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).

5.9PR5.1: Identify the variables, degree, number of terms and coefficients, including the constant term, of a given simplified polynomial expression.

5.9PR5.4: Match equivalent polynomial expressions given in simplified form.

5.9PR6: Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2).

5.9PR6.1: Identify equivalent polynomial expressions from a given set of polynomial expressions, including pictorial and symbolic representations.

5.9PR6.4: Apply a personal strategy for addition and subtraction of given polynomial expressions, and record the process symbolically.

5.9PR7: Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially and symbolically.

5.9PR7.3: Apply a personal strategy for multiplication and division of a given polynomial expression by a given monomial.

5.9PR7.4: Provide examples of equivalent polynomial expressions.

### 6: Linear Equations and Inequalities

#### 6.1PR: Patterns and Relations (Variables and Equations)

6.9PR3: Model and solve problems using linear equations of the form:

6.9PR3.a: ax = b

6.9PR3.b: x/a = b, a ≠ 0

6.9PR3.c: ax + b = c

6.9PR3.d: x/a + b= c, a ≠ 0

6.9PR3.f: a(x + b) = c

6.9PR3.i: a/x = b, x ≠ 0 where a, b, c, d, e and f are rational numbers.

6.9PR3.3: Solve a given linear equation symbolically.

6.9PR3.5: Represent a given problem using a linear equation.

6.9PR3.6: Solve a given problem using a linear equation and record the process.

6.9PR4: Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

6.9PR4.1: Translate a given problem into a single variable linear inequality using the symbols ≥, >, < or ≤.

6.9PR4.2: Determine if a given rational number is a possible solution of a given linear inequality.

6.9PR4.3: Graph the solution of a given linear inequality on a number line.

6.9PR4.6: Solve a given linear inequality algebraically and explain the process orally or in written form.

6.9PR4.7: Compare and explain the process for solving a given linear equation to the process for solving a given linear inequality.

6.9PR4.8: Compare and explain the solution of a given linear equation to the solution of a given linear inequality.

6.9PR4.10: Solve a given problem involving a single variable linear inequality and graph the solution.

### 7: Similarity and Transformations

#### 7.9SS: Shape and Space (3-D Objects and 2-D Shapes)

7.9SS3: Demonstrate an understanding of similarity of polygons.

7.9SS3.1: Determine if the polygons in a given set are similar and explain the reasoning.

7.9SS3.2: Draw a polygon similar to a given polygon and explain why the two are similar.

7.9SS3.3: Solve a given problem using the properties of similar polygons.

7.9SS4.5: Solve a given problem that involves a scale diagram by applying the properties of similar triangles.

#### 7.9SS: Shape and Space (Transformations)

7.9SS4: Draw and interpret scale diagrams of 2-D shapes.

7.9SS4.1: Identify an example in print and electronic media, e.g., newspapers, the Internet, of a scale diagram and interpret the scale factor.

7.9SS4.2: Draw a diagram to scale that represents an enlargement or reduction of a given 2-D shape.

7.9SS4.3: Determine the scale factor for a given diagram drawn to scale.

7.9SS4.4: Determine if a given diagram is proportional to the original 2-D shape and, if it is, state the scale factor.

7.9SS5: Demonstrate an understanding of line and rotation symmetry.

7.9SS5.2: Complete a 2-D shape or design given one half of the shape or design and a line of symmetry.

### 8: Circle Geometry

#### 8.9SS: Shape and Space (Measurement)

8.9SS1: Solve problems and justify the solution strategy using the following circle properties:

8.9SS1.b: the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc

8.9SS1.2: Solve a given problem involving application of one or more of the circle properties.

8.9SS1.4: Explain the relationship between the measure of the central angle and the inscribed angle subtended by the same arc.

8.9SS1.5: Determine the measure of a given angle inscribed in a semicircle using the circle properties.

8.9SS1.6: Explain the relationship between inscribed angles subtended by the same arc.

### 9: Probability and Statistics

#### 9.9SP: Statistics and Probability (Data Analysis)

9.9SP1: Describe the effect of:

9.9SP1.c: ethics

9.9SP1.d: cost

9.9SP1.e: time and timing

9.9SP1.f: privacy

9.9SP1.g: cultural sensitivity on the collection of data.

9.9SP1.1: Analyze a given case study of data collection, and identify potential problems related to bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity.

9.9SP1.2: Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity may infl uence the data.

9.9SP2: Select and defend the choice of using either a population or a sample of a population to answer a question.

9.9SP2.1: Identify whether a given situation represents the use of a sample or a population.

9.9SP2.2: Provide an example of a situation in which a population may be used to answer a question and justify the choice.

9.9SP2.3: Provide an example of a question where a limitation precludes the use of a population and describe the limitation, e.g., too costly, not enough time, limited resources.

9.9SP3: Develop and implement a project plan for the collection, display and analysis of data by:

9.9SP3.a: formulating a question for investigation

9.9SP3.b: choosing a data collection method that includes social considerations

9.9SP3.c: selecting a population or a sample

9.9SP3.d: collecting the data

9.9SP3.e: displaying the collected data in an appropriate manner

9.9SP3.f: drawing conclusions to answer the question.

9.9SP3.1: Create a rubric to assess a project that includes the assessment of:

9.9SP3.1.a: a question for investigation

9.9SP3.1.b: the choice of a data collection method that includes social considerations

9.9SP3.1.c: the selection of a population or a sample and justifying the choice

9.9SP3.1.d: the display of the collected data

9.9SP3.1.e: the conclusions to answer the question.

9.9SP3.2: Develop a project plan that describes:

9.9SP3.2.a: a question for investigation

9.9SP3.2.b: the method of data collection that includes social considerations

9.9SP3.2.c: the method for selecting a population or a sample

9.9SP3.2.d: the method to be used for collection of the data

9.9SP3.2.e: the methods for analysis and display of the data.

#### 9.9SP: Statistics and Probability (Chance and Uncertainty)

9.9SP4: Demonstrate an understanding of the role of probability in society.

9.9SP4.1: Provide an example from print and electronic media, e.g., newspapers, the Internet, where probability is used.

Correlation last revised: 9/16/2020

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