Education and Early Childhood Learning

Number sense and operations: Different representations of numbers help reveal certain properties and make calculations easier. Regardless of the type of numbers or symbols used, each operation retains the same meaning, operations are interconnected, and there are multiple ways to reach a result, some of which may be more useful depending on the situation or the problem to be solved, including using estimation to assess whether a solution is reasonable.

MAT.9.1.A.1 Demonstrate an understanding of powers with integral bases (excluding base 0) and whole-number exponents by

• representing repeated multiplication using powers
• using patterns to show that a power with an exponent of zero is equal to one

[C, CN, ME, PS, R, V]

MAT.9.1.A.2 Demonstrate how prime factorization supports reasoning of number properties by

• expressing natural numbers using prime factorization with exponents
• determining the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers using prime factorization
• applying prime factorization to determine divisibility of numbers

[C, CN, ME, PS, R, T]

MAT.9.1.A.3 Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents by determining and applying the laws of exponents to simplify and evaluate expressions:

• $a^m\cdot a^n=a^{m+n}$
• $\frac{a^m}{a^n}=a^{m-n},m\ge n$
• ${\left(a^m\right)}^n=a^{mn}$
• ${\left(ab\right)}^m=a^m\cdot b^m$
• ${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$
• $a^0=1$

where $a$ and $b$ are non-zero integers and $m$ and $n$ are whole numbers.

[C, CN, ME, PS, R]

MAT.9.1.A.4 Explain and apply the order of operations on integers, including exponents (limited to whole numbers), with and without technology.
[ME, PS, R, T]

MAT.9.1.A.5 Demonstrate an understanding of rational numbers by comparing and ordering rational numbers.
[C, CN, ME, R, V]

MAT.9.1.A.6 Demonstrate an understanding of operations on rational numbers.
[C, CN, PS, R, V]

Patterns: Recognizing and representing patterns helps us understand the world, make generalizations, and solve problems.

MAT.9.1.B.1 Generalize a pattern arising from a problem-solving context using linear equations, and verify by substitution.
[C, CN, PS, R, V]

MAT.9.1.B.2 Graph linear relations ($\mathrm{<strong>y</strong>}<strong>=</strong>\mathrm{<strong>m</strong>}\mathrm{<strong>x</strong>}<strong>+</strong>\mathrm{<strong>b</strong>}$) and analyze the graph by

• understanding slope as the rate of change and its relation to the coefficient $m$
• recognizing the $y$-intercept as the value of $y$ when $x=0$ and its relation to the constant b
• identifying the pattern in the graph that demonstrates the relationship between the independent and dependent variables
• using patterns to make predictions through interpolation and extrapolation

[C, CN, ME, PS, R, T, V]

Variables and equations: Symbols, expressions, and equations are used to represent patterns and describe relationships between quantities.

MAT.9.1.B.3 Model and solve problems using linear equations of the form:

• $ax=b$
• $\frac{x}{a}=b,a\ne 0$
• $ax+b=c$
• $a(x+b)=c$

where $a$, $b$, and $c$ are rational numbers.

[C, CN, ME, PS, V]

MAT.9.1.B.4 Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).
[C, CN, R, V]

MAT.9.1.B.5 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).
[C, CN, ME, PS, R, V]

MAT.9.1.B.6 Model and solve problems using linear equations of the form:

• $ax=b+cx$
• $ax+b=cx+d$
• $a(x+b)=cx+d$
• $a(bx+c)=d(ex+f)$
• $\frac{a}{x}=b,x\ne 0$

where $a$, $b$, $c$, $d$, $e$ and $f$ are integers.
[C, CN, ME, PS, V]

Measurement: Measurement is a useful process for comparing the dimensions of certain attributes of two-dimensional shapes and three-dimensional objects, whether through direct or indirect methods, in order to solve problems in real-world contexts.

MAT.9.1.C.1 Solve problems and justify the solution strategy using circle properties, including

• the perpendicular from the centre of a circle to a chord bisects the chord
• the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc
• the inscribed angles subtended by the same arc are congruent
• a tangent to a circle is perpendicular to the radius at the point of tangency

[C, CN, PS, R, T, V]

Three-dimensional objects and two-dimensional figures: Two-dimensional figures and three-dimensional objects can be described, classified, and analyzed based on their attributes and the relationships between them.

There are no outcomes assigned to this sub-domain.

Transformations: Two-dimensional figures can be moved using transformations and analyzed based on their position in a Cartesian plane. Their positions and movements can be described and modeled using coordinates, geometric representations, and transformations.

There are no outcomes assigned to this sub-domain.

Data analysis: Data can be collected, organized, represented, and interpreted to model situations, support decision-making, and solve problems.

MAT.9.1.D.1 Identify and analyze potential sources of bias in data collection and presentation, including

• the use of language
• ethics
• financial constraints
• time and timing
• confidentiality concerns
• cultural sensitivity
• visual representation

and explain how these factors can affect the reliability and validity of the data.

[C, CN, R, T, V]

MAT.9.1.D.2 Select and defend the choice of using either a population or a sample of a population to answer a question.
[C, CN, PS, R]

Probability and uncertainty: Probability involves determining the likelihood that an event will occur based on past experiences or the analysis of possible outcomes in order to solve problems in uncertain situations.

MAT.9.1.D.3. Demonstrate an understanding of the role of probability in society.
[C, CN, R, T]

Revenue: Understanding different types of income and how effective money management supports the development of essential skills for making informed financial decisions in everyday life.

MAT.9.1.E.1 Demonstrate an understanding of the different ways income is earned, how gross and net earnings are determined from wages and salaries, and by examining the societal role of deductions such as taxes, Canada Pension Plan (CPP), and Employment Insurance (EI).
[C, CN, PS, R, T]

Spending and borrowing: By understanding that income forms the foundation for spending decisions and that borrowing carries obligations and risks that must be managed responsibly, individuals are able to make informed financial decisions.

MAT.9.1.E.2 Demonstrate an understanding of how personal needs, wants, expectations, and experiences affect spending decisions, with attention to both individual habits and other factors that tend to impact consumer behaviour and decisions, including

• peer pressure
• social media
• advertising
• cultural influence
• digital and non-digital purchasing models.

[C, CN, PS, R, V]

MAT.9.1.E.3 Demonstrate an understanding of various payment methods, including cash, debit, and credit, and how ease of access to credit can impact spending habits and financial decision-making.
[C, CN, ME, PS, R]

Saving and investing: Managing personal finances involves saving and investing wisely to prepare for the future, handle unexpected events, and achieve personal goals.

MAT.9.1.E.4 Demonstrate an understanding of different financial service providers, including

• traditional bank
• online bank
• credit union
• fintech app

to determine the products and services they offer while recognizing their differences and their role in managing personal finances.

[C, CN, R, T, V]

MAT.9.1.E.5 Develop a budget that considers personal experiences and cultural influences on saving habits, while supporting short-term and long-term financial goals, including planning for unexpected expenses.
[C, CN, ME, PS, R, T, V]