Mathematics 9

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Big Ideas

Grandes idées

The principles and processes underlying operations with numbers

numbers

Number: Number represents and describes quantity.
Algebraic reasoning enables us to describe and analyze mathematical relationships.
Sample questions to support inquiry with students:
- How does understanding equivalence help us solve algebraic equations?
- How are the operations with polynomials connected to the process of solving equations?
- What patterns are formed when we implement the operations with polynomials?
- How can we analyze bias and reliability of studies in the media?

apply equally to algebraic situations and can be described and analyzed.

Computational fluency

fluency

Computational Fluency: Computational fluency develops from a strong sense of number.
Sample questions to support inquiry with students:
- When we are working with rational numbers, what is the relationship between addition and subtraction?
- When we are working with rational numbers, what is the relationship between multiplication and division?
- When we are working with rational numbers, what is the relationship between addition and multiplication?
- When we are working with rational numbers, what is the relationship between subtraction and division?

and flexibility with numbers extend to operations with rational numbers.

Continuous linear relationships

Patterning: We use patterns to represent identified regularities and to make generalizations.
Sample questions to support inquiry with students:
- What is a continuous linear relationship?
- How can continuous linear relationships be represented?
- How do linear relationships help us to make predictions?
- What factors can change a continuous linear relationship?
- How are different graphs and relationships used in a variety of careers?

can be identified and represented in many connected ways to identify regularities and make generalizations.

Similar shapes have proportional relationships

proportional relationships

Geometry and Measurement: We can describe, measure, and compare spatial relationships.
Proportional reasoning enables us to make sense of multiplicative relationships.
Sample questions to support inquiry with students:
- How are similar shapes related?
- What characteristics make shapes similar?
- What role do similar shapes play in construction and engineering of structures?

that can be described, measured, and compared.

Analyzing the validity, reliability, and representation of data

data

Data and Probability: Analyzing data and chance enables us to compare and interpret.
Sample questions to support inquiry with students:
- What makes data valid and reliable?
- What is the difference between valid data and reliable data?
- What factors influence the validity and reliability of data?

enables us to compare and interpret.

Curricular Competencies

Students are expected to be able to do the following:

Reasoning and analyzing

Use logic and patterns

logic and patterns

including coding

to solve puzzles and play games

Use reasoning and logic

reasoning and logic

making connections, using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences

to explore, analyze, and apply mathematical ideas

Estimate reasonably

estimating using referents, approximation, and rounding strategies (e.g., the distance to the stop sign is approximately 1 km, the width of my finger is about 1 cm)

Demonstrate and apply

apply

extending whole-number strategies to rational numbers and algebraic expressions
working toward developing fluent and flexible thinking about number

mental math strategies

Use tools or technology to explore and create patterns and relationships, and test conjectures

Model

acting it out, using concrete materials (e.g., manipulatives), drawing pictures or diagrams, building, programming

mathematics in contextualized experiences

Understanding and solving

Apply multiple strategies

multiple strategies

includes familiar, personal, and from other cultures

to solve problems in both abstract and contextualized situations

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Visualize to explore mathematical concepts

Engage in problem-solving experiences that are connected

connected

in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration
Patterns are important in First Peoples technology, architecture, and art.
Have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Communicating and representing

Use mathematical vocabulary and language to contribute to mathematical discussions

Explain and justify

using mathematical arguments

mathematical ideas and decisions

Communicate

concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos

mathematical thinking in many ways

Represent mathematical ideas in concrete, pictorial, and symbolic forms

Connecting and reflecting

Reflect

sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions

on mathematical thinking

Connect mathematical concepts to each other and to other areas and personal interests

other areas and personal interests

to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., cross-discipline, daily activities, local and traditional practices, the environment, popular media and news events, and social justice)

Use mathematical arguments to support personal choices

personal choices

including anticipating consequences

Incorporate First Peoples

Invite local First Peoples Elders and knowledge keepers to share their knowledge

worldviews and perspectives to make connections

make connections

Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)
aboriginaleducation.ca
Teaching Mathematics in a First Nations Context, FNESC (fnesc.ca/resources/math-first-peoples/)

to mathematical concepts

Content

Students are expected to know the following:

operations

includes brackets and exponents
simplifying (–3/4) ÷ 1/5 + ((–1/3) x (–5/2))
simplifying 1 – 2 x (4/5)²
paddle making

with rational numbers (addition, subtraction, multiplication, division, and order of operations)

exponents

includes variable bases
2⁷ = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n⁴= n x n x n x n
exponent laws (e.g., 6⁰ = 1; m¹ = m; n⁵ x n³ = n⁸; y⁷/y³ = y⁴; (5n)³ = 5³ x n³ = 125n³; (m/n)⁵ = m⁵/n⁵; and (3²)⁴ = 3⁸)
limited to whole-number exponents and whole-number exponent outcomes when simplified
(–3)² does not equal –3²
3x(x – 4) = 3x² – 12x

and exponent laws with whole-number exponents

operations with polynomials

polynomials

variables, degree, number of terms, and coefficients, including the constant term
(x² + 2x – 4) + (2x² – 3x – 4)
(5x – 7) – (2x + 3)
2n(n + 7)
(15k² –10k) ÷ (5k)
using algebra tiles

, of degree less than or equal to 2

two-variable linear relations

two-variable continuous linear relations; includes rational coordinates
horizontal and vertical lines
graphing relation and analyzing
interpolating and extrapolating approximate values
spirit canoe journey predictions and daily checks

, using graphing, interpolation, and extrapolation

multi-step

includes distribution, variables on both sides of the equation, and collecting like terms
includes rational coefficients, constants, and solutions
solving and verifying 1 + 2x = 3 – 2/3(x + 6)
solving symbolically and pictorially

one-variable linear equations

spatial proportional reasoning

proportional reasoning

scale diagrams, similar triangles and polygons, linear unit conversions
limited to metric units
drawing a diagram to scale that represents an enlargement or reduction of a given 2D shape
solving a scale diagram problem by applying the properties of similar triangles, including measurements
integration of scale for First Peoples mural work, use of traditional design in current First Peoples fashion design, use of similar triangles to create longhouses/models

statistics

population versus sample, bias, ethics, sampling techniques, misleading stats
analyzing a given set of data (and/or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity
using First Peoples data on water quality, Statistics Canada data on income, health, housing, population

in society

financial literacy

banking, simple interest, savings, planned purchases
creating a budget/plan to host a First Peoples event

— simple budgets and transactions

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