Big Ideas
Big Ideas
The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.
- 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?
Computational fluency and flexibility with numbers extend to operations with rational numbers.
- 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?
Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.
- 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?
Similar shapes have proportional relationships that can be described, measured, and compared.
- 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?
Analyzing the validity, reliability, and representation of data enables us to compare and interpret.
- 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?
Content
Learning Standards
Content
operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)
- includes brackets and exponents
- simplifying (–3/4) ÷ 1/5 + ((–1/3) x (–5/2))
- simplifying 1 – 2 x (4/5)2
- paddle making
exponents and exponent laws with whole-number 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
operations with polynomials, of degree less than or equal to 2
- 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
two-variable linear relations, using graphing, interpolation, and extrapolation
- 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
multi-step one-variable linear equations
- 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
spatial 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 in society
- 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
financial literacy — simple budgets and transactions
- banking, simple interest, savings, planned purchases
- creating a budget/plan to host a First Peoples event
Curricular Competency
Learning Standards
Curricular Competency
Reasoning and analyzing
Use logic and patterns to solve puzzles and play games
- including coding
Use reasoning and logic to explore, analyze, and apply mathematical ideas
- making connections, using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences
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 mental math strategies
- extending whole-number strategies to rational numbers and algebraic expressions
- working toward developing fluent and flexible thinking about number
Use tools or technology to explore and create patterns and relationships, and test conjectures
Model mathematics in contextualized experiences
- acting it out, using concrete materials (e.g., manipulatives), drawing pictures or diagrams, building, programming
Understanding and solving
Apply multiple strategies to solve problems in both abstract and contextualized situations
- includes familiar, personal, and from other cultures
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 to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures
- 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.
Communicating and representing
Use mathematical vocabulary and language to contribute to mathematical discussions
Explain and justify mathematical ideas and decisions
- using mathematical arguments
Communicate mathematical thinking in many ways
- 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
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Connecting and reflecting
Reflect on mathematical thinking
- sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions
Connect mathematical concepts to each other and to 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
- including anticipating consequences
Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts
- Invite local First Peoples Elders and knowledge keepers to share their knowledge
- 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/)