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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers.

numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- In how many ways can you represent the number ___?
- What is the relationship between decimals, fractions, and percents?
- How can you prove equivalence?
- How are parts and wholes best represented in particular contexts?

Computational fluency and flexibility with numbers extend to operations with integers and decimals.

fluency

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

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

Linear relations

- Patterning: We use patterns to represent identified regularities and to make generalizations.
*Sample questions to support inquiry with students:*- What is a linear relationship?
- In how many ways can linear relationships be represented?
- How do linear relationships differ?
- What factors can change a linear relationship?

The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships.

spatial relationships

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- What is unique about the properties of circles?
- What is the relationship between diameter and circumference?
- What are the similarities and differences between the area and circumference of circles?

Data from circle graphs can be used to illustrate proportion and to compare and interpret.

Data

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- How is a circle graph similar to and different from other types of visual representations of data?
- When would you choose to use a circle graph to represent data?
- How are circle graphs related to ratios, percents, decimals, and whole numbers?
- How would circle graphs be informative or misleading?

## Learning Standards

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### Curricular Competencies

*Students are expected to be able to do the following:*### Reasoning and analyzing

Use logic and patterns to solve puzzles and play games

logic and patterns

- including coding

Use reasoning and logic to explore, analyze, and apply mathematical ideas

reasoning and logic

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

Estimate reasonably

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

apply

- extending whole-number strategies to integers
- 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

Model

- 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

multiple strategies

- 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

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.

### Communicating and representing

Use mathematical vocabulary and language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Explain and justify

- using mathematical arguments

Communicate mathematical thinking in many ways

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

Represent mathematical ideas in concrete, pictorial, and symbolic forms

### Connecting and reflecting

Reflect on mathematical thinking

Reflect

- 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

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 worldviews and perspectives to make connections to mathematical concepts

Incorporate First Peoples

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

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/k-7/

### Content

*Students are expected to know the following:*multiplication and division facts to 100 (extending computational fluency)

facts to 100

- When multiplying 214 by 5, we can multiply by 10, then divide by 2 to get 1070.

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

operations with integers

- addition, subtraction, multiplication, division, and order of operations
- concretely, pictorially, symbolically
- order of operations includes the use of brackets, excludes exponents
- using two-sided counters
- 9–(–4) = 13 because –4 is 13 away from +9
- extending whole-number strategies to decimals

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

operations with decimals

- includes the use of brackets, but excludes exponents

relationships between decimals, fractions, ratios, and percents

relationships

- conversions, equivalency, and terminating versus repeating decimals, place value, and benchmarks
- comparing and ordering decimals and fractions using the number line
- ½ = 0.5 = 50% = 50:100
- shoreline cleanup

discrete linear relations, using expressions, tables, and graphs

discrete linear relations

- four quadrants, limited to integral coordinates
- 3n + 2; values increase by 3 starting from
*y*-intercept of 2 - deriving relation from the graph or table of values
- Small Number stories:
*Small Number and the Old Canoe*,*Small Number Counts to 100*(mathcatcher.irmacs.sfu.ca/stories)

two-step equations with whole-number coefficients, constants, and solutions

two-step equations

- solving and verifying 3
*x*+ 4 = 16 - modelling the preservation of equality (e.g., using balance, pictorial representation, algebra tiles)
- spirit canoe trip pre-planning and calculations
- Small Number stories:
*Small Number and the Big Tree*(mathcatcher.irmacs.sfu.ca/stories)

circumference and area of circles

circumference

- constructing circles given radius, diameter, area, or circumference
- finding relationships between radius, diameter, circumference, and area to develop C = π x d formula
- applying
*A*= π x*r*x*r*formula to find the area given radius or diameter - drummaking, dreamcatcher making, stories of SpiderWoman (Dene, Cree, Hopi, Tsimshian), basket making, quill box making (Note: Local protocols should be considered when choosing an activity.)

volume of rectangular prisms and cylinders

volume

- volume = area of base x height
- bentwood boxes, wiigwaasabak and mide-wiigwaas (birch bark scrolls)
*Exploring Math through Haida Legends: Culturally Responsive Mathematics*

Cartesian coordinates and graphing

Cartesian coordinates

- origin, four quadrants, integral coordinates, connections to linear relations, transformations
- overlaying coordinate plane on medicine wheel, beading on dreamcatcher, overlaying coordinate plane on traditional maps

combinations of transformations

transformations

- four quadrants, integral coordinates
- translation(s), rotation(s), and/or reflection(s) on a single 2D shape; combination of successive transformations of 2D shapes; tessellations
- First Peoples art, jewelry making, birchbark biting

circle graphs

circle graphs

- constructing, labelling, and interpreting circle graphs
- translating percentages displayed in a circle graph into quantities and vice versa
- visual representations of tidepools or traditional meals on plates

experimental probability with two independent events

experimental probability

- experimental probability, multiple trials (e.g., toss two coins, roll two dice, spin a spinner twice, or a combination thereof)
- dice games (web.uvic.ca/~tpelton/fn-math/fn-dicegames.html)

financial literacy — financial percentage

financial literacy

- financial percentage calculations
- sales tax, tips, discount, sale price

**Note:**Some of the learning standards in the PHE curriculum address topics that some students and their parents or guardians may feel more comfortable addressing at home. Refer to ministry policy regarding opting for alternative delivery.