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# Mathematics

## Core Competencies

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### Big Ideas

### Grandes idées

Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes.

numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- In how many ways can you represent the number ___?
- What are the connections between fractions, mixed numbers, and decimal numbers?
- How are mixed numbers and decimal numbers alike? Different?

Computational fluency and flexibility with numbers extend to operations with whole numbers 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 decimal numbers, what is the relationship between addition and subtraction?
- When we are working with decimal numbers, what is the relationship between multiplication and division?
- When we are working with decimal numbers, what is the relationship between addition and multiplication?
- When we are working with decimal numbers, what is the relationship between subtraction and division?

Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form 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?
- How do linear expressions and line graphs represent linear relations?
- What factors can change or alter a linear relationship?

Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles.

Properties

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- How are the areas of triangles, parallelogram, and trapezoids interrelated?
- What factors are considered when selecting a viable referent in measurement?

Data from the results of an experiment can be used to predict the theoretical probability of an event 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:*- What is the relationship between theoretical and experimental probability?
- What informs our predictions?
- What factors would influence the theoretical probability of an experiment?

## Learning Standards

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### Curricular Competencies

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*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 decimals
- 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:*small to large numbers (thousandths to billions)

small to large numbers

- place value from thousandths to billions, operations with thousandths to billions
- numbers used in science, medicine, technology, and media
- compare, order, estimate

multiplication and division facts to 100 (developing computational fluency)

facts to 100

- mental math strategies (e.g., the double-double strategy to multiply 23 x 4)

order of operations with whole numbers

order of operations

- includes the use of brackets, but excludes exponents
- quotients can be rational numbers

factors and multiples — greatest common factor and least common multiple

factors and multiples

- prime and composite numbers, divisibility rules, factor trees, prime factor phrase (e.g., 300 = 2
^{2 }x 3 x 5^{2}) - using graphic organizers (e.g., Venn diagrams) to compare numbers for common factors and common multiples

improper fractions and mixed numbers

improper fractions

- using benchmarks, number line, and common denominators to compare and order, including whole numbers
- using pattern blocks, Cuisenaire Rods, fraction strips, fraction circles, grids
- birchbark biting

introduction to ratios

ratios

- comparing numbers, comparing quantities, equivalent ratios
- part-to-part ratios and part-to-whole ratios

whole-number percents and percentage discounts

percents

- using base 10 blocks, geoboard, 10x10 grid to represent whole number percents
- finding missing part (whole or percentage)
- 50% = 1/2 = 0.5 = 50:100

multiplication and division of decimals

decimals

- 0.125 x 3 or 7.2 ÷ 9
- using base 10 block array
- birchbark biting

increasing and decreasing patterns, using expressions, tables, and graphs as functional relationships

patterns

- limited to discrete points in the first quadrant
- visual patterning (e.g., colour tiles)
- Take 3 add 2 each time, 2
*n*+ 1, and 1 more than twice a number*all*describe the pattern 3, 5, 7, … - graphing data on First Peoples language loss, effects of language intervention

one-step equations with whole-number coefficients and solutions

one-step equations

- preservation of equality (e.g., using a balance, algebra tiles)
- 3
*x*= 12, x + 5 = 11

perimeter of complex shapes

perimeter

- A complex shape is a group of shapes with no holes (e.g., use colour tiles, pattern blocks, tangrams).

area of triangles, parallelograms, and trapezoids

area

- grid paper explorations
- deriving formulas
- making connections between area of parallelogram and area of rectangle
- birchbark biting

angle measurement and classification

angle

- straight, acute, right, obtuse, reflex
- constructing and identifying; include examples from local environment
- estimating using 45°, 90°, and 180° as reference angles
- angles of polygons
- Small Number stories:
*Small Number and the Skateboard Park*(mathcatcher.irmacs.sfu.ca/stories)

volume and capacity

volume and capacity

- using cubes to build 3D objects and determine their volume
- referents and relationships between units (e.g., cm
^{3}, m^{3}, mL, L) - the number of coffee mugs that hold a litre
- berry baskets, seaweed drying

triangles

triangles

- scalene, isosceles, equilateral
- right, acute, obtuse
- classified regardless of orientation

combinations of transformations

transformations

- plotting points on Cartesian plane using whole-number ordered pairs
- translation(s), rotation(s), and/or reflection(s) on a single 2D shape
- limited to first quadrant
- transforming, drawing, and describing image
- Use shapes in First Peoples art to integrate printmaking (e.g., Inuit, Northwest coastal First Nations, frieze work) (mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/)

line graphs

line graphs

- table of values, data set; creating and interpreting a line graph from a given set of data

single-outcome probability, both theoretical and experimental

single-outcome probability

- single-outcome probability events (e.g., spin a spinner, roll a die, toss a coin)
- listing all possible outcomes to determine theoretical probability
- comparing experimental results with theoretical expectation
- Lahal stick games

financial literacy — simple budgeting and consumer math

financial literacy

- informed decision making on saving and purchasing
- How many weeks of allowance will it take to buy a bicycle?

**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.