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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Number represents, describes, and compares the quantities of ratios, rates, and percents.

Number

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- How can two quantities be compared, represented, and communicated?
- How are decimals, fractions, ratios, and percents interrelated?
- How does ratio use in mechanics differ from ratio use in architecture?

Computational fluency and flexibility extend to operations with fractions.

fluency

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

Discrete linear relationships can be represented in many connected ways and used to identify and

make generalizations.

Discrete linear relationships

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

make generalizations.

The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships.

3D objects

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- What is the relationship between the surface area and volume of regular solids?
- How can surface area and volume of regular solids be determined?
- How are the surface area and volume of regular solids related?
- How does surface area compare with volume in patterning and cubes?

Analyzing data by determining averages is one way to make sense of large data sets and enables us 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 does determining averages help us understand large data sets?
- What do central tendencies represent?
- How are central tendencies best used to describe a quality of a large data set?

## 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 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:*perfect squares and cubes

perfect squares and cubes

- using colour tiles, pictures, or multi-link cubes
- building the number or using prime factorization

square and cube roots

square and cube roots

- finding the cube root of 125
- finding the square root of 16/169
- estimating the square root of 30

percents less than 1 and greater than 100 (decimal and fractional percents)

percents

- A worker’s salary increased 122% in three years. If her salary is now ,940, what was it originally?
- What is ½% of 1 billion?
- The population of Vancouver increased by 3.25%. What is the population if it was approximately 603,500 people last year?
- beading

numerical proportional reasoning (rates, ratio, proportions, and percent)

proportional reasoning

- two-term and three-term ratios, real-life examples and problems
- A string is cut into three pieces whose lengths form a ratio of 3:5:7. If the string was 105 cm long, how long are the pieces?
- creating a cedar drum box of proportions that use ratios to create differences in pitch and tone
- paddle making

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

fractions

- includes the use of brackets, but excludes exponents
- using pattern blocks or Cuisenaire Rods
- simplifying ½ ÷ 9/6 x (7 – 4/5)
- drumming and song: 1/2, 1/4, 1/8, whole notes, dot bars, rests = one beat
- changing tempos of traditional songs dependent on context of use
- proportional sharing of harvests based on family size

discrete linear relations (extended to larger numbers, limited to integers)

discrete linear relations

- two-variable discrete linear relations
- expressions, table of values, and graphs
- scale values (e.g., tick marks on axis represent 5 units instead of 1)
- four quadrants, integral coordinates

expressions- writing and evaluating using substitution

expressions

- using an expression to describe a relationship
- evaluating 0.5n – 3n + 25, if n = 14

two-step equations with integer coefficients, constants, and solutions

two-step equations

- solving and verifying 3
*x*– 4 = –12 - modelling the preservation of equality (e.g., using a balance, manipulatives, algebra tiles, diagrams)
- spirit canoe journey calculations

surface area and volume of regular solids, including triangular and other right prisms and cylinders

surface area and volume

- exploring strategies to determine the surface area and volume of a regular solid using objects, a net, 3D design software
- volume = area of the base x height
- surface area = sum of the areas of each side

Pythagorean theorem

Pythagorean theorem

- modelling the Pythagorean theorem
- finding a missing side of a right triangle
- deriving the Pythagorean theorem
- constructing canoe paths and landings given current on a river
- First Peoples constellations

construction, views, and nets of 3D objects

3D objects

- top, front, and side views of 3D objects
- matching a given net to the 3D object it represents
- drawing and interpreting top, front, and side views of 3D objects
- constructing 3D objects with nets
- using design software to create 3D objects from nets
- bentwood boxes, lidded baskets, packs

central tendency

central tendency

- mean, median, and mode

theoretical probability with two independent events

theoretical probability

- with two independent events: sample space (e.g., using tree diagram, table, graphic organizer)
- rolling a 5 on a fair die and flipping a head on a fair coin is 1/6 x ½ = 1/12
- deciding whether a spinner in a game is fair

financial literacy — best buys

financial literacy

- coupons, proportions, unit price, products and services
- proportional reasoning strategies (e.g., unit rate, equivalent fractions given prices and quantities)

**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.