Mathematics 6

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Big Ideas

Grandes idées

Mixed 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 are the connections between fractions, mixed numbers, and decimal numbers?
- How are mixed numbers and decimal numbers alike? Different?

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

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 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?

and flexibility with numbers extend to operations with whole numbers and decimals.

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?

can be identified and represented using expressions with variables and line graphs and can be used to form generalizations.

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?

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

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?

from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.

Curricular Competencies

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Students are expected to be able to do the following:

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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 decimals
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

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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

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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

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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/k-7/

to mathematical concepts

Content

Students are expected to know the following:

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

(thousandths to billions)

multiplication and division facts to 100

facts to 100

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

(developing computational fluency)

order of operations

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

with whole numbers

factors and multiples

prime and composite numbers, divisibility rules, factor trees, prime factor phrase (e.g., 300 = 2²x 3 x 5² )
using graphic organizers (e.g., Venn diagrams) to compare numbers for common factors and common multiples

— greatest common factor and least common multiple

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

and mixed numbers

introduction to ratios

ratios

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

whole-number percents

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

and percentage discounts

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

patterns

limited to discrete points in the first quadrant
visual patterning (e.g., colour tiles)
Take 3 add 2 each time, 2n + 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

, using expressions, tables, and graphs as functional relationships

one-step equations

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

with whole-number coefficients and solutions

perimeter

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

of complex shapes

area

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

of triangles, parallelograms, and trapezoids

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)

measurement and classification

volume and capacity

using cubes to build 3D objects and determine their volume
referents and relationships between units (e.g., cm³, m³, mL, L)
the number of coffee mugs that hold a litre
berry baskets, seaweed drying

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

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

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

, both theoretical and experimental

financial literacy

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

— simple budgeting and consumer math

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Mathematics 6

Core Competencies

Big Ideas

Grandes idées

Learning Standards

Curricular Competencies

Reasoning and analyzing

Understanding and solving

Communicating and representing

Connecting and reflecting

Content