Mathematics 7

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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?

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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 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?

and flexibility with numbers extend to operations with integers 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?
- In how many ways can linear relationships be represented?
- How do linear relationships differ?
- What factors can change a linear relationship?

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

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?

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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?

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

Curricular Competencies

Students are expected to be able to do the following:

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 integers
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

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

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

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:

multiplication and division facts to 100

facts to 100

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

(extending computational fluency)

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

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

operations with decimals

includes the use of brackets, but excludes exponents

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

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

between decimals, fractions, ratios, and percents

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)

, using expressions, tables, and graphs

two-step equations

solving and verifying 3x + 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)

with whole-number coefficients, constants, and solutions

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.)

and area of circles

volume

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

of rectangular prisms and cylinders

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

and graphing

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

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

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)

with two independent events

financial literacy

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

— financial percentage

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