Big Ideas

Big Ideas

Mixed 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
  • 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.

Content

Learning Standards

Content

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
  • 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 = 22 x 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
  • comparing numbers, comparing quantities, equivalent ratios
  • part-to-part ratios and part-to-whole ratios
whole-number 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
  • 0.125 x 3 or 7.2 ÷ 9
  • using base 10 block array
  • birchbark biting
increasing and decreasing 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
  • 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

Curricular Competency

Learning Standards

Curricular Competency

Reasoning and analyzing

Use logic and patterns
  • including coding
to solve puzzles and play games
Use 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
  • 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

Understanding and solving

Apply 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
  • 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
  • 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
  • including anticipating consequences
Incorporate First Peoples
  • Invite local First Peoples Elders and knowledge keepers to share their knowledge
worldviews and perspectives to 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