Number: Number Represents and Describes Quantity

Area of Learning: Mathematics Grade 6 Big Ideas Elaborations  Mixed numbers and decimal numbers  numbers: represent quantities that can be o Number: Number represents and describes quantity. decomposed into parts and wholes.  Sample questions to support inquiry with students: o In how many ways can you represent the number ___? o What are the connections between fractions, mixed numbers, and decimal numbers? o How are mixed numbers and decimal numbers alike? Different?  Computational fluency and flexibility with  fluency: numbers extend to operations with whole o Computational Fluency: Computational fluency develops from a strong sense of number. numbers and decimals.  Sample questions to support inquiry with students: o When we are working with decimal numbers, what is the relationship between addition and subtraction? o When we are working with decimal numbers, what is the relationship between multiplication and division? o When we are working with decimal numbers, what is the relationship between addition and multiplication? o When we are working with decimal numbers, what is the relationship between subtraction and division?  Linear relations can be identified and  Linear relations: represented using expressions with o Patterning: We use patterns to represent identified regularities and to make generalizations. variables and line graphs and can be used  Sample questions to support inquiry with students: to form generalizations. o What is a linear relationship? o How do linear expressions and line graphs represent linear relations? o What factors can change or alter a linear relationship?  Properties of objects and shapes can be  Properties: described, measured, and compared using o Geometry and Measurement: We can describe, measure, and compare spatial relationships. volume, area, perimeter, and angles.  Sample questions to support inquiry with students:

o How are the areas of triangles, parallelogram, and trapezoids interrelated? o What factors are considered when selecting a viable referent in measurement?  Data from the results of an experiment can  Data: be used to predict the theoretical o Data and Probability: Analyzing data and chance enables us to compare and interpret. probability of an event and to compare and  Sample questions to support inquiry with students: interpret. o What is the relationship between theoretical and experimental probability? o What informs our predictions? o What factors would influence the theoretical probability of an experiment?

Curricular Competencies Elaborations Content Elaborations Reasoning and analyzing  logic and patterns: Students are expected to know the following:  small to large numbers:

1  Use logic and patterns to solve o including coding  small to large numbers (thousandths o place value from thousandths puzzles and play games  reasoning and logic: to billions) to billions, operations with  Use reasoning and logic to explore, o making connections, using  multiplication and division facts to thousandths to billions analyze, and apply mathematical ideas inductive and deductive 100 (developing computational o numbers used in science,  Estimate reasonably reasoning, predicting, fluency) medicine, technology, and  Demonstrate and apply mental math generalizing, drawing  order of operations with whole media strategies conclusions through numbers o compare, order, estimate  Use tools or technology to explore and experiences  factors and multiples — greatest  facts to 100: create patterns and relationships, and  Estimate reasonably: common factor and least common o mental math strategies (e.g., test conjectures o estimating using referents, multiple the double-double strategy to  Model mathematics in contextualized approximation, and rounding  improper fractions and mixed multiply 23 x 4) experiences strategies (e.g., the distance to numbers  order of operations: Understanding and solving the stop sign is approximately  introduction to ratios o includes the use of brackets,  Apply multiple strategies to solve 1 km, the width of my finger  whole-number percents and but excludes exponents problems in both abstract and is about 1 cm) percentage discounts o quotients can be rational contextualized situations  apply:  multiplication and division of numbers  Develop, demonstrate, and apply o extending whole-number decimals  factors and multiples: mathematical understanding through strategies to decimals  increasing and decreasing patterns, o prime and composite play, inquiry, and problem solving o working toward developing using expressions, tables, and graphs numbers, divisibility rules,  Visualize to explore mathematical fluent and flexible thinking as functional relationships factor trees, prime factor concepts about number  one-step equations with whole- phrase (e.g., 300 = 22 x 3 x 52 )  Engage in problem-solving  Model: number coefficients and solutions o using graphic organizers (e.g., experiences that are connected to o acting it out, using concrete  perimeter of complex shapes Venn diagrams) to compare place, story, cultural practices, and materials (e.g.,  area of triangles, parallelograms, and numbers for common factors perspectives relevant to local First manipulatives), drawing trapezoids and common multiples Peoples communities, the local pictures or diagrams, building,  angle measurement and classification  improper fractions: community, and other cultures programming  volume and capacity o using benchmarks, number Communicating and representing o http://www.nctm.org/Publicati  triangles line, and common  Use mathematical vocabulary and ons/Teaching-Children-  combinations of transformations denominators to compare and language to contribute to Mathematics/Blog/Modeling-  line graphs order, including whole mathematical discussions with-Mathematics-through-  single-outcome probability, both numbers Three-Act-Tasks/  Explain and justify mathematical theoretical and experimental o using pattern blocks, ideas and decisions  multiple strategies:  financial literacy — simple Cuisenaire Rods, fraction includes familiar, personal,  Communicate mathematical thinking o budgeting and consumer math strips, fraction circles, grids in many ways and from other cultures o birchbark biting  Represent mathematical ideas in  connected:  ratios: concrete, pictorial, and symbolic o in daily activities, local and o comparing numbers, forms traditional practices, the comparing quantities,

2 Connecting and reflecting environment, popular media equivalent ratios  Reflect on mathematical thinking and news events, cross- o part-to-part ratios and part-to-  Connect mathematical concepts to curricular integration whole ratios each other and to other areas and o Patterns are important in o traditional Aboriginal personal interests Aboriginal technology, language speakers to English  Use mathematical arguments to architecture, and art. speakers or French speakers, support personal choices o Have students pose and solve dual-language speakers  Incorporate First Peoples problems or ask questions  percents: worldviews and perspectives to make connected to place, stories, o using base 10 blocks, connections to mathematical and cultural practices. geoboard, 10x10 grid to concepts  Explain and justify: represent whole number o using mathematical arguments percents  Communicate: o finding missing part (whole or o concretely, pictorially, percentage) symbolically, and by using o 50% = 1/2 = 0.5 = 50:100 spoken or written language to  decimals: express, describe, explain, o 0.125 x 3 or 7.2 ÷ 9 justify, and apply o using base 10 block array mathematical ideas; may use o birchbark biting technology such as  patterns: screencasting apps, digital o limited to discrete points in photos the first quadrant Reflect:  o visual patterning (e.g., colour o sharing the mathematical tiles) thinking of self and others, o Take 3 add 2 each time, 2n + including evaluating strategies 1, and 1 more than twice a and solutions, extending, and number all describe the posing new problems and pattern 3, 5, 7, … questions o graphing data on Aboriginal  other areas and personal interests: language loss, effects of o to develop a sense of how language intervention mathematics helps us  one-step equations: understand ourselves and the o preservation of equality (e.g., world around us (e.g., cross- using a balance, algebra tiles) discipline, daily activities, 3x = 12, x + 5 = 11 local and traditional practices, o the environment, popular  perimeter media and news events, and o A complex shape is a group of social justice) shapes with no holes (e.g., use

3  personal choices: colour tiles, pattern blocks, o including anticipating tangrams). consequences  area:  Incorporate First Peoples: o grid paper explorations o Invite local First Peoples o deriving formulas Elders and knowledge keepers o making connections between to share their knowledge area of parallelogram and area of rectangle  make connections: o birchbark biting o Bishop’s cultural practices:  angle: counting, measuring, locating, o straight, acute, right, obtuse, designing, playing, reflex explaining(http://www.csus.ed o constructing and identifying; u/indiv/o/oreyd/ACP.htm_file include examples from local s/abishop.htm ) environment o First Nations Education o estimating using 45°, 90°, and Steering Committee (FNESC) 180° as reference angles Place-Based Themes and o angles of polygons Topics: family and ancestry; o Small Number stories: Small travel and navigation; games; Number and the Skateboard land, environment, and Park resource management; (http://mathcatcher.irmacs.sfu. community profiles; art; ca/stories) nutrition; dwellings  volume and capacity: o Teaching Mathematics in a o using cubes to build 3D First Nations Context, FNESC objects and determine their (http://www.fnesc.ca/k-7/) volume o referents and relationships between units (e.g., cm3, m3, mL, L) o the number of coffee mugs that hold a litre o berry baskets, seaweed drying  triangles: o scalene, isosceles, equilateral o right, acute, obtuse o classified regardless of orientation

4  transformations: o plotting points on Cartesian plane using whole-number ordered pairs o translation(s), rotation(s), and/or reflection(s) on a single 2D shape o limited to first quadrant o transforming, drawing, and describing image o Use shapes in First Peoples art to integrate printmaking (e.g., Inuit, Northwest coastal First Nations, frieze work) (http://mathcentral.uregina.ca/ RR/database/RR.09.01/mcdon ald1/).  line graphs: o table of values, data set; creating and interpreting a line graph from a given set of data o fish runs versus time  single-outcome probability: o single-outcome probability events (e.g., spin a spinner, roll a die, toss a coin) o listing all possible outcomes to determine theoretical probability o comparing experimental results with theoretical expectation o Lahal bone game  financial literacy: o informed decision making on saving and purchasing o How many weeks of

5 allowance will it take to buy a bicycle?

6 Area of Learning: Mathematics Grade 7 Big Ideas Elaborations  Decimals, fractions, and percents are  numbers: used to represent and describe parts o Number: Number represents and describes quantity. and wholes of numbers.  Sample questions to support inquiry with students: o In how many ways can you represent the number ___? o What is the relationship between decimals, fractions, and percents? o How can you prove equivalence? o How are parts and wholes best represented in particular contexts?  Computational fluency and  fluency: flexibility with numbers extend to o Computational Fluency: Computational fluency develops from a strong sense of number. operations with integers and  Sample questions to support inquiry with students: decimals. o When we are working with integers, what is the relationship between addition and subtraction? o When we are working with integers, what is the relationship between multiplication and division? o When we are working with integers, what is the relationship between addition and multiplication? o When we are working with integers, what is the relationship between subtraction and division?  Linear relations can be represented in  Linear relations: many connected ways to identify o Patterning: We use patterns to represent identified regularities and to make generalizations. regularities and make generalizations.  Sample questions to support inquiry with students: o What is a linear relationship? o In how many ways can linear relationships be represented? o How do linear relationships differ? o What factors can change a linear relationship?  The constant ratio between the  spatial relationships: circumference and diameter of circles o Geometry and Measurement: We can describe, measure, and compare spatial relationships. can be used to describe, measure, and  Sample questions to support inquiry with students: compare spatial relationships. o What is unique about the properties of circles? o What is the relationship between diameter and circumference? o What are the similarities and differences between the area and circumference of circles?  Data from circle graphs can be used to  Data: illustrate proportion and to compare and o Data and Probability: Analyzing data and chance enables us to compare and interpret. interpret.  Sample questions to support inquiry with students: o How is a circle graph similar to and different from other types of visual representations of data? o When would you choose to use a circle graph to represent data? o How are circle graphs related to ratios, percents, decimals, and whole numbers? o How would circle graphs be informative or misleading?

7 Curricular Competencies Elaborations Content Elaborations Reasoning and analyzing  logic and patterns: Students are expected to know the following:  facts to 100:  Use logic and patterns to solve o including coding  multiplication and division facts o When multiplying 214 by 5, we can puzzles and play games  reasoning and logic: to 100 (extending computational fluency) multiply by 10, then divide by 2 to get  Use reasoning and logic to explore, o making connections, using  operations with integers (addition, 1070. analyze, and apply mathematical inductive and deductive subtraction, multiplication, division, and  operations with integers: ideas reasoning, predicting, order of operations) o addition, subtraction,  Estimate reasonably generalizing, drawing  operations with decimals (addition, multiplication, division, and order of  Demonstrate and apply mental math conclusions through subtraction, multiplication, division, and operations strategies experiences order of operations) o concretely, pictorially, symbolically  Use tools or technology to explore  Estimate reasonably:  relationships between decimals, fractions, o order of operations includes the use and create patterns and relationships, o estimating using referents, ratios, and percents of brackets, excludes exponents and test conjectures approximation, and rounding  discrete linear relations, using o using two-sided counters  Model mathematics in contextualized strategies (e.g., the distance to expressions, tables, and graphs o 9–(–4) = 13 because –4 is 13 away experiences the stop sign is approximately  two-step equations with whole-number from +9 Understanding and solving 1 km, the width of my finger coefficients, constants, and solutions o extending whole-number strategies  Apply multiple strategies to solve is about 1 cm)  circumference and area of circles to decimals problems in both abstract and  apply:  volume of rectangular prisms and cylinders  operations with decimals: contextualized situations o extending whole-number  Cartesian coordinates and graphing o includes the use of brackets, but  Develop, demonstrate, and apply strategies to integers  combinations of transformations excludes exponents mathematical understanding through o working toward developing  circle graphs  relationships: play, inquiry, and problem solving fluent and flexible thinking  experimental probability with two o conversions, equivalency, and  Visualize to explore mathematical about number independent events terminating versus repeating decimals, concepts  Model:  financial literacy — financial percentage place value, and benchmarks  Engage in problem-solving o acting it out, using concrete o comparing and ordering decimals experiences that are connected to materials (e.g., and fractions using the number line place, story, cultural practices, and manipulatives), drawing o ½ = 0.5 = 50% = 50:100 perspectives relevant to local First pictures or diagrams, o shoreline cleanup Peoples communities, the local building, programming  discrete linear relations: community, and other cultures o http://www.nctm.org/Publicat four quadrants, limited to integral Communicating and representing o ions/Teaching-Children- coordinates  Use mathematical vocabulary and Mathematics/Blog/Modeling- o 3n + 2; values increase by 3 starting language to contribute to with-Mathematics-through- from y-intercept of 2 mathematical discussions Three-Act-Tasks/ o deriving relation from the graph or  Explain and justify mathematical  multiple strategies: table of values ideas and decisions o includes familiar, personal, o Small Number stories: Small  Communicate mathematical thinking and from other cultures Number and the Old Canoe, Small Number

8 in many ways  connected: Counts to 100  Represent mathematical ideas in o in daily activities, local and (http://mathcatcher.irmacs.sfu.ca/stories) concrete, pictorial, and symbolic traditional practices, the  two-step equations: forms environment, popular media o solving and verifying 3x + 4 = 16 Connecting and reflecting and news events, cross- o modelling the preservation of  Reflect on mathematical thinking curricular integration equality (e.g., using balance, pictorial  Connect mathematical concepts to o Patterns are important in representation, algebra tiles) each other and to other areas and Aboriginal technology, o spirit canoe trip pre-planning and personal interests architecture, and art. calculations  Use mathematical arguments to o Have students pose and solve o Small Number stories: Small support personal choices problems or ask questions Number and the Big Tree  Incorporate First Peoples connected to place, stories, (http://mathcatcher.irmacs.sfu.ca/stories) worldviews and perspectives to and cultural practices.  circumference make connections to mathematical  Explain and justify: o constructing circles given radius, concepts o using mathematical diameter, area, or circumference arguments o finding relationships between  Communicate: radius, diameter, circumference, and area to o concretely, pictorially, develop C = π x d formula symbolically, and by using o applying A = π x r x r formula to spoken or written language to find the area given radius or diameter express, describe, explain, o drummaking, dreamcatcher making, justify and apply stories of SpiderWoman (Dene, Cree, Hopi, mathematical ideas; may use Tsimshian), basket making, quill box technology such as making (Note: Local protocols should be screencasting apps, digital considered when choosing an activity.) photos  volume:  Reflect: o volume = area of base x height o sharing the mathematical o bentwood boxes, wiigwaasabak and thinking of self and others, mide-wiigwaas (birch bark scrolls) including evaluating o Exploring Math through Haida strategies and solutions, Legends: Culturally Responsive extending, and posing new Mathematics problems and questions (http://www.haidanation.ca/Pages/language/  other areas and personal interests: haida_legends/media/Lessons/RavenLes4- o to develop a sense of how 9.pdf) mathematics helps us  Cartesian coordinates: understand ourselves and the o origin, four quadrants, integral world around us (e.g., cross- coordinates, connections to linear relations,

9 discipline, daily activities, transformations local and traditional practices, o overlaying coordinate plane on the environment, popular medicine wheel, beading on dreamcatcher, media and news events, and overlaying coordinate plane on traditional social justice) maps  personal choices:  transformations: o including anticipating o four quadrants, integral coordinates consequences o translation(s), rotation(s), and/or  Incorporate First Peoples: reflection(s) on a single 2D shape; o Invite local First Peoples combination of successive transformations Elders and knowledge of 2D shapes; tessellations keepers to share their o Aboriginal art, jewelry making, knowledge birchbark biting  circle graphs:  make connections: o constructing, labelling, and o Bishop’s cultural practices: interpreting circle graphs counting, measuring, o translating percentages displayed in locating, designing, playing, a circle graph into quantities and vice versa explaining(http://www.csus.e o visual representations of tidepools du/indiv/o/oreyd/ACP.htm_fil or tradional meals on plates es/abishop.htm )  experimental probability: o First Nations Education o experimental probability, multiple Steering Committee (FNESC) trials (e.g., toss two coins, roll two dice, Place-Based Themes and spin a spinner twice, or a combination Topics: family and ancestry; thereof) travel and navigation; games; o Puim, Hubbub land, environment and o dice games resource management; (http://web.uvic.ca/~tpelton/fn-math/fn- community profiles; art; dicegames.html ) nutrition; dwellings  financial literacy: o Teaching Mathematics in a o financial percentage calculations First Nations Context, o sales tax, tips, discount, sale price FNESC (http://www.fnesc.ca/k-7/)

10 11 Area of Learning: Mathematics Grade 8 Big Ideas Elaborations  Number represents, describes, and compares the  numbers: quantities of ratios, rates, and percents. o Number: Number represents and describes quantity.  Sample questions to support inquiry with students: o How can two quantities be compared, represented, and communicated? o How are decimals, fractions, ratios, and percents interrelated? o How does ratio use in mechanics differ from ratio use in architecture?  Computational fluency and flexibility extend to  fluency: operations with fractions. o Computational Fluency: Computational fluency develops from a strong sense of number.  Sample questions to support inquiry with students: o When we are working with fractions, what is the relationship between addition and subtraction? o When we are working with fractions, what is the relationship between multiplication and division? o When we are working with fractions, what is the relationship between addition and multiplication? o When we are working with fractions, what is the relationship between subtraction and division?  Discrete linear relationships can be represented in  Discrete linear relationships: many connected ways and used to identify and make o Patterning: We use patterns to represent identified regularities and to make generalizations. generalizations.  Sample questions to support inquiry with students: o What is a discrete linear relationship? o How can discrete linear relationships be represented? o What factors can change a discrete linear relationship?  The relationship between surface area and volume of  3D objects: 3D objects can be used to describe, measure, and o Geometry and Measurement: We can describe, measure, and compare spatial relationships. compare spatial relationships.  Sample questions to support inquiry with students: o What is the relationship between the surface area and volume of regular solids? o How can surface area and volume of regular solids be determined? o How are the surface area and volume of regular solids related? o How does surface area compare with volume in patterning and cubes?  Analyzing data by determining averages is one way to  data: make sense of large data sets and enables us to compare o Data and Probability: Analyzing data and chance enables us to compare and interpret. and interpret.  Sample questions to support inquiry with students: o How does determining averages help us understand large data sets? o What do central tendencies represent? o How are central tendencies best used to describe a quality of a large data set?

Curricular Competencies Elaborations Content Elaborations

12 Reasoning and analyzing  logic and patterns: Students are expected to know the  perfect squares and cubes:  Use logic and patterns to solve o including coding following: o using colour tiles, pictures, or multi-link puzzles and play games  reasoning and logic:  perfect squares and cubes cubes  Use reasoning and logic to o making connections,  square and cube roots o building the number or using prime explore, analyze, and apply using inductive and  percents less than 1 and greater factorization mathematical ideas deductive reasoning, than 100 (decimal and fractional  square and cube roots  Estimate reasonably predicting, generalizing, percents) o finding the cube root of 125  Demonstrate and apply mental drawing conclusions  numerical proportional o finding the square root of 16/169 math strategies through experiences reasoning (rates, ratio, o estimating the square root of 30  Use tools or technology to explore  Estimate reasonably: proportions, and percent)  percents: and create patterns and o estimating using  operations with fractions o A worker’s salary increased 122% in three relationships, and test conjectures referents, approximation, (addition, subtraction, years. If her salary is now $93,940, what  Model mathematics in and rounding strategies multiplication, division, and order was it originally? contextualized experiences (e.g., the distance to the of operations) o What is ½% of 1 billion? Understanding and solving stop sign is approximately  discrete linear relations o The population of Vancouver increased by  Apply multiple strategies to solve 1 km, the width of my (extended to larger numbers, 3.25%. What is the population if it was problems in both abstract and finger is about 1 cm) limited to integers) approximately 603,500 people last year? contextualized situations  apply:  expressions- writing and o beading evaluating using substitution  Develop, demonstrate, and apply o extending whole-number  proportional reasoning: mathematical understanding  two-step equations with integer strategies to decimals and o two-term and three-term ratios, real-life through play, inquiry, and problem coefficients, constants, and fractions examples and problems solving working toward solutions o o A string is cut into three pieces whose  Visualize to explore mathematical  surface area and volume of developing fluent and lengths form a ratio of 3:5:7. If the string concepts regular solids, including triangular flexible thinking of was 105 cm long, how long are the and other right prisms and  Engage in problem-solving number pieces? experiences that are connected to Model: cylinders  o creating a cedar drum box of proportions place, story, cultural practices, and  Pythagorean theorem o acting it out, using that use ratios to create differences in perspectives relevant to local First concrete materials (e.g.,  construction, views, and nets of pitch and tone Peoples communities, the local 3D objects manipulatives), drawing o paddle making community, and other cultures pictures or diagrams,  central tendency  fractions: Communicating and representing building, programming  theoretical probability with two o includes the use of brackets, but excludes  Use mathematical vocabulary and o http://www.nctm.org/Publ independent events exponents language to contribute to ications/Teaching-  financial literacy — best buys using pattern blocks or Cuisenaire Rods mathematical discussions Children- o  Explain and justify mathematical Mathematics/Blog/Model o simplifying ½ ÷ 9/6 x (7 – 4/5) ideas and decisions ing-with-Mathematics- o drumming and song: 1/2, 1/4, 1/8, whole  Communicate mathematical through-Three-Act-Tasks/ notes, dot bars, rests = one beat thinking in many ways  multiple strategies: o changing tempos of traditional songs dependent on context of use

13  Represent mathematical ideas in o includes familiar, o proportional sharing of harvests based on concrete, pictorial, and symbolic personal, and from other family size forms cultures  discrete linear relations: Connecting and reflecting  connected: o two-variable discrete linear relations  Reflect on mathematical thinking o in daily activities, local o expressions, table of values, and graphs  Connect mathematical concepts to and traditional practices, o scale values (e.g., tick marks on axis each other and to other areas and the environment, popular represent 5 units instead of 1) personal interests media and news events, o four quadrants, integral coordinates  Use mathematical arguments to cross-curricular  expressions: support personal choices integration o using an expression to describe a  Incorporate First Peoples o Patterns are important in relationship worldviews and perspectives to Aboriginal technology, o evaluating 0.5n – 3n + 25, if n = 14 make connections to architecture, and art.  two-step equations: mathematical concepts Have students pose and o o solving and verifying 3x – 4 = –12 solve problems or ask o modelling the preservation of equality questions connected to (e.g., using a balance, manipulatives, place, stories, and cultural algebra tiles, diagrams) practices. o spirit canoe journey calculations  Explain and justify:  surface area and volume: o using mathematical exploring strategies to determine the arguments o surface area and volume of a regular solid  Communicate: using objects, a net, 3D design software o concretely, pictorially, o volume = area of the base x height symbolically, and by surface area = sum of the areas of each using spoken or written o language to express, side describe, explain, justify,  Pythagorean theorem: and apply mathematical o modelling the Pythagorean theorem ideas; may use o finding a missing side of a right triangle technology such as o deriving the Pythagorean theorem screencasting apps, digital o constructing canoe paths and landings photos given current on a river (First Nations  Reflect: Education Steering Committee) o sharing the mathematical o Aboriginal constellations and adaus thinking of self and  3D objects: others, including o top, front, and side views of 3D objects evaluating strategies and o matching a given net to the 3D object it solutions, extending, and represents posing new problems and

14 questions o drawing and interpreting top, front, and  other areas and personal side views of 3D objects interests: o constructing 3D objects with nets o to develop a sense of how o using design software to create 3D objects mathematics helps us from nets understand ourselves and o bentwood boxes, lidded baskets, packs the world around us (e.g.,  central tendency: cross-discipline, daily o mean, median, and mode activities, local and  theoretical probability: traditional practices, the o with two independent events: sample environment, popular space (e.g., using tree diagram, table, media and news events, graphic organizer) and social justice) o rolling a 5 on a fair die and flipping a  personal choices: head on a fair coin is 1/6 x ½ = 1/12 including anticipating o o deciding whether a spinner in a game is consequences fair  Incorporate First Peoples:  financial literacy: Invite local First Peoples o o coupons, proportions, unit price, products Elders and knowledge and services keepers to share their o proportional reasoning strategies (e.g., knowledge unit rate, equivalent fractions given prices and quantities)  make connections: o Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining(http://www.cs us.edu/indiv/o/oreyd/ACP .htm_files/abishop.htm ) o First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and

15 resource management; community profiles; art; nutrition; dwellings o Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/reso urces/math-first-peoples/)

16 Area of Learning: Mathematics Grade 9 Big Ideas Elaborations  The principles and processes underlying operations with  numbers: numbers apply equally to algebraic situations and can be o Number: Number represents and describes quantity. (Algebraic reasoning enables us to describe and described and analyzed. analyze mathematical relationships.)

 Sample questions to support inquiry with students:

o How does understanding equivalence help us solve algebraic equations? o How are the operations with polynomials connected to the process of solving equations? o What patterns are formed when we implement the operations with polynomials? o How can we analyze bias and reliability of studies in the media?  Computational fluency and flexibility with numbers  fluency: extend to operations with rational numbers. o Computational Fluency: Computational fluency develops from a strong sense of number.  Sample questions to support inquiry with students: o When we are working with rational numbers, what is the relationship between addition and subtraction?

o When we are working with rational numbers, what is the relationship between multiplication and division?

o When we are working with rational numbers, what is the relationship between addition and multiplication?

o When we are working with rational numbers, what is the relationship between subtraction and division?

 Continuous linear relationships can be identified and  Continuous linear relationships: represented in many connected ways to identify o Patterning: We use patterns to represent identified regularities and to make generalizations. regularities and make generalizations.  Sample questions to support inquiry with students: o What is a continuous linear relationship? o How can continuous linear relationships be represented? o How do linear relationships help us to make predictions? o What factors can change a continuous linear relationship? o How are different graphs and relationships used in a variety of careers?  Similar shapes have proportional relationships that  proportional relationships: can be described, measured, and compared. o Geometry and Measurement: We can describe, measure, and compare spatial relationships. (Proportional reasoning enables us to make sense of multiplicative relationships.)  Sample questions to support inquiry with students: o How are similar shapes related?

17 o What characteristics make shapes similar? o What role do similar shapes play in construction and engineering of structures?  Analyzing the validity, reliability, and representation  data: of data enables us to compare and interpret. o Data and Probability: Analyzing data and chance enables us to compare and interpret.  Sample questions to support inquiry with students: o What makes data valid and reliable? o What is the difference between valid data and reliable data? o What factors influence the validity and reliablity of data?

Curricular Competencies Elaborations Content Elaborations Reasoning and analyzing  logic and patterns: Students are expected to know the  operations:  Use logic and patterns to solve o including coding following: o includes brackets and exponents puzzles and play games  reasoning and logic:  operations with rational numbers o simplifying (-3/4) ÷ 1/5 + ((-1/3) x (-5/2))  Use reasoning and logic to o making connections, using (addition, subtraction, multiplication, o simplifying 1 – 2 x (4/5)2 explore, analyze, and apply inductive and deductive division, and order of operations) o paddle making mathematical ideas reasoning, predicting,  exponents and exponent laws with  exponents:  Estimate reasonably generalizing, drawing whole-number exponents o includes variable bases  Demonstrate and apply mental conclusions through  operations with polynomials, of o 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n4 = n math strategies experiences degree less than or equal to 2 x n x n x n  Use tools or technology to explore  Estimate reasonably:  two-variable linear relations, using o exponent laws (e.g., 60 = 1; m1 = m; n5 x and create patterns and o estimating using referents, graphing, interpolation, and n3 = n8; y7/y3 = y4; (5n)3 = 53 x n3 = 125n3; relationships, and test conjectures approximation, and extrapolation (m/n)5 = m5/n5; and (32)4 = 38)  Model mathematics in rounding strategies (e.g.,  multi-step one-variable linear o limited to whole-number exponents and contextualized experiences the distance to the stop equations whole-number exponent outcomes when Understanding and solving sign is approximately 1  spatial proportional reasoning simplified  Apply multiple strategies to solve km, the width of my finger  statistics in society o (–3)2 does not equal –32 is about 1 cm) 2 problems in both abstract and  financial literacy — simple budgets o 3x(x – 4) = 3x – 12x contextualized situations  apply: and transactions  polynomials:  Develop, demonstrate, and apply o extending whole-number o variables, degree, number of terms, and mathematical understanding strategies to rational coefficients, including the constant term through play, inquiry, and problem numbers and algebraic o (x2 + 2x – 4) + (2x2 – 3x – 4) solving expressions o (5x – 7) – (2x + 3)  Visualize to explore mathematical o working toward concepts o 2n(n + 7) developing fluent and 2  Engage in problem-solving flexible thinking of number o (15k -10k) ÷ (5k) experiences that are connected to  Model: o using algebra tiles place, story, cultural practices, and o acting it out, using  two-variable linear relations: perspectives relevant to local First concrete materials (e.g., o two-variable continuous linear relations;

18 Peoples communities, the local manipulatives), drawing includes rational coordinates community, and other cultures pictures or diagrams, o horizontal and vertical lines Communicating and representing building, programming o graphing relation and analyzing  Use mathematical vocabulary and o http://www.nctm.org/Publi o interpolating and extrapolating language to contribute to cations/Teaching-Children- approximate values mathematical discussions Mathematics/Blog/Modeli o spirit canoe journey predictions and daily  Explain and justify mathematical ng-with-Mathematics- checks ideas and decisions through-Three-Act-Tasks/  multi-step:  Communicate mathematical  multiple strategies: o includes distribution, variables on both thinking in many ways o includes familiar, personal, sides of the equation, and collecting like  Represent mathematical ideas in and from other cultures terms concrete, pictorial, and symbolic  connected: o includes rational coefficients, constants, forms o in daily activities, local and and solutions Connecting and reflecting traditional practices, the o solving and verifying 1 + 2x = 3 – 2/3(x +  Reflect on mathematical thinking environment, popular 6)  Connect mathematical concepts to media and news events, o solving symbolically and pictorially each other and to other areas and cross-curricular integration  proportional reasoning: personal interests o Patterns are important in o scale diagrams, similar triangles and  Use mathematical arguments to Aboriginal technology, polygons, linear unit conversions support personal choices architecture, and art. o limited to metric units Have students pose and  Incorporate First Peoples o o drawing a diagram to scale that represents worldviews and perspectives to solve problems or ask an enlargement or reduction of a given 2D make connections to questions connected to shape mathematical concepts place, stories, and cultural o solving a scale diagram problem by practices. applying the properties of similar  Explain and justify: triangles, including measurements using mathematical o o integration of scale for Aboriginal mural arguments work, use of traditional design in current  Communicate: Aboriginal fashion design, use of similar o concretely, pictorially, triangles to create longhouses/models symbolically, and by using  statistics: spoken or written language o population versus sample, bias, ethics, to express, describe, sampling techniques, misleading stats explain, justify and apply o analyzing a given set of data (and/or its mathematical ideas; may representation) and identifying potential use technology such as problems related to bias, use of language, screencasting apps, digital ethics, cost, time and timing, privacy, or photos cultural sensitivity

19  Reflect: o using First Peoples data on water quality, o sharing the mathematical Statistics Canada data on income, health, thinking of self and others, housing, population including evaluating  financial literacy strategies and solutions, o banking, simple interest, savings, planned extending, and posing new purchases problems and questions o creating a budget/plan to host a First  other areas and personal Peoples event interests: o 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)  personal choices: o including anticipating consequences  Incorporate First Peoples: o Invite local First Peoples Elders and knowledge keepers to share their knowledge

 make connections: o Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining(http://www.csu s.edu/indiv/o/oreyd/ACP.ht m_files/abishop.htm ) o First Nations Education Steering Committee

20 (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and resource management; community profiles; art; nutrition; dwellings o Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resou rces/math-first-peoples/)