Grade Four Grade Five Grade Six Grade Seven Grade Eight number concepts to 10 000 number concepts to 1 000 000 number concepts: small to large numbers (thousandths to billions) ◦ counting: ◦ counting: ◦ place value from thousandths to ▪ multiples ◦ multiples billions, operations with ▪ flexible counting strategies ◦ flexible counting strategies thousandths to billions ▪ whole number benchmarks ◦ whole number benchmarks ◦ numbers used in science, medicine, ◦ Numbers to 10 000 can be arranged ◦ Numbers to 1 000 000 can be technology, and media and recognized: arranged and recognized: ◦ compare, order, estimate ▪ comparing and ordering ◦ comparing and ordering numbers numbers ◦ estimating large quantities ▪ estimating large quantities ◦ place value: ◦ place value: ◦ 100 000s, 10 000s, 1000s, 100s, ▪ 1000s, 100s, 10s, and 1s 10s, and 1s ▪ understanding the ◦ understanding the relationship relationship between digit between digit places and their places and their value, to 10 value, to 1 000 000 000 ◦ First Peoples use unique counting systems (e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers e.g., 10 = two hands, 20 = one person) Decimals: to hundredths & addition and Decimals: to thousandths and addition and subtraction of decimals to hundredths subtraction of decimals to thousandths ◦ Fractions and decimals are ◦ estimating decimal sums and numbers that represent an amount differences or quantity. ◦ using visual models such as base ◦ Fractions and decimals can 10 blocks, place-value mats, grid represent parts of a region, set, or paper, and number lines linear model. ◦ using addition and subtraction in ◦ Fractional parts and decimals are real-life contexts and problem- equal shares or equal-sized based situations portions of a whole or unit. ◦ whole-class number talks ◦ understanding the relationship between fractions and decimals ◦ estimating decimal sums and differences ◦ using visual models, such as base 10 blocks, place-value mats, grid paper, and number lines ◦ using addition and subtraction in real-life contexts and problem- based situations ◦ whole-class number talks Fractions: Comparing and ordering Fractions: Equivalent fractions and Fractions: Fractions: Fractions: fractions whole-number, fraction, and decimal ◦ improper fractions and mixed ◦ relationships between decimals, ◦ percents less than 1 and greater benchmarks numbers fractions, ratios, and percents than 100 (decimal and fractional ◦ introduction to ratios percents) ◦ whole-number percents and ◦ numerical proportional reasoning percentage discounts (rates, ratio, proportions, and percent) ◦ operations with fractions (addition, subtraction, multiplication, division, and order of operations) ◦ comparing and ordering of ◦ Two equivalent fractions are two ◦ using benchmarks, number line, ◦ conversions, equivalency, and ◦ A worker’s salary increased 122% fractions with common ways to represent the same amount and common denominators to terminating versus repeating in three years. If her salary is now denominators (having the same whole). compare and order, including decimals, place value, and $93,940, what was it originally? ◦ estimating fractions with ◦ comparing and ordering of whole numbers benchmarks ◦ What is ½% of 1 billion? benchmarks (e.g., zero, half, fractions and decimals ◦ using pattern blocks, Cuisenaire ◦ comparing and ordering decimals ◦ The population of Vancouver whole) ◦ addition and subtraction of Rods, fraction strips, fraction and fractions using the number line increased by 3.25%. What is the ◦ using concrete and visual models decimals to thousandths circles, grids ◦ ½ = 0.5 = 50% = 50:100 population if it was approximately ◦ equal partitioning ◦ estimating decimal sums and ◦ birchbark biting ◦ shoreline cleanup 603,500 people last year? differences ◦ comparing numbers, comparing ◦ ◦ Beading ◦ estimating fractions with quantities, equivalent ratios ◦ two-term and three-term ratios, benchmarks (e.g., zero, half, ◦ part-to-part ratios and part-to- real-life examples and problems whole) whole ratios ◦ A string is cut into three pieces ◦ equal partitioning ◦ using base 10 blocks, geoboard, whose lengths form a ratio of 10x10 grid to represent whole 3:5:7. If the string was 105 cm number percents long, how long are the pieces? ◦ finding missing part (whole or ◦ creating a cedar drum box of percentage) proportions that use ratios to create ◦ 50% = 1/2 = 0.5 = 50:100 differences in pitch and tone ◦ paddle making ◦ 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 Addition and Subtraction: to 10 000 Addition and Subtraction: of whole numbers to 1 000 000 ◦ using flexible computation ◦ using flexible computation strategies, involving taking apart strategies involving taking apart (e.g., decomposing using friendly (e.g., decomposing using friendly numbers and compensating) and numbers and compensating) and combining numbers in a variety of combining numbers in a variety of ways, regrouping ways, regrouping ◦ estimating sums and differences to ◦ estimating sums and differences to 10 000 10 000 ◦ using addition and subtraction in ◦ using addition and subtraction in real-life contexts and problem- real-life contexts and problem- based situations based situations ◦ whole-class number talks ◦ whole-class number talks Multiplication and Division: of 2 or 3 Multiplication and Division: to three Multiplication and Division: Multiplication and Division: digit numbers by a one digit number digits, including division with remainders ◦ order of operations with whole ◦ operations with integers numbers (addition, subtraction, ◦ factors and multiples — greatest multiplication, division, and order common factor and least common of operations) multiple ◦ operations with decimals ◦ multiplication and division of (addition, subtraction, decimals multiplication, division, and order of operations) ◦ understanding the relationships ◦ understanding the relationships ◦ includes the use of brackets, but ◦ addition, subtraction, ◦ between multiplication and between multiplication and excludes exponents multiplication, division, and order division, multiplication and division, multiplication and ◦ quotients can be rational numbers of operations addition, division and subtraction addition, and division and ◦ prime and composite numbers, ◦ concretely, pictorially, ◦ using flexible computation subtraction divisibility rules, factor trees, symbolically strategies (e.g., decomposing, ◦ using flexible computation prime factor phrase (e.g., 300 = 22 ◦ order of operations includes the use distributive principle, commutative strategies (e.g., decomposing, x 3 x 52 ) of brackets, excludes exponents principle, repeated addition and distributive principle, commutative ◦ using graphic organizers (e.g., ◦ using two-sided counters repeated subtraction) principle, repeated addition, Venn diagrams) to compare ◦ 9–(–4) = 13 because –4 is 13 away ◦ using multiplication and division in repeated subtraction) numbers for common factors and from +9 real-life contexts and problem- ◦ using multiplication and division in common multiples ◦ extending whole-number strategies based situations real-life contexts and problem- ◦ 0.125 x 3 or 7.2 ÷ 9 to decimals ◦ whole-class number talks based situations ◦ using base 10 block array ◦ includes the use of brackets, but ◦ whole-class number talks ◦ birchbark biting excludes exponents ◦ Fact Fluency: Fact Fluency: Fact Fluency: Fact Fluency: ◦ addition and subtraction facts to 20 ◦ addition and subtraction facts to ◦ multiplication and division facts to ◦ multiplication and division facts to (developing computational 20 (extending computational 100 (developing computational 100 (extending computational fluency) fluency) fluency) fluency) ◦ multiplication and division facts to ◦ multiplication and division facts to 100 (introductory computational 100 (emerging computational strategies) fluency) ◦ Provide opportunities for authentic ◦ Provide opportunities for authentic ◦ mental math strategies (e.g., the ◦ When multiplying 214 by 5, we practice, building on previous practice, building on previous double-double strategy to multiply can multiply by 10, then divide by grade-level addition and grade-level addition and 23 x 4) 2 to get 1070. subtraction facts. subtraction facts. ◦ flexible use of mental math ◦ applying strategies and knowledge strategies of addition and subtraction facts in ◦ Provide opportunities for concrete real-life contexts and problem- and pictorial representations of based situations, as well as when multiplication. making math-to-math connections ◦ building computational fluency (e.g., for 800 + 700, you can annex ◦ Use games to provide opportunities the zeros and use the knowledge of for authentic practice of 8 + 7 to find the total) multiplication computations. ◦ Provide opportunities for concrete ◦ looking for patterns in numbers, and pictorial representations of such as in a hundred chart, to multiplication. further develop understanding of ◦ Use games to provide opportunities multiplication computation for authentic practice of ◦ Connect multiplication to skip- multiplication computations. counting. ◦ looking for patterns in numbers, ◦ Connecting multiplication to such as in a hundred chart, to division and repeated addition. further develop understanding of ◦ Memorization of facts is not multiplication computation intended for this level. ◦ Connect multiplication to skip- ◦ Students will become more fluent counting. with these facts. ◦ Connect multiplication to division ◦ using mental math strategies, such and repeated addition. as doubling or halving ◦ Memorization of facts is not ◦ Students should be able to recall intended this level. the following multiplication facts ◦ Students will become more fluent by the end of Grade 4 (2s, 5s, 10s). with these facts. ◦ using mental math strategies such as doubling and halving, annexing, and distributive property ◦ Students should be able to recall many multiplication facts by the end of Grade 5 (e.g., 2s, 3s, 4s, 5s, 10s). ◦ developing computational fluency with facts to 100 Patterns: increasing and decreasing Patterns: rules for increasing and Patterns: increasing and decreasing patterns, using tables and charts decreasing patterns with words, numbers, patterns, using expressions, tables, and symbols, and variables graphs as functional relationships ◦ Change in patterns can be ◦ limited to discrete points in the first represented in charts, graphs, and quadrant tables. ◦ visual patterning (e.g., colour tiles) ◦ using words and numbers to ◦ Take 3 add 2 each time, 2n + 1, describe increasing and decreasing and 1 more than twice a number all patterns describe the pattern 3, 5, 7, … ◦ fish stocks in lakes, life ◦ graphing data on First Peoples expectancies language loss, effects of language intervention Algebra: Algebra: Algebra: Algebra: Algebra: ◦ algebraic relationships among ◦ one-step equations with variables ◦ one-step equations with whole- ◦ discrete linear relations, using ◦ perfect squares and cubes quantities number coefficients and solutions expressions, tables, and graphs ◦ square and cube roots ◦ one-step equations with an ◦ two-step equations with whole- ◦ discrete linear relations (extended unknown number, using all number coefficients, constants, and to larger numbers, limited to operations solutions integers) ◦ expressions- writing and evaluating using substitution ◦ two-step equations with integer coefficients, constants, and solutions ◦ representing and explaining one- ◦ solving one-step equations with a ◦ preservation of equality (e.g., using ◦ four quadrants, limited to integral ◦ using colour tiles, pictures, or step equations with an unknown variable a balance, algebra tiles) coordinates multi-link cubes number ◦ expressing a given problem as an ◦ 3x = 12, x + 5 = 11 ◦ 3n + 2; values increase by 3 ◦ building the number or using prime ◦ describing pattern rules, using equation, using symbols (e.g., 4 + starting from y-intercept of 2 factorization words and numbers from concrete X = 15) ◦ deriving relation from the graph or ◦ finding the cube root of 125 and pictorial representations table of values ◦ finding the square root of 16/169 ◦ planning a camping or hiking trip; ◦ Small Number stories: Small ◦ estimating the square root of 30 planning for quantities and Number and the Old Canoe, Small ◦ two-variable discrete linear materials needed per individual and Number Counts to 100 relations group over time (mathcatcher.irmacs.sfu.ca/stories) ◦ expressions, table of values, and ◦ one-step equations for all ◦ solving and verifying 3x + 4 = 16 graphs operations involving an unknown ◦ modelling the preservation of ◦ scale values (e.g., tick marks on number (e.g., ___ + 4 = 15, 15 – equality (e.g., using balance, axis represent 5 units instead of 1) □ = 11) pictorial representation, algebra ◦ four quadrants, integral coordinates ◦ start unknown (e.g., n + 15 = 20; tiles) ◦ using an expression to describe a 20 – 15 = □) ◦ spirit canoe trip pre-planning and relationship ◦ change unknown (e.g., 12 + n = calculations ◦ evaluating 0.5n – 3n + 25, if n = 14 20) ◦ Small Number stories: Small ◦ solving and verifying 3x – 4 = –12 ◦ result unknown (e.g., 6 + 13 = __) Number and the Big Tree ◦ modelling the preservation of (mathcatcher.irmacs.sfu.ca/stories) equality (e.g., using a balance, manipulatives, algebra tiles, diagrams) ◦ spirit canoe journey calculations ◦ Measurement: how to tell time with Measurement: Measurement: Measurement: Measurement: analog and digital clocks, using 12- and ◦ area measurement of squares and • perimeter of complex shapes ◦ circumference and area of circles ◦ surface area and volume of 24-hour clocks rectangles • area of triangles, parallelograms, ◦ volume of rectangular prisms and regular solids, including triangular ◦ relationships between area and and trapezoids cylinders and other right prisms and perimeter • angle measurement and cylinders ◦ duration, using measurement of classification time • volume and capacity ◦ understanding how to tell time with ◦ measuring area of squares and ◦ A complex shape is a group of ◦ exploring strategies to determine analog and digital clocks, using 12- rectangles, using tiles, geoboards, shapes with no holes (e.g., use ◦ constructing circles given radius, the surface area and volume of a and 24-hour clocks grid paper colour tiles, pattern blocks, diameter, area, or circumference regular solid using objects, a net, ◦ understanding the concept of a.m. ◦ investigating perimeter and area tangrams). ◦ finding relationships between 3D design software and p.m. and how they are related to but not ◦ grid paper explorations radius, diameter, circumference, ◦ volume = area of the base x height ◦ understanding the number of dependent on each other ◦ deriving formulas and area to develop C = π x d ◦ surface area = sum of the areas of minutes in an hour ◦ use traditional dwellings ◦ making connections between area formula each side ◦ understanding the concepts of ◦ Invite a local Elder or knowledge of parallelogram and area of ◦ applying A = π x r x r formula to using a circle and of using fractions keeper to talk about traditional rectangle find the area given radius or in telling time (e.g., half past, measuring and estimating ◦ birchbark biting diameter quarter to) techniques for hunting, fishing, and ◦ straight, acute, right, obtuse, reflex ◦ drummaking, dreamcatcher ◦ telling time in five-minute intervals building. ◦ constructing and identifying; making, stories of SpiderWoman ◦ telling time to the nearest minute ◦ understanding elapsed time and include examples from local (Dene, Cree, Hopi, Tsimshian), ◦ First Peoples use of numbers in duration environment basket making, quill box making time and seasons, represented by ◦ applying concepts of time in real- ◦ estimating using 45°, 90°, and 180° (Note: Local protocols should be seasonal cycles and moon cycles life contexts and problem-based as reference angles considered when choosing an (e.g., how position of sun, moon, situations ◦ angles of polygons activity.) and stars is used to determine times ◦ daily and seasonal cycles, moon ◦ Small Number stories: Small ◦ volume = area of base x height for traditional activities, cycles, tides, journeys, events Number and the Skateboard Park ◦ bentwood boxes, wiigwaasabak navigation) (mathcatcher.irmacs.sfu.ca/stories) and mide-wiigwaas (birch bark ◦ using cubes to build 3D objects and scrolls) determine their volume ◦ Exploring Math through Haida ◦ referents and relationships between Legends: Culturally Responsive units (e.g., cm3, m3, mL, L) Mathematics ◦ the number of coffee mugs that (haidanation.ca/Pages/language hold a litre /haida_legends/media/Lessons ◦ berry baskets, seaweed drying /RavenLes4-9.pdf) ◦ Geometry: Geometry: Geometry: Geometry: ◦ regular and irregular polygons • classification of prisms and ◦ triangles ◦ Pythagorean theorem ◦ perimeter of regular and irregular pyramids ◦ construction, views, and nets of 3D shapes objects ◦ line symmetry ◦ describing and sorting regular and ◦ investigating 3D objects and 2D ◦ scalene, isosceles, equilateral ◦ modelling the Pythagorean irregular polygons based on shapes, based on multiple attributes ◦ right, acute, obtuse theorem multiple attributes ◦ describing and sorting ◦ classified regardless of orientation ◦ finding a missing side of a right ◦ investigating polygons (polygons quadrilaterals triangle are closed shapes with similar ◦ describing and constructing ◦ deriving the Pythagorean theorem attributes) rectangular and triangular prisms ◦ constructing canoe paths and ◦ Yup’ik border patterns ◦ identifying prisms in the landings given current on a river ◦ using geoboards and grids to environment ◦ First Peoples constellations create, represent, measure, and ◦ top, front, and side views of 3D calculate perimeter objects ◦ using concrete materials such as ◦ matching a given net to the 3D pattern blocks to create designs object it represents that have a mirror image within ◦ drawing and interpreting top, front, them and side views of 3D objects ◦ First Peoples art, borders, ◦ constructing 3D objects with nets birchbark biting, canoe building ◦ using design software to create 3D ◦ Visit a structure designed by First objects from nets Peoples in the local community ◦ bentwood boxes, lidded baskets, and have the students examine the packs symmetry, balance, and patterns ◦ within the structure, then replicate simple models of the architecture focusing on the patterns they noted in the original.

Transformations Transformations: Transformations: Transformations: ◦ single transformations ◦ combinations of transformations ◦ combinations of transformations ◦ single transformations ◦ plotting points on Cartesian plane ◦ four quadrants, integral coordinates (slide/translation, flip/reflection, using whole-number ordered pairs ◦ translation(s), rotation(s), and/or turn/rotation) ◦ translation(s), rotation(s), and/or reflection(s) on a single 2D shape; ◦ using concrete materials with a reflection(s) on a single 2D shape combination of successive focus on the motion of ◦ limited to first quadrant transformations of 2D shapes; transformations ◦ transforming, drawing, and tessellations ◦ weaving, cedar baskets, designs describing image ◦ First Peoples art, jewelry making, ◦ Use shapes in First Peoples art to birchbark biting integrate printmaking (e.g., Inuit, Northwest coastal First Nations, frieze work) (mathcentral.uregina.ca/RR/ database/RR.09.01/mcdonald1/) Graphing: Graphing: Graphing: Graphing: ◦ one-to-one correspondence and ◦ one-to-one correspondence and ◦ line graphs ◦ Cartesian coordinates and many-to-one correspondence, many-to-one correspondence, graphing using bar graphs and pictographs using double bar graphs ◦ circle graphs ◦ many-to-one correspondence: one ◦ many-to-one correspondence: one ◦ table of values, data set; creating ◦ origin, four quadrants, integral symbol represents a group or value symbol represents a group or value and interpreting a line graph from a coordinates, connections to linear (e.g., on a bar graph, one square (e.g., on a bar graph, one square given set of data relations, transformations may represent five cookies) may represent five cookies) ◦ overlaying coordinate plane on ◦ medicine wheel, beading on dreamcatcher, overlaying coordinate plane on traditional maps ◦ 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 Probability: probability experiments Probability: probability experiments, Probability: single-outcome probability, Probability: experimental probability Probability: single events or outcomes both theoretical and experimental with two independent events ◦ central tendency ◦ theoretical probability with two independent event ◦ predicting single outcomes (e.g., ◦ predicting outcomes of ◦ single-outcome probability events ◦ experimental probability, multiple ◦ mean, median, and mode when you spin using one spinner independent events (e.g., when you (e.g., spin a spinner, roll a die, toss trials (e.g., toss two coins, roll two ◦ with two independent events: and it lands on a single colour) spin using a spinner and it lands on a coin) dice, spin a spinner twice, or a sample space (e.g., using tree ◦ using spinners, rolling dice, pulling a single colour) ◦ listing all possible outcomes to combination thereof) diagram, table, graphic organizer) objects out of a bag ◦ predicting single outcomes (e.g., determine theoretical probability ◦ dice games ◦ rolling a 5 on a fair die and flipping ◦ recording results using tallies when you spin using a spinner and ◦ comparing experimental results (web.uvic.ca/~tpelton/fn-math/fn- a head on a fair coin is 1/6 x ½ = ◦ Dene/Kaska hand games, Lahal it lands on a single colour) with theoretical expectation dicegames.html) 1/12 stick games ◦ using spinners, rolling dice, pulling ◦ Lahal stick games ◦ deciding whether a spinner in a objects out of a bag game is fair ◦ representing single outcome probabilities using fractions Financial Literacy: monetary Financial Literacy: monetary Financial Literacy: — simple budgeting Financial Literacy: financial percentage Financial Literacy: best buys calculations, including making change calculations, including making change and consumer math with amounts to 100 dollars and making with amounts to 1000 dollars and simple financial decisions developing simple financial plans ◦ making monetary calculations, ◦ making monetary calculations, ◦ informed decision making on ◦ financial percentage calculations ◦ coupons, proportions, unit price, including decimal notation in real- including making change and saving and purchasing ◦ sales tax, tips, discount, sale price products and services life contexts and problem-based decimal notation to $1000 in real- ◦ How many weeks of allowance ◦ proportional reasoning strategies situations life contexts and problem-based will it take to buy a bicycle? (e.g., unit rate, equivalent fractions ◦ applying a variety of strategies, situations given prices and quantities) such as counting up, counting ◦ applying a variety of strategies, back, and decomposing, to such as counting up, counting calculate totals and make change back, and decomposing, to ◦ making simple financial decisions calculate totals and make change involving earning, spending, ◦ making simple financial plans to saving, and giving meet a financial goal ◦ equitable trade rules ◦ developing a budget that takes into account income and expenses