Connecting and reflecting Reflect on mathematical thinking Connect mathematical concepts to each other and to other areas and personal interests Use mathematical arguments to support personal choices Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts Have students pose and solve problems or ask questions connected to place, stories, and cultural practices. Explain and justify: using mathematical arguments 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 Reflect: sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions 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) personal choices: including anticipating percents finding missing part (whole or percentage) 50% = 1/2 = 0.5 = 50:100 decimals: 0.125 x 3 or 7.2 ÷ 9 using base 10 block array birchbark biting 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 Aboriginal language loss, effects of language intervention one-step equations: preservation of equality (e.g., using a balance, algebra tiles) 3x = 12, x + 5 = 11 perimeter A complex shape is a group of shapes with no holes (e.g., use colour tiles, pattern blocks, tangrams). area: grid paper explorations deriving formulas making connections between area of parallelogram and area of rectangle birchbark biting 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
Communicating and representing Use mathematical vocabulary and language to contribute to mathematical discussions Explain and justify mathematical ideas and decisions Communicate mathematical thinking in many ways Represent mathematical ideas in concrete, pictorial, and symbolic forms Connecting and reflecting Reflect on mathematical thinking Connect mathematical concepts to each other and to other areas and personal interests Use mathematical arguments to support personal choices Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts includes familiar, personal, and from other cultures connected: in daily activities, local and traditional practices, the environment, popular media and news events, integration Patterns are important in Aboriginal technology, architecture, and art. Have students pose and solve problems or ask questions connected to place, stories, and cultural practices. Explain and justify: using mathematical arguments 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 Reflect: sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions other areas and personal interests: to develop a sense of how mathematics helps us understand ourselves and the 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 () 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 () 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.) volume: volume = area of base x height bentwood boxes, wiigwaasabak and mide-wiigwaas (birch bark scrolls)
world around us (e.g., daily activities, local and traditional practices, the environment, popular media and news events, and social justice) personal choices: including anticipating consequences Incorporate First Peoples: Invite local First Peoples Elders and knowledge keepers to share their knowledge make connections: Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining() First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment and resource management; community profiles; art; nutrition; dwellings Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/k-7/) Exploring Math through Haida Legends: Culturally Responsive Mathematics () 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 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 Aboriginal 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 tradional 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) Puim, Hubbub dice games () financial literacy: financial percentage calculations sales tax, tips, discount, sale price
Communicating and representing Use mathematical vocabulary and language to contribute to mathematical discussions Explain and justify mathematical ideas and decisions Communicate mathematical thinking in many ways Represent mathematical ideas in concrete, pictorial, and symbolic forms Connecting and reflecting Reflect on mathematical thinking Connect mathematical concepts to each other and to other areas and personal interests Use mathematical arguments to support personal choices Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts multiple strategies: includes familiar, personal, and from other cultures connected: in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration Patterns are important in Aboriginal technology, architecture, and art. Have students pose and solve problems or ask questions connected to place, stories, and cultural practices. Explain and justify: using mathematical arguments 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 Reflect: sharing the mathematical thinking of self and others, including evaluating strategies and theoretical probability with two independent events financial literacy — best buys 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 discrete linear relations: two-variable discrete linear relations expressions, table of values, and graphs scale values (e.g., tick marks on axis represent 5 units instead of 1) four quadrants, integral coordinates expressions: using an expression to describe a relationship evaluating 0.5n – 3n + 25, if n = 14 two-step equations: solving and verifying 3x – 4 = –12 modelling the preservation of equality (e.g., using a balance, manipulatives, algebra tiles, diagrams) spirit canoe journey calculations surface area and volume: exploring strategies to determine the surface area and volume of a regular solid using objects, a net, 3D design software volume = area of the base x height surface area = sum of the areas of each side Pythagorean theorem: modelling the Pythagorean theorem finding a missing side of a right triangle deriving the Pythagorean theorem constructing canoe paths and landings given current on a river (First Nations Education Steering Committee)
solutions, extending, and posing new problems and questions 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) personal choices: including anticipating consequences Incorporate First Peoples: Invite local First Peoples Elders and knowledge keepers to share their knowledge make connections: Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining() First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and resource management; Aboriginal constellations and adaus 3D objects: top, front, and side views of 3D objects matching a given net to the 3D object it represents drawing and interpreting top, front, and side views of 3D objects constructing 3D objects with nets using design software to create 3D objects from nets bentwood boxes, lidded baskets, packs central tendency: mean, median, and mode theoretical probability: with two independent events: sample space (e.g., using tree diagram, table, graphic organizer) rolling a 5 on a fair die and flipping a head on a fair coin is 1/6 x ½ = 1/12 deciding whether a spinner in a game is fair financial literacy: coupons, proportions, unit price, products and services proportional reasoning strategies (e.g., unit rate, equivalent fractions given prices and quantities)