Elaborations (from BC curriculum)

• Number: Number represents and describes quantity. Sample questions to support inquiry with students: In how many ways can you represent the fraction ____? What is the relationship between parts and wholes when we think about fractions? How do these materials help you think about fractions? What stories live in numbers? How do numbers help us communicate and think about place? How do numbers help us communicate and think about ourselves?

Elaborations (from BC curriculum)

• Computational Fluency: Computational fluency develops from a strong sense of number. Sample questions to support inquiry with students: What is the relationship between addition and multiplication? How can we decompose and compose numbers to help us add, subtract, multiply, and divide? How might we use mental math strategies to solve equations?

Elaborations (from BC curriculum)

• Patterning: We use patterns to represent identified regularities and to make generalizations. Sample questions to support inquiry with students: How are these patterns alike and different (e.g., increasing and decreasing)? How are place value patterns repeated in large numbers? How do numbers help us describe patterns?

Elaborations (from BC curriculum)

• Geometry and Measurement: We can describe, measure, and compare spatial relationships. Sample questions to support inquiry with students: Where do 2D shapes live in 3D objects? How do standard units help us to compare and communicate measurements? How do the properties of shapes contribute to buildings and designs?

Elaborations (from BC curriculum)

• Data and Probability: Analyzing data and chance enables us to compare and interpret. Sample questions to support inquiry with students: How is the probability of an event determined and described? What events in our lives are left to chance? What are the possible outcomes of these events?

Elaborations (from BC curriculum)

• counting: skip-counting by any number from any starting point, increasing and decreasing (i.e., forward and backward) skip-counting is related to multiplication investigating place-value based counting patterns (e.g., counting by 10s, 100s; bridging over a century; noticing the role of zero as a placeholder 698, 699, 700, 701; noticing the predictability of our number system) Numbers to 1000 can be arranged and recognized: comparing and ordering numbers estimating large quantities place value: 100s, 10s, and 1s understanding the relationship between digit places and their values, to 1000 (e.g., the digit 4 in 342 has the value of 40 or 4 tens) understanding the importance of 0 as a place holder (e.g., in the number 408, the zero indicates that there are 0 tens) instructional resource: Math in a Cultural Context, by Jerry Lipka

Elaborations (from BC curriculum)

• Fractions are numbers that represent an amount or quantity. Fractions can represent parts of a region, set, or linear model. Fraction parts are equal shares or equal-sized portions of a whole or unit. Provide opportunities to explore and create fractions with concrete materials. recording pictorial representations of fraction models and connecting to symbolic notation equal partitioning equal sharing, pole ratios as visual parts, medicine wheel, seasons

Elaborations (from BC curriculum)

• using flexible computation strategies, involving taking apart (e.g., decomposing using friendly numbers and compensating) and combining numbers in a variety of ways, regrouping estimating sums and differences of all operations to 1000 using addition and subtraction in real-life contexts and problem-based situations whole-class number talks

Elaborations (from BC curriculum)

• adding and subtracting of numbers to 20 demonstrating fluency with math strategies for addition and subtraction (e.g., decomposing, making and bridging 10, related doubles, and commutative property) Addition and subtraction are related. At the end of Grade 3, most students should be able to recall addition facts to 20.

Elaborations (from BC curriculum)

• understanding concepts of multiplication (e.g., groups of, arrays, repeated addition) understanding concepts of division (e.g., sharing, grouping, repeated subtraction) Multiplication and division are related. Provide opportunities for concrete and pictorial representations of multiplication. Use games to develop opportunities for authentic practice of multiplication computations. looking for patterns in numbers, such as in a hundred chart, to further develop understanding of multiplication computation Connect multiplication to skip-counting. Connect multiplication to division and repeated addition. Memorization of facts is not intended for this level. fish drying on rack; sharing of food resources in First Peoples communities

Elaborations (from BC curriculum)

• creating patterns using concrete, pictorial, and numerical representations representing increasing and decreasing patterns in multiple ways generalizing what makes the pattern increase or decrease (e.g., doubling, adding 2)

Elaborations (from BC curriculum)

• from a concrete pattern, describing the pattern rule using words and numbers predictability in song rhythm and patterns Share examples of local First Peoples art with the class, and ask students to notice patterns in the artwork.

Elaborations (from BC curriculum)

• start unknown (e.g., n + 15 = 20 or □ + 15 + 20) change unknown ( e.g., 12 + n = 20 or 12 + □ = 20) result unknown (e.g., 6 + 13 = n or 6 + 13 = □;) investigating even and odd numbers

Elaborations (from BC curriculum)

• linear measurements, using standard units (e.g., centimetre, metre, kilometre) capacity measurements, using standard units (e.g., millilitre, litre) Introduce concepts of perimeter, area, and circumference (the distance around); use of formula and pi to calculate not intended — the focus is on the concepts. area measurement, using square units (standard and non-standard) mass measurements, using standard units (e.g., gram, kilogram) estimation of measurements, using standard referents (e.g., If this cup holds 100 millilitres, about how much does this jug hold?)

Elaborations (from BC curriculum)

• understanding concepts of time (e.g., second, minute, hour, day, week, month, year) understanding the relationships between units of time Telling time is not expected at this level. estimating time, using environmental references and natural daily/seasonal cycles, temperatures based on weather systems, traditional calendar

Elaborations (from BC curriculum)

• identifying 3D objects according to the 2D shapes of the faces and the number of edges and vertices (e.g., construction of nets, skeletons) describing the attributes of 3D objects (e.g., faces, edges, vertices) identifying 3D objects by their mathematical terms (e.g., sphere, cube, prism, cone, cylinder) comparing 3D objects (e.g., How are rectangular prisms and cubes the same or different?) understanding the preservation of shape (e.g., the orientation of a shape will not change its properties) jingle dress bells, bentwood box, birch bark baskets, pithouses

Elaborations (from BC curriculum)

• collecting data, creating a graph, and describing, comparing, and discussing the results choosing a suitable representation

Elaborations (from BC curriculum)

• using comparative language (e.g., certain, uncertain; more, less, or equally likely) developing an understanding of chance (e.g., tossing a coin creates a 50-50 chance of landing a head or tail; drawing from a bag, using spinners, and rolling dice all simulate probability events) story: The Snowsnake Game (yukon-ed-show-me-your-math.wikispaces.com/file/view/The%20Snowsnake%20Game.pdf/203828506/The%20Snowsnake%20Game.pdf)

Elaborations (from BC curriculum)

• counting mixed combinations of coins and bills up to $100: totalling up a set of coins and bills using different combinations of coins and bills to make the same amount understanding that payments can be made in flexible ways (e.g., cash, cheques, credit, electronic transactions, goods and services) understanding that there are different ways of earning money to reach a financial goal (e.g., recycling, holding bake sales, selling items, walking a neighbour’s dog) Using pictures of First Peoples trade items (e.g., dentalium shells, dried fish, or tools when available) with the values indicated on the back, have students play a trading game.

Elaborations (from BC curriculum)

• estimating by comparing to something familiar (e.g., more than 5, taller than me)

Elaborations (from BC curriculum)

• working toward developing fluent and flexible thinking about number

Elaborations (from BC curriculum)

• calculators, virtual manipulatives, concept-based apps

Elaborations (from BC curriculum)

• acting it out, using concrete materials, drawing pictures

Elaborations (from BC curriculum)

• visual, oral, play, experimental, written, symbolic

Elaborations (from BC curriculum)

• in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration Have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

Elaborations (from BC curriculum)

• concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas using technology such as screencasting apps, digital photos

Elaborations (from BC curriculum)

• using mathematical arguments “Prove it!”

Elaborations (from BC curriculum)

• Use local materials gathered outside for concrete and pictorial representations.

Elaborations (from BC curriculum)

• sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions

Elaborations (from BC curriculum)

• to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, the environment, popular media and news events, social justice, and cross-curricular integration)

Elaborations (from BC curriculum)

• Invite local First Peoples Elders and knowledge keepers to share their knowledge.
• 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/