## We are Mathematicians.

**Big Ideas:** Development of computational fluency in addition, subtraction, multiplication, and division of whole numbers requires flexible decomposing and composing.

**Term Three – Grade 3**

Financial literacy — fluency with coins and bills to 100 dollars, and earning and payment

- 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.

Multiplication and division concepts

- 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

Measurement, using standard units (linear, mass, and capacity)

- 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?)

**Term Two – Grade 2**

Addition and subtraction facts to 20 (introduction of computational strategies)

- adding and subtracting numbers to 20
- fluency with math strategies for addition and subtraction (e.g., making or bridging 10, decomposing, identifying related doubles, adding on to find the difference)

Addition and subtraction to 100

- decomposing numbers to 100
- estimating sums and differences to 100
- using strategies such as looking for multiples of 10, friendly numbers (e.g., 48 + 37, 37 = 35 + 2, 48 + 2 = 50, 50 + 35 = 85), decomposing into 10s and 1s and recomposing (e.g., 48 + 37, 40 + 30 = 70, 8 +7 = 15, 70 +15 = 85), and compensating (e.g., 48 + 37, 48 +2 = 50, 37 – 2 = 35, 50 + 35 = 80)
- adding up to find the difference
- using an open number line, hundred chart, ten-frames
- using addition and subtraction in real-life contexts and problem-based situations
- whole-class number talks

Multiple attributes of 2D shapes and 3D objects

- sorting 2D shapes and 3D objects, using two attributes, and explaining the sorting rule
- describing, comparing, and constructing 2D shapes, including triangles, squares, rectangles, circles
- identifying 2D shapes as part of 3D objects
- using traditional northwest coast First Peoples shapes (ovoids, U, split U, and local art shapes) reflected in the natural environment

**Term Two – Grade 3**

Addition and subtraction to 1000

- 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

Addition and subtraction facts to 20 (emerging computational fluency)

- 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.

Construction of 3D objects

- 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

- 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

**Term One**

**The grade 3 curriculum: Fraction Concepts**

**Big Ideas:**

- Fractions are a type of number that can represent quantities.

*Students are expected to know the following:*

- 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

**Number Concepts **– Students are expected to know the following:

**Big Ideas:**

- Numbers to 100 represent quantities that can be decomposed into 10s and 1s. (Gr. 2)
- Numbers to 1000 represent quantities that can be decomposed into 100s, 10s and 1s. (Gr. 3)

**The grade 2 curriculum: Number Concepts to 100**

- counting:
- skip-counting by 2, 5, and 10:
- using different starting points
- increasing and decreasing (forward and backward)

- skip-counting by 2, 5, and 10:
- Quantities to 100 can be arranged and recognized:
- comparing and ordering numbers to 100
- benchmarks of 25, 50, and 100
- place value:
- understanding of 10s and 1s
- understanding the relationship between digit places and their value, to 99 (e.g., the digit 4 in 49 has the value of 40)
- decomposing two-digit numbers into 10s and 1s

- even and odd numbers
- Benchmarks
- seating arrangements at ceremonies/feasts of 25, 50, and 100 and personal referents

**The grade 3 curriculum: Number Concepts to 1000**

- 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

**Patterns** – Students are expected to know the following:

**Big Ideas: **

- The regular change in increasing patterns can be identified and used to make generalizations. (Gr. 2)
- Regular increases and decreases in patterns can be identified and used to make generalizations. (Gr. 3)

**The grade 2 curriculum:**

- repeating and increasing patterns
- exploring more complex repeating patterns (e.g., positional patterns, circular patterns)
- identifying the core of repeating patterns (e.g., the pattern of the pattern that repeats over and over)
- increasing patterns using manipulatives, sounds, actions, and numbers (0 to 100)

**The grade 3 curriculum:**

- increasing and decreasing patterns using words and numbers, based on concrete experiences
- 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)

- pattern rules
- 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.