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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Fractions are a type of number that can represent quantities.

number

- 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?

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

fluency

- 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?

Regular increases and decreases in patterns can be identified and used to make generalizations.

patterns

- 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?

Standard units are used to describe, measure, and compare attributes of objects’ shapes.

attributes

- 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?

The likelihood of possible outcomes can be examined, compared, and interpreted.

outcomes

- 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?

## Learning Standards

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### Curricular Competencies

*Students are expected to be able to do the following:*### Reasoning and analyzing

Use reasoning to explore and make connections

Estimate reasonably

Estimate reasonably

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

Develop mental math strategies and abilities to make sense of quantities

mental math strategies

- working toward developing fluent and flexible thinking about number

Use technology to explore mathematics

technology

- calculators, virtual manipulatives, concept-based apps

Model mathematics in contextualized experiences

Model

- acting it out, using concrete materials, drawing pictures

### Understanding and solving

Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Visualize to explore mathematical concepts

Develop and use multiple strategies to engage in problem solving

multiple strategies

- visual, oral, play, experimental, written, symbolic

Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

connected

- 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.

### Communicating and representing

Communicate mathematical thinking in many ways

Communicate

- 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

Use mathematical vocabulary and language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Explain and justify

- using mathematical arguments
- “Prove it!”

Represent mathematical ideas in concrete, pictorial, and symbolic forms

concrete, pictorial, and symbolic forms

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

### Connecting and reflecting

Reflect on mathematical thinking

Reflect

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

Connect mathematical concepts to each other and to other areas and personal interests

other areas and personal interests

- 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)

Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Incorporate

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

make connections

- 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/

### Content

*Students are expected to know the following:*number concepts to 1000

number concepts

- 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

fraction concepts

fraction concepts

- 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

addition and subtraction to 1000

addition and subtraction

- 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)

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.

multiplication and division concepts

multiplication and division

- 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

increasing and decreasing patterns

patterns

- 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 using words and numbers, based on concrete experiences

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.

one-step addition and subtraction equations with an unknown number

equations

- 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

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

standard units

- 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?)

time concepts

time

- 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

construction of 3D objects

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

one-to-one correspondence with bar graphs, pictographs, charts, and tables

one-to-one correspondence

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

likelihood of simulated events, using comparative language

simulated events

- 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)

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

financial literacy

- counting mixed combinations of coins and bills up to 0:
- 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.

**Note:**Some of the learning standards in the PHE curriculum address topics that some students and their parents or guardians may feel more comfortable addressing at home. Refer to ministry policy regarding opting for alternative delivery.