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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Numbers to 20 represent quantities that can be decomposed into 10s and 1s.

Numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- How does understanding 5 or 10 help us think about other numbers?
- What is the relationship between 10s and 1s?
- Why is it useful to use 10 frames to represent quantities?
- 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?

Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.

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 subtraction?
- How does knowing that 4 and 6 make 10 help you understand other ways to make 10?
- How many different ways can you solve…? (e.g., 8 + 5)

Repeating elements in patterns can be identified.

patterns

- Patterning: We use patterns to represent identified regularities and to make generalizations.
*Sample questions to support inquiry with students:*- How can patterns be used to make predictions?
- What is the relationship between increasing patterns and addition?
- What do you notice about this pattern? What is the part that repeats?
- What number patterns live in a hundred chart?

Objects and shapes have attributes that can be described, measured, and compared.

attributes

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- How are these shapes alike and different?
- What stories live in these shapes?
- What 2D shapes can you find in nature?

Concrete graphs help us to compare and interpret data and show one-to-one correspondence.

data

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- What stories can data tell us?
- When might we use words like never, sometimes, always, more likely, and less likely?
- How does organizing concrete data help us understand the data?

## 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)
- First Peoples people used specific estimating and measuring techniques in daily life (e.g., estimating time using environmental references and natural daily/seasonal cycles, estimating temperatures based on weather systems).

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
- Patterns are important in First Peoples technology, architecture, and artwork.
- 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

- how ovoid has different look to represent different animal parts
- 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 20

number concepts

- counting:
- counting on and counting back
- skip-counting by 2 and 5
- sequencing numbers to 20
- comparing and ordering numbers to 20
- Numbers to 20 can be arranged and recognized.
- subitizing
- base 10
- 10 and some more

- books published by Native Northwest:
*Learn to Count*, by various artists;*Counting Wild Bears*, by Gryn White;*We All Count*, by Jason Adair;*We All Count*, by Julie Flett (nativenorthwest.com) using counting collections made of local materials; counting in different languages; different First Peoples counting systems (e.g., Tsimshian) *Tlingit Math Book*(yukon-ed-show-me-your-math.wikispaces.com/file/detail/Tlingit Math Book.pdf)

ways to make 10

make 10

- decomposing 10 into parts
- Numbers to 10 can be arranged and recognized.
- benchmarks of 10 and 20
- Traditional First Peoples counting methods involved using fingers to count to 5 and for groups of 5.
- traditional songs/singing and stories

addition and subtraction to 20 (understanding of operation and process)

addition and subtraction to 20

- decomposing 20 into parts
- mental math strategies:
- counting on
- making 10
- doubles

- Addition and subtraction are related.
- whole-class number talks
- nature scavenger hunt in
*Kaska Counting Book*(yukon-ed-show-me-your-math.wikispaces.com/file/detail/Kaska Counting Book.pdf)

repeating patterns with multiple elements and attributes

repeating patterns

- identifying sorting rules
- repeating patterns with multiple elements/attributes
- translating patterns from one representation to another (e.g., an orange-blue pattern could be translated to a circle-square pattern)
- letter coding of pattern
- predicting an element in repeating patterns using a variety of strategies
- patterns using visuals (ten-frames, hundred charts)
- investigating numerical patterns (e.g., skip-counting by 2s or 5s on a hundred chart)
- beading using 3–5 colours

change in quantity to 20, concretely and verbally

change in quantity to 20

- verbally describing a change in quantity (e.g., I can build 7 and make it 10 by adding 3)

meaning of equality and inequality

equality and inequality

- demonstrating and explaining the meaning of equality and inequality
- recording equations symbolically, using = and ≠

direct measurement with non-standard units (non-uniform and uniform)

direct measurement

- Non-uniform units are not consistent in size (e.g., children’s hands, pencils); uniform units are consistent in size (e.g., interlocking cubes, standard paper clips).
- understanding the importance of using a baseline for direct comparison in linear measurement
- using multiple copies of a unit
- iterating a single unit for measuring (e.g., to measure the length of a string with only one cube, a student iterates the cube over and over, keeping track of how many cubes long the string is)
- tiling an area
- rope knots at intervals
- using body parts to measure
- book:
*An Anishnaabe Look at Measurement,*by Rhonda Hopkins and Robin King-Stonefish (strongnations.com/store/item_display.php?i=3494&f=) - hand/foot tracing for mitten/moccasin making

comparison of 2D shapes and 3D objects

2D shapes and 3D objects

- sorting 3D objects and 2D shapes using one attribute, and explaining the sorting rule
- comparing 2D shapes and 3D objects in the environment
- describing relative positions, using positional language (e.g., up and down, in and out)
- replicating composite 2D shapes and 3D objects (e.g., putting two triangles together to make a square)

concrete graphs, using one-to-one correspondence

concrete graphs

- creating, describing, and comparing concrete graphs

likelihood of familiar life events, using comparative language

familiar life events

- using the language of probability (e.g., never, sometimes, always, more likely, less likely)
- cycles (Elder or knowledge keeper to speak about ceremonies and life events)

financial literacy — values of coins, and monetary exchanges

financial literacy

- identifying values of coins (nickels, dimes, quarters, loonies, and toonies)
- counting multiples of the same denomination (nickels, dimes, loonies, and toonies)
- Money is a medium of exchange.
- role-playing financial transactions (e.g., using coins and whole numbers), integrating the concept of wants and needs
- trade games, with understanding that objects have variable value or worth (shells, beads, furs, tools)

**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.