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# Mathematics

## Core Competencies

### Big Ideas

### Grandes idées

Numbers to 100 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?
- What patterns do you notice in numbers?
- 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 and subtraction with numbers to 100 requires an understanding of place value.

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 can you use addition to help you subtract?
- How does understanding 10 help us to add and subtract two-digit numbers?

The regular change in increasing 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 can we represent patterns in different ways/modes?
- How can you create repeating patterns with objects that are all one colour?
- What stories live in patterns?

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:*- What 2D shapes live in objects in our world?
- How can you combine shapes to make new shapes?

Concrete items can be represented, compared, and interpreted pictorially in graphs.

graphs

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- When you look at this graph, what do you notice? What do you wonder?
- How do graphs help us understand data?
- What are some different ways to represent data pictorially?

## 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.
- Elder communication to explain harvest traditions and sharing 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 100

number concepts

- 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 of 25, 50, and 100 and personal referents

benchmarks

- seating arrangements at ceremonies/feasts

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

facts to 20

- 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

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 + 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

repeating and increasing patterns

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)
- Métis finger weaving
- First Peoples head/armband patterning
- online video and text:
*Small Number Counts to 100*(mathcatcher.irmacs.sfu.ca/story/small-number-counts-100)

change in quantity, using pictorial and symbolic representation

change in quantity

- numerically describing a change in quantity (e.g., for 6 + n = 10, visualize the change in quantity by using ten-frames, hundred charts, etc.)

symbolic representation of equality and inequality

direct linear measurement, introducing standard metric units

direct linear measurement

- centimetres and metres
- estimating length
- measuring and recording length, height, and width, using standard units

multiple attributes of 2D shapes and 3D objects

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

pictorial representation of concrete graphs, using one-to-one correspondence

pictorial representation

- collecting data, creating a concrete graph, and representing the graph, using a pictorial representation through grids, stamps, drawings
- one-to-one correspondence

likelihood of familiar life events, using comparative language

familiar life events

- using comparative language (e.g., certain, uncertain; more, less, or equally likely)

financial literacy — coin combinations to 100 cents, and spending and saving

financial literacy

- counting simple mixed combinations of coins to 100 cents
- introduction to the concepts of spending and saving, integrating the concepts of wants and needs
- role-playing financial transactions (e.g., using bills and coins)

**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.