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# Mathematics K

2016/17

Curriculum Mathematics Kindergarten
PDF Grade-Set: k-9

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### Big Ideas

### Grandes idées

Numbers represent quantities that can be decomposed into smaller parts.

Numbers

- Number: Number represents and describes quantity.
- Sample questions to support inquiry with students:
- How do these materials help us think about numbers and parts of numbers?
- Which numbers of counters/dots are easy to recognize and why?
- In how many ways can you decompose ____?
- 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?

- Sample questions to support inquiry with students:

One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.

fluency

- Computational Fluency: Computational fluency develops from a strong sense of number.
- Sample questions to support inquiry with students:
- If you know that 4 and 6 make 10, how does that help you understand other ways to make 10?
- How does understanding 5 help us decompose and compose numbers to 10?
- What parts make up the whole?

- Sample questions to support inquiry with students:

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:
- What makes a pattern a pattern?
- How are these patterns alike and different?
- Do all patterns repeat?

- Sample questions to support inquiry with students:

Objects 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 do you notice about these shapes?
- How are these shapes alike and different?

- Sample questions to support inquiry with students:

Familiar events can be described as likely or unlikely and compared.

Familiar events

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
- Sample questions to support inquiry with students:
- When might we use words like unlikely and likely?
- How does data/information help us predict the likeliness of an event (e.g., weather)?
- What stories can data tell us?

- Sample questions to support inquiry with students:

## Learning Standards

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### Curricular Competencies

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*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 used specific estimating and measuring techniques in daily life (e.g., seaweed drying and baling).

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

- 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 10

number concepts

- counting:
- one-to-one correspondence
- conservation
- cardinality
- stable order counting
- sequencing 1-10
- linking sets to numerals
- subitizing

- using counting collections made of local materials
- counting to 10 in more than one language, including local First Peoples language or languages

ways to make 5

ways to make 5

- perceptual subitizing (e.g., I see 5)
- conceptual subitizing (e.g., I see 4 and 1)
- comparing quantities, 1-10
- using concrete materials to show ways to make 5
- Traditional First Peoples counting methods involved using fingers to count to 5 and for groups of 5.
- aboriginalperspectives.uregina.ca/rosella/lessons/math/numberconcepts.shtml
- ankn.uaf.edu/curriculum/Tlingit/Salmon/graphics/mathbook.pdf
- youtube.com/watch?v=6-k_5hezWPE

decomposition of numbers to 10

decomposition

- decomposing and recomposing quantities to 10
- Numbers can be arranged and recognized.
- benchmarks of 5 and 10
- making 10
- part-part-whole thinking
- using concrete materials to show ways to make 10
- whole-class number talks

repeating patterns with two or three elements

repeating patterns

- sorting and classifying using a single attribute
- identifying patterns in the world
- repeating patterns with 2-3 elements
- identifying the core
- representing repeating patterns in various ways
- noticing and identifying repeating patterns in First Peoples and local art and textiles, including beadwork and beading, and frieze work in borders

change in quantity to 10, using concrete materials

change in quantity to 10

- generalizing change by adding 1 or 2
- modeling and describing number relationships through change (eg., build and change tasks - begin with four cubes, what do you need to do to change it to six? to change it to 3?)

equality as a balance and inequality as an imbalance

equality as a balance

- modeling equality as balanced and inequality as imbalanced using concrete and visual models (e.g., using a pan balance with cubes on each side to show equal and not equal)
- fish drying and sharing

direct comparative measurement (e.g., linear, mass, capacity)

direct comparative measurement

- understanding the importance of using a baseline for direct comparison in linear measurement
- linear height, width, length (e.g., longer than, shorter than, taller than, wider than)
- mass (e.g., heavier than, lighter than, same as)
- capacity (e.g., holds more, holds less)

single attributes of 2D shapes and 3D objects

single attributes

- At this level, using specific math terminology to name and identify 2D shapes and 3D objects is not expected.
- sorting 2D shapes and 3D objects using a single attribute
- building and describing 3D objects (e.g., shaped like a can)
- exploring, creating, and describing 2D shapes
- using positional language, such as beside, on top of, under, and in front of

concrete or pictorial graphs as a visual tool

graphs

- creating concrete and pictorial graphs to model the purpose of graphs and provide opportunities for mathematical discussions (e.g., survey the students about how they got to school, then represent the data in a graph and discuss together as a class).

likelihood of familiar life events

familiar life events

- using the language of probability, such as unlikely or likely (e.g., Could it snow tomorrow?)

financial literacy — attributes of coins, and financial role-play

financial literacy

- noticing attributes of Canadian coins (colour, size, pictures)
- identifying the names of coins
- role-playing financial transactions, such as in a restaurant, bakery, or store, using whole numbers to combine purchases (e.g., a muffin is $2.00 and a juice is $1.00), and integrating the concept of wants and needs
- token value (e.g., wampum bead/trade beads for furs)

**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.