Science- Kindergarten · Web viewdiscrete linear relations: two-variable discrete linear relations...

Area of Learning: Mathematics KindergartenBig Ideas Elaborations

Numbers represent quantities that can be decomposed into smaller parts.

Numbers:o Number: Number represents and describes quantity.

Sample questions to support inquiry with students:o How do these materials help us think about numbers and parts of numbers?o Which numbers of counters/dots are easy to recognize and why?o In how many ways can you decompose ____?o What stories live in numbers?o How do numbers help us communicate and think about place?o How do numbers help us communicate and think about ourselves?

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

fluency:o Computational Fluency: Computational fluency develops from a strong sense of number.

Sample questions to support inquiry with students:o If you know that 4 and 6 make 10, how does that help you understand other ways to make 10?o How does understanding 5 help us decompose and compose numbers to 10?o What parts make up the whole?

Repeating elements in patterns can be identified. patterns:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o What makes a pattern a pattern?o How are these patterns alike and different?o Do all patterns repeat?

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

attributes:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.

Sample questions to support inquiry with students:o What do you notice about these shapes?o How are these shapes alike and different?

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

Familiar events:o Data and Probability: Analyzing data and chance enables us to compare and interpret.

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

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Curricular Competencies Elaborations Content ElaborationsStudents are expected to do the following:Reasoning and analyzing

Use reasoning to explore and make connections

Estimate reasonably Develop mental math strategies and

abilities to make sense of quantities Use technology to explore

mathematics Model mathematics in contextualized

experiencesUnderstanding 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

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

Communicating and representing Communicate mathematical thinking

in many ways Use mathematical vocabulary and

language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Represent mathematical ideas in concrete, pictorial, and symbolic forms

Estimate reasonably:o estimating by

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

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

mental math strategies:o working toward

developing fluent and flexible thinking about number

technology:o calculators, virtual

manipulatives, concept-based apps

Model:o acting it out, using

concrete materials, drawing pictures

multiple strategies:o visual, oral, play,

experimental, written, symbolic

connected:o in daily activities, local

and traditional practices, the environment, popular media and news events, cross-curricular

Students are expected to know the following: number concepts to 10 ways to make 5 decomposition of numbers to 10 repeating patterns with two or three

elements change in quantity to 10, using

concrete materials equality as a balance and inequality

as an imbalance direct comparative measurement

(e.g., linear, mass, capacity) single attributes of 2D shapes and 3D

objects concrete or pictorial graphs as a

visual tool likelihood of familiar life events financial literacy — attributes of

coins, and financial role-play

number concepts:o counting:

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

o using counting collections made of local materials

o counting to 10 in more than one language, including local First Peoples language or languages

ways to make 5:o perceptual subitizing (e.g., I see 5)o conceptual subitizing (e.g., I see 4 and

1)o comparing quantities, 1-10o using concrete materials to show ways

to make 5o Traditional First Peoples counting

methods involved using fingers to count to 5 and for groups of 5.

http:// aboriginalperspectives.uregina.ca/rosella/lessons/math/numberconcepts.shtml

http://www.ankn.uaf.edu/ curriculum/Tlingit/Salmon/graphics/mathbook.pdf

https://www.youtube.com/ watch?v=6-k_5hezWPE

decomposition:o decomposing and recomposing

quantities to 10

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https://www.youtube.com/watch?v=6-k_5hezWPE

https://www.youtube.com/watch?v=6-k_5hezWPE

http://www.ankn.uaf.edu/curriculum/Tlingit/Salmon/graphics/mathbook.pdf



http://aboriginalperspectives.uregina.ca/rosella/lessons/math/numberconcepts.shtml



Connecting and reflecting Reflect on mathematical thinking Connect mathematical concepts to

each other and to other areas and personal interests

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

integrationo Patterns are important

in First Peoples technology, architecture, and artwork.

o Have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

communicate:o concretely, pictorially,

symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas

o using technology such as screencasting apps, digital photos

Explain and justify:o using mathematical

argumentso “Prove it!”

concrete, pictorial, and symbolic forms:

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

Reflect:o sharing the

mathematical thinking of self and others, including evaluating

o Numbers can be arranged and recognized.

o benchmarks of 5 and 10o making 10o part-part-whole thinkingo using concrete materials to show ways

to make 10o whole-class number talks

repeating patterns:o sorting and classifying using a single

attributeo identifying patterns in the worldo repeating patterns with two to three

elementso identifying the coreo representing repeating patterns in

various wayso 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:o generalizing change by adding 1 or 2o modelling and describing number

relationships through change (e.g., build and change tasks — begin with 4 cubes; what do you need to do to change it to 6? to change it to 3?)

equality as a balance:o modelling 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)

o fish drying and sharing direct comparative measurement:

o understanding the importance of using a baseline for direct comparison in

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strategies and solutions, extending, and posing new problems and questions

other areas and personal interests:

o 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:o Invite local First

Peoples Elders and knowledge keepers to share their knowledge

make connections:o Bishop’s cultural

practices: counting, measuring, locating, designing, playing, explaining (http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)

o www.aboriginaleducati on.ca

o Teaching Mathematics in a First Nations

linear measuremento linear height, width, length (e.g.,

longer than, shorter than, taller than, wider than)

o mass (e.g., heavier than, lighter than, same as)

o capacity (e.g., holds more, holds less) single attributes:

o At this level, using specific math terminology to name and identify 2D shapes and 3D objects is not expected.

o sorting 2D shapes and 3D objects, using a single attribute

o building and describing 3D objects (e.g., shaped like a can)

o exploring, creating, and describing 2D shapes

o using positional language, such as beside, on top of, under, and in front of

familiar life events:o using the language of probability,

such as unlikely or likely (e.g., could it snow tomorrow?)

graphs:o 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)

financial literacy:o noticing attributes of Canadian coins

(colour, size, pictures)o identifying the names of coinso role-playing financial transactions,

such as in a restaurant, bakery, or

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http://www.aboriginaleducation.ca/


http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm



Context, FNESC http://www.fnesc.ca/k-7/

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

o token value (e.g., wampum bead/trade beads for furs)

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Area of Learning: Mathematics Grade 1Big Ideas Elaborations

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


Sample questions to support inquiry with students:o How does understanding 5 or 10 help us think about other numbers?o What is the relationship between 10s and 1s?o Why is it useful to use 10 frames to represent quantities?o What stories live in numbers?o How do numbers help us communicate and think about place?o 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:o Computational Fluency: Computational fluency develops from a strong sense of number.Sample questions to

support inquiry with students:o What is the relationship between addition and subtraction?o How does knowing that 4 and 6 make 10 help you understand other ways to make 10?o How many different ways can you solve…? (e.g., 8 + 5)

Repeating elements in patterns can be identified. patterns:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o How can patterns be used to make predictions?o What is the relationship between increasing patterns and addition?o What do you notice about this pattern? What is the part that repeats?o What number patterns live in a hundred chart?

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


Sample questions to support inquiry with students:o How are these shapes alike and different?o What stories live in these shapes?o What 3D shapes can you find in nature?

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

data:o Data and Probability: Analyzing data and chance enables us to compare and interpret.

Sample questions to support inquiry with students:o What stories can data tell us?o When might we use words like never, sometimes, always, more likely, and less likely?o How does organizing concrete data help us understand the data?

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Estimate reasonably Develop mental math strategies

and abilities to make sense of quantities

Use technology to explore mathematics

Model mathematics in contextualized experiences

Understanding and solving Develop, demonstrate, and apply

mathematical understanding through play, inquiry, and problem solving




Communicating and representing Communicate mathematical

thinking in many ways Use mathematical vocabulary and





o 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).










and traditional practices,

Students are expected to know the following: number concepts to 20 ways to make 10 addition and subtraction to 20

(understanding of operation and process)

repeating patterns with multiple elements and attributes

change in quantity to 20, concretely and verbally

meaning of equality and inequality direct measurement with non-standard

units (non-uniform and uniform) comparison of 2D shapes and 3D

objects concrete graphs, using one-to-one

correspondence likelihood of familiar life events, using

comparative language financial literacy — values of coins,

and monetary exchanges

number concepts to 20:o 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

o 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 (http://nativenorthwest.com)using counting collections made of local materialscounting in different languages; different First Peoples counting systems (e.g., Tsimshian)

o Tlingit Math Book (http://yukon-ed-show-me-your-math.wikispaces.com/file/detail/Tlingit Math Book.pdf)

make 10:o decomposing 10 into partso Numbers to 10 can be arranged and

recognized.o benchmarks of 10 and 20o Traditional First Peoples counting

methods involved using fingers to count to 5 and for groups of 5.

o traditional songs/singing and stories addition and subtraction to 20:

o decomposing 20 into parts

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http://yukon-ed-show-me-your-math.wikispaces.com/file/detail/Tlingit%20Math%20Book.pdf



http://nativenorthwest.com/





the environment, popular media and news events, cross-curricular integration

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

o Have students pose and solve problems or ask questions connected to place, stories and cultural practices.









mathematical thinking of self and others,

o mental math strategies: counting on making 10 doubles

o Addition and subtraction are related.o whole-class number talkso nature scavenger hunt in Kaska

Counting Book (http://yukon-ed-show-me-your-math.wikispaces.com/file/detail/Kaska Counting Book.pdf)

repeating patterns:o identifying sorting ruleso repeating patterns with multiple

elements/attributeso translating patterns from one

representation to another (e.g., an orange-blue pattern could be translated to a circle-square pattern)

o letter coding of patterno predicting an element in repeating

patterns using a variety of strategieso patterns using visuals (ten-frames,

hundred charts)o investigating numerical patterns (e.g.,

skip-counting by 2s or 5s on a hundred chart)

o beading using 3-5 colours change in quantity to 20:

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

equality and inequality:o demonstrating and explaining the

meaning of equality and inequalityo recording equations symbolically,

using = and ≠ direct measurement:

o Non-uniform units are not consistent

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http://yukon-ed-show-me-your-math.wikispaces.com/file/detail/Kaska%20Counting%20Book.pdf



including evaluating strategies and solutions, extending, and posing new problems and questions


o 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:o how ovoid has different

look to represent different animal parts

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



o www.aboriginaleducatio n.ca

in size (e.g., children’s hands, pencils); uniform units are consistent in size (e.g., interlocking cubes, standard paper clips).

o understanding the importance of using a baseline for direct comparison in linear measurement

o using multiple copies of a unito 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)

o tiling an areao rope knots at intervalso using body parts to measureo book: An Anishnaabe Look at

Measurement, by Rhonda Hopkins and Robin King-Stonefish (http://www.strongnations.com/store/item_display.php?i=3494&f=)

o hand/foot tracing for mitten/moccasin making

2D shapes and 3D objects:o sorting 3D objects and 2D shapes

using one attribute, and explaining the sorting rule

o comparing 2D shapes and 3D objects in the environment

o describing relative positions, using positional language (e.g., up and down, in and out)

o replicating composite 2D shapes and 3D objects (e.g., putting two triangles together to make a square)

concrete graphs:o creating, describing, and comparing

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http://www.strongnations.com/store/item_display.php?i=3494&f=

http://www.strongnations.com/store/item_display.php?i=3494&f=






o Teaching Mathematics in a First Nations Context, FNESC) http://www.fnesc.ca/k-7/

concrete graphs familiar life event:

o using the language of probability (e.g., never, sometimes, always, more likely, less likely)

o cycles (Elder or knowledge keeper to speak about ceremonies and life events)

financial literacy:o identifying values of coins (nickels,

dimes, quarters, loonies, and toonies )o counting multiples of the same

denomination (nickels, dimes, loonies, and toonies)

o Money is a medium of exchange.o role-playing financial transactions

(e.g., using coins and whole numbers), integrating the concept of wants and needs

o trade games, with understanding that objects have variable value or worth (shells, beads, furs, tools)

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Numbers to 100 represent quantities that can be decomposed into 10s and 1s.


Sample questions to support inquiry with students:o How does understanding 5 or 10 help us think about other numbers?o What is the relationship between 10s and 1s?o What patterns do you notice in numbers?o What stories live in numbers?o How do numbers help us communicate and think about place?o 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.


Sample questions to support inquiry with students:o What is the relationship between addition and subtraction?o How can you use addition to help you subtract?o 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:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o How can we represent patterns in different ways/modes?o How can you create repeating patterns with objects that are all one colour?o What stories live in patterns?

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


Sample questions to support inquiry with students:o What 2D shapes live in objects in our world?o How can you combine shapes to make new shapes?

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

graphs:o Data and Probability: Analyzing data and chance enables us to compare and interpret.

Sample questions to support inquiry with students:o When you look at this graph, what do you notice? What do you wonder?o How do graphs help us understand data?o What are some different ways to represent data pictorially?

Curricular Competencies Elaborations Content Elaborations

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Students are expected to do the following:Reasoning and analyzing
















Connecting and reflecting Reflect on mathematical thinking











connected:o in daily activities,

local and traditional practices, the environment, popular media and news events, cross-curricular integration


o Elder

Students are expected to know the following: number concepts to 100 benchmarks of 25, 50, and 100 and

personal referents addition and subtraction facts to 20

(introduction of computational strategies)

addition and subtraction to 100 repeating and increasing patterns change in quantity, using pictorial and

symbolic representation symbolic representation of equality and

inequality direct linear measurement,

introducing standard metric units multiple attributes of 2D shapes and 3D

objects pictorial representation of concrete

graphs, using one-to-one correspondence

likelihood of events, using comparative language

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


skip-counting by 2, 5, and 10: using different starting

points increasing and

decreasing (forward and backward)

o 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:

o seating arrangements at ceremonies/feasts

facts to 20:o adding and subtracting numbers to 20o 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:o decomposing numbers to 100o estimating sums and differences to 100

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


communication to explain harvest traditions and sharing practices

communicate:o concretely,

pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas







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

other areas and personal

o 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)

o adding up to find the differenceo using an open number line, hundred

chart, ten-frameso using addition and subtraction in real-

life contexts and problem-based situations

o whole-class number talks patterns:

o exploring more complex repeating patterns (e.g., positional patterns, circular patterns)

o identifying the core of repeating patterns (e.g., the pattern of the pattern that repeats over and over)

o increasing patterns using manipulatives, sounds, actions, and numbers (0 to 100)

o Metis finger weavingo First Peoples head/armband patterningo online video and text: Small Number

Counts to 100 (http://mathcatcher.irmacs.sfu.ca/story/small-number-counts-100)

change in quantity:o numerically describing a change in

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

direct linear measurement:o centimetres and metres

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http://mathcatcher.irmacs.sfu.ca/story/small-number-counts-100

http://mathcatcher.irmacs.sfu.ca/story/small-number-counts-100

interests:o 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)


Peoples Elders and knowledge keepers to share their knowledge.



o www.aboriginaleduc ation.ca

o Teaching Mathematics in a First Nations Context, FNESC)

o estimating lengtho measuring and recording length, height,

and width, using standard units 2D shapes and 3D objects:

o sorting 2D shapes and 3D objects, using two attributes, and explaining the sorting rule

o describing, comparing, and constructing 2D shapes, including triangles, squares, rectangles, circles

o identifying 2D shapes as part of 3D objects

o using traditional northwest coast First Peoples shapes (ovoids, U, split U, and local art shapes) reflected in the natural environment

pictorial representation:o collecting data, creating a concrete

graph, and representing the graph, using a pictorial representation through grids, stamps, drawings

o one-to-one correspondence likelihood of events:

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

financial literacy:o counting simple mixed combinations of

coins to 100 centso introduction to the concepts of spending

and saving, integrating the concepts of wants and needs

o role-playing financial transactions (e.g., using bills and coins)

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http://www.fnesc.ca/k-7/


Fractions are a type of number that can represent quantities.

number:o Number: Number represents and describes quantity.

Sample questions to support inquiry with students:o In how many ways can you represent the fraction ____?o What is the relationship between parts and wholes when we think about fractions?o How do these materials help you think about fractions?o What stories live in numbers?o How do numbers help us communicate and think about place?o 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.


Sample questions to support inquiry with students:o What is the relationship between addition and multiplication?o How can we decompose and compose numbers to help us add, subtract, multiply, and divide?o 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:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o How are these patterns alike and different (e.g., increasing and decreasing)?o How are place value patterns repeated in large numbers?o How do numbers help us describe patterns?

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


Sample questions to support inquiry with students:o Where do 2D shapes live in 3D shapes?o How do standard units help us to compare and communicate measurements?o How do the properties of shapes contribute to buildings and designs?

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

outcomes:o Data and Probability: Analyzing data and chance enables us to compare and interpret.

Sample questions to support inquiry with students:

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o How is the probability of an event determined and described?o What events in our lives are left to chance?o What are the possible outcomes of these events?



























and traditional practices, the environment, popular media and news events, cross-curricular integration

o Have students pose and solve problems or ask

Students are expected to know the following: number concepts to 1000 fraction concepts addition and subtraction to 1000 addition and subtraction facts to 20

(emerging computational fluency) multiplication and division concepts increasing and decreasing patterns pattern rules using words and numbers,

based on concrete experiences one-step addition and subtraction

equations with an unknown number measurement, using standard units

(linear, mass, and capacity) time concepts construction of 3D shapes one-to-one correspondence with bar

graphs, pictographs, charts, and tables likelihood of simulated events, using

comparative language financial literacy — fluency with coins

and bills to 100 dollars, and earning and payment


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)

o Numbers to 1000 can be arranged and recognized:

comparing and ordering numbers

estimating large quantitieso 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

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questions connected to place, stories, and cultural practices.











o to develop a sense of how mathematics helps us understand ourselves and the world around us

408, the zero indicates that there are 0 tens)

o instructional resource: Math in a Cultural Context, by Jerry Lipka

fraction concepts:o Fractions are numbers that

represent an amount or quantity.o Fractions can represent parts of a

region, set, or linear model.o Fraction parts are equal shares or

equal-sized portions of a whole or unit.

o Provide opportunities to explore and create fractions with concrete materials.

o recording pictorial representations of fraction models and connecting to symbolic notation

o equal partitioningo equal sharing, pole ratios as visual

parts, medicine wheel, seasons addition and subtraction:

o using flexible computation strategies, involving taking apart (e.g., decomposing using friendly numbers and compensating) and combining numbers in a variety of ways, regrouping

o estimating sums and differences of all operations to 1000

o using addition and subtraction in real-life contexts and problem-based situations

o whole-class number talks computational fluency:

o adding and subtracting of numbers to 20

o demonstrating fluency with math

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(e.g., daily activities, local and traditional practices, the environment, popular media and news events, social justice, and cross-curricular integration)






o Teaching Mathematics in a First Nations Context, FNESC http://www.fnesc.ca/k-7/

strategies for addition and subtraction (e.g., decomposing, making and bridging 10, related doubles, and commutative property)

o Addition and subtraction are related.

o At the end of Grade 3, most students should be able to recall addition facts to 20.

multiplication and division:o understanding concepts of

multiplication (e.g., groups of, arrays, repeated addition)

o understanding concepts of division (e.g., sharing, grouping, repeated subtraction)

o Multiplication and division are related.

o Provide opportunities for concrete and pictorial representations of multiplication.

o Use games to develop opportunities for authentic practice of multiplication computations.

o looking for patterns in numbers, such as in a hundred chart, to further develop understanding of multiplication computation

o Connect multiplication to skip-counting.

o Connect multiplication to division and repeated addition.

o Memorization of facts is not intended for this level.

o fish drying on rack; sharing of food resources in First Peoples communities

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patterns:o creating patterns using concrete,

pictorial, and numerical representations

o representing increasing and decreasing patterns in multiple ways

o generalizing what makes the pattern increase or decrease (e.g., doubling, adding 2)

pattern rules:o from a concrete pattern, describing

the pattern rule using words and numbers

o predictability in song rhythm and patterns

o Share examples of local First Peoples art with the class, and ask students to notice patterns in the artwork.

equations:o start unknown (e.g., n + 15 = 20 or

□ + 15 + 20)o change unknown ( e.g., 12 + n =

20 or 12 + □ = 20)o result unknown (e.g., 6 + 13 = n or

6 + 13 = □)o investigating even and odd

numbers standard units:

o linear measurements, using standard units (e.g., centimetre, metre, kilometre)

o capacity measurements, using standard units (e.g., millilitre, litre)

o Introduce concepts of perimeter, area, and circumference (the distance around); use of formula

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and pi to calculate not intended — the focus is on the concepts.

o area measurement, using square units (standard and non-standard)

o mass measurements, using standard units (e.g., gram, kilogram)

o estimation of measurements, using standard referents (e.g., If this cup holds 100 millilitres, about how much does this jug hold?)

time:o understanding concepts of time

(e.g., second, minute, hour, day, week, month, year)

o understanding the relationships between units of time

o Telling time is not expected at this level.

o estimating time, using environmental references and natural daily/seasonal cycles, temperatures based on weather systems, traditional calendar

3D shapes:o identifying 3D shapes according to

the 2D shapes of the faces and the number of edges and vertices (e.g., construction of nets, skeletons)

o describing the attributes of 3D shapes (e.g., faces, edges, vertices)

o identifying 3D shapes by their mathematical terms (e.g., sphere, cube, prism, cone, cylinder)

o comparing 3D shapes (e.g., How are rectangular prisms and cubes the same or different?)

o understanding the preservation of

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shape (e.g., the orientation of a shape will not change its properties)

o jingle dress bells, bentwood box, birch bark baskets, pithouses

one-to-one correspondence:o collecting data, creating a graph,

and describing, comparing, and discussing the results

o choosing a suitable representation simulated events:

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

o 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)

o story: The Snowsnake Game (http://yukon-ed-show-me-your-math.wikispaces.com/file/view/The%20Snowsnake%20Game.pdf/203828506/The%20Snowsnake%20Game.pdf )

financial literacy:o 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

o understanding that payments can be made in flexible ways (e.g., cash, cheques, credit, electronic transactions, goods and services)

21

http://yukon-ed-show-me-your-math.wikispaces.com/file/view/The%20Snowsnake%20Game.pdf/203828506/The%20Snowsnake%20Game.pdf



o 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)

o 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.

22


Fractions and decimals are types of numbers that can represent quantities.

numbers:o Number: Number represents and describes quantity.

Sample questions to support inquiry with students:o What is the relationship between fractions and decimals?o How are these fractions (e.g., 1/2 and 7/8) alike and different?o How do we use fractions and decimals in our daily life?o What stories live in numbers?o How do numbers help us communicate and think about place?o How do numbers help us communicate and think about ourselves?

Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.

fluencyo Computational Fluency: Computational fluency develops from a strong sense of number.

Sample questions to support inquiry with students:o What is the relationship between multiplication and division?o What patterns in our number system connect to our understanding of multiplication?o How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex

multiplication facts? Regular changes in patterns can be identified and

represented using tools and tables. patterns:

o Patterning: We use patterns to represent identified regularities and to make generalizations. Sample questions to support inquiry with students:

o What regularities can you identify in these patterns?o Where do we see patterns in the world around us?o How can we represent increasing and decreasing regularities that we see in number patterns?o How do tables and charts help us understand number patterns?

Polygons are closed shapes with similar attributes that can be described, measured, and compared.


Sample questions to support inquiry with students:o How are these polygons alike and different?o How can we measure polygons?o How do the properties of shapes contribute to buildings and design?

Analyzing and interpreting experiments in data probability develops an understanding of chance.


Sample questions to support inquiry with students:o How is the probability of an event determined and described?o What events in our lives are left to chance?o How do probability experiments help us understand chance?

23




























and traditional practices, the environment, popular media and news events, cross-curricular integration


communicate:

Students are expected to know the following: number concepts to 10 000 decimals to hundredths ordering and comparing fractions addition and subtraction to 10 000 multiplication and division of two- or

three-digit numbers by one-digit numbers

addition and subtraction of decimals to hundredths

addition and subtraction facts to 20 (developing computational fluency)

multiplication and division facts to 100 (introductory computational strategies)

increasing and decreasing patterns, using tables and charts

algebraic relationships among quantities

one-step equations with an unknown number, using all operations

how to tell time with analog and digital clocks, using 12- and 24-hour clocks

regular and irregular polygons perimeter of regular and irregular

shapes line symmetry one-to-one correspondence and

many-to-one correspondence, using bar graphs and pictographs

probability experiments financial literacy — monetary

calculations, including making change with amounts to 100 dollars and making simple financial decisions


multiples flexible counting strategies whole number benchmarks

o Numbers to 10 000 can be arranged and recognized:

comparing and ordering numbers

estimating large quantitieso place value:

1000s, 100s, 10s, and 1s understanding the relationship

between digit places and their value, to 10 000

decimals to hundredths:o Fractions and decimals are numbers

that represent an amount or quantity.o Fractions and decimals can represent

parts of a region, set, or linear model.o Fractional parts and decimals are

equal shares or equal-sized portions of a whole or unit.

o understanding the relationship between fractions and decimals

fractions:o comparing and ordering of fractions

with common denominatorso estimating fractions with benchmarks

(e.g., zero, half, whole)o using concrete and visual modelso equal partitioning

addition and subtraction:o using flexible computation strategies,

involving taking apart (e.g., decomposing using friendly numbers

24




o concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas









o 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

and compensating) and combining numbers in a variety of ways, regrouping

o estimating sums and differences to 10 000


o whole-class number talks multiplication and division:

o understanding the relationships between multiplication and division, multiplication and addition, division and subtraction

o using flexible computation strategies (e.g., decomposing, distributive principle, commutative principle, repeated addition and repeated subtraction)

o using multiplication and division in real-life contexts and problem-based situations

o whole-class number talks decimals:

o estimating decimal sums and differences

o using visual models, such as base 10 blocks, place-value mats, grid paper, and number lines


o whole-class number talks computational fluency:

o Provide opportunities for authentic practice, building on previous grade-level addition and subtraction facts.

o flexible use of mental math strategies

25

environment, popular media and news events, social justice, and cross-curricular integration)






o Teaching Mathematics in a First Nations Context, FNESC)http://www.fnesc.ca/k-7/

facts:o Provide opportunities for concrete and

pictorial representations of multiplication.

o building computational fluencyo Use games to provide opportunities

for authentic practice of multiplication computations.



o Connecting multiplication to division and repeated addition.

o Memorization of facts is not intended for this level.

o Students will become more fluent with these facts.

o using mental math strategies, such as doubling or halving

o Students should be able to recall the following multiplication facts by the end of Grade 4 (2s, 5s, 10s).

patterns:o Change in patterns can be represented

in charts, graphs, and tables.o using words and numbers to describe

increasing and decreasing patternso fish stocks in lakes, life expectencies

algebraic relationships:o representing and explaining one-step

equations with an unknown numbero describing pattern rules, using words

and numbers from concrete and pictorial representations

o planning a camping or hiking trip;

26



planning for quantities and materials needed per individual and group over time

one-step equations:o one-step equations for all operations

involving an unknown number (e.g., ___ + 4 = 15, 15 – □ = 11)

o start unknown (e.g., n + 15 = 20; 20 – 15 = □)

o change unknown (e.g., 12 + n = 20)o result unknown (e.g., 6 + 13 = __)

tell time:o understanding how to tell time with

analog and digital clocks, using 12- and 24-hour clocks

o understanding the concept of a.m. and p.m.

o understanding the number of minutes in an hour

o understanding the concepts of using a circle and of using fractions in telling time (e.g., half past, quarter to)

o telling time in five-minute intervalso telling time to the nearest minuteo First Peoples use of numbers in time

and seasons, represented by seasonal cycles and moon cycles (e.g., how position of sun, moon, and stars is used to determine times for traditional activities, navigation)

polygons:o describing and sorting regular and

irregular polygons based on multiple attributes

o investigating polygons (polygons are closed shapes with similar attributes)

o Yup’ik border patterns perimeter:

27

o using geoboards and grids to create, represent, measure, and calculate perimeter

line symmetry:o using concrete materials such as

pattern blocks to create designs that have a mirror image within them

o First Peoples art, borders, birchbark biting, canoe building

o Visit a structure designed by First Peoples in the local community and have the students examine the symmetry, balance, and patterns within the structure, then replicate simple models of the architecture focusing on the patterns they noted in the original.

one-to-one correspondence:o many-to-one correspondence: one

symbol represents a group or value (e.g., on a bar graph, one square may represent five cookies)

probability experiments:o predicting single outcomes (e.g.,

when you spin using one spinner and it lands on a single colour)

o using spinners, rolling dice, pulling objects out of a bag

o recording results using tallieso Dene/Kaska hand games, Lahal stick

games financial literacy:

o making monetary calculations, including decimal notation in real-life contexts and problem-based situations

o applying a variety of strategies, such as counting up, counting back, and decomposing, to calculate totals and make change

28

o making simple financial decisions involving earning, spending, saving, and giving

o equitable trade rules

29


Numbers describe quantities that can be represented by equivalent fractions.


Sample questions to support inquiry with students:o How can you prove that two fractions are equivalent?o In how many ways can you represent the fraction ___?o How do we use fractions and decimals in our daily life?o What stories live in numbers?o How do numbers help us communicate and think about place?o How do numbers help us communicate and think about ourselves?

Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.


Sample questions to support inquiry with students:o How many different ways can you solve…? (e.g., 16 x 7)o What flexible strategies can we apply to use operations with multi-digit numbers?o How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex

multiplication facts? Identified regularities in number patterns can be

expressed in tables. patterns:

o Patterning: We use patterns to represent identified regularities and to make generalizations. Sample questions to support inquiry with students:

o How do tables and charts help us understand number patterns?o How do tables help us see the relationship between a variable within number patterns?o How do rules for increasing and decreasing patterns help us solve equations?

Closed shapes have area and perimeter that can be described, measured, and compared.

area and perimeter:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.

Sample questions to support inquiry with students:o What is the relationship between area and perimeter?o What standard units do we use to measure area and perimeter?o When might an understanding of area and perimeter be useful?

Data represented in graphs can be used to show many-to-one correspondence.

Data:o Data and Probability: Analyzing data and chance enables us to compare and interpret.

Sample questions to support inquiry with students:o How do graphs help us understand data?o In what different ways can we represent many-to-one correspondence in a graph?o Why would you choose many-to-one correspondence rather than one-to-one correspondence in a graph?

30



Estimate reasonably Develop mental math

strategies and abilities to make sense of quantities



Understanding and solving Develop, demonstrate, and

apply mathematical understanding through play, inquiry, and problem solving





thinking in many ways Use mathematical vocabulary

and language to contribute to mathematical discussions

Explain and justify

Estimate reasonably:o estimating by comparing to

something familiar (e.g., more than 5, taller than me)

mental math strategies:o working toward developing fluent

and flexible thinking of number technology:

o calculators, virtual manipulatives, concept-based apps

Model:o acting it out, using concrete

materials, drawing pictures multiple strategies:

o visual, oral, play, experimental, written, symbolic

connected:o in daily activities, local and

traditional practices, the environment, popular media and news events, cross-curricular integration

o First Peoples people value recognize and utilize balance and symmetry within art and structural design; have students pose and solve problems or ask questions connected to place, stories, and cultural practices.

communicate:o concretely, pictorially, symbolically,

and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos

Explain and justify:

Students are expected to know the following:

number concepts to 1 000 000 decimals to thousandths equivalent fractions whole-number, fraction, and

decimal benchmarks addition and subtraction of whole

numbers to 1 000 000 multiplication and division to

three digits, including division with remainders

addition and subtraction of decimals to thousandths

addition and subtraction facts to 20 (extending computational fluency)

multiplication and division facts to 100 (emerging computational fluency)

rules for increasing and decreasing patterns with words, numbers, symbols, and variables

one-step equations with variables area measurement of squares and

rectangles relationships between area and

perimeter duration, using measurement of

time classification of prisms and

pyramids single transformations one-to-one correspondence and

many-to-one correspondence, using double bar graphs

probability experiments, single


multiples flexible counting

strategies whole number

benchmarkso Numbers to 1 000 000 can be

arranged and recognized: comparing and ordering

numbers estimating large

quantitieso place value:

100 000s, 10 000s, 1000s, 100s, 10s, and 1s

understanding the relationship between digit places and their value, to 1 000 000

o First Peoples use unique counting systems e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers e.g., 10 = two hands, 20 = one person

benchmarks:o Two equivalent fractions are two

ways to represent the same amount (having the same whole).

o comparing and ordering of fractions and decimals

o addition and subtraction of decimals to thousandths


31

mathematical ideas and decisions


Connecting and reflecting Reflect on mathematical

thinking Connect mathematical concepts

to each other and to other areas and personal interests


o using mathematical argumentso “Prove it!”

concrete, pictorial, and symbolic forms:o Use local materials gathered outside

for concrete and pictorial representations.

Reflect:o sharing the mathematical thinking of

self and others, including evaluating strategies and solutions, extending, and posing new problems and questions

other areas and personal interests:o 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:o Invite local First Peoples Elders and

knowledge keepers to share their knowledge.

make connections:o Bishop’s cultural practices: counting,

measuring, locating, designing, playing, explaining (http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)

o www.aboriginaleducation.ca o Teaching Mathematics in a First

Nations Context, FNESC: http://www.fnesc.ca/k-7/

events or outcomes financial literacy — monetary

calculations, including making change with amounts to 1000 dollars and developing simple financial plans

o estimating fractions with benchmarks (e.g., zero, half, whole)

o equal partitioning whole numbers:

o using flexible computation strategies involving taking apart (e.g., decomposing using friendly numbers and compensating) and combining numbers in a variety of ways, regrouping

o estimating sums and differences to 10 000


o whole-class number talks multiplication and division:

o understanding the relationships between multiplication and division, multiplication and addition, and division and subtraction

o using flexible computation strategies (e.g., decomposing, distributive principle, commutative principle, repeated addition, repeated subtraction)

o using multiplication and division in real-life contexts and problem-based situations

o whole-class number talks decimals:


o using visual models such as base 10 blocks, place-value mats, grid

32


paper, and number lineso using addition and subtraction in

authentic contexts and problem-based situations

o whole-class number talks addition and subtraction facts to 20:

o Provide opportunities for authentic practice, building on previous grade-level addition and subtraction facts.

o applying strategies and knowledge of addition and subtract facts in real-life contexts and problem-based situations, as well as when making math-to-math connections (e.g., for 800 + 700, you can annex the zeros and use the knowledge of 8 + 7 to find the total)

facts to 100:o Provide opportunities for

concrete and pictorial representations of multiplication.

o Use games to provide opportunities for authentic practice of multiplication computations.



o Connect multiplication to division and repeated addition.

o Memorization of facts is not intended this level.

o Students will become more fluent with these facts.

33

o using mental math strategies such as doubling and halving, annexing, and distributive property

o Students should be able to recall many multiplication facts by the end of Grade 5 (e.g., 2s, 3s, 4s, 5s, 10s).

o developing computational fluency with facts to 100

one-step equations:o solving one-step equations with a

variableo expressing a given problem as an

equation, using symbols (e.g., 4 + X = 15)

area and perimeter:o measuring area of squares and

rectangles, using tiles, geoboards, grid paper

o investigating perimeter and area and how they are related to but not dependent on each other

o use traditional dwellingso Invite a local Elder or knowledge

keeper to talk about traditional measuring and estimating techniques for hunting, fishing, and building.

time:o understanding elapsed time and

durationo applying concepts of time in

real-life contexts and problem-based situations

o daily and seasonal cyles, moon cycles, tides, journeys, events

classification:

34

o investigating 3D objects and 2D shapes, based on multiple attributes

o describing and sorting quadrilaterals

o describing and constructing rectangular and triangular prisms

o identifying prisms in the environment

transformations:o single transformations

(slide/translation, flip/reflection, turn/rotation)

o using concrete materials with a focus on the motion of transformations

o weaving, cedar baskets, designs many-to-one correspondence:

o many-to-one correspondence: one symbol represents a group or value (e.g., on a bar graph, one square may represent five cookies)

probability experiments:o predicting outcomes of

independent events (e.g., when you spin using a spinner and it lands on a single colour)

o predicting single outcomes (e.g., when you spin using a spinner and it lands on a single colour)

o using spinners, rolling dice, pulling objects out of a bag

o representing single outcome probabilities using fractions

financial literacy:o making monetary calculations,

including making change and

35

decimal notation to $1000 in real-life contexts and problem-based situations

o applying a variety of strategies, such as counting up, counting back, and decomposing, to calculate totals and make change

o making simple financial plans to meet a financial goal

o developing a budget that takes into account income and expenses

36


Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes.


Sample questions to support inquiry with students:o In how many ways can you represent the number ___?o What are the connections between fractions, mixed numbers, and decimal numbers?o How are mixed numbers and decimal numbers alike? Different?

Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.


Sample questions to support inquiry with students:o When we are working with decimal numbers, what is the relationship between addition and subtraction?o When we are working with decimal numbers, what is the relationship between multiplication and division?o When we are working with decimal numbers, what is the relationship between addition and multiplication?o When we are working with decimal numbers, what is the relationship between subtraction and division?

Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form generalizations.

Linear relations:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o What is a linear relationship?o How do linear expressions and line graphs represent linear relations?o What factors can change or alter a linear relationship?

Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles.

Properties:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.

Sample questions to support inquiry with students:o How are the areas of triangles, parallelogram, and trapezoids interrelated?o What factors are considered when selecting a viable referent in measurement?

Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.


Sample questions to support inquiry with students:o What is the relationship between theoretical and experimental probability?o What informs our predictions?o What factors would influence the theoretical probability of an experiment?

37

Curricular Competencies Elaborations Content ElaborationsReasoning and analyzing

Use logic and patterns to solve puzzles and play games

Use reasoning and logic to explore, analyze, and apply mathematical ideas

Estimate reasonably Demonstrate and apply mental

math strategies Use tools or technology to explore

and create patterns and relationships, and test conjectures


Understanding and solving Apply multiple strategies to solve

problems in both abstract and contextualized situations




Communicating and representing Use mathematical vocabulary and



Communicate mathematical

logic and patterns:o including coding

reasoning and logic:o making connections, using

inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences

Estimate reasonably:o estimating using referents,

approximation, and rounding strategies (e.g., the distance to the stop sign is approximately 1 km, the width of my finger is about 1 cm)

apply:o extending whole-number

strategies to decimalso working toward developing

fluent and flexible thinking about number

Model:o acting it out, using concrete

materials (e.g., manipulatives), drawing pictures or diagrams, building, programming

multiple strategies:o includes familiar, personal,

and from other cultures connected:

o in daily activities, local and traditional practices, the environment, popular media and news events,


small to large numbers (thousandths to billions)

multiplication and division facts to 100 (developing computational fluency)

order of operations with whole numbers

factors and multiples — greatest common factor and least common multiple

improper fractions and mixed numbers

introduction to ratios whole-number percents and

percentage discounts multiplication and division of

decimals increasing and decreasing patterns,

using expressions, tables, and graphs as functional relationships

one-step equations with whole-number coefficients and solutions

perimeter of complex shapes area of triangles, parallelograms,

and trapezoids angle measurement and

classification volume and capacity triangles combinations of transformations line graphs single-outcome probability, both

theoretical and experimental financial literacy — simple

budgeting and consumer math

small to large numbers:o place value from thousandths to

billions, operations with thousandths to billions

o numbers used in science, medicine, technology, and media

o compare, order, estimate facts to 100:

o mental math strategies (e.g., the double-double strategy to multiply 23 x 4)

order of operations:o includes the use of brackets, but

excludes exponentso quotients can be rational numbers

factors and multiples:o prime and composite numbers,

divisibility rules, factor trees, prime factor phrase (e.g., 300 = 22 x 3 x 52 )

o using graphic organizers (e.g., Venn diagrams) to compare numbers for common factors and common multiples

improper fractions:o using benchmarks, number line, and

common denominators to compare and order, including whole numbers

o using pattern blocks, Cuisenaire Rods, fraction strips, fraction circles, grids

o birchbark biting ratios:

o comparing numbers, comparing quantities, equivalent ratios

o part-to-part ratios and part-to-whole ratios

percents:

38

thinking in many ways Represent mathematical ideas in

concrete, pictorial, and symbolic forms



Use mathematical arguments to support personal choices


cross-curricular integrationo Patterns are important in

First Peoples technology, architecture, and art.



arguments Communicate:

o concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos

Reflect:o sharing the mathematical

thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions


o to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., cross-discipline, daily activities, local and traditional practices, the environment, popular

o using base 10 blocks, geoboard, 10x10 grid to represent whole number percents

o finding missing part (whole or percentage)

o 50% = 1/2 = 0.5 = 50:100 decimals:

o 0.125 x 3 or 7.2 ÷ 9o using base 10 block arrayo birchbark biting

patterns:o limited to discrete points in the first

quadranto visual patterning (e.g., colour tiles)o Take 3 add 2 each time, 2n + 1, and 1

more than twice a number all describe the pattern 3, 5, 7, …

o graphing data on First Peoples language loss, effects of language intervention

one-step equations:o preservation of equality (e.g., using a

balance, algebra tiles)o 3x = 12, x + 5 = 11

perimetero A complex shape is a group of shapes

with no holes (e.g., use colour tiles, pattern blocks, tangrams).

area:o grid paper explorationso deriving formulaso making connections between area of

parallelogram and area of rectangleo birchbark biting

angle:o straight, acute, right, obtuse, reflexo constructing and identifying; include

examples from local environment

39

media and news events, and social justice)

personal choices:o including anticipating

consequences Incorporate First Peoples:

o Invite local First Peoples Elders and knowledge keepers to share their knowledge

make connections:o Bishop’s cultural practices:

counting, measuring, locating, designing, playing, explaining(http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm )

o www.aboriginaleducation.c a

o Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/k-7/ )

o estimating using 45°, 90°, and 180° as reference angles

o angles of polygonso Small Number stories: Small Number

and the Skateboard Park (http://mathcatcher.irmacs.sfu.ca/stories )

volume and capacity:o using cubes to build 3D objects and

determine their volumeo referents and relationships between

units (e.g., cm3, m3, mL, L)o the number of coffee mugs that hold a

litreo berry baskets, seaweed drying

triangles:o scalene, isosceles, equilateralo right, acute, obtuseo classified regardless of orientation

transformations:o plotting points on Cartesian plane

using whole-number ordered pairso translation(s), rotation(s), and/or

reflection(s) on a single 2D shapeo limited to first quadranto transforming, drawing, and describing

imageo Use shapes in First Peoples art to

integrate printmaking (e.g., Inuit, Northwest coastal First Nations, frieze work) (http://mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/ ).

line graphs:o table of values, data set; creating and

interpreting a line graph from a given

40

http://mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/

http://mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/

http://mathcatcher.irmacs.sfu.ca/stories

http://mathcatcher.irmacs.sfu.ca/stories



set of data single-outcome probability:

o single-outcome probability events (e.g., spin a spinner, roll a die, toss a coin)

o listing all possible outcomes to determine theoretical probability

o comparing experimental results with theoretical expectation

o Lahal stick games financial literacy:

o informed decision making on saving and purchasing

o How many weeks of allowance will it take to buy a bicycle?


Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers.


Sample questions to support inquiry with students:o In how many ways can you represent the number ___?o What is the relationship between decimals, fractions, and percents?o How can you prove equivalence?o How are parts and wholes best represented in particular contexts?

Computational fluency and flexibility with numbers extend to operations with integers and decimals.


Sample questions to support inquiry with students:o When we are working with integers, what is the relationship between addition and subtraction?o When we are working with integers, what is the relationship between multiplication and division?o When we are working with integers, what is the relationship between addition and multiplication?o When we are working with integers, what is the relationship between subtraction and division?

Linear relations can be represented in many connected ways to identify regularities and make generalizations.

Linear relations:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o What is a linear relationship?o In how many ways can linear relationships be represented?

41

o How do linear relationships differ?o What factors can change a linear relationship?

The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships.

spatial relationships:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.

Sample questions to support inquiry with students:o What is unique about the properties of circles?o What is the relationship between diameter and circumference?o What are the similarities and differences between the area and circumference of circles?

Data from circle graphs can be used to illustrate proportion and to compare and interpret.


Sample questions to support inquiry with students:o How is a circle graph similar to and different from other types of visual representations of data?o When would you choose to use a circle graph to represent data?o How are circle graphs related to ratios, percents, decimals, and whole numbers?o How would circle graphs be informative or misleading?




Estimate reasonably Demonstrate and apply mental math

strategies Use tools or technology to explore












strategies to integerso working toward developing

fluent and flexible thinking

Students are expected to know the following: multiplication and division facts to 100

(extending computational fluency) operations with integers (addition,

subtraction, multiplication, division, and order of operations)

operations with decimals (addition, subtraction, multiplication, division, and order of operations)

relationships between decimals, fractions, ratios, and percents

discrete linear relations, using expressions, tables, and graphs

two-step equations with whole-number coefficients, constants, and solutions

circumference and area of circles volume of rectangular prisms and cylinders Cartesian coordinates and graphing combinations of transformations circle graphs experimental probability with two

facts to 100:o When multiplying 214 by 5, we can

multiply by 10, then divide by 2 to get 1070.

operations with integers:o addition, subtraction,

multiplication, division, and order of operations

o concretely, pictorially, symbolicallyo order of operations includes the use

of brackets, excludes exponentso using two-sided counterso 9–(–4) = 13 because –4 is 13 away

from +9o extending whole-number strategies

to decimals operations with decimals:

o includes the use of brackets, but excludes exponents

relationships:o conversions, equivalency, and

42






Communicate mathematical thinking in many ways






about number Model:

o acting it out, using concrete materials (e.g., manipulatives), drawing pictures or diagrams, building, programming



o in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration

o Patterns are important in First Peoples technology, architecture, and art.




o concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify and apply mathematical ideas; may use technology such as screencasting apps, digital photos


thinking of self and others,

independent events financial literacy — financial percentage

terminating versus repeating decimals, place value, and benchmarks

o comparing and ordering decimals and fractions using the number line

o ½ = 0.5 = 50% = 50:100o shoreline cleanup

discrete linear relations:o four quadrants, limited to integral

coordinateso 3n + 2; values increase by 3 starting

from y-intercept of 2o deriving relation from the graph or

table of valueso Small Number stories: Small

Number and the Old Canoe, Small Number Counts to 100 (http://mathcatcher.irmacs.sfu.ca/stories )

two-step equations:o solving and verifying 3x + 4 = 16o modelling the preservation of

equality (e.g., using balance, pictorial representation, algebra tiles)

o spirit canoe trip pre-planning and calculations

o Small Number stories: Small Number and the Big Tree (http://mathcatcher.irmacs.sfu.ca/stories )

circumferenceo constructing circles given radius,

diameter, area, or circumferenceo finding relationships between

radius, diameter, circumference,

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including evaluating strategies and solutions, extending, and posing new problems and questions

other areas and personal interests:o to develop a sense of how

mathematics helps us understand ourselves and the world around us (e.g., cross-discipline, daily activities, local and traditional practices, the environment, popular media and news events, and social justice)






o www.aboriginaleducation.ca o Teaching Mathematics in a

First Nations Context, FNESC ( http://www.fnesc.ca/k-7/ )

and area to develop C = π x d formula

o applying A = π x r x r formula to find the area given radius or diameter

o drummaking, dreamcatcher making, stories of SpiderWoman (Dene, Cree, Hopi, Tsimshian), basket making, quill box making (Note: Local protocols should be considered when choosing an activity.)

volume:o volume = area of base x heighto bentwood boxes, wiigwaasabak and

mide-wiigwaas (birch bark scrolls)o Exploring Math through Haida

Legends: Culturally Responsive Mathematics (http://www.haidanation.ca/Pages/language/haida_legends/media/Lessons/RavenLes4-9.pdf )

Cartesian coordinates:o origin, four quadrants, integral

coordinates, connections to linear relations, transformations

o overlaying coordinate plane on medicine wheel, beading on dreamcatcher, overlaying coordinate plane on traditional maps

transformations:o four quadrants, integral coordinateso translation(s), rotation(s), and/or

reflection(s) on a single 2D shape; combination of successive transformations of 2D shapes; tessellations

44

o First Peoples art, jewelry making, birchbark biting

circle graphs:o constructing, labelling, and

interpreting circle graphso translating percentages displayed in

a circle graph into quantities and vice versa

o visual representations of tidepools or tradional meals on plates

experimental probability:o experimental probability, multiple

trials (e.g., toss two coins, roll two dice, spin a spinner twice, or a combination thereof)

o dice games (http://web.uvic.ca/~tpelton/fn-math/fn-dicegames.html )

financial literacy:o financial percentage calculationso sales tax, tips, discount, sale pric

45


Number represents, describes, and compares the quantities of ratios, rates, and percents.


Sample questions to support inquiry with students:o How can two quantities be compared, represented, and communicated?o How are decimals, fractions, ratios, and percents interrelated?o How does ratio use in mechanics differ from ratio use in architecture?

Computational fluency and flexibility extend to operations with fractions.


Sample questions to support inquiry with students:o When we are working with fractions, what is the relationship between addition and subtraction?o When we are working with fractions, what is the relationship between multiplication and division?o When we are working with fractions, what is the relationship between addition and multiplication?o When we are working with fractions, what is the relationship between subtraction and division?

Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations.

Discrete linear relationships:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o What is a discrete linear relationship?o How can discrete linear relationships be represented?o What factors can change a discrete linear relationship?

The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships.

3D objects:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.

Sample questions to support inquiry with students:o What is the relationship between the surface area and volume of regular solids?o How can surface area and volume of regular solids be determined?o How are the surface area and volume of regular solids related?o How does surface area compare with volume in patterning and cubes?

Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret.


Sample questions to support inquiry with students:o How does determining averages help us understand large data sets?o What do central tendencies represent?o How are central tendencies best used to describe a quality of a large data set?

Curricular Competencies Elaborations Content Elaborations

46

Reasoning and analyzing Use logic and patterns to solve

puzzles and play games Use reasoning and logic to

explore, analyze, and apply mathematical ideas














Represent mathematical ideas in


reasoning and logic:o making connections,

using inductive and deductive reasoning, predicting, generalizing, drawing conclusions through experiences

Estimate reasonably:o estimating using

referents, approximation, and rounding strategies (e.g., the distance to the stop sign is approximately 1 km, the width of my finger is about 1 cm)


strategies to decimals and fractions

o working toward developing fluent and flexible thinking of number


concrete materials (e.g., manipulatives), drawing pictures or diagrams, building, programming

multiple strategies:o includes familiar,

personal, and from other cultures


and traditional practices, the environment, popular


perfect squares and cubes square and cube roots percents less than 1 and greater

than 100 (decimal and fractional percents)

numerical proportional reasoning (rates, ratio, proportions, and percent)

operations with fractions (addition, subtraction, multiplication, division, and order of operations)

discrete linear relations (extended to larger numbers, limited to integers)

expressions- writing and evaluating using substitution

two-step equations with integer coefficients, constants, and solutions

surface area and volume of regular solids, including triangular and other right prisms and cylinders

Pythagorean theorem construction, views, and nets of

3D objects central tendency theoretical probability with two

independent events financial literacy — best buys

perfect squares and cubes:o using colour tiles, pictures, or multi-link

cubeso building the number or using prime

factorization square and cube roots

o finding the cube root of 125o finding the square root of 16/169o estimating the square root of 30

percents:o A worker’s salary increased 122% in three

years. If her salary is now $93,940, what was it originally?

o What is ½% of 1 billion?o The population of Vancouver increased by

3.25%. What is the population if it was approximately 603,500 people last year?

o beading proportional reasoning:

o two-term and three-term ratios, real-life examples and problems

o A string is cut into three pieces whose lengths form a ratio of 3:5:7. If the string was 105 cm long, how long are the pieces?

o creating a cedar drum box of proportions that use ratios to create differences in pitch and tone

o paddle making fractions:

o includes the use of brackets, but excludes exponents

o using pattern blocks or Cuisenaire Rodso simplifying ½ ÷ 9/6 x (7 – 4/5)o drumming and song: 1/2, 1/4, 1/8, whole

notes, dot bars, rests = one beato changing tempos of traditional songs

dependent on context of use

47

concrete, pictorial, and symbolic forms





media and news events, cross-curricular integration





o concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos




o to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g.,

o proportional sharing of harvests based on family size

discrete linear relations:o two-variable discrete linear relationso expressions, table of values, and graphso scale values (e.g., tick marks on axis

represent 5 units instead of 1)o four quadrants, integral coordinates

expressions:o using an expression to describe a

relationshipo evaluating 0.5n – 3n + 25, if n = 14

two-step equations:o solving and verifying 3x – 4 = –12o modelling the preservation of equality

(e.g., using a balance, manipulatives, algebra tiles, diagrams)

o spirit canoe journey calculations surface area and volume:

o exploring strategies to determine the surface area and volume of a regular solid using objects, a net, 3D design software

o volume = area of the base x heighto surface area = sum of the areas of each

side Pythagorean theorem:

o modelling the Pythagorean theoremo finding a missing side of a right triangleo deriving the Pythagorean theoremo constructing canoe paths and landings

given current on a rivero First Peoples constellations

3D objects:o top, front, and side views of 3D objectso matching a given net to the 3D object it

representso drawing and interpreting top, front, and

side views of 3D objects

48

cross-discipline, daily activities, local and traditional practices, the environment, popular media and news events, and social justice)





practices: counting, measuring, locating, designing, playing, explaining(http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm )

o www.aboriginaleducation .ca

o Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resources/math-first-peoples/ )

o constructing 3D objects with netso using design software to create 3D objects

from netso bentwood boxes, lidded baskets, packs

central tendency:o mean, median, and mode

theoretical probability:o with two independent events: sample

space (e.g., using tree diagram, table, graphic organizer)

o rolling a 5 on a fair die and flipping a head on a fair coin is 1/6 x ½ = 1/12

o deciding whether a spinner in a game is fair

financial literacy:o coupons, proportions, unit price, products

and serviceso proportional reasoning strategies (e.g.,

unit rate, equivalent fractions given prices and quantities)

49


The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

numbers:o Number: Number represents and describes quantity.o Algebraic reasoning enables us to describe and analyze mathematical relationships.

Sample questions to support inquiry with students:o How does understanding equivalence help us solve algebraic equations?o How are the operations with polynomials connected to the process of solving equations?o What patterns are formed when we implement the operations with polynomials?o How can we analyze bias and reliability of studies in the media?

Computational fluency and flexibility with numbers extend to operations with rational numbers.


Sample questions to support inquiry with students:o When we are working with rational numbers, what is the relationship between addition and subtraction?o When we are working with rational numbers, what is the relationship between multiplication and division?o When we are working with rational numbers, what is the relationship between addition and multiplication?o When we are working with rational numbers, what is the relationship between subtraction and division?

Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.

Continuous linear relationships:o Patterning: We use patterns to represent identified regularities and to make generalizations.

Sample questions to support inquiry with students:o What is a continuous linear relationship?o How can continuous linear relationships be represented?o How do linear relationships help us to make predictions?o What factors can change a continuous linear relationship?o How are different graphs and relationships used in a variety of careers?

Similar shapes have proportional relationships that can be described, measured, and compared.

proportional relationships:o Geometry and Measurement: We can describe, measure, and compare spatial relationships.o Proportional reasoning enables us to make sense of multiplicative relationships.

Sample questions to support inquiry with students:o How are similar shapes related?o What characteristics make shapes similar?o What role do similar shapes play in construction and engineering of structures?

Analyzing the validity, reliability, and representation of data enables us to compare and interpret.


Sample questions to support inquiry with students:

50

o What makes data valid and reliable?o What is the difference between valid data and reliable data?o What factors influence the validity and reliablity of data?





















strategies to rational numbers and algebraic expressions

o working toward developing fluent and flexible thinking of number


concrete materials (e.g., manipulatives), drawing pictures or diagrams, building, programming


Students are expected to know the following: operations with rational numbers

(addition, subtraction, multiplication, division, and order of operations)

exponents and exponent laws with whole-number exponents

operations with polynomials, of degree less than or equal to 2

two-variable linear relations, using graphing, interpolation, and extrapolation

multi-step one-variable linear equations

spatial proportional reasoning statistics in society financial literacy — simple budgets

and transactions

operations:o includes brackets and exponentso simplifying (-3/4) ÷ 1/5 + ((-1/3) x (-5/2))o simplifying 1 – 2 x (4/5)2

o paddle making exponents:

o includes variable baseso 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n4 = n

x n x n x no exponent laws (e.g., 60 = 1; m1 = m; n5 x

n3 = n8; y7/y3 = y4; (5n)3 = 53 x n3 = 125n3; (m/n)5 = m5/n5; and (32)4 = 38)

o limited to whole-number exponents and whole-number exponent outcomes when simplified

o (–3)2 does not equal –32

o 3x(x – 4) = 3x2 – 12x polynomials:

o variables, degree, number of terms, and coefficients, including the constant term

o (x2 + 2x – 4) + (2x2 – 3x – 4)o (5x – 7) – (2x + 3)o 2n(n + 7)o (15k2 -10k) ÷ (5k)o using algebra tiles

two-variable linear relations:o two-variable continuous linear relations;

includes rational coordinateso horizontal and vertical lineso graphing relation and analyzingo interpolating and extrapolating

approximate values

51









o in daily activities, local and traditional practices, the environment, popular media and news events, cross-curricular integration





o concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify and apply mathematical ideas; may use technology such as screencasting apps, digital photos




o to develop a sense of how mathematics helps us

o spirit canoe journey predictions and daily checks

multi-step:o includes distribution, variables on both

sides of the equation, and collecting like terms

o includes rational coefficients, constants, and solutions

o solving and verifying 1 + 2x = 3 – 2/3(x + 6)

o solving symbolically and pictorially proportional reasoning:

o scale diagrams, similar triangles and polygons, linear unit conversions

o limited to metric unitso drawing a diagram to scale that represents

an enlargement or reduction of a given 2D shape

o solving a scale diagram problem by applying the properties of similar triangles, including measurements

o integration of scale for First Peoples mural work, use of traditional design in current First Peoples fashion design, use of similar triangles to create longhouses/models

statistics:o population versus sample, bias, ethics,

sampling techniques, misleading statso analyzing a given set of data (and/or its

representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity

o using First Peoples data on water quality, Statistics Canada data on income, health, housing, population

financial literacy

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understand ourselves and the world around us (e.g., cross-discipline, daily activities, local and traditional practices, the environment, popular media and news events, and social justice)






o www.aboriginaleducation. ca

o Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resources/math-first-peoples/ )

o banking, simple interest, savings, planned purchases

o creating a budget/plan to host a First Peoples event

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