Science- Kindergarten · Web view2016/05/06 · surface area and volume of regular solids,...

Area of Learning: Mathematics Grade 6Big Ideas Elaborations

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

numbers:o Number: Number represents and describes quantity.

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.

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

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.

Data:o Data and Probability: Analyzing data and chance enables us 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?

Curricular Competencies Elaborations Content ElaborationsReasoning and analyzing

Use logic and patterns to solve logic and patterns:

o including codingStudents are expected to know the following:

small to large numbers:o place value from thousandths to

1

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

Model mathematics in contextualized experiences

Understanding and solving Apply multiple strategies to solve

problems in both abstract and contextualized situations

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

Visualize to explore mathematical concepts

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 Use mathematical vocabulary and

language to contribute to mathematical discussions

Explain and justify mathematical ideas and decisions

Communicate mathematical thinking in many ways

Represent mathematical ideas in concrete, pictorial, and symbolic forms

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

o http://www.nctm.org/ Publications/Teaching-Children-Mathematics/Blog/Modeling-with-Mathematics-through-Three-Act-Tasks/

multiple strategies:o includes familiar, personal,

and from other cultures connected:

o in daily activities, local and traditional practices, the

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

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

o traditional Aboriginal language speakers to English speakers or French speakers, dual-language speakers

percents:

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http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Modeling-with-Mathematics-through-Three-Act-Tasks/



Connecting and reflecting Reflect on mathematical thinking Connect mathematical concepts to

each other and to other areas and personal interests

Use mathematical arguments to support personal choices

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

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

o Patterns are important in Aboriginal technology, architecture, and art.

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

Explain and justify:o using mathematical

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

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

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 Aboriginal 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 environmento estimating using 45°, 90°, and 180° as

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traditional practices, the environment, popular 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 First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and resource management; community profiles; art; nutrition; dwellings

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

reference angleso 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 set of data

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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


o fish runs versus time 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 bone game financial literacy:

o informed decision making on saving and purchasing

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

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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?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.

Data:o Data and Probability: Analyzing data and chance enables us 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?

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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












logic and patterns:o including coding






strategies to integerso 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



and from other cultures

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

independent events financial literacy — financial percentage

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

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

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connected: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



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,

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, 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)

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local and traditional practices, the environment, popular media and news events, and social justice)






o First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment and resource management; community profiles; art; nutrition; dwellings

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

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

o Aboriginal 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)

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http://www.haidanation.ca/Pages/language/haida_legends/media/Lessons/RavenLes4-9.pdf



o Puim, Hubbubo dice games

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

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

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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.

data:o Data and Probability: Analyzing data and chance 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

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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

Model:o acting it out, using

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


multiple strategies:o includes familiar,

Students are expected to know the following:

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

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concrete, pictorial, and symbolic forms





personal, and from other cultures

connected: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 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 river (First Nations Education Steering Committee)

o Aboriginal constellations and adaus 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

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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)




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 First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and resource management;

side views of 3D objectso 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)

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community profiles; art; nutrition; dwellings

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

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http://www.fnesc.ca/resources/math-first-peoples/



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. (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. (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.

data: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 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?


Use logic and patterns to solve puzzles and play games

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


















strategies to rational numbers and algebraic expressions

o working toward developing fluent and flexible thinking of number

Model:o acting it out, using

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

o http://www.nctm.org/ Publications/Teaching-

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

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Children-Mathematics/Blog/Modeling-with-Mathematics-through-Three-Act-Tasks/


and from other cultures connected:

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


thinking of self and others, including evaluating strategies and solutions,

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 Aboriginal mural work, use of traditional design in current Aboriginal 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 literacyo banking, simple interest, savings, planned

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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 media and news events, and social justice)






o First Nations Education Steering Committee (FNESC) Place-Based Themes and Topics: family and ancestry; travel and navigation; games; land, environment, and resource

purchaseso creating a budget/plan to host a First

Peoples event

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management; community profiles; art; nutrition; dwellings

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

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Science- Kindergarten · Web view2016/05/06 · surface area and volume of regular solids,...

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Transcript of Science- Kindergarten · Web view2016/05/06 · surface area and volume of regular solids,...