ontario curriculum - national council of teachers of ... · 4. grade number measurement geometry...

1

Grade Number Measurement Geometry Patterning and Algebra Data Management and Probability

KCCSSMDomain

K: K.CC

K: K.OA

K: K.MD

Grade 1: 1.MD (length only)

K: K.G Not supported in the CCSSM K: K.MD

Not covered in the CCSSM

• counting back (explicitly)

• subitizing (explicitly)

• estimating amounts (explicitly)

• use of ordinal numbers

• use of Canadian coins

• non-standard units for area, capacity, mass, or time

• work with temperature

• sorting (explicitly)

• exploration of the 2-D shapes that make up a 3-D shape (explicitly)

• concrete graphs

• work on probability until grade 7

1CCSSMDomain

K: K.CC

K: K.NBT

Grade 1: 1.OA

Grade 1: 1.NBT

Grade 1: 1.G

Grade 2: 2.OA

Grade 2: 2.G

K: K.MD

Grade 1: 1.MD

K: K.G

Grade 1: 1.G

K: K.CC Grade 1: 1.MD


• writing numbers in words

• anchoring to the number 5 (explicitly)

• identification of coins or representing money amounts

• estimating numbers of objects (explicitly)

• constructing given lengths

• creating measuring tools

• measuring area, mass, capacity, or time with non-standard units

• work with the calendar

• tracing or recognizing 2-D shapes as faces of 3-D figures (explicitly)

• covering of outline puzzles with shapes

• using maps to describe location

• creating symmetrical designs (explicitly)

• repeating patterns

• requirement for a pan balance model for equality

• probability until grade 7

Ontario Curriculum Matching Ontario overall and specific expectations to the Common Core State Standards for Mathematics (CCSSM)

Elementary Courses • K–4

sbarker

Sticky Note

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http://www.corestandards.org/Math/Content/K/CC

http://www.corestandards.org/Math/Content/K/OA

http://www.corestandards.org/Math/Content/K/MD

http://www.corestandards.org/Math/Content/1/MD

http://www.corestandards.org/Math/Content/K/G



http://www.corestandards.org/Math/Content/K/NBT

http://www.corestandards.org/Math/Content/1/OA

http://www.corestandards.org/Math/Content/1/NBT

http://www.corestandards.org/Math/Content/1/G









2



• use of ordinal numbers

• skip counting by 2s and 5s until Grade 2 and then it’s to 1000, not 100


• use of money amounts


• metre as a benchmark (explicitly)

2CCSSMDomain

Grade 1: 1.OA

Grade 1: 1.NBT

Grade 1: 1.G

Grade 2: 2.OA

Grade 2: 2.NBT

Grade 2: 2.G

Grade 3: 3.OA

Grade 2: 2.MD

Grade 3: 3.MD

K: K.G

Grade 1:1.G

Grade 4: 4.G

Grade 1: 1.OA

Grade 4: 4.OA

Grade 1: 1.MD

Grade 2: 2.MD


• writing number words

• determining nearest multiple of 10 (until larger numbers are involved)


• skip counting by 25s

• placing numbers on a number line (explicitly)

Note: CCSSM skip counting is to 1,000 rather than 200. The x sign is introduced in grade 2 rather than grade 3.

• developing benchmarks for units

• justifying unit selection

• representing measures in a variety of ways

• measuring around round objects

• measurement of capacity with non-standard units

• calendar work

• relating time units (days, weeks, months, years)

• constructing time measurement tools


Note: Reading the clock in the CCSSM is to the nearest 5 minutes, rather than nearest quarter hour.

• contrasting geometric to non-geometric attributes of objects

• covering outline puzzles

• drawing simple maps


Note: Pattern work in the CCSSM is in grade 4 and focuses more on applying pattern rules than identifying, describing, representing, or creating patterns.

• sorting using two attributes

• distinguishing data value from data frequency numbers


Elementary Courses • K–4Matching Ontario overall and specific expectations to the Common Core State Standards for Mathematics (CCSSM)

















3


3CCSSMDomain

Grade 2: 2.NBT

Grade 2: 2.MD

Grade 3: 3.OA

Grade 3: 3.NBT

Grade 3: 3.NF

Grade 2: 2.MD

Grade 3: 3.MD

K: K.G

Grade 3: 3.G

Grade 4: 4.MD

Grade 4: 4.G

Grade 1: 1.OA

Grade 3: 3.OA

Grade 4: 4.OA

Grade 1: 1.MD



• decomposing 3-digit numbers other than in the standard way

• use of place value materials (explicitly)

• skip counting backwards (explicitly)

• visual representations or real life uses to focus on magnitude (explicitly)

• skip counting by 25s

• skip counting backwards

• student-generated algorithms

• requirement for estimation to test reasonableness of computations

Note: Standard fraction notation is used instead of words when fractions are introduced in the CCSSM.

• drawing items of a particular length


• development of 1 kg or 1 L benchmarks

• unit selection justification

• exploration of effect of unit size on a measured area

• solving problems based on time units

• solving problems based on greatest or least number of shapes to compose another shape

• 2-D shapes found in 3-D figures (explicitly)

• movement on a grid

• transformations until grade 8

Note: re CCSSM approaches: The introduction of right angles and angle comparison is not until grade 4. The word congruent is used much later.


• representing geometric patterns

Note: Most of the pattern work in the CCSSM is applying pattern rules, not describing or creating patterns.

• sorting using two or more attributes

• use of surveys

• concept of mode


4 CCSSMDomain

Grade 3: 3.OA

Grade 3: 3.NBT

Grade 3: 3.NF

Grade 4: 4.OA

Grade 3: 3.MD

Grade 4: 4.MD

Grade 5: 5.MD

Grade 4: 4.MD

Grade 4: 4.G

Grade 6: 6.G

Grade 3: 3.OA

Grade 4: 4.OA

Grade 6: 6.SP

Grade 7: 7.SP






http://www.corestandards.org/Math/Content/3/NF























http://www.corestandards.org/Math/Content/6/SP


4


4CCSSMDomain

Grade 4: 4.NBT

Grade 4: 4.NF

Grade 5: 5.NBT



• required use of money contexts

• required use of estimation when solving problems to judge reasonableness of solutions

• drawing items of given lengths

• work with time units like decade or centuries

• justifying selection of most appropriate unit

• classification of prisms and pyramids (explicitly)

• use of grid system for location

• repeating patterns based on geometric transformations

Note: Most of the pattern work in the CCSSM is applying pattern rules, not identifying, describing, or creating patterns.

• data collection

• distinguishing between primary and secondary data

• stem and leaf plots





5


5CCSSMDomain

Grade 4: 4.OA

Grade 4: 4.NBT

Grade 4: 4.NF

Grade 5: 5.NBT

Grade 6: 6.RP

Grade 3: 3.MD

Grade 4: 4.MD

Grade 5: 5.MD

Grade 4: 4.MD

Grade 4: 4.G

Grade 5: 5.G

Grade 6: 6.G

Grade 7: 7.G

Grade 8: 8.G

Grade 4: 4.OA

Grade 6: 6.EE

Grade 6: 6.SP

Grade 7: 7.SP



• working with money problems with large numbers (explicitly)

• counting up by hundredths using decimals (explicitly)

• representing time to nearest second

• measuring time in days, weeks, months or years

• work with temperatures

• work with 24-hour clock

• relating volume to capacity


• choosing and justifying most appropriate unit choice

• distinguishing between regular or irregular shapes

• classifying triangles based on angle size or side lengths (explicitly)

• recognizing 3-D objects from nets

• using grids and cardinal direction

• creating tables of values to describe patterns

• repeating patterns involving geometric transformations

Note: Most of the pattern work in the CCSSM is applying pattern rules, not identifying, describing, or creating patterns.

• distinguishing between discrete and continuous data

• distinguishing between primary and secondary data

• alternative ways to collect samples

• describing data collection

6CCSSMDomain

Grade 4: 4.OA

Grade 4: 4.NBT

Grade 4: 4.NF

Grade 5: 5.OA

Grade 5: 5.NBT

Grade 6: 6.RP

Grade 4: 4.MD

Grade 5: 5.MD

Grade 6: 6.G

Grade 4: 4.MD

Grade 5: 5.G

Grade 8: 8.G

High School: G-CO

Grade 4: 4.OA

Grade 6: 6.EE

Grade 6: 6.SP

Grade 7: 7.SP


• writing numbers in words • measurement precision

• selecting the most appropriate measurement unit

• using isometric or orthographic drawings

• identifying geometric patterns

• alternate types of pattern rules

• repeating patterns based on geometric transformations

• distinction between quantities that vary and constants (explicitly)

• collecting data

• distinguishing between discrete and continuous data, or primary and secondary data

• considering alternate types of graphs to display data

• considering effect of scale in data presentation

Elementary Courses • 5–8Matching Ontario overall and specific expectations to the Common Core State Standards for Mathematics (CCSSM)





http://www.corestandards.org/Math/Content/6/RP











http://www.corestandards.org/Math/Content/6/EE















http://www.corestandards.org/Math/Content/HSG/CO





6


7CCSSMDomain

Grade 4: 4.OA

Grade 4: 4.NF

Grade 5: 5.OA

Grade 5: 5.NBT

Grade 5: 5.NF

Grade 6: 6.RP

Grade 6: 6.NS

Grade 7: 7.NS

Grade 5: 5.MD

Grade 6: 6.G

Grade 7: 7.G

Grade 5: 5.G

Grade 6: 6.NS

Grade 7: 7.G

Grade 8: 8.G

High School: Congruence G-CO

Grade 5: 5.OA

Grade 6: 6.EE

Grade 7: 7.RP

Grade 6: 6.SP

Grade 7: 7.SP


• selecting among decimal, fraction, or percent representations (explicitly)

• representing perfect squares and their square roots

• relating exponential notation to measurement units

• mandating use of estimation when solving problems

• research on real-life applications of area measurement

• conversion between volume and capacity units

• measuring angles at vertices of prisms

• determining shapes that tile

• expression of general terms of patterns

• collecting survey data

• distinguishing between discrete and continuous data, or primary and secondary data

• considering alternate types of graphs for display

• misleading graphs

• concept of mode

• making convincing arguments from graphs and tables (explicitly)

8CCSSMDomain

Grade 5: 5.NBT

Grade 5: 5.NF

Grade 6: 6.RP

Grade 6: 6.NS

Grade 6: 6.EE

Grade 7: 7.NS

Grade 8: 8.EE

Grade 5: 5.MD

Grade 7: 7.G

Grade 8: 8.G

Grade 8: 8.G

High School: Congruence G-CO

Grade 6: 6.EE

Grade 7: 7.RP

Grade 7: 7.EE

Grade 6: 6.SP

Grade 7: 7.SP

Grade 8: 8.F

Grade 8: 8.SP








http://www.corestandards.org/Math/Content/6/NS
































http://www.corestandards.org/Math/Content/8/F


7



• requirement to estimate when solving problems

• research on applications of volume/capacity measurement

• surface area of a cylinder

• circle construction

• investigating application of geometry in real world

• investigating relationship in area and volume of similar shapes/figures

• Euler’s theorem

• expression of general term of pattern algebraically

• conducting surveys

• distinguishing between categorical, discrete, or continuous data

• distinguishing between primary or secondary data

• selecting and justifying appropriate graphs for data

• identification of complementary events for probability


8

Grade 9 Academic (MPM1D)

Number Sense and Algebra Linear Relations Analytic Geometry Measurement and Geometry

9CCSSM Domain

Grade 6: 6.RP

Grade 6: 6.EE

Grade 7: 7.EE

Grade 8: 8.EE

High School: A-APR

High School: A-CED

Grade 7: 7.RP

Grade 7: 7.EE

Grade 8: 8.F

Grade 8: 8.SP

High School: S-ID

Grade 8: 8.EE

Grade 8: 8.F

High School: G-GPE

Grade 8: 8.G

High School: N-Q

High School: G-CO

High School: G-MD

High School: G-MG


• relating square and cube of a number to area and volume measures

• distinction between different algebraic forms for a line (explicitly)

• explaining significance of optimal area or volume

• surface area of a cylinder or cone

Grade 9 Applied (MFM1P)

Number Sense and Algebra Linear Relations Measurement and Geometry

9CCSSM Domain

Grade 6: 6.RP

Grade 6: 6.EE

Grade 7: 7.RP

Grade 7: 7.EE

Grade 8: 8.EE

High School: A-APR

Grade 7: 7.RP

Grade 7: 7.EE

Grade 8: 8.EE

Grade 8: 8.F

Grade 8: 8.SP

High School: S-ID

Grade 8: 8.G

High School: N-Q

High School: G-CO

High School: G-MD

High School: G-MG


• expression of decimals, fractions, or percents in equivalent form (explicitly)

• relating the square and cube of a number to area and volume measures

Grade 10 Academic (MPM2D)

Quadratic Relations Analytic Geometry Trigonometry

10CCSSM Domain

High School: A-SSE

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: S-ID

Grade 8: 8.EE

Grade 8: 8.G

High School: G-CO

High School: G-GPE

High School: N-Q

High School: G-SRT


• specific reference to second differences (explicitly)

High School Courses • 9–12Matching Ontario overall and specific expectations to the Common Core State Standards for Mathematics (CCSSM)





http://www.corestandards.org/Math/Content/HSA/APR

http://www.corestandards.org/Math/Content/HSA/CED






http://www.corestandards.org/Math/Content/HSS/ID



http://www.corestandards.org/Math/Content/HSG/GPE


http://www.corestandards.org/Math/Content/HSN/Q


http://www.corestandards.org/Math/Content/HSG/GMD

http://www.corestandards.org/Math/Content/HSG/MG


















http://www.corestandards.org/Math/Content/HSA/SSE


http://www.corestandards.org/Math/Content/HSA/REI

http://www.corestandards.org/Math/Content/HSF/IF

http://www.corestandards.org/Math/Content/HSF/BF







http://www.corestandards.org/Math/Content/HSG/SRT

9

Grade 10 Applied (MFM2P)

Measurement and Trigonometry Modelling Linear Relations Quadratic Relations

10CCSSM Domain

High School: N-Q

High School: G-SRT

Grade 8: 8.EE

High School: G-GPE

High School: A-SSE

High School: A-CED

High School: A-REI

High School: F-IF

High School: S-ID


• discussion of occupations that use trigonometry

• calculation of surface area of cylinders, cones, or spheres

• distinction between different algebraic forms for a line (explicitly) • second differences (explicitly)

Grade 11 Functions (MCR3U)

Characteristics of Functions Exponential Functions Discrete Functions Trigonometric Functions

11CCSSM Domain

High School: N-RN

High School: A-APR

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: N-RN

High School: A-SSE

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-LE

High School: S-ID

High School: A-SSE

High School: F-IF

High School: F-BF

High School: F-LE

High School: N-Q

High School: F-IF

High School: F-BF

High School: F-TF

High School: G-SRT

High School: S-ID


• exploration of the Fibonacci sequence or Pascal’s triangle (explicitly)

• formula for sum of arithmetic series

• financial applications of exponential functions

Grade 11 Functions and Applications (MCF3M)

Quadratic Functions Exponential Functions Trigonometric Functions

11CCSSM Domain

High School: A-SSE

High School: A-CED

High School: A-REI

High School: F-IF

High School: N-RN

High School: A-SSE

High School: A-CED

High School: A-REI

High School: N-Q

High School: F-IF

High School: F-BF

High School: F-TF











http://www.corestandards.org/Math/Content/HSN/RN












http://www.corestandards.org/Math/Content/HSF/LE









http://www.corestandards.org/Math/Content/HSF/TF















10

Grade 11 Functions and Applications (MCF3M)

Quadratic Functions Exponential Functions Trigonometric Functions

11CCSSM Domain

High School: F-BF

High School: S-ID

High School: F-IF

High School: F-BF

High School: F-LE

High School: S-ID

High School: G-SRT

High School: S-ID

Grade 11 Foundations for College Math (MBF3C)

Mathematical Models Personal Finance Geometry and Trigonometry Data Management

11CCSSM Domain

High School: N-RN

High School: A-SSE

High School: A-CED

High School: F-IF

High School: F-BF

High School: F-LE

High School: S-ID

Not covered in the CCSSM High School: N-Q

High School: G-SRT

High School: G-MG

High School: S-ID

High School: S-IC


• changing expressed form for a quadratic (explicitly)

• isometric or orthographic drawings • design of a questionnaire or statistical experiment

• distinguishing among sampling techniques

• classification of data sources

• analysis of probability in the media

Grade 11 Workplace (MEL3E)

Not supported in the CCSSM

Grade 12 Advanced Functions (MHF4U)

Exponential and Logarithmic Functions Trigonometric Functions Polynomial and Rational Functions Characteristics of Functions

12CCSSM Domain

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-LE

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-TF

High School: A-APR

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-IF

High School: F-BF

High School: S-ID





















http://www.corestandards.org/Math/Content/HSS/IC



















11

Grade 12 Calculus and Vectors (MCV4U)

Rate of Change Derivatives and their Applications Geometry and Algebra of Vectors


• graphing reciprocal functions (explicitly)

• graphing in radians

• compound angle formulas

• instantaneous rate of change

12CCSSM Domain

High School: F-IF Not supported in the CCSSM High School: N-VM


• instantaneous rate of change • dot product

• cross product

• describing lines or planes using scalar, vector, parametric form

• describing planes using Cartesian form

Grade 12 Mathematics of Data Management (MDM4U)

Counting and Probability Probability Distributions Organization of Data for Analysis Statistical Analysis

12CCSSM Domain

High School: S-CP High School: S-ID

High School: S-MD

High School: S-ID

High School: S-IC

High School: S-ID

High School: S-IC


• exploring Pascal’s triangle (explicitly) • creation of a probability histogram

• exploration of conditions that lead to various distributions

• distinguishing between continuous or discrete, qualitative or quantitative, primary or secondary, or between discrete, qualitative, and quantitative data

• data in the media

Note: There is no requirement for a culminating project in the CCSSM.

Grade 12 Mathematics for College Technology (MCT4C)

Exponential Functions Polynomial Functions Trigonometric Functions Applications of Geometry

12CCSSM Domain

High School: A-SSE

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-LE

High School: A-APR

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-BF

High School: F-TF

High School: G-SRT

High School: N-Q

High School: N-VM

High School: G-C

High School: G-GMD



http://www.corestandards.org/Math/Content/HSN/VM

http://www.corestandards.org/Math/Content/HSS/CP


http://www.corestandards.org/Math/Content/HSS/MD
























http://www.corestandards.org/Math/Content/HSG/C


12

Grade 12 Mathematics for College Technology (MCT4C)

Exponential Functions Polynomial Functions Trigonometric Functions Applications of Geometry


• graphing reciprocal functions (explicitly)

• graphing in radians

• compound angle formulas

Grade 12 Foundations for College Mathematics MAP4C

Mathematical Models Personal Finance Geometry and Trigonometry Data Management

12CCSSM Domain

High School: N-RN

High School: A-CED

High School: A-REI

High School: F-IF

High School: F-LE

Not supported in the CCSSM Grade 6: 6.RP

Grade 6: 6.G

Grade 7: 7.G

High School: N-Q

High School: N-VM

High School: G-SRT

High School: G-CO

High School: G-MD

High School: G-MG

High School: S-ID

High School: S-IC


• surface area of a cylinder or sphere

• presentation to showcase occupations that use trigonometry

• collection of data

• use of data from the media

• use of language, such as 19 times out of 20


















13

Grade 12 Mathematics for Work and Everyday Life (MEL4E)

Reasoning with Data Personal Finance Applications of Measurement

12CCSSM Domain

Grade 6: 6.SP

Grade 7: 7.SP

High School: S-ID

High School: S-IC

Not supported in the CCSSM Grade 5: 5.MD

Grade 6: 6.RP

Grade 7: 7.G

Grade 8: 8.G

High School: N-Q


• collection of data

• use of data from the media

• use of circle graphs or broken line graphs

• 3-D scale models

• preparing budget for household improvement

• discussion of consequences of errors in proportional reasoning











ontario curriculum - national council of teachers of ... · 4. grade number measurement geometry...

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