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Skills available for Ontario grade 6 math curriculum

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Ontario Curriculum (2005) Ontario Curriculum (2005)

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6.B Number

6.B1 Number Sense
- Rational Numbers
  - 6.B1.1 read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life
    - Place values in whole numbers up to 1 million (6-A.1)
    - Word names for numbers (6-A.3)
  - 6.B1.2 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines
  - 6.B1.3 compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts
- Fractions, Decimals and Percents
  - 6.B1.4 read, represent, compare, and order decimal numbers up to thousandths, in various contexts
  - 6.B1.5 round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts
    - Round decimals (6-B.6)
    - Round whole numbers and decimals: find the missing digit (6-B.7)
  - 6.B1.6 describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts
6.B2 Operations
- Properties and Relationships
  - 6.B2.1 use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations
- Math Facts
  - 6.B2.2 understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and 10
    - Divisibility rules (6-F.1)
- Mental Math
  - 6.B2.3 use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used
- Addition and Subtraction
  - 6.B2.4 represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms
  - 6.B2.5 add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts
- Multiplication and Division
  - 6.B2.6 represent composite numbers as a product of their prime factors, including through the use of factor trees
    - Prime factorization (6-I.3)
  - 6.B2.7 represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms
    - Multiply a decimal up to tenths by a whole number (6-G.5)
    - Multiply a decimal up to tenths by a whole number: word problems (6-G.7)
  - 6.B2.8 represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate
    - Divide whole numbers by decimals (6-G.20)
  - 6.B2.9 multiply whole numbers by proper fractions, using appropriate tools and strategies
  - 6.B2.10 divide whole numbers by proper fractions, using appropriate tools and strategies
  - 6.B2.11 represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies
  - 6.B2.12 solve problems involving ratios, including percents and rates, using appropriate tools and strategies

6.C Algebra

6.C1 Patterns and Relationships
- Patterns
  - 6.C1.1 identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear
  - 6.C1.2 create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations
  - 6.C1.3 determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns
  - 6.C1.4 create and describe patterns to illustrate relationships among whole numbers and decimal numbers
    - Division patterns with zeroes (6-F.6)
    - Decimal division patterns over increasing place values (6-G.15)
6.C2 Equations and Inequalities
- Variables and Expressions
  - 6.C2.1 add monomials with a degree of 1 that involve whole numbers, using tools
    - Identify equivalent expressions using strip models (6-W.13)
    - Identify equivalent expressions (6-W.14)
  - 6.C2.2 evaluate algebraic expressions that involve whole numbers and decimal tenths
    - Evaluate variable expressions with whole numbers (6-W.3)
    - Evaluate variable expressions with decimals (6-W.5)
- Equalities and Inequalities
  - 6.C2.3 solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions
  - 6.C2.4 solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions
6.C3 Coding
- Coding Skills
  - 6.C3.1 solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves conditional statements and other control structures
  - 6.C3.2 read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code

6.D Data

6.D1 Data Literacy
- Data Collection and Organization
  - 6.D1.1 describe the difference between discrete and continuous data, and provide examples of each
    - Identify discrete and continuous data (6-FF.8)
  - 6.D1.2 collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals
    - Interpret categorical data (6-EE.8)
- Data Visualization
  - 6.D1.3 select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs
    - Choose the best type of graph (6-EE.20)
  - 6.D1.4 create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data
- Data Analysis
  - 6.D1.5 determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets
  - 6.D1.6 analyse different sets of data presented in various ways, including in histograms and broken-line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions
6.D2 Probability
- Probability
  - 6.D2.1 use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions
  - 6.D2.2 determine and compare the theoretical and experimental probabilities of two independent events happening
    - Experimental probability (6-GG.6)

6.E Spatial Sense

6.00E+01 Geometric and Spatial Reasoning
- Geometric Reasoning
  - 6.E1.1 create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry
  - 6.E1.2 construct three-dimensional objects when given their top, front, and side views
    - Front, side and top view (6-CC.4)
- Location and Movement
  - 6.E1.3 plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another
  - 6.E1.4 describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations
6.00E+02 Measurement
- The Metric System
  - 6.E2.1 measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa
    - Convert and compare metric units (6-R.2)
    - Multi-step problems with metric unit conversions (6-R.8)
- Angles
  - 6.E2.2 use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise
  - 6.E2.3 use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures
- Area and Surface Area
  - 6.E2.4 determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas
  - 6.E2.5 create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas
    - Nets of three-dimensional figures (6-CC.3)
  - 6.E2.6 determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together

6.F Financial Literacy

6.F.1 Money and Finances
- Money Concepts
  - 6.F.1.1 describe the advantages and disadvantages of various methods of payment that can be used to purchase goods and services
    - Identify advantages and disadvantages of payment methods (6-HH.2)
- Financial Management
  - 6.F.1.2 identify different types of financial goals, including earning and saving goals, and outline some key steps in achieving them
  - 6.F.1.3 identify and describe various factors that may help or interfere with reaching financial goals
- Consumer and Civic Awareness
  - 6.F.1.4 explain the concept of interest rates, and identify types of interest rates and fees associated with different accounts and loans offered by various banks and other financial institutions
    - Simple interest (6-T.7)
  - 6.F.1.5 describe trading, lending, borrowing, and donating as different ways to distribute financial and other resources among individuals and organizations
    - Financial institution vocabulary (6-HH.1)

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6.B Number

6.B1 Number Sense

Rational Numbers

6.B1.1 read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life

6.B1.2 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines

6.B1.3 compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts

Fractions, Decimals and Percents

6.B1.4 read, represent, compare, and order decimal numbers up to thousandths, in various contexts

6.B1.5 round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts

6.B1.6 describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts

6.B2 Operations

Properties and Relationships

6.B2.1 use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations

Math Facts

6.B2.2 understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4, 5, 6, 8, 9, and 10

Mental Math

6.B2.3 use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used

Addition and Subtraction

6.B2.4 represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms

6.B2.5 add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts

Multiplication and Division

6.B2.6 represent composite numbers as a product of their prime factors, including through the use of factor trees

6.B2.7 represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms

6.B2.8 represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate

6.B2.9 multiply whole numbers by proper fractions, using appropriate tools and strategies

6.B2.10 divide whole numbers by proper fractions, using appropriate tools and strategies

6.B2.11 represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies

6.B2.12 solve problems involving ratios, including percents and rates, using appropriate tools and strategies

6.C Algebra

6.C1 Patterns and Relationships

Patterns

6.C1.1 identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear

6.C1.2 create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations

6.C1.3 determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns

6.C1.4 create and describe patterns to illustrate relationships among whole numbers and decimal numbers

6.C2 Equations and Inequalities

Variables and Expressions

6.C2.1 add monomials with a degree of 1 that involve whole numbers, using tools

6.C2.2 evaluate algebraic expressions that involve whole numbers and decimal tenths

Equalities and Inequalities

6.C2.3 solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions

6.C2.4 solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions

6.C3 Coding

Coding Skills

6.C3.1 solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves conditional statements and other control structures

6.C3.2 read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code

6.D Data

6.D1 Data Literacy

Data Collection and Organization

6.D1.1 describe the difference between discrete and continuous data, and provide examples of each

6.D1.2 collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals

Data Visualization

6.D1.3 select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs

6.D1.4 create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data

Data Analysis

6.D1.5 determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets

6.D2 Probability

Probability

6.D2.1 use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions

6.D2.2 determine and compare the theoretical and experimental probabilities of two independent events happening

6.E Spatial Sense

6.00E+01 Geometric and Spatial Reasoning

Geometric Reasoning

6.E1.1 create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry

6.E1.2 construct three-dimensional objects when given their top, front, and side views

Location and Movement

6.E1.3 plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another

6.E1.4 describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations

6.00E+02 Measurement

The Metric System

6.E2.1 measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa

Angles

6.E2.2 use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise

6.E2.3 use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures

Area and Surface Area

6.E2.4 determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas

6.E2.5 create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas