Grade 6 math in Ontario: what your child learns

Your child reads whole numbers to one million, places integers (including negative numbers) on number lines, and compares integers, decimals and fractions. They use divisibility rules, find percents mentally (like 10%, 15% and 25%), add and subtract fractions with unlike denominators, make factor trees, multiply and divide by decimal tenths and by fractions, and solve ratio, rate and percent problems.

Typical homework, with a hint

What your child learns in Number

• Numbers to one millionB1.1

  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.

• Integers on number linesB1.2

  Read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines.

• Comparing integers, decimals, fractionsB1.3

  Compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts.

• Decimals to thousandthsB1.4

  Read, represent, compare, and order decimal numbers up to thousandths, in various contexts.

• Rounding decimalsB1.5

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

• Fractions and decimalsB1.6

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

• Properties of operationsB2.1

  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.

• Divisibility rulesB2.2

  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 percentsB2.3

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

• Adding and subtracting decimalsB2.4

  Represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms.

• Adding fractions, unlike denominatorsB2.5

  Add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts.

• Prime factors and treesB2.6

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

• Multiplying by decimal tenthsB2.7

  Represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms.

• Dividing by decimal tenthsB2.8

  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.

• Multiplying by fractionsB2.9

  Multiply whole numbers by proper fractions, using appropriate tools and strategies.

• Dividing by fractionsB2.10

  Divide whole numbers by proper fractions, using appropriate tools and strategies.

• Dividing decimalsB2.11

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

• Ratios, rates, and percentsB2.12

  Solve problems involving ratios, including percents and rates, using appropriate tools and strategies.

Kids identify linear growing patterns and describe them with algebraic expressions and equations, then use those rules to find unknown values. They add like terms with a variable (like 2x + 3x), evaluate expressions with decimals, solve equations with several terms, and solve two-step inequalities. In coding, they write and improve efficient code.

Typical homework, with a hint

What your child learns in Algebra

• Linear growing patternsC1.1

  Identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear.

• Patterns as equationsC1.2

  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.

• Pattern rules and unknownsC1.3

  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.

• Decimal number patternsC1.4

  Create and describe patterns to illustrate relationships among whole numbers and decimal numbers.

• Adding monomialsC2.1

  Add monomials with a degree of 1 that involve whole numbers, using tools.

• Evaluating expressionsC2.2

  Evaluate algebraic expressions that involve whole numbers and decimal tenths.

• Solving multi-term equationsC2.3

  Solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions.

• Two-step inequalitiesC2.4

  Solve inequalities that involve two operations and whole numbers up to 100 and verify and graph the solutions.

• Writing efficient codeC3.1

  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.

• Reading and improving codeC3.2

  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.

Mathematical Modelling (C4): Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

Kids learn the difference between discrete data (counted, like number of siblings) and continuous data (measured, like height), group data into intervals, and use histograms and broken-line graphs. They find the range and the mean, median and mode to compare data sets, spot misleading graphs, and find the probability of two independent events, like flipping a coin and rolling a die.

Typical homework, with a hint

What your child learns in Data

• Discrete vs continuous dataD1.1

  Describe the difference between discrete and continuous data, and provide examples of each.

• Collecting data in intervalsD1.2

  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.

• Histograms and line graphsD1.3

  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.

• Making an infographicD1.4

  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.

• Range and central tendencyD1.5

  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.

• Spotting misleading graphsD1.6

  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.

• Probability as percentsD2.1

  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.

• Probability of two eventsD2.2

  Determine and compare the theoretical and experimental probabilities of two independent events happening.

Geometry covers the properties of quadrilaterals (including diagonals and symmetry), building objects from top, front and side views, plotting points in all four quadrants, and combining translations, reflections and rotations. Measurement includes metric conversions both ways, angles up to 360°, unknown angles (supplementary, complementary, opposite), areas of trapezoids, rhombuses and kites, nets, and surface area of prisms and pyramids.

Typical homework, with a hint

What your child learns in Spatial Sense

• Properties of quadrilateralsE1.1

  Create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry.

• Building from viewsE1.2

  Construct three-dimensional objects when given their top, front, and side views.

• Four-quadrant coordinatesE1.3

  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.

• Combining transformationsE1.4

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

• Converting metric unitsE2.1

  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.

• Protractor to 360°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.

• Finding unknown anglesE2.3

  Use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures.

• Area of composite shapesE2.4

  Determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas.

• Nets and surface areaE2.5

  Create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas.

• Surface area of prismsE2.6

  Determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together.

Financial literacy in Grade 6 covers the pros and cons of different ways to pay, setting earning and saving goals and what helps or gets in the way of reaching them, interest rates and bank fees, and different ways to share resources (trading, lending, borrowing and donating).

Typical homework, with a hint

What your child learns in Financial Literacy

• Comparing ways to payF1.1

  Describe the advantages and disadvantages of various methods of payment that can be used to purchase goods and services.

• Setting financial goalsF1.2

  Identify different types of financial goals, including earning and saving goals, and outline some key steps in achieving them.

• Reaching financial goalsF1.3

  Identify and describe various factors that may help or interfere with reaching financial goals.

• Interest rates and feesF1.4

  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.

• Trading, lending, donatingF1.5

  Describe trading, lending, borrowing, and donating as different ways to distribute financial and other resources among individuals and organizations.

The Ontario curriculum also has a strand A that runs through all the others. It’s about how kids approach math: managing frustration, keeping at a hard problem, and using the mathematical processes (such as problem solving, reasoning, connecting, representing and communicating). It has no homework of its own, but it’s exactly what a patient, hint-based tutor helps build.

How to help with Grade 6 math at home

• Talk about negative numbers with temperatures in winter and bank balances.
• For unlike denominators, go back to drawings or fraction strips before the rule.
• Encourage neat, step-by-step work. In Grade 6 the method matters as much as the answer.
• Keep practice calm and routine. Short, regular sessions beat cramming.

More ideas: how to help with math homework without giving the answer.

Grade 6 is an EQAO year in Ontario. Read our parent guide: EQAO Grade 6 math: what parents should know.

How Astuzo helps with Grade 6 math

Grade 6 problems are often multi-step. Spark keeps your child moving one step at a time: what do you know, what’s the first step, does the answer make sense? Those are the habits they’ll need in Grades 7 and 8.

You set your child’s grade once, and Spark pitches every hint at that level. You get a short report after each session showing what they worked on. See how Astuzo works.