Grade 5 math in Ontario: what your child learns

Your child works with numbers to 100 000, fractions from halves to twelfths (including improper fractions and mixed numbers), and decimals to hundredths, and connects fractions, decimals and whole-number percents. They recall facts to 12 × 12, multiply two-digit by two-digit numbers with the area model and a written method, divide three-digit numbers by two-digit numbers, add and subtract fractions with like denominators, and work with equivalent ratios and rates.

Typical homework, with a hint

What your child learns in Number

• Reading numbers to 100 000B1.1

  Read, represent, compose, and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in everyday life.

• Comparing numbers to 100 000B1.2

  Compare and order whole numbers up to and including 100 000, in various contexts.

• Equivalent fractionsB1.3

  Represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts.

• Comparing fractionsB1.4

  Compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts.

• Decimals to hundredthsB1.5

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

• Rounding decimals to tenthsB1.6

  Round decimal numbers to the nearest tenth, in various contexts.

• Fractions, decimals, and percentsB1.7

  Describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, 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 and decimal numbers, including those requiring more than one operation, and check calculations.

• Times tables to 12×12B2.2

  Recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts.

• Mental math with decimalsB2.3

  Use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used.

• Adding and subtracting decimalsB2.4

  Represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms.

• Adding fractions, like denominatorsB2.5

  Add and subtract fractions with like denominators, in various contexts.

• Two-digit multiplicationB2.6

  Represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods.

• Dividing by two digitsB2.7

  Represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately.

• Multiplying by unit fractionsB2.8

  Multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings.

• Equivalent ratios and ratesB2.9

  Represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts.

Patterns can now shrink as well as grow. Kids translate between words and algebraic expressions (“3 more than a number” becomes n + 3), evaluate expressions by substituting a value, solve equations with whole numbers up to 100, and solve one-step inequalities. Code uses conditional statements (“if this, then that”).

Typical homework, with a hint

What your child learns in Algebra

• Growing and shrinking patternsC1.1

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

• Patterns in tables, graphsC1.2

  Create and translate growing and shrinking patterns using various representations, including tables of values and graphs.

• Pattern rules and predictionsC1.3

  Determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns.

• Decimal number patternsC1.4

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

• Words to algebraic expressionsC2.1

  Translate among words, algebraic expressions, and visual representations that describe equivalent relationships.

• Evaluating expressionsC2.2

  Evaluate algebraic expressions that involve whole numbers.

• Solving equationsC2.3

  Solve equations that involve whole numbers up to 100 in various contexts, and verify solutions.

• Solving inequalitiesC2.4

  Solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions.

• Code with conditionsC3.1

  Solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves conditional statements and other control structures.

• Reading and changing 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.

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

Kids learn why a good sample matters, organise data in relative-frequency tables, choose graphs (including stacked-bar graphs), and spot misleading graphs. They find the mean, median and mode with decimals too. Probability is written as a fraction, and they compare what should happen (theoretical) with what did happen (experimental).

Typical homework, with a hint

What your child learns in Data

• Sampling techniquesD1.1

  Explain the importance of various sampling techniques for collecting a sample of data that is representative of a population.

• Relative-frequency tablesD1.2

  Collect data, using appropriate sampling techniques as needed, to answer questions of interest about a population, and organize the data in relative-frequency tables.

• Choosing the right graphD1.3

  Select from among a variety of graphs, including stacked-bar 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 relative-frequency tables and stacked-bar graphs, and incorporating any other relevant information that helps to tell a story about the data.

• Mean, median, and modeD1.5

  Determine the mean and the median and identify the mode(s), if any, for various data sets involving whole numbers and decimal numbers, and explain what each of these measures indicates about the data.

• Spotting misleading graphsD1.6

  Analyse different sets of data presented in various ways, including in stacked-bar 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 fractionsD2.1

  Use fractions to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions.

• Theoretical vs experimental probabilityD2.2

  Determine and compare the theoretical and experimental probabilities of an event happening.

Geometry covers types of triangles, congruent shapes, and drawing top, front and side views. Kids plot points with different scales and do translations, reflections and rotations up to 180°. In measurement they convert metric units (like metres to centimetres), use a protractor, find the area of triangles and parallelograms, and see that shapes with the same area can have different perimeters.

Typical homework, with a hint

What your child learns in Spatial Sense

• Types of trianglesE1.1

  Identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements.

• Congruent shapesE1.2

  Identify and construct congruent triangles, rectangles, and parallelograms.

• Top, front, side viewsE1.3

  Draw top, front, and side views of objects, and match drawings with objects.

• Coordinates with scalesE1.4

  Plot and read coordinates in the first quadrant of a Cartesian plane using various scales, and describe the translations that move a point from one coordinate to another.

• Translations, reflections, rotationsE1.5

  Describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations.

• Choosing metric unitsE2.1

  Use appropriate metric units to estimate and measure length, area, mass, and capacity.

• Converting metric unitsE2.2

  Solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units.

• Comparing anglesE2.3

  Compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units.

• Using a protractorE2.4

  Explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles.

• Area of triangles, parallelogramsE2.5

  Use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle, and solve related problems.

• Same area, different perimeterE2.6

  Show that two-dimensional shapes with the same area can have different perimeters, and solve related problems.

Money gets real: how money moves between people and businesses, totals with sales tax, simple budgets, credit and debt, unit rates to find the best value, and the kinds of taxes collected by different levels of government in Canada.

Typical homework, with a hint

What your child learns in Financial Literacy

• How money movesF1.1

  Describe several ways money can be transferred among individuals, organizations, and businesses.

• Costs with sales taxF1.2

  Estimate and calculate the cost of transactions involving multiple items priced in dollars and cents, including sales tax, using various strategies.

• Making a budgetF1.3

  Design sample basic budgets to manage finances for various earning and spending scenarios.

• Credit and debtF1.4

  Explain the concepts of credit and debt, and describe how financial decisions may be impacted by each.

• Unit rates, best valueF1.5

  Calculate unit rates for various goods and services, and identify which rates offer the best value.

• Taxes in CanadaF1.6

  Describe the types of taxes that are collected by the different levels of government in Canada, and explain how tax revenue is used to provide services in the community.

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 5 math at home

• Use money to make decimals and percents concrete: 25¢ is 0.25 of a dollar and 25% of a dollar.
• For fractions, draw it. A quick sketch of pieces clears up most confusion.
• Ask “is your answer reasonable?” after every calculation. Estimating first catches big mistakes.
• Let your child compare unit prices at the grocery store.

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

How Astuzo helps with Grade 5 math

In Grade 5 many mistakes hide in the middle of a long calculation. When an answer is off, Spark doesn’t just say “wrong”. It asks your child to walk through their steps and helps them find the slip themselves, which is how kids learn to check their own work.

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.