Canada · Ontario Curriculum Expectations
Grade 5 Mathematics
This course guides students through the deepening of number sense and the introduction of algebraic reasoning. Students move beyond basic computation to analyze relationships between decimals, fractions, and integers while developing spatial reasoning through geometric transformations.
01The Power of Place: Large Numbers and Decimals
Students explore the base ten system to understand how place value extends infinitely in both directions. This unit focuses on comparing, ordering, and representing numbers from millions to thousandths.
Students will investigate the structure of the base ten system for whole numbers up to millions, identifying the value of each digit.
Students will practice reading and writing multi-digit whole numbers using base-ten numerals, number names, and expanded form.
Students will extend their understanding of place value to include decimals, identifying the value of digits in the tenths, hundredths, and thousandths places.
Students will read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
Students will compare and order decimals to the thousandths using various strategies, including place value charts and number lines.
Students will round decimals to any given place, understanding the purpose of rounding in real-world contexts.
Students will explore the patterns that emerge when multiplying whole numbers and decimals by powers of ten.
Students will explore the patterns that emerge when dividing whole numbers and decimals by powers of ten.
02Operating with Flexibility: Multi-Digit Thinking
Moving beyond rote algorithms to master mental math and estimation strategies for multiplication and division. Students develop a toolkit of strategies to tackle complex multi-step problems.
Students will use various strategies, including area models, partial products, and the standard algorithm, to multiply multi-digit whole numbers.
Students will estimate products and quotients of multi-digit numbers using rounding and compatible numbers to check for reasonableness.
Students will divide whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, and the relationship between multiplication and division.
Students will interpret remainders in division problems based on the context of the problem, deciding whether to ignore, round up, or express as a fraction/decimal.
Students will evaluate numerical expressions using the order of operations, including parentheses, brackets, and braces.
03Fractions and Decimals: Different Names for the Same Parts
Students bridge the gap between fractions and decimals, learning to treat them as interchangeable representations of the same values.
Students will generate equivalent fractions and express fractions in simplest form using visual models and multiplication/division.
Students will compare and order fractions with unlike denominators using strategies such as finding common denominators or comparing to benchmark fractions.
Students will add fractions with unlike denominators by finding common denominators and using visual models.
Students will subtract fractions with unlike denominators by finding common denominators and using visual models.
Students will add and subtract mixed numbers with unlike denominators, converting between mixed numbers and improper fractions as needed.
Students will understand a fraction a/b as a result of dividing a by b, solving word problems involving division of whole numbers leading to fractional answers.
Students will multiply a fraction by a whole number, interpreting the product as repeated addition or scaling.
Students will multiply fractions by fractions, including mixed numbers, using area models and the standard algorithm.
Students will divide whole numbers by unit fractions and unit fractions by whole numbers, using visual models and the relationship between multiplication and division.
04Algebraic Patterns and Functional Thinking
An introduction to variables, expressions, and the use of patterns to predict future results in a sequence.
Students will write and interpret simple numerical expressions without evaluating them, using mathematical language.
Students will generate two numerical patterns using two given rules and identify relationships between corresponding terms.
Students will form ordered pairs from corresponding terms of two numerical patterns and graph them on a coordinate plane.
05Space and Shape: Geometry and Measurement
Students explore the properties of 2D and 3D shapes while mastering the measurement of perimeter, area, and volume.
Students will understand the coordinate plane, identifying and plotting points in the first quadrant.
Students will plot points on the coordinate plane to represent real-world problems and draw geometric shapes.
Students will classify two-dimensional figures into categories based on their properties, such as number of sides, angles, and parallel/perpendicular lines.
Students will understand volume as an attribute of solid figures and measure volume by counting unit cubes.
Students will relate volume to the operations of multiplication and addition, applying the formulas V = l × w × h and V = B × h for rectangular prisms.
Students will find the volume of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.
Students will convert among different-sized standard measurement units within the metric system (e.g., convert 5 cm to 0.05 m).
06Data Analysis and Financial Literacy
Students will collect, organize, and interpret data, and apply mathematical concepts to real-world financial situations.
Students will make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
Students will use information presented in line plots to solve problems involving addition and subtraction of fractions.
Students will explore basic financial concepts such as income, expenses, saving, and spending.
Students will create simple budgets, track spending, and make informed financial decisions.
07Advanced Operations with Decimals
Students will extend their understanding of operations to include decimals, applying strategies learned with whole numbers to decimal computation.
Students will add and subtract decimals to the hundredths using concrete models or drawings and strategies based on place value.
Students will multiply decimals by whole numbers using strategies based on place value and properties of operations.
Students will multiply decimals by decimals using concrete models or drawings and strategies based on place value.
Students will divide decimals by whole numbers using concrete models or drawings and strategies based on place value.
Students will divide whole numbers by decimals, understanding the concept of making the divisor a whole number.
08Review and Application
This unit provides an opportunity for students to consolidate their learning from the year, applying various mathematical concepts to solve complex, multi-step problems and prepare for future grades.
Students will solve multi-step word problems involving all four operations with whole numbers, assessing the reasonableness of answers.
Students will solve multi-step word problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers.
Students will solve multi-step word problems involving all four operations with decimals, including problems involving money and measurement.
Students will solve complex, real-world problems that require integrating knowledge of whole numbers, fractions, and decimals across all operations.
Students will apply their understanding of geometric properties, coordinate planes, and measurement conversions to solve practical problems.