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Grade 5 Mathematics

This course builds on the Grade 4 curriculum to further develop students’ understanding of fundamental mathematical concepts by exploring topics related to number sense and numeration, measurement, geometry and spatial sense, patterning and algebra, and data management and probability. Students work with numbers up to 100 000, proper and improper fractions, and mixed numbers, and develop the concept of place value up to hundredths. Students count forward and backwards by 0.01, and build on addition, subtraction, multiplication, and division skills by solving problems with multiplication of whole digit numbers and solving problems with addition and subtraction of decimal numbers to hundredths. They also explore proportional reasoning by investigating whole-number rates. Through investigations, students measure and record perimeter, area, temperature change, and elapsed time. Students also determine the relationships among units and measureable attributes, specifically looking at the area of a rectangle and the volume of a rectangular prism. They identify and classify two-dimensional shapes by side and angle properties, compare and sort three-dimensional figures, and identify and construct nets of prisms and pyramids. Students identify and describe the location of an object using cardinal directions, and translate two-dimensional shapes. Furthermore, students investigate a table of values to determine relationships in growing and shrinking patterns, and investigate repeating patterns involving translations. Students demonstrate, through investigation, an understanding of the use of variables in equations. In addition, students collect and organize discrete or continuous primary and secondary data and display the data using charts and graphs. Students read, describe and interpret primary data and secondary data presenting in charts and graphs, and represent as a fraction the probability that an outcome will occur through a simple probability experiment, using systematic lists and area models. Throughout the course, students reinforce the mathematical processes of problem-solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating. Through investigation of real-life problems, students develop a strong foundation of mathematical knowledge and skills. This course prepares students for Grade 6 mathematics. The course relies on the assistance of a learning coach to support young students through the content.

Full Grade 5 Mathematics Course Outline

Course Code: MAT5
Curriculum Policy Document: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)
Department: Junior
Course Developer: Virtual Elementary School
Development Date: 2019

Numbers Up to 100 000

In the Numbers Up to 100 000 unit, students learn to read and write numbers up to 10 000, explore place value up to 100 000, and represent numbers up to 100 000. Students also compare and order whole numbers and solve problems up to 100 000.


In the Patterning unit, students identify, extend and create geometric and numeric patterns, and build models from a table to show numeric patterns. Students make tables of values by adding or subtracting a rule in words and make a table of values for a pattern generated by multiplying or dividing. Students also make predictions related to growing and shrinking geometric and numeric patterns. Finally, students extend and create repeating patterns using translations.

Multiplication and Division

In the Multiplication and Division unit, students solve addition and subtraction problems, solve multiplication problems mentally, multiply two-digit numbers, and multiply decimal numbers by 10, 100, 1000, and 10 000. Students also investigate relationships involving whole number rates, divide with concrete materials and algorithms, and divide three-digit whole numbers with standard algorithms. Furthermore, students divide decimal numbers by 10 and 100, solve problems using division, develop an understanding that letters or symbols can be used to show unknown values, and use letters or symbols in equations involving simple rates. Students also find the missing number in addition, subtraction, multiplication, and division equations.


In the Geometry unit, students identify and classify polygons as regular or irregular, identify acute, right, obtuse, and straight angles, and measure and construct angles up to 90°. Students identify and classify triangles from their angle and side properties, construct triangles, and identify and classify three-dimensional figures including prisms, right prisms, and pyramids. Students also identify prisms and pyramids from nets and construct nets of prisms and pyramids. Furthermore, students locate an object using cardinal directions and a coordinate system, compare grid systems used on maps, identify, describe and perform translations, and create and analyse designs by translating and reflecting shapes.

Working with Decimal Numbers

In the Working with Decimal Numbers unit, students read and write decimal numbers, read and write money amounts to $1000, explore place value of decimal numbers and represent, compare, and order decimal numbers. Students round decimal numbers to the nearest tenth, count forward by hundredths, and count backwards by hundredths. Students show equivalent decimal numbers, and add and subtract decimal numbers.


In the Fractions unit, students represent proper and improper fractions, represent mixed numbers, convert improper fractions and mixed numbers, and show equivalent fractions. Students also compare proper and improper fractions, as well as compare and order fractions and mixed numbers. Furthermore, students explore equivalent fractions and decimal numbers and investigate the relationship between fractions and decimal numbers.

Data Management and Probability

In the Data Management and Probability unit, students develop an understanding of discrete and continuous data and data collection methods. Students explore samples of larger populations, collect and record data, organize data in charts, tables and graphs, as well as read, interpret, and draw conclusions from data. Students calculate the mean and use it to describe data and compare sets of data. To investigate probability, students explore possible outcomes in a probability experiment, represent probability using fractions, and perform a probability experiment.


In the measurement unit, students estimate and measure the perimeter of polygons, find unknown side lengths, estimate and measure the area of polygons, and create 2D shapes with the same perimeter or area. Students find the perimeter and area of a rectangle, solve perimeter problems, and solve problems by estimating and calculating the area of rectangles, converting metres into centimetres, and converting kilometres into metres. Furthermore, students investigate measuring the mass of an object using the appropriate unit, find the volume of a rectangular prism, and determine the relationship between capacity and volume. Students also measure time and intervals with seconds and elapsed time, solve problems between 12- and 24-hour clocks, as well as measure, record, and represent temperature changes over time.

The Final Grade (Courses with Qualified Teacher)

Student evaluation in this course is based on the student's achievement of curriculum expectations. The final letter grade represents the quality of the student's overall fulfillment of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline. The final grade reflects the student’s most consistent level of achievement across all units in the course, although special consideration is given to more recent evidence of achievement. There is no final assessment, such as an exam, in this course.