## Grade 5 Mathematics

**Number Sense and Numeration**

Number sense refers to a general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgements and to develop useful strategies for solving problems. In this strand, students develop their understanding of number by learning about different ways of representing numbers and about the relationships among numbers. They learn how to count in various ways, developing a sense of magnitude. They also develop a solid understanding of the four basic operations and learn to compute fluently, using a variety of tools and strategies. A well-developed understanding of number includes a grasp of more-and-less relationships, part-whole relationships, the role of special numbers such as five and ten, connections between numbers and real quantities and measures in the environment, and much more. Online Unit: Number Sense - Grade 5

**Measurement**

Measurement concepts and skills are directly applicable to the world in which students live. Many of these concepts are also developed in other subject areas, such as science, social studies, and physical education. In this strand, students learn about the measurable attributes of objects and about the units and processes involved in measurement. Students begin to learn how to measure by working with non-standard units, and then progress to using the basic metric units to measure quantities such as length, area, volume, capacity, mass, and temperature. They identify benchmarks to help them recognize the magnitude of units such as the kilogram, the litre, and the metre. Skills associated with telling time and computing elapsed time are also developed. Students learn about important relationships among measurement units and about relationships involved in calculating the perimeters, areas, and volumes of a variety of shapes and figures. Concrete experience in solving measurement problems gives students the foundation necessary for using measurement tools and applying their understanding of measurement relationships. Estimation activities help students to gain an awareness of the size of different units and to become familiar with the process of measuring. As students’ skills in numeration develop, they can be challenged to undertake increasingly complex measurement problems, thereby strengthening their facility in both areas of mathematics.

Online Unit: Measurement - Grade 5

**Geometry and Spatial Sense**

Spatial sense is the intuitive awareness of one’s surroundings and the objects in them. Geometry helps us represent and describe objects and their interrelationships in space. A strong sense of spatial relationships and competence in using the concepts and language of geometry also support students’ understanding of number and measurement. Spatial sense is necessary for understanding and appreciating the many geometric aspects of our world. Insights and intuitions about the characteristics of two-dimensional shapes and three-dimensional figures, the interrelationships of shapes, and the effects of changes to shapes are important aspects of spatial sense. Students develop their spatial sense by visualizing, drawing, and comparing shapes and figures in various positions. In this strand, students learn to recognize basic shapes and figures, to distinguish between the attributes of an object that are geometric properties and those that are not, and to investigate the shared properties of classes of shapes and figures. Mathematical concepts and skills related to location and movement are also addressed in this strand.

Online Unit: Geometry and Spatial Sense - Grade 5

**Patterning and Algebra**

One of the central themes in mathematics is the study of patterns and relationships. This study requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of real-world phenomena that exhibit observable patterns. Young students identify patterns in shapes, designs, and movement, as well as in sets of numbers. They study both repeating patterns and growing and shrinking patterns and develop ways to extend them. Concrete materials and pictorial displays help students create patterns and recognize relationships. Through the observation of different representations of a pattern, students begin to identify some of the properties of the pattern. In the junior grades, students use graphs, tables, and verbal descriptions to represent relationships that generate patterns. Through activities and investigations, students examine how patterns change, in order to develop an understanding of variables as changing quantities. In the intermediate grades, students represent patterns algebraically and use these representations to make predictions. A second focus of this strand is on the concept of equality. Students look at different ways of using numbers to represent equal quantities.Variables are introduced as “unknowns”, and techniques for solving equations are developed. Problem solving provides students with opportunities to develop their ability to make generalizations and to deepen their understanding of the relationship between patterning and algebra.

Online Unit: Pattering and Algebra - Grade 5

**Data Management and Probability**

The related topics of data management and probability are highly relevant to everyday life. Graphs and statistics bombard the public in advertising, opinion polls, population trends, reliability estimates, descriptions of discoveries by scientists, and estimates of health risks, to name just a few. In this strand, students learn about different ways to gather, organize, and display data. They learn about different types of data and develop techniques for analysing the data that include determining measures of central tendency and examining the distribution of the data. Students also actively explore probability by conducting probability experiments and using probability models to simulate situations. The topic of probability offers a wealth of interesting problems that can fascinate students and that provide a bridge to other topics, such as ratios, fractions, percents, and decimals. Connecting probability and data management to real-world problems helps make the learning relevant to students.

Online Unit: Data Manangement and Probability - Grade 5

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