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This course builds on the Grade 5 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 represent and order numbers to 1 000 000, develop the concept of place value to thousandths, compare and order fractional amounts with unlike denominators, and estimate 10%, 25%, 50%, and 75% of a quantity. Students add and subtract decimal amounts to thousandths, multiply and divide four-digit whole numbers by two-digit whole numbers, and multiply and divide decimals to tenths by whole numbers and two-digit by two-digit whole numbers. Furthermore, students divide three-digit whole numbers by one-digit whole numbers, apply order of operations in expressions without brackets, and relate simple fractions, decimals and percentages. Students measure quantities using metric units, convert from larger to smaller metric units, including square metres to square centimetres, and develop and apply area relationships for a parallelogram and a triangle. Students develop and apply the volume relationships for a triangular prism, determine and apply surface area relationships for rectangular and triangular prisms, and relate square metres and square centimetres. Students classify quadrilaterals by geometric properties, sort polygons by lines of symmetry and by rotational symmetry, measure angles to 180° with a protractor, and construct polygons. Students represent figures using views and isometric sketches, perform and describe rotations, and plot points in the first quadrant. Students represent patterns using ordered pairs and graphs, describe pattern rules in words, and calculate any term when given the term number. Students investigate variables as changing quantities and solve equations using concrete materials and the guess and check strategy. Furthermore, students collect and organize discrete and continuous data, display data using continuous line graphs, select appropriate geographical representations, use continuous line graphs and mean to compare sets of data, find theoretical probabilities, and predict the frequency of an outcome based on the theoretical probability. 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 7 mathematics. The course relies on the assistance of a learning coach to support students through the content.

Full Grade 6 Mathematics Course Outline**Course Code:** MAT6

**Curriculum Policy Document:** The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)

**Department:** Junior

**Course Developer:** Virtual Elementary School

**Development Date:** 2019

In the Numbers unit, students read and write numbers up to 100 000, understand, represent, compare, and order numbers, and solve word problems up to 1 000 000. Students identify prime and composite numbers and find the prime factors for composite numbers. Students also understand place value and represent, compare, and order decimal numbers.

In the Patterning unit, students sort and classify quadrilaterals, sort and construct polygons, and classify, measure, and construct angles. Students build 3D models using drawings and sketch isometric perspectives and different views. Furthermore, students plot points and represent location, identify, perform, and describe rotations, and create and analyze designs made by transformations.

In the Operations unit, students solve addition, subtraction, multiplication, and division problems. Students multiply and divide four-digit numbers by two-digit numbers, add and subtract decimal numbers to thousandths, and multiply and divide decimal numbers by whole numbers using concrete materials and algorithms. Students multiply whole numbers by 0.1, 0.01, and 0.001 and multiply and divide decimal numbers by 10, 100, 1000, and 10 000. Furthermore, students solve equations using the order of operations.

In the Fractions, Percentages, Ratios, and Unit Rates unit, students represent fractions, compare fractions and mixed numbers using tools and fraction notation, and order fractions and mixed numbers. Students represent ratios using materials, drawings, and fractions. Students estimate using percentage benchmarks and explore fractions, decimal numbers, and unit rates.

In the Data Management and Probability unit, students collect and organize data, select appropriate graphs, use technology, and determine how well a set of data represents a population. Students also read primary and secondary data, compare different graphical representations of the same data, and understand mean. Furthermore, students express theoretical probability as a ratio, represent probability on a range of 0 to 1, and predict the outcome of a probability experiment.

In the Algebra unit, students understand variables, identify variables and constants in an equation, and solve equations with one, two, and three variables.

In the Patterning unit, students identify geometric patterns and represent them numerically, plot ordered pairs, and determine the term number. Students also describe pattern rules, determine a term by extending a pattern, and extend and create rotation patterns.

In the Measurement unit, students select the appropriate unit of measurement and estimate, measure, and record length, area, mass, and capacity. Students justify when an estimate or precise measurement is needed, convert metric units, and construct rectangles and squares given their area or perimeter. Students also find the area of a parallelogram and a triangle and solve related problems. Students construct parallelograms and triangles given the area, find the relationship between area units, and estimate and calculate the surface area of a rectangular prism and triangular prism. Furthermore, students calculate the volume of rectangular and triangular prisms and solve problems related to the volume of rectangular and triangular prisms.

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.