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This course builds on the Grade 7 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 rational numbers, represent numbers using exponential notation, and solve multi-step problems involving whole numbers and decimals. Students multiply and divide fractions and integers, multiply and divide decimals by powers of ten, and apply order of operations in expressions with brackets and exponents. Students solve problems involving percents to one decimal place and percents greater than 100, and solve problems involving rates and proportions. Students convert between cubic centimetres and cubic metres and between millilitres and cubic centimetres. Students develop circumference and area relationships for a circle, develop and apply the formula for the volume of a cylinder, and determine and apply surface-area relationships for cylinders. Students sort quadrilaterals by geometric properties involving diagonals, construct circles, investigate relationships among similar shapes, and determine and apply angle relationships for parallel and intersecting lines. Furthermore, students relate the number of faces, edges, and vertices of a polyhedron, determine and apply the Pythagorean relationship geometrically, and plot the image of a point on the coordinate plane after applying a transformation. Students represent the general term in a linear sequence, use one or more algebraic expressions, translate statements, and use algebraic equations. Students find the term number in a pattern algebraically when given any term, and solve linear equations involving one-variable terms with integer solutions using a “balance” model. Students collect categorical, discrete, and continuous data, organize data into intervals, display data using histograms and scatter plots, and use measures of central tendency to compare sets of data. Students compare two attributes using data management tools, compare experimental and theoretical probabilities, and calculate the probability of complementary events. 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 9 mathematics. The course relies on the assistance of a learning coach to support students through the content.

Course Code: MAT8
Curriculum Policy Document: The Ontario Curriculum Grades 1-8: Mathematics, 2005 (revised)
Department: Intermediate
Course Developer: Virtual Elementary School
Development Date: 2019

#### Representing Numbers

In the Representing Numbers unit, students investigate exponential notation, expanded form using powers of ten, prime factorization, and translating between decimal numbers, fractions, and percentages. Students also represent, compare, and order rational numbers.

#### Geometry

In the Geometry unit, students sort and classify quadrilaterals, construct circles, and explore applications of geometric properties. Students investigate and solve problems associated with area, perimeter, side length, angle relationships, and line relationships. Students explore the Pythagorean theorem, examine polyhedron relationships, graph on the Cartesian coordinate plane, and investigate real-world movements.

#### Operations

In the Operations unit, students multiply and divide decimal numbers by decimal numbers and solve problems involving whole numbers and decimal numbers, percentages, and percentages over 100. Students multiply and divide decimal numbers by powers of ten, explore positive square roots, and multiply and divide integers. Students solve problems involving integers and utilize order of operations.

#### Fractions

In the Fractions unit, students add and subtract fractions and solve problems involving fraction addition and subtraction. Students multiply and divide fractions and solve problems involving fraction multiplication and division.

#### Proportional Reasoning

In the Proportional Reasoning unit, students explore real-life proportional relationships and solve problems involving proportional relationships, proportions by using variables, percentages, and rates.

#### Data Management and Probability

In the Data Management and Probability unit, students understand census, samples, and population. They also collect and organize data and investigate histograms and scatter plots. Students select the appropriate graph, explore measures of central tendency, and compare data using scatter plots and different tools and strategies. Students analyze data and develop an understanding of theoretical and experimental probability and probability of complementary events.

#### Patterning and Algebra

In the Patterning and Algebra unit, students develop an understanding of the general term, represent linear patterns graphically, determine a term value, and explore algebra in real life. Students model linear relationships, evaluate algebraic expressions, and solve equations using inspection, guess and check, and a balance model.

#### Measurement

In the Measurement unit, students convert units of area, volume, and capacity, investigate circumferences and areas of circles, and measure the surface area and volume of a cylinder.

#### The Final Grade (Courses with Qualified Teacher)

Student evaluation in this course is based on the student's achievement of curriculum expectations. The final percentage 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.