Mathematics

Grade 8: Number Sense and Numeration	Planning: Term # Tracking: Ach. Level
Overall Expectations	1	2	3	4
• represent, compare, and order equivalent representations of numbers, including those involving positive exponents;
• solve problems involving whole numbers, decimal numbers, fractions, and integers, using a variety of computational strategies;
• solve problems by using proportional reasoning in a variety of meaningful contexts.
Specific Expectations
Quantity Relationships
– express repeated multiplication using exponential notation (e.g., 2 x 2 x 2 x 2 = 24);
– represent whole numbers in expanded form using powers of ten
– represent, compare, and order rational numbers (i.e., positive and negative fractions and decimals to thousandths);
– translate between equivalent forms of a number (i.e., decimals, fractions, percents) (e.g., 3/4 = 0.75);
– determine common factors and common multiples using the prime factorization of numbers (e.g., the prime factorization of 12 is 2 x 2 x 3; the prime factorization of 18 is 2 x 3 x 3; the greatest common factor of 12 and 18 is 2 x 3 or 6; the least common multiple of 12 and 18 is 2 x 2 x 3 x 3 or 36).
Operational Sense
– solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools (e.g., graphs, calculators) and strategies (e.g., estimation, algorithms);
– solve problems involving percents expressed to one decimal place (e.g., 12.5%) and whole-number percents greater than 100 (e.g., 115%) (Sample problem: The total cost of an item with tax included [115%] is $23.00. Use base ten materials to determine the price before tax.);
– use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
– represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent 1/4 muitiplied by 1/3);
– solve problems involving addition, subtraction, multiplication, and division with simple fractions;
– represent the multiplication and division of integers, using a variety of tools [e.g., if black counters represent positive amounts and red counters represent negative amounts, you can model 3 x (–2) as three groups of two red counters];
– solve problems involving operations with integers, using a variety of tools (e.g., two colour counters, virtual manipulatives, number lines);
– evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations;
– multiply and divide decimal numbers by various powers of ten (e.g.,“To convert 230 000 cm3 to cubic metres, I calculated in my head 230 000 ÷ 106 to get 0.23 m3.”) (Sample problem: Use a calculator to help you generalize a rule for dividing numbers by 1 000 000.);
– estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not (Sample problem: Explain why a square with an area of 20 cm2 does not have a whole-number side length.).
Proportional Relationships
– identify and describe real-life situations involving two quantities that are directly proportional (e.g., the number of servings and the quantities in a recipe, mass and volume of a substance, circumference and diameter of a circle);
– solve problems involving proportions, using concrete materials, drawings, and variables (Sample problem: The ratio of stone to sand in HardFast Concrete is 2 to 3. How much stone is needed if 15 bags of sand are used?);
– solve problems involving percent that arise from real-life contexts (e.g., discount, sales tax, simple interest) (Sample problem: In Ontario, people often pay a provincial sales tax [PST] of 8% and a federal sales tax [GST] of 7% when they make a purchase. Does it matter which tax is calculated first? Explain your reasoning.);
– solve problems involving rates (Sample problem: A pack of 24 CDs costs $7.99. A pack of 50 CDs costs $10.45. What is the most economical way to purchase 130 CDs?).
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Expectations: Copyright The Queen's Printer for Ontario, 2005.  Format: Copyright B.Phillips, 1998.