Gr. 8 - Operational Sense, Multiples, Factors, Decimal Numbers and Fractions / Percent, Rate and RatioOur first unit in Math will focus on Multiples, Factors, Decimal Numbers (Multiplication / Division), Proportional Relationships (rate / ratio), and Operational Sense. Students can begin to review multiplication and division at home. Students should have a strong understanding of place value (including whole numbers and decimal numbers to hundredths). You may need to spend some time reviewing this with your child.
You can also help at home by reviewing with your child percent and fractions so they can switch back and forth easily between the two. (E.g. 2 / 5 = 40%) They also need to be able to reason this out and show how they arrived at the answer. We will spend some time working with Math manipulatives to help students have a strong understanding of fractions, percent and decimal numbers. Below you will find a list of the Ontario Curriculum Expectations that we will be covering the first 5 weeks of school. Please encourage your child to check their UG Cloud calendar for homework, assignments, projects, quizzes and tests. In this unit, students will: – 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 (e.g., 347 = 3 x 10^2 + 4 x 10 + 7); – 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) – 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). – 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 multiplied by 1/3); – solve problems involving addition, subtraction, multiplication, and division with simple fractions; – evaluate expressions, 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 ÷ 10^6 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.). – 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?). |