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 multistep problems arising from reallife 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 wholenumber 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 wholenumber 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 wholenumber side
length.). 




Proportional Relationships 




–
identify and describe reallife 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 reallife 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?). 




Student Name: 




Expectations: Copyright The Queen's Printer for Ontario, 2005. Format: Copyright B.Phillips, 1998.