Mathematics
Grade 6: Number Sense and Numeration 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
•
read, represent, compare, and order whole numbers to 1 000 000, decimal
numbers to thousandths, proper and improper fractions, and mixed numbers; 




•
solve problems involving the multiplication and division of whole numbers,
and the addition and subtraction of decimal numbers to thousandths, using a
variety of strategies; 




•
demonstrate an understanding of relationships involving percent, ratio, and
unit rate. 




Specific Expectations 




Quantity Relationships 




–
represent, compare, and order whole numbers and decimal numbers from 0.001 to
1 000 000, using a variety of tools (e.g., number lines with appropriate increments,
base ten materials for decimals); 




–
demonstrate an understanding of place value in whole numbers and decimal numbers
from 0.001 to 1 000 000, using a variety of tools and strategies (e.g. use base
ten materials to represent the relationship between 1, 0.1, 0.01, and 0.001)
(Sample problem: How many thousands cubes would be needed to make a base ten
block for 1 000 000?); 




–
read and print in words whole numbers to one hundred thousand, using meaningful
contexts (e.g., the Internet, reference books); 




–
represent, compare, and order fractional amounts with unlike denominators, including
proper and improper fractions and mixed numbers, using a variety of tools
(e.g., fraction circles, Cuisenaire rods, drawings, number lines,
calculators) and using standard fractional notation (Sample problem: Use
fraction strips to show that 1 1/2 is greater than 5/4); 




–
estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100% (e.g.,
the container is about 75% full; approximately 50% of our students walk to
school); 




–
solve problems that arise from reallife situations and that relate to the
magnitude of whole numbers up to 1 000 000 (Sample problem: How would you determine
if a person could live to be 1 000 000 hours old? Show your work.); 




–
identify composite numbers and prime numbers, and explain the relationship between
them (i.e., any composite number can be factored into prime factors) (e.g.,
42 = 2 x 3 x 7). 




Operational Sense 




–
use a variety of mental strategies to solve addition, subtraction, multiplication, and
division problems involving whole numbers (e.g., use the commutative
property: 4 x 16 x 5 = 4 x 5 x 16, which gives 20 x 16 = 320; use the
distributive property: (500 + 15) ÷ 5 = 500 ÷ 5 + 15 ÷ 5, which gives 100 + 3
= 103); 




–
multiply whole numbers by 0.1, 0.01, and 0.001 using mental strategies (e.g.,
use a calculator to look for patterns and generalize to develop a rule); 




–
multiply and divide decimal numbers by 10, 100, 1000, and 10 000 using mental
strategies (e.g., “To convert 0.6 m2 to square centimetres, I calculated in
my head 0.6 x 10 000 and got 6000 cm2.”) (Sample problem: Use a calculator to
help you generalize a rule for multiplying numbers by 10 000.); 




–
solve problems involving the multiplication and division of whole numbers
(four digit by twodigit), using a variety of tools (e.g., concrete
materials, drawings, calculators) and strategies (e.g., estimation,
algorithms); 




–
add and subtract decimal numbers to thousandths, using concrete materials, estimation,
algorithms, and calculators; 




–
multiply and divide decimal numbers to tenths by whole numbers, using
concrete materials, estimation, algorithms, and calculators (e.g., calculate
4 x 1.4 using base ten materials; calculate 5.6 ÷ 4 using base ten
materials); 




–
use estimation when solving problems involving the addition and subtraction
of whole numbers and decimals, to help judge the reasonableness of a
solution; 




–
explain the need for a standard order for performing operations, by
investigating the impact that changing the order has when performing a series
of operations (Sample problem: Calculate and compare the answers to 3 + 2 x 5
using a basic four function calculator and using a scientific calculator.). 




Proportional Relationships 




–
represent ratios found in reallife contexts, using concrete materials,
drawings, and standard fractional notation (Sample problem: In a classroom of
28 students, 12 are female. What is the ratio of male students to female
students?); 




–
determine and explain, through investigation using concrete materials,
drawings, and calculators, the relationships among fractions (i.e., with
denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents
(e.g., use a 10 x 10 grid to show that 1/4 = 0.25 or 25%); 




–
represent relationships using unit rates (Sample problem: If 5 batteries cost
$4.75, what is the cost of 1 battery?). 




Student Name: 




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