Mathematics
Grade 7: Number Sense and Numeration 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
•
represent, compare, and order numbers, including integers; 




•
demonstrate an understanding of addition and subtraction of fractions and
integers, and apply a variety of computational strategies to solve problems
involving whole numbers and decimal numbers; 




•
demonstrate an understanding of proportional relationships using percent,
ratio, and rate. 




Specific Expectations 




Quantity Relationships 




–
represent, compare, and order decimals to hundredths and fractions, using a
variety of tools (e.g., number lines, Cuisenaire rods, base ten materials,
calculators); 




–
generate multiples and factors, using a variety of tools and strategies
(e.g., identify multiples on a hundreds chart; create rectangles on a
geoboard) (Sample problem: List all the rectangles that have an area of 36
cm2 and have wholenumber dimensions.); 




–
identify and compare integers found in reallife contexts (e.g., –10°C is
much colder than +5°C); 




–
represent and order integers, using a variety of tools (e.g., twocolour
counters, virtual manipulatives, number lines); 




–
select and justify the most appropriate representation of a quantity (i.e.,
fraction, decimal, percent) for a given context (e.g., “I would use a decimal
for recording the length or mass of an object, and a fraction for part of an
hour.”); 




–
represent perfect squares and square roots, using a variety of tools (e.g.,
geoboards, connecting cubes, grid paper); 




–
explain the relationship between exponential notation and the measurement of
area and volume (Sample problem: Explain why area is expressed in square units
[units2] and volume is expressed in cubic units [units3].). 




Operational Sense 




–
divide whole numbers by simple fractions and by decimal numbers to
hundredths, using concrete materials (e.g., divide 3 by ½ using fraction
strips; divide 4 by 0.8 using base ten materials and estimation); 




–
use a variety of mental strategies to solve problems involving the addition
and subtraction of fractions and decimals (e.g., use the commutative
property: 3 x 2/5 x 1/3 = 3 x 1/3 x 2/5, which gives 1 x 2/5 = 2/5 ; use the
distributive property: 16.8 ÷ 0.2 can be thought of as (16 + 0.8) ÷ 0.2 = 16
÷ 0.2 + 0.8 ÷ 0.2, which gives 80 + 4 = 84); 




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




–
solve multistep problems arising from reallife contexts and involving whole
numbers and decimals, using a variety of tools (e.g., concrete
materials, drawings,
calculators) and strategies (e.g., estimation, algorithms); 




–
use estimation when solving problems involving operations with whole numbers,
decimals, and percents, to help judge the reasonableness of a solution
(Sample problem: A book costs $18.49. The salesperson tells you that the
total price, including taxes, is $22.37. How can you tell if the total price
is reasonable without using a calculator?); 




–
evaluate expressions that involve whole numbers and decimals, including
expressions that contain brackets, using order of operations; 




–
add and subtract fractions with simple like and unlike denominators, using a
variety of tools (e.g., fraction circles, Cuisenaire rods, drawings,
calculators) and algorithms; 




–
demonstrate, using concrete materials, the relationship between the repeated
addition of fractions and the multiplication of that fraction by a whole
number (e.g., 1/2 + 1/2 + 1/2 = 3 x 1/2); 




–
add and subtract integers, using a variety of tools (e.g., twocolour
counters, virtual manipulatives, number lines). 




Proportional Relationships 




–
determine, through investigation, the relationships among fractions,
decimals, percents, and ratios; 




–
solve problems that involve determining whole number percents, using a
variety of tools (e.g., base ten materials, paper and pencil, calculators)
(Sample problem: If there are 5 blue marbles in a bag of 20 marbles, what
percent of the marbles are not blue?); 




–
demonstrate an understanding of rate as a comparison, or ratio, of two
measurements with different units (e.g., speed is a rate that compares
distance to time and that can be expressed as kilometres per hour); 




–
solve problems involving the calculation of unit rates (Sample problem: You
go shopping and notice that 25 kg of Ryan’s Famous Potatoes cost $12.95, and
10 kg of Gillian’s Potatoes cost $5.78. Which is the better deal? Justify
your answer.). 




Student Name: 




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