Mathematics
Grade 4: Number Sense and Numeration 
Planning: Term # Tracking: Ach. Level 

Overall Expectations 
1 
2 
3 
4 
•
read, represent, compare, and order whole numbers to 10 000, decimal numbers
to tenths, and simple fractions, and represent money amounts to $100; 




•
demonstrate an understanding of magnitude by counting forward and backwards
by 0.1 and by fractional amounts; 




•
solve problems involving the addition, subtraction, multiplication, and
division of single and multidigit whole numbers, and involving the addition
and subtraction of decimal numbers to tenths and money amounts, using a
variety of strategies; 




•
demonstrate an understanding of proportional reasoning by investigating
wholenumber unit rates. 




Specific Expectations 




Quantity Relationships 




–
represent, compare, and order whole numbers to 10 000, using a variety of
tools (e.g., drawings of base ten materials, number lines with increments of 100
or other appropriate amounts); 




–
demonstrate an understanding of place value in whole numbers and decimal
numbers from 0.1 to 10 000, using a variety of tools and strategies (e.g.,
use base ten materials to represent 9307 as 9000 + 300 + 0 + 7) (Sample
problem: Use the digits 1, 9, 5, 4 to create the greatest number and the
least number possible, and explain your thinking.); 




–
read and print in words whole numbers to one thousand, using meaningful contexts
(e.g., books, highway distance signs); 




–
round fourdigit whole numbers to the nearest ten, hundred, and thousand, in
problems arising from reallife situations; 




– represent,
compare, and order decimal numbers to tenths, using a variety of tools (e.g.,
concrete materials such as paper strips divided into tenths and base ten
materials, number lines, drawings) and using standard decimal notation
(Sample problem: Draw a partial number line that extends from 4.2 to 6.7, and
mark the location of 5.6.); 




–
represent fractions using concrete materials, words, and standard fractional
notation, and explain the meaning of the denominator as the number of the fractional
parts of a whole or a set, and the numerator as the number of fractional
parts being considered; 




–
compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths)
by considering the size and the number of fractional parts (e.g., 4/5 us
greater than 3/5 because there are more parts in 4/5; 1/4 is greater than 1/5
because the size of the part is larger in 1/4) 





compare fractions to the benchmarks of 0, 1/2, and 1 (e.g., 1/8 is closer to 0
than 1/2; 3/5 more than 1/2); demonstrate and explain the relationship
between equivalent fractions, using concrete materials (e.g., fraction
circles, fraction strips, pattern blocks) and drawings (e.g., “I can say that
3/6 of my cubes are white, or half of the cubes are white. This means that
3/6 and 1/2 are equal.”); 




–
read and represent money amounts to $100 (e.g., five dollars, two quarters,
one nickel, and four cents is $5.59); 




– solve
problems that arise from reallife situations and that relate to the
magnitude of whole numbers up to 10 000 (Sample problem: How high would a
stack of 10 000 pennies be? Justify your answer.). 




Counting 




– count
forward by halves, thirds, fourths, and tenths to beyond one whole, using
concrete materials and number lines (e.g., use fraction circles to count
fourths: “One fourth, two fourths, three fourths, four fourths, five fourths,
six fourths, …”); 




–
count forward by tenths from any decimal number expressed to one decimal
place, using concrete materials and number lines (e.g., use base ten
materials to represent 3.7 and count forward: 3.8, 3.9, 4.0, 4.1, …; “Three
and seven tenths, three and eight tenths, three and nine tenths, four, four
and one tenth, …”) (Sample problem: What connections can you make between
counting by tenths and measuring lengths in millimetres and in centimetres?). 




Operational Sense 




–
add and subtract twodigit numbers, using a variety of mental strategies
(e.g., one way to calculate 73  39 is to subtract 40 from 73 to get 33, and
then add 1 back to get 34); 




– solve
problems involving the addition and subtraction of fourdigit numbers, using
studentgenerated algorithms and standard algorithms (e.g., “I added 4217 +
1914 using 5000 + 1100 + 20 + 11.”); 




– add
and subtract decimal numbers to tenths, using concrete materials (e.g., paper
strips divided into tenths, base ten materials) and studentgenerated
algorithms (e.g., “When I added 6.5 and 5.6, I took five tenths in fraction
circles and added six tenths in fraction circles to give me one whole and one
tenth. Then I added 6 + 5 + 1.1, which equals 12.1.”); 




–
add and subtract money amounts by making simulated purchases and providing change
for amounts up to $100, using a variety of tools (e.g., currency
manipulatives, drawings); 




–
multiply to 9 x 9 and divide to 81 ÷ 9, using a variety of mental strategies
(e.g., doubles, doubles plus another set, skip counting); 




–
solve problems involving the multiplication of onedigit whole numbers, using
a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x
8); 




– multiply
whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100,
using mental strategies (e.g., use a calculator to look for patterns and
generalize to develop a rule); 




–
multiply twodigit whole numbers by onedigit whole numbers, using a variety
of tools (e.g., base ten materials or drawings of them, arrays),
studentgenerated algorithms, and standard algorithms; 




–
divide twodigit whole numbers by one digit whole numbers, using a variety of
tools (e.g., concrete materials, drawings) and studentgenerated algorithms; 




–
use estimation when solving problems involving the addition, subtraction, and
multiplication of whole numbers, to help judge the reasonableness of a solution
(Sample problem: A school is ordering pencils that come in boxes of 100. If
there are 9 classes and each class needs about 110 pencils, estimate how many
boxes the school should buy.). 




Proportional Relationships 




– describe
relationships that involve simple wholenumber multiplication (e.g.,“If you
have 2 marbles and I have 6 marbles, I can say that I have three times the
number of marbles you have.”); 




–
determine and explain, through investigation, the relationship between
fractions (i.e., halves, fifths, tenths) and decimals to tenths, using a
variety of tools (e.g., concrete materials, drawings, calculators) and
strategies (e.g., decompose 2/5 into 4/10 by dividing each fifth into two
equal parts to show that 2/5 can be represented as 0.4); 




–
demonstrate an understanding of simple multiplicative relationships involving
unit rates, through investigation using concrete materials and drawings (e.g.,
scale drawings in which 1 cm represents 2 m) (Sample problem: If 1 book costs
$4, how do you determine the cost of 2 books?… 3 books?…4 books?). 




Student Name: 




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