Children learn about division both as the inverse of multiplication and
through the idea of equal sharing, which leads to fractions. At first
these two connections can be made separately, with the idea of equal sharing
coming first in grade 2. In grade 3 division as equal sharing is
elaborated to include the number of items in n groups, the number
of groups of n items, and the result of repeated subtraction of
n.
In grade 4 the idea of a rate is introduced and children learn to divided
two and three digit numbers by single digits. In grade 5 they begin
to explore dividing by two digit numbers and dividing decimals by whole
numbers, and should learn to mentally divide by 10 and to divide even multiplies
of single digit numbers (e.g., 56÷7). In grade 6 they continue
to learn about dividing decimals, including changing a division problem
involving decimals into and equivalent one in whole numbers.
Note: many curriculum outcomes related to fractions and multiplication
also involve division. The outcomes listed here are only those specific
to division.
Grade 2
B2: recognize that division can mean determining how many groups of fixed
size are in a larger group or fair sharing
Grade 3
B2: recognize several meanings for division
B3: recognize the relationship between multiplication and division
B5: solve and create problems involving multiplication and division
with small numbers
Grade 4
B3: demonstrate an understanding of the various meanings of division
B5: divide 2- and 3-digit whole numbers by a single-digit divisor
B8: relate multiplication and division facts, using principles of these
operations
B10: demonstrate an understanding of various treatments of remainders
in division situations
B14: estimate the product or quotient of 2- or 3-digit numbers and
single digit numbers
Grade 5
B4: divide 2- 3- and 4-digit numbers by single digit divisors and investigate
division by 2-digit divisors
B6: divide decimal numbers by single digit whole numbers
B14: divide numbers mentally when appropriate
Grade 6
B3: compute quotients of whole numbers and decimals
B4: model and calculate the quotients of two decimals
B10: divide numbers by 0.1, 0.01 and 0.001 mentally
Resources
Additional information on teaching division can be found in the APEF Mathematics
Curriculum guides, and texts on teaching mathematics in elementary schools,
such as van der Walle, or Cathcart, Poithier and Vance. The NCTM
journal Teaching Children Mathematics (formerly Arithmetic
Teacher) is also an excellent source of ideas. An index of articles
is available at the NCTM website nctm.org.