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Division Strategies
We’ve just begun our division unit! As I introduce new division strategies I’ll
add them to this document. Many of the strategies will be stepping stones
to another more abstract strategy. In third grade, the students were
introduced to the concept of division through problems related to known
multiplication facts. The state’s third grade TEKS also specified that all
problems were to be supported with pictures because the goal was for the
students to learn that division is the process of breaking a total up into equal
sized groups. This year students are expected to be able to divide three digit
by one digit numbers without the support of pictures. To get them to this
point, we introduce them to a variety of strategies that will bridge the gap.
Many of the strategies will be stepping stones to another more abstract
strategy.
1)Multiplication/Division inverse relationships
Students use their knowledge of fact families to solve simple division
problems. For example, 63 ÷ 9 = _____ could be interpreted as 9 x ___ = 63.
2)Break the problem apart using known multiplication facts
Students will use facts that they know to solve division problems piece by
piece.
For example: 56 ÷ 4 = _____
Students will choose a 4’s fact that they are comfortable using, such as 4x10
or 4x12. They will then subtract the product of this equation from 56, which
should result in another total that they can easily divide by 4 using another
known multiplication fact.
Step #1: 4x10 = 40
Start with a known 4’s fact.
Step #2: 56 – 40 = 16
Subtract the product from step #1 from the
dividend.
Step #3: 4 x 4 = 16
Identify the 4’s fact that will equal the total from
step #2.
Step #4: (4x10) + (4x4) = (14x4)
Add up the groups of 4.
Since there are 14 groups of 4, then 56 ÷ 4 = 14
In the beginning, students often use tile manipulatives or draw arrays on
graph paper to represent the problem:
4 x 10 = 40
4 x 4 = 16
Students first arrange the 56 tiles into one array with 4 rows. They then
separate the large array into two smaller arrays that represent known facts.
Finally, they can add the 10 groups and 4 groups to determine that the array
represents 14 groups of 4. This visual representation usually helps them see
how to break up a larger dividend into smaller parts. Students can break
the array into any combination of facts they are comfortable using.