|
|
Teaching Decimal Operations
This resource is principally concerned with student's understanding
of decimal notation, not with their ability to compute with decimals.
This is because understanding the meaning of the numbers is fundamental
to both interpreting answers to computation and remembering algorithms.
Inadequate understanding underlies many of the difficulties that
students have with computation and "simple" procedures
such as rounding and understanding significant figures and scientific
notation.
Here is a summary of some key points. The CD-ROM resource "Foundations
for Teaching Arithmetic" explains these ideas fully.
Key Ideas for Addition and Subtraction
 |
Only quantities of the same magnitude can be added
or subtracted, so tenths must be added to or subtracted from
tenths, hundredths with hundredths, etc.
|
|
In the base ten system, "trading" bundles of ten
for one in the next column on the left is needed so that no
column holds more than nine. Concrete models, such as LAB,
MAB or an abacus, demonstrate this well.
|
|
The similarity of the algorithms for addition and subtraction
for whole numbers and decimals means that students have few
problems. The main difficulty is dealing with "ragged
decimals" (e.g. 0.38 + 0.4), which requires understanding
of decimal notation.
|
Key Ideas for Multiplication and Division
|
|
A range of meanings of multiplication must be understood.
If multiplication is only understood as repeated addition,
multiplication by a decimal does not make sense. For example,
if 3 x 0.98 is only understood as 0.98+0.98 +0.98,
then 0.29 x 0.98 is meaningless. Click here
to see one approach using an area model.
|
|
|
A range of meanings of division must be understood. If division
is only understood as sharing then division by a decimal does
not make sense. For example, if 0.45 divided by 3 is only
understood as "share 0.45 into 3 equal parts", then
0.45 divided by 0.15 does not make any sense.
|
|
|
Teach operations in the following order:
Phase 1:
Multiplying and dividing by ten (it fits the decimal system!)
Multiplying and dividing by powers of ten (e.g. 1000)(
Lesson plan)
Phase 2:
Multiplying/dividing decimals by small whole numbers (e.g.
3)
Multiplying/dividing by multiples of ten (e.g. 20)
Multiplying/dividing by any whole number (e.g. 23)
Phase 3:
Multiplying/dividing by decimals less than one. (This requires
special activities to develop meanings).
Note that concrete models cannot adequately explain all of
the ideas involved. Students need to understand and generalize
the mathematical principles.
|
|
