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Activity Instructions:
1. Firstly revise basic ideas of multiplication, place value
properties and the endless
base ten chain. From this students can understand that it is
the digits that move when multiplied or divided by a power of ten
whilst the decimal point remains stationary. For example:
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Illustrative examples, focusing on why the digits
need to be placed into new columns.
3 multiplied by 10 is 3 groups of ten
i.e. a 3 in the tens
column: 3 x 10 = 30
3 multiplied by 100 is 3 groups of a hundred
i.e. a 3 in
the hundreds column: 3 x 100 = 300
3 multiplied by 1000000 is 3 groups of a million
i.e. a
3 in the millions column: 3 x 1000000 = 3000000
86 multiplied by 100 is 86 groups of a hundred
i.e. 80 groups
of a hundred and 6 groups of a hundred.
The 6 groups of a
hundred is easy - just 6 in the hundreds column. The 80 groups
of a hundred is 8 groups of ten groups of a hundred,
i.e.
8 groups of a thousand.
86 x 100 = 8600
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2. The final answer of a multiplication by 10, 100 can be
shown using a number slide (photocopy
master of number slides) to your students (although step one
is important - a number slide is a strong visual reminder, not a
reason).
3. Students are guided through the completion of two tables
(one multiplication and one division - Worksheet).
Overhead Transparencies - blank and completed tables:
* Note that the powers of 10 notation for the division table is not
strictly "scientific notation" as the main number being considered
is 24 ( it is not written as 2.4 x10). 4. Students are asked to add more multiplications to the
following: 24 = 3 x 8 = 30 x 0.8 =....... While they should be able
to read exactly 3 more multiplications from the table, encourage
them to make up their own as there is no limit!
5. Likewise with the division: 8 = 24 ÷ 3 = 240 ÷
30 =....There are 3more in the table, but no need to stop there!
6. Students are then asked to make the link between multiplication
and division. Firstly they write a multiplication fact, such as
4 x 8 = 32. They then make up their own 5 multiplications (using
these numbers multiplied by a power of 10) for their partner to
do, e.g. (1) 4 x 80 =__, (2) 400 x 0.8=__ etc. Similarly, they are
then asked to make up 5 divisions (1) 3200 ÷ 8 = __, (2) 0.32
÷ 0.008=__ etc. They swap problems with their partner to try,
then swap back to mark (checking on the calculator).
Comments:
While completing the table, encourage the students to look for
patterns and predict, before checking with a calculator. This
is to encourage them to extend their sense of number to include
decimals. The reason for doing this is because it is quite common
for students (and even adults) to resort to using a calculator whenever
a problem involving a decimal is encountered. It is important to
have "decimal number sense" to estimate answers and to check the
feasibility of the calculator result.
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