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The purpose of this lesson is to teach equality of decimals
and place value with visual
models in order to teach these concepts
with understanding. Students can be shown
this square with the decimal six tenths
and asked to find or describe
the hundredths square with the same share amount
and
write the decimal equality for the two squares.
The hundredths squares have
heavy vertical lines and horizontal lines that aren't so heavy,
and these heavy lines help students to think in terms of columns.
So both squares have 6 full column shaded,
and there decimals are equal. There are nine such pairs of
red squares for tenths, and green squares from hundreds
whose decimals are equal. Here's their list
equalities. Students are quick to see
the pattern here, of adding zeros, but often when given such equations
they cannot explain why is zero can be placed at the end of the tenths
decimal to get an equal hundredths decimal. For example,
they might be asked to explain why 3 tenths is equal to
30 hundreds, or .3 is equal to .30.
Using visual models, such as we been using,
and the meaning of decimals, .3
means 3 parts out of 10, and .30
means 30 parts out a hundred, and these two amounts
and the same. Another activity is finding all red squares
for tenths and yellow squares for thousands
with the same shade amount and writing an equality
for their decimals.
One part out of 10 and 100 parts out of 1000. These pairs of decimals can also be listed
with an obvious pattern.
Some pairs of green squares
for hundreds and yellow squares for thousands have the
same amount of shading, 5 parts out of 100
has the same amount of shading as 50 parts, 10, 20, 30, 40, 50, parts out of 1000. So
their decimals are equal.
There are nineteen pairs of hundredths squares
and thousands squares with equal decimals in this deck.
This shows the beginning that list.
The number of full columns shaded
is four, the same amount of sharing as the
decimal four tenths. So we say four
is a tenths digit or in the tenths
place. The number of small squares,
1, 2, 3, 4, 5, is the same
as in the decimal for 5 hundredths.
So 5 is the hundreds digit, or
we say its in the hundreds place. this square
has 325 parts out of 1000 shaded.
Its decimal is 325 thousands.
But we can think of each on these digits
separately. The 3
is for the number of full columns, so 3
is the tenths digit and we say 3 is in the tenths
place. Two is a number of small hundreds squares,
so we say 2 is the hundred digit
and 2 is in the hundreds place. Finally
there are five, 1, 2, 3, 4, 5, tiny
thousands parts, so 5
is called the thousands digit and it's in
the thousands place. Place value tables
are a common method of recording the digits in decimals.
For a table with 4 tenths, 2 hundreds,
and 5 thousands, the decimal
will be 425 thousands.
For a table with only 8
in the first column,
the decimal will be .8. The table for the decimal .8
might look like this, 8 full columns shaded
and 0 hundreds squares shaded.
Or,
the table for .8 could look like this,
8 tenths, 0
hundredths shaded, and 0 thousandths shaded. When we look at inequality of decimals, and
operations on decimals,
there will be times when we want to include the zero in the hundredths column
and zero in the thousand column to represent the decimal
8 tens. Conversely, given a table
students can describe the corresponding
square for the decimal. In this case there is 7 full columns,
0 small hundredths squares, and 4
tiny thousand squares. There are two
interactive games in decimalsquares.com
that are related to this lesson. In the game Concentration,
the object is to turn over two squares
whose decimals are equal. In this example,
the decimals are not equal. The second game
is played against the robot, with players
spinning the spinner and placing numbers
in a three-place or four-place table.
Students often learn rules
for equality of decimals and place value my rote
methods. But, this lesson
has shown it is possible to teach these concepts
will understanding.