• Zero is essential as a place holder, for example
Decimal number place value
0.023 is not the same as 0.23. However, it is
not written when the number makes sense
Number Sequence progression, 5th step;
without it, for example 0.230 is written as 0.23.
Place Value progression, 5th step
The 0 is written, however, when it is necessary
to show the accuracy of a measurement, for
The purpose of the activity
example, 2.230 metres indicates that the
In this activity, the learners develop their
measurement has been made to the nearest
understanding of the place value system to include
millimetre.
the decimal numbers tenths, hundredths and
thousandths. They learn to name any decimal
• When selecting a context for developing an
understanding of decimal place value, be aware
number in tenths, hundredths and thousandths.
of the difficulties that arise when using money
The teaching points
or measurement. For example, $12.35 is usually
• The system for whole numbers, where each
treated as two whole number parts, 12 dollars
and 35 cents rather than 12.35 dollars.
place to the right is smaller by a factor of 10,
continues for the decimal numbers.
Resources
For example:
-
• Decimal number place value templates (see
The value of the first place to the right of ‘one’
Appendix B), for each learner with four strips
is ‘tenths’ – 0.1 is / 10 of 1, 0.2 is / 10 of 1, etc
of equal length placed directly underneath
1
2
each other: one left unmarked, one divided into
- The value of the second place to the right of
tenths, one divided into hundredths and one
‘one’ is 1 / 10 of 1 / 10 of 1 or 1 / 100 of 1 – 0.01 is 1 / 100 ,
divided into thousandths.
0.23 is 23/ 100 or 2/ 10 and 3/ 100 .
- The value of the third place to the right of
‘one’ is 1 / 10 of 1 / 10 of 1 / 10 or 1 / 1000 of 1. 0.001
The guided teaching and learning sequence
1. Point to the strip divided into tenths and ask
the learners what fraction one segment of the
is 1 / 1000 , 0.012 is 12/ 1000 or 1 / 100 and 2/ 1000 and
strip is. When the learners respond correctly by
0.345 is 345/ 1000 or 3/ 10, 4/ 1000 and 5/ 1000 .
saying “one tenth”, ask, “How do you write that?”
• A decimal point is used to separate the whole
Listen for “1 / 10”, “tenth”, “0.1” – ensure that all
numbers on the left (the ones, tens, hundreds,
etc.) from the decimal parts on the right (the
tenths, hundredths, thousandths, etc.).
responses are included and written down.
2. Ask the learners to cover portions of the tenths
strip, using the variety of possible names, for
Note: If using place-value charts, the decimal
point does not hold a place
HUNDREDS
TENS
example, 0.2, seven tenths, 4 / 10.
3. Ask the learners to answer questions such as:
ONES
TENTHS
•
HUNDREDTHS
“Of 0.2 and 0.6, which is smaller and why?”
“How else could 10/ 10 be written?”
“How else could 11/ 10 be written?”
“Put 0.6, 0.9, 1.1 in order and explain the reason
for this order.”
78    Tertiary Education Commission  Teaching Adults to Make Sense of Number to Solve Problems: Using the Learning Progressions
4. Point to the strip that is divided into
hundredths and ask the learners what fraction
one segment of the strip is. When the learners
respond correctly by saying “one hundredth”,
ask, “How do you write that?” Listen for “1/ 100”,
11. Ask the learners to answer questions such as:
“Of 0.294 and 0.615, which is smaller and why?”
“Of 0.09 and 0.009, which is smaller and why?”
“Of 0.8 and 0.699, which is smaller and why?”
“hundredth”, “0.01” – ensure all responses are
Follow-up activity
included and written down.
Using the decimals sheet for support, ask the
5. Ask the learners to cover 20/ 100 and discuss the
ways in which this could be written. Record
all responses. Listen for and encourage “20
hundredths”, “20/ 100”, “0.20”, “2/ 10”, “0.2”.
Discuss the fact 0.20 and 0.2 are the same
learners to put the following number in order from
smallest to largest:
• 0.4, 0.05, 0.45, 0.448
• 3.387, 3.4, 3.09, 3.199.
and that 0 is usually not written unless it is
essential as a place holder or used to indicate a
level of accuracy.
6. Ask the learners to answer questions such as :
“Of 0.29 and 0.61, which is smaller and why”?
“How else could 0.7 be written?”
“Of 0.7 and 0.69, which is smaller and why?”
7. Point to the strip divided into thousandths
and ask the learners what fraction is one
segment of the strip. When the learners
respond correctly by saying “one thousandth”,
ask, “How do you write that?” Listen for
“1 / 1000”, “thousandth”, “0.001” – ensure that all
responses are included and written down.
8. Ask the learners to cover 400/ 1000 and discuss
the ways in which this could be written. Record
all responses. Listen for and encourage “400
thousandths”, “40 hundredths”, “4 tenths”,
“0.400”, “0.40”, “0.4”, etc. Again discuss the
role of 0 as a place holder.
9. Ask the learners to cover 0.3 on all strips and
record all the ways it could be written. Ask
them to explain their thinking (0.3, 3/ 10, 30/ 100 ,
300
/ 1000).
10.Repeat with 0.65, 250/ 1000 , 1.4.
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