Number Sequence progression, 5th step;
Place Value progression, 5th step
The purpose of the activity
In this activity, the learners develop their understanding of the place value system to include the decimal numbers tenths, hundredths and thousandths. They learn to name any decimal number in tenths, hundredths and thousandths.
The teaching points

The system for whole numbers, where each place ato the right is smaller by a factor of 10, continues for the decimal numbers.
For example:

The value of the first place to the right of ‘one’ is ‘tenths’ – 0.1 is 1/10 of 1, 0.2 is 2/10 of 1, etc

The value of the second place to the right of ‘one’ is 1/10 of 1/10 of 1 or 1/100 of 1 – 0.01 is 1/100, 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 is 1/1000, 0.012 is 12/1000 or 1/100 and 2/1000 and 0.345 is 345/1000 or 3/10, 4/1000 and 5/1000.

A decimal point is used to separate the whole numbers on the left (the ones, tens, hundreds, etc.) from the decimal parts on the right (the tenths, hundredths, thousandths, etc.).
Note: If using placevalue charts, the decimal point does not hold a place

Zero is essential as a place holder, for example 0.023 is not the same as 0.23. However, it is not written when the number makes sense without it, for example 0.230 is written as 0.23. The 0 is written, however, when it is necessary to show the accuracy of a measurement, for example, 2.230 metres indicates that the measurement has been made to the nearest millimetre.

When selecting a context for developing an understanding of decimal place value, be aware of the difficulties that arise when using money or measurement. For example, $12.35 is usually treated as two whole number parts, 12 dollars and 35 cents rather than 12.35 dollars.
Resources
Decimal number place value templates (see Appendix B (PDF, 31kB)), for each learner with four strips of equal length placed directly underneath each other: one left unmarked, one divided into tenths, one divided into hundredths and one divided into thousandths.
The guided teaching and learning sequence
1. Point to the strip divided into tenths and ask the learners what fraction one segment of the strip is. When the learners respond correctly by saying “one tenth”, ask, “How do you write that?” Listen for “1/10”, “tenth”, “0.1” – ensure that all responses are included and written down.
2. Ask the learners to cover portions of the tenths strip, using the variety of possible names, for example, 0.2, seven tenths, 4/10.
3. Ask the learners to answer questions such as:
“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.”
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”, “hundredth”, “0.01” – ensure all responses are included and written down.
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 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.
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?”
Followup activity
Using the decimals sheet for support, ask the 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.
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