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Decimal Concepts
Although students begin to develop place value
understandings in primary one, they are formally introduced to
decimal numbers usually from primary four.
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By the time students reach primary four, they would have been
introduced to both whole number place value and fractions.
Hence, at this point we will assume that students have some
knowledge of whole number place value as well as of fractions
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to include at least , , and .
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Let us consider these place value and fractional prerequisites
in more detail.
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As with most topics, effective mathematics place value
instruction begins with using some relevant concrete material.
As highlighted in Figure 1, let us assume that students
became familiar with base ten blocks. At some point the
teacher compared the actual blocks to a picture of the
base-ten blocks perhaps in a textbook or a PowerPoint slide.
Likely, the teacher would have stated the value of those blocks
and eventually written the value on the whiteboard.
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Concrete
Number symbol
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Word
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Figure 1 Concrete-pictorial-abstract inter-relationships for
place value concepts for whole number
Place value
Teaching to Mastery Mathematics: Teaching of Decimals
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Place Value
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Concept of Tenths
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With prerequisites in place, students will likely be presented with experiences similar to those
shown in Figure 2 and followed by instruction to highlight key points beginning with decimal ideas
as suggested by Figure 3.
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I folded the strip of paper
into 10 equal parts.
Divide 1 whole into 10 equals parts.
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10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
We can write 1 tenth as
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0.1 is 1 tenth.
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We write 5 tenths as 0.5.
We read 0.5 as zero point five.
Notes
0.1 and 0.5 are decimals.
These are decimal points.
Figure 3 Writing tenths in decimal form
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or 0.5.
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or 0.1.
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Teaching to Mastery Mathematics: Teaching of Decimals
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Figure 2 Modeling tenths
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I coloured one tenth
of the rectangle.
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Pedagogy-based Task
How might you use the number line to reinforce
mixed-number decimal concepts?
• Give number; find number on the
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Three illustrations are given. For each one, what
additional questions would you consider asking?
• Use the number line to show the number 2.6.
number line
• Show point on number line;
name the number
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• Find the value of Points A and B on the following
number line.
A
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0
B
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Questions: What is 0.1 more than 0.6?
What is 0.1 less than 0.6?
What is 0.1 more than 0.9?
What is 0.1 less than 0.9?
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Develop one or two other illustrations that also make
use of the number line.
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Chapter 1: Developing Decimal Number Concepts
number line
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• Compare numbers using the
• Use the following number line to help you answer
the questions.
Solution on p.34
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Number Line
The number line, although perhaps not as “concrete” as
some other illustrations, has a distinct advantage of allowing
representations of tenths, hundredths and thousandths. At
some point, a unit has to be established. Then within that unit
if necessary a pair of end points must be chosen so that
subsequent discussion of points between those points can be
made. The diagram and examples below help show how units
and sub-units can be modeled.
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number line
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
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0.1
0.30
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EXAMPLE 1
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In the first set of examples below, although some
concentration is required, students are basically asked to read
the numbers off the number line.
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What decimal does each letter represent?
A
B
C
a)
0.01
b)
0.02
J
9.97
0.03
K
9.98
0.04
L
9.99
M
10.00
10.01
Solution on p.34
Teaching to Mastery Mathematics: Teaching of Decimals
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As was suggested with the activity with number discs,
number lines can also be used to promote various levels of
conceptual understanding.
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