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✎Although students begin to develop place value

understandings in primary one, they are formally introduced to

decimal numbers usually from primary four.

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

to include at least 12

, 15

, and 110

.

Let us consider these place value and fractional prerequisites

in more detail.

Place Value

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.

Place value

Decimal Concepts

Figure 1 Concrete-pictorial-abstract inter-relationships for

place value concepts for whole number

Concrete

Number symbol

23

Word

Twenty three

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Divide 1 whole into 10 equals parts.

We write 5 tenths as 0.5.

We read 0.5 as zero point fi ve.

Figure 3 Writing tenths in decimal form

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.

I folded the strip of paper into 10 equal parts.

I coloured one tenth of the rectangle.

We can write 1 tenth as 110

or 0.1.110

0

0.1 is 1 tenth.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Notes

0.1 and 0.5 are decimals.

These are decimal points.

Concept of Tenths

510

or 0.5.

Figure 2 Modeling tenths

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How might you use the number line to reinforce

mixed-number decimal concepts?

Three illustrations are given. For each one, what

additional questions would you consider asking?

• Use the number line to show the number 2.6.

0 1 2 3

• Find the value of Points A and B on the following

number line.

0 1

A B

2 3

• Use the following number line to help you answer

the questions.

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?

0 1 2

Develop one or two other illustrations that also make

use of the number line.

Solution on p.34

Pedagogy-based Task

• Give number; fi nd number on the

number line

• Show point on number line;

name the number

• Compare numbers using the

number line

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✎

number line

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.

As was suggested with the activity with number discs,

number lines can also be used to promote various levels of

conceptual understanding.

In the fi rst set of examples below, although some

concentration is required, students are basically asked to read

the numbers off the number line.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.210.20 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30

EXAMPLE 1

What decimal does each letter represent?

a)

0.01 0.02

A B C

0.03 0.04

b)

9.97 9.98 9.99 10.00 10.01

J K L M

Solution on p.34

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