Decimal Fraction Models
Visual models for tenths, hundredths and thousandths may be used for investigations of decimal fraction
notation, equivalent fractions, or decimal fraction multiplication.
Suggested Uses

Write decimal fractions on board. Have students color in fractions to match the written symbols.

Shade different fractions onto grids, duplicate for students. Have students write appropriate names and
symbols, as common fractions and decimals.

Have students shade a fraction in tenths. Ask students to draw vertical lines to show hundredths, write
the shaded area in both tenths and hundredths, as common fractions and as decimal fractions. This
may be extended to include percent.

Use multiplication models to represent the product of decimals visually. Mark off the size of each factor
on the horizontal or vertical axis, shade the rectangle marked out. Students can use the model to match
the shaded area with the algorithm for multiplying ones and tenths, by checking the partial products. In
the above diagram, for example, the following partial products can be identified in the shaded area:
o
2.3 x 0.7 = 1.61
o
2.3 x 2 = 4.6
Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Tenths
Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Name:
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Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Date:
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Hundredths
Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Name:
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Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Date:
................................................
Thousandths
Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Name:
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Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Date:
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Multiplication Grids
Name:
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Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Date:
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Name:
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Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price
Date:
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Common Fractions
1
Drawing Fractions
Draw halves and then quarters or fourths on these circles. Cross out any that are
not even. Try drawing the first line at different angles.
Draw eighths, thirds, sixths and fifths
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Common Fractions
2
Finding and Folding Thirds and Sixths
Rectangle Finding a third is trickier than finding a half or quarter.
This is a good way to find thirds of a rectangle:
1. Take a sheet of paper.
Fold one edge and slide it until the folded
part looks the same size as the remaining
page.
3. Fold the last
edge across
2.
fold the paper here
halfway point
4.
fold the paper
Circle
To find a third of a
circle, think of a clock:
find 10, 2 & 6 o’clock
and connect the lines to
the centre.
5. Open the sheet
and you will see
that the page is
folded into thirds.
Or think of holding a
steering wheel. Your
hands and the bottom of
the steering wheel divide
it into thirds.
1
—
3
1
—
3
1
—
3
To find a sixth of a
circle, first draw thirds,
then draw lines to
divide each third in half.
Try dividing your own circles into thirds and sixths.
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Common Fractions
3
Fractions on a Number Line
1. fourths or quarters
0
1
2. thirds
1
0
3. fifths
0
1
4. sixths
1
0
Count the hops on these lines and write the fractions above the markers.
1. How many hops?_______ The fractional parts are _______________
0
1
—
4
1
2. How many hops?_______ The fractional parts are _______________
0
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Common Fractions
4
Cross out any number lines that do not show equal hops.
Write the fractions on any lines that are show equal hops.
1.
2.
3.
4.
0
1
0
1
0
1
0
1
A half is always found at the midway point regardless of the number of other
markers on the number line. (Use the finger slide or count the hops)
1
—
2
0
1
—
6
2
—
6
3
—
6
0
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1
4
—
6
5
—
6
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Common Fractions
5
Cut each Fractional Piece into Two Pieces
Draw lines to cut each fractional piece in two to make
new fractions.
Equivalent fractions
example:
2
3
1
3

4
6
Write the equivalent fraction that each shape now
shows.
 62____
1
2
 24
____
3
4
 86____
1
4

2
8____
5
8
 10
16____
Write the equivalent fraction of each of these if each fractional piece was cut in
two.
x2
x2
6
—
8
= ——
3
—
4
x2
2
= ——
—
7
= ——
x2
Equivalent fractions
example:
2
3
1
4
 96
Draw lines to cut each fractional piece in three
pieces to make new fractions.
Write the equivalent fraction that each shape now
shows.
 123____
1
2

3
____
6
3
4
5
8

15
____
24
1
3

9
12
____
 39____
x3
2
7
= ——
6
8
= ——
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4
= ——
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Common Fractions
6
Fill in the missing numbers and shade the shapes to match.
1)
0
—
8
1
—
8
3
—
8
—
8
4
—
—
—
8
8
—
8
—
8
2) Counting in fifths
1
2—
5
8
—
5
12
—
5
3)
1
—
4
0
1
4)
—
one fifth
0
1
Tenths: Draw or write the missing common or decimal fraction and place it on
the number line.
1)
0.4
—–
0
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Common Fractions
7
Percentages: Write the missing common or decimal fraction and place it on the number line.
When drawing the fraction use the divisions as a guide. N.B. You will need to find the
equivalent fraction first.
1)
1
—––
=
2
——
100
—–– =
——
100
%
1
0
2)
%
1
0
Ratio
3)
%
—— = ——
100
4)
:
1
0
(Remember to show as recurring decimals and percent,
and round to the nearest hundredth)
%
—— = ——
100
0
:
1
Operations
1)
+
3
6
+
=
2
6
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Common Fractions
8
Shade then add the fractions below. Remember to use 2 different colors.
1)
=
+
=
1 34  1 42 
+
+
=
=
Add these. Add the whole numbers, then add the fractions.
2)
1 36  3 56 
3)
3 92  3 79 
_________________= ______________ = _________
_________________ = ______________ = _______-
To add mixed numbers, add the whole numbers then add the fractions. It may be
necessary to convert the fractions to the Lowest Common Denominator. Once
added, change any improper fractions to mixed numbers and then simplify where
possible.
+
9
—
2 12
=
=
+
3
3—
8
=
2
+
3+
18
9
—
—
+
24
24 =
27
5—
24 6
3
—
24
6
1
—
8
Add these. Remember to simplify any fractions in the answer.
1)
2 62  1 87  _________________= _____________ = ______
2)
2 54  3 24  _________________= _____________ = ______
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