Representing Thousandths
Visualizing Thousandths
Materials
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overhead transparency of a 10x10 grid (attached)
overhead projector
Activity
Display an overhead transparency of a 10x10 grid. Explain that the grid represents one whole and
ask students to point to sections of the grid that represent different quantities of tenths and
hundredths (e.g., 1 tenth, 7 tenths, 20 hundredths, 92 hundredths).
Next, ask students to imagine what one thousandth of the grid would look like. Discuss how a
thousandth is one-tenth of a hundredth (a small square). Help students to understand this idea by
using an overhead marker (preferably with a fine tip) to divide a small square into ten sections.
Alternatively, place 10 toothpick pieces, cut to the length of a small square, lengthwise in the
square to divide it into 10 parts. Discuss how one thousandth is a small quantity compared to the
whole grid.
Note: Base-ten materials provide another powerful way to visualize thousandths. Start with a cube
of 10 flats to represent the whole. One flat represents a tenth, a rod represents a hundredth, and a
unit cube represents a thousandth.
Decimal Numbers – Grade 4 to Grade 6
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Representing Thousandths
Thinking about a Thousandth
Materials
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overhead transparency of a 10x10 Grid (attached)
overhead projector
copies of 10x10 Grids (6 grids on a page) – 2 pages per pair of students
scissors – for each pair of students
tape – 1 roll per pair of students
Activity
Display an overhead transparency of a 10x10 Grid. Cover nine columns of the grid with a sheet of
paper so that only one column is visible on the screen. Ask students to imagine that the column
represents the whole and to explain the relationship between a small square and the column (i.e., a
small square is one tenth of the column). Have students come to the overhead projector and indicate
what 3 tenths, 5 tenths, and 9 tenths would look like.
Next, reveal the entire 10x10 grid and tell the students that the entire grid now represents one whole.
Again, ask them to explain the relationship between a small square and the entire grid. (A small square
is one hundredth of the grid.) Have students indicate on the overhead transparency different numbers
of hundredths (e.g., 3 hundredths, 20 hundredths, 89 hundredths).
Arrange students in pairs. Provide students with copies of 10x10 Grids, scissors, and tape and explain
that they are to work with their partner to create a model that represents one whole in which one small
square represents a thousandth. Students should discover that 10 grids taped together in any
configuration form a whole that is composed of 1000 small squares and that each square is one
thousandth of the whole.
A Possible Model for Thousandths
Have students share their models with the class and ask them to explain the relationship between a
small square and one whole.
Record 0.325 on the board and instruct pairs of students to shade part of their model to show the
decimal number. Record other decimal numbers on the board and have students discuss with their
partner how their model could be shaded to show the numbers.
Decimal Numbers – Grade 4 to Grade 6
2
© Queen's Printer for Ontario, 2006
Representing Thousandths
Thousandths on a Metre Stick
Materials
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metre stick (calibrated in centimetres and millimetres)
Activity
Tape a metre stick to the board. Ensure that students are close enough to the metre stick to see
the centimetre markings and numbers.
Discuss how one metre is divided into 10 decimetres, 100 centimetres, and 1000 millimetres. Ask
the following questions and have students explain their answers:
– “What fraction is a decimetre of a metre?” [one tenth]
– “What fraction is a centimetre of a metre?” [one hundredth]
– “What fraction is a millimetre of a metre?” [one thousandth]
Draw a line segment that extends from 0 to 8 cm below the metre stick on the board.
Ask:
– “What is the length of the line segment in centimetres? in millimetres?”
– “What fraction is the line segment of the metre?”
Have students explain why the line segment can be described as 8 hundredths of a metre and 80
thousandths of a metre. Record these amounts as decimal numbers and have students explain
why 0.08 (8 hundredths) and 0.080 (80 thousandths) represent the same quantity.
Continue by drawing other line segments below the metre stick and asking students to identify the
number of hundredths and thousandths that each line segment is of one metre.
Decimal Numbers – Grade 4 to Grade 6
3
© Queen's Printer for Ontario, 2006
Representing Thousandths
Thousandths on a Number Line
Materials
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metre stick (calibrated in centimetres and millimetres)
Activity
On the board, draw a line that is 1 m long. Label 0 and 1 at opposite ends.
0
1
Explain that the length of the line is one metre. Clarify that a metre is composed of 1000 millimetres
and that each millimetre is one thousandth of a metre.
On the board, record a decimal number expressed as thousandths (e.g., 0.564) and ask students
to estimate the location of the decimal number on the number line. Invite a few students to indicate
their estimates on the number line and have them explain their thinking. For example, students
might explain that 0.564 would be located slightly to the right of the midway point between 0 and 1
1
1
because 564 thousandths is close to 5 tenths ( ) or 56 hundredths (close to ).
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Ask students to use a metre stick to check estimated positions of numbers on the line segment.
Two students could hold the metre stick directly below the number line and a third student could
indicate how the markings on the metre stick can be used to locate the position of the decimal
number (e.g., 0.564 would be located 4 millimetres to the right of the 56 centimetre mark).
Repeat by having students estimate the location of other thousandths (e.g., 0.764, 0.911, 0.005).
For each number, ask students to explain how they made their estimate and to check their
estimates using the metre stick.
Decimal Numbers – Grade 4 to Grade 6
4
© Queen's Printer for Ontario, 2006
10x10 Grid
Decimal Numbers – Grade 4 to Grade 6
5
© Queen's Printer for Ontario, 2006
10x10 Grids
Decimal Numbers – Grade 4 to Grade 6
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© Queen's Printer for Ontario, 2006