Conceptual Learning Materials’
Insight into Math Concepts
www.conceptuallearning.com
Roman Numerals
Because of historical interest as well as enhanced critical
thinking skills, Roman numerals offer a great enrichment math
topic that can be presented at almost any age. Typically,
lower elementary students have exposure to Roman numerals
through their clock work, and older students must be able to
decipher Roman numerals in literature and research.
Below are details on an incremented series of concept
presentations lessons on Roman numerals (We chose to
enumerate these in Roman numeral notation). Younger
children focus on lessons I, II, and III. Older children with a
good background in place value will have an intuitive feel for
Roman numerals, will move at a much faster pace, and can
easily master Roman numerals through lesson VII and beyond.
In addition to the series of concept presentations, three specific
sample exercises are included. These random exercises were
numbered in a logical order for the children to follow. (Note that
there are more exercises than concepts, so the Roman numbers on
the presentation page do not necessarily correspond to the Arabic
number of a specific exercise.) The exercise Roman Numerals 1
serves as an introduction. Roman Numerals 4 illustrates the
Romans’ use of expanded form in developing their numeration
system, and Roman Numerals 11 focuses on random Arabic and
Roman equivalents up to 100. These are only three representative
samples from the entire 15-exercise set.
The entire series of 15 incremental exercises is available through Conceptual Learning Materials’ website
www.conceptuallearning.com. Culminating with concepts through several thousand, The Roman Numeral
cardstock series features 15 sets of cards that can be used as matching exercises or free-response exercises
with a control. The same exercises are also available in blackline master workpage format .
Conceptual Learning Materials, Inc.
3515-B Longmire #225
College Station, TX 77845
281-488-3252
Roman Numerals
Lesson I
Through the three-period lesson, introduce the symbols and values of I, V, and X.
I=1
V=5
X = 10
Have the child practice matching or writing the Arabic symbol for the Roman symbol, as well as
the Roman symbol for the Arabic symbol.
Lesson II
Romans avoided using four of the same symbols in a row. Instead, they used the practice of
placing an I before a V or X for “less than” and an I after a V or X for more for “more than”.
IV (one less than five) = 4.
VI (one more than five) = 6
IX (one less than 10) = 9.
XI (one more than 10) = 11.
Practice association of Arabic with Roman numeral for these four values.
Lesson III
Have the child practice the Roman symbol for values of one through ten. He or she can do this by
associating Roman symbols with concrete materials such as number rods or the colored beads. The
child could also practice association of Arabic and Roman symbols. After this, it would be a good
time to add the symbols for 11 and 12 so the child can begin clock work with Roman numerals.
Lesson IV
Review the concept of ten plus any one-digit number. This can be done with the teen board, golden
beads, stamp game, and/or Montessori numeral cards. Draw the correlation with Roman
Numerals.
10 + 1 = 11
10 + 2 = 12
10 + 3 = 13
10 + 4 = 14
10 + 5 = 15
10 + 6 = 16
10 + 7 = 17
10 + 8 = 18
10 + 9 = 19
X + I = XI
X + II = XII
X + III = XIII
X + IV = XIV
X + V = XV
X + VI = XVI
X + VII = XVII
X + VIII = XVIII
X + IX = XIX
Extensions can include a teen board with Roman numerals instead of with Arabic numerals,
matching exercises, or free-response written practice.
Lesson V
Introduce Roman symbols L and C.
L = 50
C = 100
As with the symbol I placed before or after a V or X, an X before L or C means “less than” and an
X after L or C means more than.
XL (ten less than fifty) = 40.
LX (ten more than fifty) = 60
XC (ten less than 100) = 90.
CX (ten more than 100) = 110
Lesson VI
Encourage the child to discover the pattern with Roman numeral multiples of 10.
10 = X
20 = XX
30 = XXX
40 = XL
50 = L
60 = LX
70 = LXX
80 = LXXX
90 = XC
100 = C
Extensions can include Roman numerals with the tens board, hundred chain, matching exercises, and freeresponse written exercises.
Lesson VII
Review concept of place value involving two digit numbers. Then draw the correlation with Roman
numerals.
30 + 4 = 34
XXX + IV = XXXIV
40 + 5 = 45
XL + V = XLV
50 +8 = 58
L + VIII = LVIII
90 + 9 = 99
XL + IX = XLIX
Extensions can include correlating Roman numerals with golden beads, stamp game values, small bead
frame, random numbers on the hundred chain, matching exercises, and free-response written exercises.
Lessons VIII+
Provide incremental exercises based on the concept that 500 = D and 1000 = M. 400 = CD, and 900 = CM.
As with two-digit numeration, three- and four-digit numeration is based on place value concepts.
314 = 300 + 10 + 4
449 = 400 + 40 + 9
993 = 900 + 90 + 3
1492 = 1000 + 400 + 90 + 2
3769 = 3000 + 700 + 60 + 9
CCCXIV = CCC + X + IV
CDXLIX = CD + XL + IX
CMXCIII = CM + XC + III
MCDXCII = M + CD + XC + II
MMMDCCLXIX = MMM + DCC + LX + IX
1
2
3
4
I
Roman 1A
Roman 1A
Roman 1A
III
Roman 1A
5
Roman 1A
Roman 1A
10
Roman 1A
VI
6
Roman 1A
Conceptual Learning Materials
Insights Into Math Concepts
Roman 1B
IX
Roman 1B
Roman 1B
X
Roman 1B
Roman 1B
XI
Roman 1B
12
Roman 1A
Roman 1B
VIII
11
V
Roman 1A
Roman 1B
Roman 1B
9
IV
Roman 1A
VII
8
II
Roman 1A
7
Roman 1B
XII
Roman 1B
www.conceptuallearning.com
Roman 1B
Copyright 1993, 1998, 2005 Dianne M. Knesek
10 + 1 = 11
Roman 4A
10 + 2 = 12
Roman 4A
10 + 4 = 14
Roman 4A
20 + 6 = 26
X + I = XI
Roman 4A
Roman 4B
20 + 9 = 29
X + II = XII
Roman 4A
Roman 4B
30 + 2 = 32
X + IV = XIV
Roman 4A
Roman 4B
XX + VI = XXVI
Roman 4B
XX + IX = XXIX
Roman 4B
XXX + II = XXXII
Roman 4B
souvnrdi.ttf
souvnrd.ttf
souvnrli.ttf
10 + 6 = 16
Roman 4A
10 + 9 = 19
Roman 4A
20 + 5 = 25
Roman 4A
Conceptual Learning Materials
X + VI = XVI
Roman 4A
X + IX = XIX
Roman 4A
XX + V = XXV
Roman 4A
Insights Into Math Concepts
30 + 4 = 34
Roman 4B
40 + 6 = 46
Roman 4B
40 + 9 = 49
Roman 4B
www.conceptuallearning.com
XXX + IV = XXXIV
Roman 4B
XL + VI = XLVI
Roman 4B
XL + IX = XLIX
Roman 4B
Copyright 1993, 1998, 2005 Dianne M. Knesek
4
64
IV
Roman 11A
11
Roman 11A
38
Roman 11A
XXXVIII
Roman 11A
46
Roman 11A
62
Conceptual Learning Materials
Roman 11B
XCIV
Roman 11B
XCVI
Roman 11B
100
Insights Into Math Concepts
Roman 11B
Roman 11B
Roman 11A
Roman 11A
Roman 11B
LXXXIII
96
LXII
Roman 11A
83
Roman 11A
Roman 11A
LXXV
94
LIX
Roman 11B
Roman 11B
Roman 11A
XLVI
59
Roman 11B
75
XI
Roman 11A
LXIV
Roman 11B
C
Roman 11B
www.conceptuallearning.com
Roman 11B
Copyright 1993, 1998, 2005 Dianne M. Knesek