Conceptual Learning Materials Insight into Math Concepts. Roman Numerals

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1 Conceptual Learning Materials Insight into Math Concepts 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 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 B Longmire #225 College Station, TX

2 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. IX (one less than 10) = 9. VI (one more than five) = 6 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 = 11 X + I = XI = 12 X + II = XII = 13 X + III = XIII = 14 X + IV = XIV = 15 X + V = XV = 16 X + VI = XVI = 17 X + VII = XVII = 18 X + VIII = XVIII = 19 X + IX = XIX Extensions can include a teen board with Roman numerals instead of with Arabic numerals, matching exercises, or free-response written practice.

3 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. XC (ten less than 100) = 90. LX (ten more than fifty) = 60 CX (ten more than 100) = 110 Lesson VI Encourage the child to discover the pattern with Roman numeral multiples of = 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 = 34 XXX + IV = XXXIV = 45 XL + V = XLV = 58 L + VIII = LVIII = 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 = CCCXIV = CCC + X + IV 449 = CDXLIX = CD + XL + IX 993 = CMXCIII = CM + XC + III 1492 = MCDXCII = M + CD + XC + II 3769 = MMMDCCLXIX = MMM + DCC + LX + IX

4 1 I 7 VII 2 II 8 VIII 3 4 III 9 10 IX IV X 5 V 11 XI 6 VI 12 XII Conceptual Learning Materials Insights Into Math Concepts Copyright 1993, 1998, 2005 Dianne M. Knesek

5 = 11 X + I = XI = 26 XX + VI = XXVI = 12 X + II = XII = 29 XX + IX = XXIX = 14 X + IV = XIV = 32 XXX + II = XXXII = 16 X + VI = XVI souvnrdi.ttf souvnrd.ttf souvnrli.ttf = 34 XXX + IV = XXXIV = 19 X + IX = XIX = 46 XL + VI = XLVI = 25 XX + V = XXV = 49 XL + IX = XLIX Conceptual Learning Materials Insights Into Math Concepts Copyright 1993, 1998, 2005 Dianne M. Knesek

6 4 IV 64 LXIV 11 XI 75 LXXV 38 XXXVIII 83 LXXXIII 46 XLVI 94 XCIV 59 LIX 96 XCVI 62 LXII 100 C Conceptual Learning Materials Insights Into Math Concepts Copyright 1993, 1998, 2005 Dianne M. Knesek

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