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WEEK 2
ORDERING OF WHOLE NUMBERS WITH SYMBOLS
Comparing quantities or amounts in terms of more, fewer, or the same as helps with understanding the relationship between numbers. Quantity is related to ‘how many’ rather than size, shape, or position. Numbers can be compared by determining which one is greater than, less than, or equal to another number. For example,
Sometimes it is useful to arrange numbers in ascending or descending order.
For example, 20, 30, 40, 50 is arranged in ascending order (least to greatest) 50, 40, 30, 20 is arranged in descending order (greatest to least)
Understanding place value can help with comparing and ordering numbers. In our decimal number system the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right. For example in the number 42• the digit 2 is in the ones place• the digit 4 is in the tens place
Mathematical Words/Symbols used in ordering number include
Fewer – less than (<)
More – greater than (>)
Same as – equal to (=)
Digits – are the numerals 0 to 9 that form numbers. For example, the digits 2 and 7 can form the two- digit numbers 27 and 72. Mathematical Statement – consists of numbers and symbols defining a relationship of equality or inequality. An example of equality is 3+ 5 = 2 + 6. An example of inequality is 3+ 5 < 2 + 5.Place value – the value of any digit depending on its location in a number e.g., for the number 84 the place value of the 8 is 80.
Quiz
Rewrite the following from least to the greatest
- 340, 043 304, 043 340, 340 430, 040 430, 004
- 609,229 69, 929 609292 690, 229 69, 292
WEEK 3
THE ROMAN NUMERALS
Roman numerals use seven letters: I, V, X, L, C, D and M to represent the numbers 1, 5, 10, 50, 100, 500 and 1000. These seven letters make up thousands of numbers. Romans Numerals are based on the following symbols:
| 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
| I | V | X | L | C | D | M |
Basic Combinations
Which can be combined like this:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| I | II | III | IV | V | VI | VII | VIII | IX |
| 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |
| X | XX | XXX | XL | L | LX | LXX | LXXX | XC |
| 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 |
| C | CC | CCC | CD | D | DC | DCC | DCCC | CM |
Forming Numbers – The Rules
When a symbol appears after a larger (or equal) symbol it is added
- Example: VI = V + I = 5 + 1 = 6
- Example: LXX = L + X + X = 50 + 10 + 10 = 70
But if the symbol appears before a larger symbol it is subtracted
- Example: IV = V − I = 5 − 1 = 4
- Example: IX = X − I = 10 − 1 = 9
To Remember: After Larger is Added
Don’t use the same symbol more than three times in a row (but IIII is sometimes used for 4, particularly on clocks)
How to Convert to Roman Numerals
Break the number into Thousands, Hundreds, Tens, and Ones, and write down each in turn
Example: Convert 1984 to Roman Numerals.
Break 1984 into 1000, 900, 80 and 4, then do each conversion
- 1000 = M
- 900 = CM
- 80 = LXXX
- 4 = IV
1000 + 900 + 80 + 4 = 1984, so 1984 = MCMLXXXIV
Really Big Numbers
Numbers greater than 1,000 are formed by placing a dash over the symbol, meaning “times 1,000”, but these are not commonly used:
| 5,000 | 10,000 | 50,000 | 100,000 | 500,000 | 1,000,000 |
| V | X | L | C | D | M |
i-1 vi-6 xi-11 xvi-16 xxiv-24 L-50 cc-200
ii-2 vii-7 xii-12 xvii-17 xxix-29 Lv-55 ccc-300
iii-3 viii-8 xiii-13 xviii-18 xxxix-39 xc-90 CD-400
iv-4 ix-9 xiv-14 xix-19 xL-40 xcvi-96 CDXL-440
v-5 x-10 xv-15 xx-20 xLv-45 c-100 CDL-450
D-500 DCC-700 CM-900 M-1000 MMM-3000
IV-4000 IVD-4500 V-5000 VM-6000 X-10000
L-5000 C-100000 D-500000 M-1000000
Application of Roman figures
LXX +MC =MCLXX
CCCIX +DIV = DCCCXIII
MCMXCIX + DI = MMD
XXXII – XIX = XIII
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