Lesson 2

The Coat of Many Bits

Est. Class Sessions: 3

Summarizing the Lesson

Use Questions 15–17 to summarize the key concepts of the lesson. Ask students to discuss Questions 15 and 16 in small groups and then talk about them as a whole class.

Read the Comparing Number Systems section together as a class, then assign Question 17. Students are asked to compare three representations of the same numbers: standard form in the base-ten system, base-ten shorthand, and Roman Numerals.

One similarity between the Roman Numeral System and base-ten shorthand is that they each have special symbols for ones, tens, hundreds and so on, that have to be written repeatedly to show how many the number has. Neither of these representations depend on place value. Since writing numbers in standard form in the base-ten system depends on place value, it does not use special symbols for ones, tens, and hundreds. You just let the place tell the value. And you do not have to write things many times, you just have to tell how many ones, tens, and so on there would be if you did write them all.

X

Roman Numerals. The lesson only describes a few Roman Numeral symbols. There are seven basic symbols: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000. They are combined to produce numbers in between these values. So, the number 725 is represented as DCCXXV. Symbols are usually written in order with the largest on the left and the values of the symbols are added to get the number. But the system has evolved to show subtraction: if a smaller symbol is written to the left of another, it means subtract. So, IX means 10 – 1 = 9, while XI means 10 + 1 = 11. Similarly, instead of writing IIII, you can write IV. Roman numerals are commonly used today in the introductory pages of books, on clock faces, on old buildings, and on the numbering of sports events such as the Super Bowl. Some students might enjoy looking for Roman numerals in their everyday lives and rewriting them in standard form.

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