Chapter 2: Counting & Recording of Numbers

Chapter 2: Counting & Recording of Numbers Presented by Erin O’Halloran

Historical Perspective • Oldest mathematical skill for which we have evidence • May have preceded written language

Tally Sticks • Notches denote numbers • Connected to Roman numerals • Made of animal bone, wood, stone

Egyptian Numerals • ~3400 BC • One of the earliest forms of numbers • Base-10 numerical system • Could be expressed as fractions

Roman Numerals • ~800 BC • Still taught in elementary and middle • Combination of Latin symbols

Attic Greek Numerals • ~700 BC • Similar to Roman numerals • Expressed in exponents for larger numbers

Greek Alphabet Numerals • Ciphered numeral number • 1-9 • 10-90 • 100-900

Chinese-Japanese Numerals • 1400 BC • Written vertically not horizontally

Developmental Perspective • Natural human endeavor • Early months: discriminate one from two objects • 2-3 years: compare large groups of objects • 4-5 years: ordinality and cardinality

Scenario Five year old Peter is doing an activity with his teacher. Ms. Jannat holds out a canister of candies and asks Peter "'How many do you think there are?' Peter looks into the can and, carefully touching each of the wrapped candies, he counts, 'One, two, three, four, five, six.' Ms. Jannet smiles and pours the candies out on the floor... She says 'Are you sure?' Peter moves the candy that has fallen behind a toy car so it is together with the rest, and he again counts. He then lines the candies in a column- the two blue candies are on top- and, as he counts, he tags each candy with a number, 'One, two, three, four, five, six, seven.' 'How many?' Ms. Jannat asks. Peter again begins to count, 'One, two, three.' He hesitates and then he says, 'Seven.'"

Art of Counting • Sets • Functions • Combinatorics

Sets • Union & intersection • Misconceptions • “and” = bigger • “or” = smaller Activity!

Functions Misconceptions • Surjective • Injective

Combinatorics • Permutations • Misconceptions • Permutation vs. combination Problem Set 2.6

Positional Number Systems • Number zero is CRUCIAL in math • Calculus • Finance • Arithmetic • Computers • Placeholder for bases • Expanded notation Who knew I was so important? Video

Problem Set 2.7 & Activity! 61 60 62

Large Numbers • How big is a billion? • What’s the largest number you could write? • Idea of infinity • Fractals • Number lines • Misconception • Infinity is a hard concept • Using number line to give idea of real numbers

Chapter 2: Counting & Recording of Numbers