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

ScenarioFive 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 Surjective Injective

Misconceptions

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!

62 61 60

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