Representing and Analyzing
Mathematical Situations
Overview Day One, AM
“Making Sense of Algebra in Grades PK - 2”
Expectations
Illustrate general principles and properties
of operations, such as commutativity, using
specific numbers;
Use concrete, pictorial, and verbal
representations to develop an understanding
of invented and conventional symbolic
notations.
“Making Sense of Algebra in Grades PK - 2”
Concrete Representations
“Making Sense of Algebra in Grades PK - 2”
Concrete Model:
Ten Thousand
“Making Sense of Algebra in Grades PK - 2”
Concrete Model:
Hundred Thousand
“Making Sense of Algebra in Grades PK - 2”
Pictorial Representations
“Making Sense of Algebra in Grades PK - 2”
Verbal Representations
“When I count my fingers REAL
fast, I get six!”
“The bus driver doesn’t count….
He lives there!”
“Stick, Stick, Stick, Stick, (cha-ka),
Gate!”
“Making Sense of Algebra in Grades PK - 2”
Symbolic Notations: Invented
“Making Sense of Algebra in Grades PK - 2”
Symbolic Notations:
Conventional
7=7
3+4=5+2
5+1=7
7=2+5
Which one is wrong?
“Making Sense of Algebra in Grades PK - 2”
General Principles and
Properties of Operations
“Five is always a 2 and a 3 or a 3 and a
2 or a 4 and a 1 or a 1 and a 4 or even a
5 and a 0 or a 0 and a 5!” ….a five
year old
“Can it be anything else?” … teacher
“Nope… unless you use half of stuff…
and I don’t think I can do that yet!”…
a rather amazing five year old
“Making Sense of Algebra in Grades PK - 2”
Commutativity
“Making Sense of Algebra in Grades PK - 2”
Expectations AGAIN
Illustrate general PRINCIPLES and
PROPERTIES of operations, such as
COMMUTATIVITY, using specific
numbers;
Use CONCRETE, PICTORIAL, and
VERBAL representations to develop an
understanding of INVENTED and
conventional SYMBOLIC notations.
“Making Sense of Algebra in Grades PK - 2”