Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Coordinates on the plane, distance formula, equations and their graphs June 20, 2012
I once asked a class of undergraduates why the graph of a linear equation is a line. One student
looked at me, kind
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Order of Operations
Some arithmetic expressions appear to allow dierent interpretations. For example, most people
will simplify 6 3 + 2 as follows:
63+2
=
(6 3) + 2
=
3+2
=
5,
but a few may read 6 3 +
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Mathematical Foundations for the Common Core
A Course for Middle and Secondary Teachers
James J. Madden
Department of Mathematics, Louisiana State University
Topic: Expressions and Trees
An expression
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
June 7, 2012
The Distributive Law
If x, y and z are any numbers, then
x (y + z ) = x y + x z.
Of course, it does not matter in what order we write the factors in a multiplication, so the distributive
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
M6302, June 5, 2012
The Number Line
The Number Line is the most important picture in mathematics.
3
52
2
32
1
12
0
12
1
32
2
52
3
To make a number line, one decorates a naked line. Follow these steps:
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Mathematical Foundations for the Common Core
A Course for Middle and Secondary Teachers
James J. Madden
Department of Mathematics, Louisiana State University
Conversion Factors, and some speculations
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
June 13, 2012
Logic
Friedrich Ludwig Gottlob Frege (b. 1848, d. 1925) was a German mathematician, logician, and
philosopher who worked at the University of Jena. Frege essentially reconceived the disc
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Logic II: Simple Sentences
June 14, 2012
CCSS for Grade 6 (page 39)
Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Mathematical Foundations for the Common Core
A Course for Middle and Secondary Teachers
James J. Madden
Department of Mathematics, Louisiana State University
Exposition: Measure numbers
M6302 June 4,
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Order of operations and other oddities in school
mathematics
H. Wu
September 13, 2007
One of the aws of the school mathematics curriculum is that it wastes time
in fruitless exercises in notation, den
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Mathematical Foundations for the Common Core
A Course for Middle and Secondary Teachers
James J. Madden
Department of Mathematics, Louisiana State University
Measurement, Ratio and Number Systems: A U
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Mathematical Foundations for the Common Core
A Course for Middle and Secondary Teachers
James J. Madden
Department of Mathematics, Louisiana State University
Topic: Why is the graph of a linear equati
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
June 18, 2012
And, Or, Not
So far, we have seen that the language of mathematics starts with constant symbols and variable
symbols . With the inclusion of functions symbols , we gain the ability to cr
Math 6302 "Mathematical Foundations for the Common Core
MATH 6302

Summer 2011
Coordinates on the line
June 19, 2012
We have seen that to solve an equationor an inequality, or a combination of equations and/or inequalities
joined by ANDs and ORsmeans to nd the numbers which, whe