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 of tilted her head, and said, Well, duh! Why do you th
June 10, 2010
Lecture 7: 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 create
expressions . An expression summarizes
Seminar Notes: Franois Vi`te and his Zetetica
c
e
Franois Vi`te was born in 1540 in Poitou in westcentral France. Vi`te was educated as a lawyer,
c
e
e
and in the 1570s, having established a good reputation, he was invited by King Henry III to act
as an
Writing assignment 8(a)
June 22, 2011
Name_
PART I: Please work on this for 10 minutes your own, without discussing with your classmates. After
10 minutes, turn this sheet over and DO NOT WRITE FURTHER ON IT.
1. Express the perimeter of a square as a func
Writing assignment 7
June 20, 2011
Name_
Write a SOLUTION and EXPLANATION of the following problem that will be informative AS WRITTEN to a 7thgrader.
Which is a better deal: A 10 inch diameter pizza for $8 or a 15 inc
Writing assignment 6
June 15, 2011
Name_
The Extended Golf Problem concerned a green that we represented as a circular region about the origin of radius 35. A ball
travels along a straight line from a point outside the green in the left halfpane across a
Writing assignment 5
June 13, 2011
Name_
How has your view of problem solving changed as a result of the MNS course, so far?
Please describe ONE (ONLY!) SPECIFIC GOAL related to problemsolving that you will bring to
Writing assignment 4
June 10, 2011
Name_
Review the CCSS document for High School Algebra. Make up a 15minute quiz for highschool students that would be
useful in testing the material on inequalities that is outlined there. Write out the quiz and soluti
Writing assignment 3
June 8, 2011
Name_
Think about the things you have been learning in the MNS and the curriculum that you teach. Do you have any plans for
modifying what you will be doing in your own classroom, based on what you are experiencing in the
Writing assignment 2
June 6, 2011
Name_
Show how to set up variables and equations to translate the following problem into algebra. Then solve the problem.
Given two numbers that are less than a third number and the ratio of their deficiencies, find the t
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, when inserted in place of the variables, yield
a true sent
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 create expressions .
An expression summarizes a calculati
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 + 2 as 6 (3 + 2), which equals 1. Most people will simpl
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 is a written record of a computation. On page 62 of th
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 law implies that (y + z ) x = x y + x z , and that (y +
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:
STAGE I (setting things up)
Choose a unit of length.
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 about student errors
June 6, 2012
What is a conversion
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 discipline
of logic by constructing the rst predicate calcu
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 situations, evaluate expressions, and use expressions a
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, 2012
Each act of measuring involves: 1) the thing measu
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, denitions, and conventions, when it should be
spending the
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 Unifying Theme in K8
1. The K5 Measurement Strand
The
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 equation a straight line?
The Common Core State Standards sta