Establishing
Foundations to
Support Student
Success
What are your goals when
teaching a math class?
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Students succeed in this course.
Students succeed in the next course.
Why is it Important for
Students to Study Math?
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Remove a barrier to a vocation.
Solve practical problems.
Develop problem-solving skills.
Be a better consumer.
Be part of an informed citizenry.
Build confidence.
Evaluate payday loans.
Supporting Success
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Understand the four basic operations.

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Selecting the correct operation.
Creating problems with a certain operation.
Explain the meaning of an answer.
Explain the Meaning
of an Answer
A chef is making 120 meatballs from 6
pounds of hamburger. Six pounds of
hamburger contain 7200 calories.
 Explain the meaning of the quotient of 120
and 6.
120 meatballs
6 lb of hamburger
= 20 meatballs per pound of hamburger
Explain the Meaning
of an Answer
A chef is making 120 meatballs from 6
pounds of hamburger. Six pounds of
hamburger contain 7200 calories.
 Explain the meaning of the quotient of 6
and 120.
6 pounds
120 meatballs
= 0.05 pound of hamburger per meatball
Supporting Success

Develop comprehension.
 Number sense
 Percent
 Mixture
 Uniform motion
 Work
Percent Mixture
The large square
contains 100 smaller
squares. The large
square represents 1 liter
of a solution.
1 liter
Percent Mixture
 Each
small square
represents 1%. To
show, for instance, a
10% solution, shade
any 10 of the smaller
squares.
Percent Mixture
 Begin
with 10 liters of a 10% acid solution.
Percent Mixture
 Add
5 liters of a 4% acid solution.
Percent Mixture
 There
are 15 liters. This
is represented by the
1500 small squares.
There are 120 shaded
small squares. The
percent concentration of
the new solution is
120
 0.08  8%
1500
Progress Gradually
 Begin
with a numerical example. (p. 7,
Percent Problems, part A, #1)
 Give the same example with one variable.
(p. 7, #2)
 Give an example of the intended problem
type. (p. 7, #3)
Move from Concrete
to Abstract
A
candy manufacturer has x pieces of
chocolate. If each piece of chocolate
weighs y pounds, how many pounds of
chocolate does the manufacturer have?
Concept of Variable

A variable is a symbol that represents a
quantity capable of assuming any of a set
of values.
𝜋, e, i
 ax2 + bx + c = 0
a2 + 3a – 10 = 0
 y = mx + b

Why Two Variables?
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Michael and Sara take turns driving on a
45-hour drive across country. How long
did Sara drive?
A 10-pound mixture contains walnuts and
pecans. How many pounds of each are in
the mixture?
Effect of Language
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At this college, there are six times as
many students as professors.
At this college, the number of students is
six times the number of professors.
Effect of Language
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At this college, there are six times as
many students as professors. This can
be expressed by the equation y = 6x.
What does the letter x represent?
a.
b.
c.
d.
e.
f.
Professors
Students
Number of professors
Number of students
More than one of the above (which ones)
None of the above
Projects
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Quantitative reasoning
Percent Increase and Decrease
Population and Land Allocation
Linear Business Model
Gasoline Station Choices
Magnitude of Numbers
Closing Questions
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How much time are you spending
teaching concept development?
How much time are you spending
teaching algorithm?