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February 19, 2010 Math 132: Foundations of Mathematics

1.1 Homework Solutions17. 3, 7, 12, 18, 25, 33, 42 .

22. 2, 5, 7, 12, 19, 31, 50 .

26. 2, 6, 5, 15, 14, 42, 41, 123, 122 . (What’s

the next term in the pattern?)

47. b. ax # ay = ax+2y

56. 1 5 10 10 5 1

61. (11 – 7)2 = 121 – 154 + 49

62. Area = 360 square units

63. Answers vary.

One example: 2, 5, 7, 10, 12,


Math 132:Math 132:

Foundations of MathematicsFoundations of Mathematics

Amy LewisMath Specialist

IU1 Center for STEM Education


1.2 Estimation, Graphs, and

Mathematical Models

• Objectives

– Use estimation techniques to arrive at an

approximate answer to a problem.

– Apply estimation techniques to information

given by graphs.

– Develop mathematical models that estimate

relationships between variables.


Estimation

• Turn to the horizontal bar graph on page

24.

• Answer questions 45 and 46 using

MENTAL MATH.

• What strategies did you use to solve the

problem?


Estimation• Estimation is the process of arriving at an

approximate answer to a question.

• In the era of calculators and computers,

why is estimation important?

– What does an ability to estimate tell us

about a student?

• How do you use estimation in your shop?

• “≈” means approximately equal to.


Rounding• The first 7 digits of pi (π) are 3.141592.

– Round this number to the nearest tenth.

– Round this number to the nearest ten-thousandth.

• What are the rules for rounding?

• What question are we really asking?

• How is rounding different from truncating?

– Which do you use in your shop?


Estimation with Graphs

• Circle Graphs (aka Pie Charts) are used to

show percentages.

– Circle is divided into sectors.

– Shows part of a whole.

• Consider the graph on page 16.

– If there are 43,143,849 dog owners in the US,

how many think that dogs are company?

– What strategy did you use?


Estimation with Graphs

• Bar Graphs show comparisons among discrete amounts.

– Can be vertical or horizontal; may contain a “double bar”

– See example on page 18.

• Line Graphs show trends (usually, but not always, over time).

– See example on page 20.


Mathematical Modeling

• Mathematical Modeling is the process of

finding formulas to describe real-world

phenomena.

– Example 8 on page 21.

– We will spend more time on mathematical

modeling in the Algebra course.


1.3 Problem Solving

• Objective

– Solve problems using the organization of the

four-step problem-solving process.


Shopping Problem

• Which is the better value: a 15.3 oz. box of

cereal for $3.37 or a 1½ lb. box of cereal

for $4.59?

• Write out the steps that you took to solve

this problem.

• Does your answer make sense?


Polya’s Four Steps

in Problem Solving

Step 1: Understand the problem

Step 2: Devise a plan

Step 3: Carry out the plan and solve the

problem

Step 4: Look back and check the answer


A Mathematical TugA Mathematical Tug--ofof--WarWar

• Your job in this mathematical contest is too

decide who will win the final tug-of war.

Listen carefully and take notes, the first two

rounds give you the information you need.

From Math for Smarty Pants by Marilyn Burns



• What Algebraic thinking was

evident in the solutions

presented?

• Contrast the different solutions

presented—were there any

similarities? Differences?


55thth GradersGraders’’ ThinkingThinking

Keith and Andy

assigned

“strength points”

to the different

characters to

determine who

would win.


SubstitutionSubstitution


More 5More 5thth Grade ThinkingGrade Thinking


Fractions!Fractions!


So What?!?• How do you learn problem solving

strategies?

• YOU SOLVE PROBLEMS!

• Most importantly, you explain and justify your reasoning. This process makes students have to think about the strategies they use.

• The process is more important than the answer.


Homework

• 1.2: 49, 50, 51, 67-70

• 1.3: 28, 35, 39

Next Class: MONDAY! February 22, 2010

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