1.1 homework solutions -...
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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,
February 19, 2010 Math 132: Foundations of Mathematics
Math 132:Math 132:
Foundations of MathematicsFoundations of Mathematics
Amy LewisMath Specialist
IU1 Center for STEM Education
February 19, 2010 Math 132: Foundations of Mathematics
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.
February 19, 2010 Math 132: Foundations of Mathematics
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?
February 19, 2010 Math 132: Foundations of Mathematics
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.
February 19, 2010 Math 132: Foundations of Mathematics
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?
February 19, 2010 Math 132: Foundations of Mathematics
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?
February 19, 2010 Math 132: Foundations of Mathematics
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.
February 19, 2010 Math 132: Foundations of Mathematics
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.
February 19, 2010 Math 132: Foundations of Mathematics
1.3 Problem Solving
• Objective
– Solve problems using the organization of the
four-step problem-solving process.
February 19, 2010 Math 132: Foundations of Mathematics
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?
February 19, 2010 Math 132: Foundations of Mathematics
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
February 19, 2010 Math 132: Foundations of Mathematics
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
February 19, 2010 Math 132: Foundations of Mathematics
A Mathematical TugA Mathematical Tug--ofof--WarWar
February 19, 2010 Math 132: Foundations of Mathematics
A Mathematical TugA Mathematical Tug--ofof--WarWar
• What Algebraic thinking was
evident in the solutions
presented?
• Contrast the different solutions
presented—were there any
similarities? Differences?
February 19, 2010 Math 132: Foundations of Mathematics
55thth GradersGraders’’ ThinkingThinking
Keith and Andy
assigned
“strength points”
to the different
characters to
determine who
would win.
February 19, 2010 Math 132: Foundations of Mathematics
More 5More 5thth Grade ThinkingGrade Thinking
February 19, 2010 Math 132: Foundations of Mathematics
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.