MATH 2160 2nd Exam Review

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MATH 2160 2nd Exam Review

• Problem Solving and Proportional Reasoning

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Problem SolvingPolyas 4 Steps

• Understand the problem
• What does this mean?
• How do you understand?
• Devise a plan
• What goes into this step?
• Why is it important?
• Carry out the plan
• What happens here?
• What belongs in this step?
• Look back
• What does this step imply?
• How do you show you did this?

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Problem SolvingStrategies for Problem Solving

• Make a chart
• Make a table
• Draw a picture
• Draw a diagram
• Guess, test, and revise
• Form an algebraic model
• Look for a pattern
• Try a simpler version of the problem
• Work backward
• Restate the problem differently
• Eliminate impossible situations
• Use reasoning

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Proportional ReasoningPiaget

• Concrete
• A manipulative
• Something I can move around and investigate
  things with
• Semi-concrete
• A picture of the things I have been moving around
• If I have never moved it around before this
  becomes semi-abstract for me

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Proportional Reasoning Piaget

• Semi-abstract
• Symbols or alternate representations for my
  semi-concrete models
• Good time to use algebraic thinking with students
• Abstract
• Using numbers to represent all parts of the
  original concrete model

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Proportional ReasoningEquivalent Representations

• Percents
• Decimals
• Ratios
• Fractions
• 25 0.25 25/100 ¼
• Need to be able to fill in missing equivalent
  values on a table

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Proportional Reasoning Circle Graph
Representations

• 5/3
• 12.5
• 1.25
• All circles contain exactly 100

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Proportional ReasoningInteger Rods

• White 1 cm x 1 cm W
• Red 2 cm x 1 cm R
• Lime 3 cm x 1 cm L
• Purple 4 cm x 1 cm P
• Yellow 5 cm x 1 cm Y
• Green 6 cm x 1 cm G
• Black 7 cm x 1 cm K
• Brown 8 cm x 1 cm N
• Blue 9 cm x 1 cm B
• Orange 10 cm x 1 cm O

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Proportional Reasoning Integer Rods

• Equivalents / Combinations
• Number of Equivalents 2n-1

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Proportional Reasoning Integer Rods

• Equivalent Fractions
• ½
• 1/3
• ¼
• Etc.

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Proportional Reasoning Scale Factors

• Enlargement gt100
• Reduction lt100
• Original 100
• Percent per 100

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Proportional Reasoning Types of Percent Problems

• A x B C
• What is 27.37 of 123.4 to the nearest
  thousandth?
• 0.2737 x 123.4 C
• C 33.775
• What percent of 785.46 is 800.03 to the nearest
  thousandth?
• A x 785.46 800.03
• A 1.019
• A 101.9

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Proportional Reasoning Types of Percent Problems

• A x B C
• 237.9 of what number is 48.37 to the nearest
  thousandth?
• 2.379 x B 48.37
• B 20.332

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Proportional Reasoning Bar Graphs

• ALL graphs must have the following
• Title
• Scales
• Labels

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Proportional Reasoning Bar Graphs

• A survey was taken and the following results were
  obtained from a group of 25 people Hats 5
  Glasses 10 Neither ?

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Proportional Reasoning Circle Graphs

• A survey was taken and the following results were
  obtained from a group of 25 people Hats 5
  Glasses 10 Neither ?

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Proportional Reasoning Additive Models

• A factory builds 500 widgets a week. They want
  to increase productivity by 25 widgets a week
  over the next 3 months. What is the factories
  production rate per week for any given week?
• 500 25W P
• where P Production rate
• and W the number of weeks

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Proportional Reasoning Multiplicative Models

• A factory builds 500 widgets a week. They want
  to increase productivity by 2.5 widgets a week
  over the next 3 months. What is the factories
  production rate per week for any given week?
• 5001.025W P
• where P Production rate
• and W the number of weeks

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Proportional Reasoning Tangrams

• Recognizing pieces
• Whole to part
• Part to whole
• Conservation of area

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Proportional Reasoning Tangrams

• Recognizing pieces
• 1 whole square or large square composed of 7
  pieces
• 2 large triangles
• 2 small triangles
• 1 medium triangle
• 1 small square
• 1 parallelogram

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Proportional Reasoning Tangrams

• Whole to part
• If the whole tangram has an area of 36 units2,
  what is the area of the parallelogram?

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Proportional Reasoning Tangrams

• Part to whole
• If the parallelogram and a small triangle have an
  area of 3/8 units2, what is the area of the whole
  large square?

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Test Taking Tips

• Get a good nights rest before the exam
• Prepare materials for exam in advance (scratch
  paper, pencil, and calculator)
• Read questions carefully and ask if you have a
  question DURING the exam
• Remember If you are prepared, you need not fear