Looking closer ' ' '

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Looking closer . . .

• Chapter 9
• Generating and Testing Hypotheses

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Research and Theory onGenerating and Testing
Hypotheses

• By definition, the process of generating and
  testing hypotheses involves the application of
  knowledge

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Research and Theory onGenerating and Testing
Hypotheses

• Deductive reasoning

• Inductive Reasoning

Know general rule
Action or events happen
Shape your understanding of the general rule
Predict future action or event
Refer to Effect Sizes - Pg. 106
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Inductive Reasoning

• How do you come up with the answer 8?
• 4(423)
• 6
• Students use a problem to find the rule.

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Deductive Reasoning

• Given the order of operations
• Parentheses, exponents, mult./div, add/subtract.
• What is the answer to 4(423) ?
• 6
• Students use the rule to find the answer.

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Justifying the Conjecture a b b a

• As you watch the video, look for examples of
  inductive and deductive reasoning.

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Research and Theory onGenerating and Testing
Hypotheses

• Explaining the hypotheses and the conclusions,
  particularly in writing, leads to deeper
  understanding of the principles.

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Research and Theory onGenerating and Testing
Hypotheses

• Not Just for Science, It Can Be Used For All
  Subjects!!

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Classroom Practice forGenerating and Testing
Hypotheses

• A variety of structured tasks
• Systems Analysis
• Problem Solving
• Historical Investigation
• Invention
• Experimental Inquiry
• Decision Making

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Systems Analysis

• Students predict what will happen if some part
  of a system changes.
• Skip-Counting on a Hundreds Chart
• Count by 2s from 1 to 49. If you continue the
  pattern, will you land on 100?
• How would the pattern change if we started on 2
  instead of on 1?

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Problem Solving

• Problems involve obstacles and constraints
• Problems have several possible solutions
• A solution can be tried or simulated
• Success is obvious students can tell if the
  problem has been solved

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Invention

• Create a model that fits a set of data
• Build a shape that meets given criteria
• Invent an algorithm for a particular procedure

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Experimental Inquiry

• Students make observations from an experiment,
  ask questions about what they have observed, then
  apply what they have learned.

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Decision Making
Using a framework, students use hypothetical
situations to make decisions.
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Classroom Practice forGenerating and Testing
Hypotheses

• Read from the bottom of page 109 (Making Sure
  Students Can Explain Their Hypotheses and Their
  Conclusions) to the end of the chapter.
• At your tables, consider the five bulleted
  suggestions on page 110
• Which of these strategies have you tried?
• Which would you like to try?

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Perfect Solids

• A perfect solid is a three-dimensional figure,
  such as a cube, whose sides are all identical.
• There are only five perfect solids.
• Each perfect solid can be inscribed in and
  circumscribed around a sphere.
• In the beginning of his career, Kepler believed
  that the planetary orbits could all be inscribed
  in one of the perfect solids.

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Characteristics of the 5 Perfect Solids

• Faces on one perfect 3-D shape are all the same.
• At every vertex, the same number of faces come
  together.
• If you turn one face from edge to edge, it always
  looks the same.

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Exploring Perfect Solids Grade 3

• As you watch the video, look for examples of
• Systems Analysis
• Problem Solving
• Historical Investigation
• Invention
• Experimental Inquiry
• Decision Making

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The 5 Perfect Solids

• tetrahedron (four triangular sides)
• cube (six square sides)
• octahedron (eight triangular sides)
• dodecahedron (twelve pentagonal sides)
• icosahedron (twenty triangular sides)

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Generating and Testing Hypotheses

• Deeper understanding develops through the process
  of explaining, orally or in writing, your
  thinking.

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Research and Theory onGenerating and Testing
Hypotheses

• Deductive reasoning

• Inductive Reasoning

Know general rule
Action or events happen
Shape your understanding of the general rule
Predict future action or event
Refer to Effect Sizes - Pg. 106
22
Justifying the Conjecture a b b a

• As you watch the video, look for examples of
  inductive and deductive reasoning.

23
Research and Theory onGenerating and Testing
Hypotheses

• Explaining the hypotheses and the conclusions,
  particularly in writing, leads to deeper
  understanding of the principles.

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Systems Analysis

• Consider an equation of the form
• y mx b.
• What happens to the graph of the function when
  the value of b is increased?

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Systems Analysis Function Families

• Transformation Graphing Application
• Works on TI-83 Plus or TI-84 Plus
• Activities available online
• www.education.ti.com
• http//education.ti.com/educationportal/sites/US/n
  onProductSingle/activitybook_transgraphapp_explori
  ng.html