Problem SolvingProblem Solving

A Scientific ProcessA Scientific Process

A Scientific Process… A Scientific Process…

Is Based on Observed FactsIs Based on Observed Facts

Has Repeatable ResultsHas Repeatable Results

Produces Verifiable OutcomesProduces Verifiable Outcomes

Is Carried Out in a Standard, Systematic Is Carried Out in a Standard, Systematic WayWay

Scientific MethodScientific Method

The Standard, Systematic Way to Carry The Standard, Systematic Way to Carry Out a Scientific ProcessOut a Scientific ProcessHypothesis (Untested Idea)Hypothesis (Untested Idea)Experiment (Test to Check Validity of Experiment (Test to Check Validity of

Hypothesis)Hypothesis)Theory (Valid Explanation of Observations)Theory (Valid Explanation of Observations)

Model – Simplified Theory with AssumptionsModel – Simplified Theory with Assumptions

Law (Summary of Key Experimental Law (Summary of Key Experimental Observations)Observations)

The Scientific MethodThe Scientific Method

Experiment

TheoryLaw

Hypothesis

Scientific Problem SolvingScientific Problem Solving

HypothesisHypothesis

ExperimentExperiment

Theory/LawTheory/Law

Understand Problem ConceptsUnderstand Problem Concepts

Propose Solution Based on Propose Solution Based on Applicable RelationshipsApplicable Relationships

Try Proposal (ie – Do the Try Proposal (ie – Do the Math!)Math!)

Check Results – Do they Make Check Results – Do they Make Sense?Sense?

Document/Summarize ResultsDocument/Summarize Results

It’s All About MeasurementsIt’s All About Measurements

Measurement – 3 PartsMeasurement – 3 PartsA Number or Value; MagnitudeA Number or Value; MagnitudeA Unit: Provides the Standard ScaleA Unit: Provides the Standard Scale

One of the Standard Scale – Known and ConstantOne of the Standard Scale – Known and Constant

Eg, pound, gram, liter, newtonEg, pound, gram, liter, newton

What is Being Measured – Sometimes Very What is Being Measured – Sometimes Very ImportantImportant

Examples of MeasurementsExamples of Measurements

3.98 calories of heat3.98 calories of heat

5.67 newtons force of bowling ball striking 5.67 newtons force of bowling ball striking pinspins

10.0 liters of water10.0 liters of water

57 km/hour auto speed57 km/hour auto speed

7.65 gallons gasoline7.65 gallons gasoline

Not MeasurementsNot MeasurementsObjects CountedObjects CountedDefinitions – eg. Exactly 2.54 cm = 1 inchDefinitions – eg. Exactly 2.54 cm = 1 inchWhy Not?Why Not?Counted Items and Definitions are not Counted Items and Definitions are not

debatabledebatableThey are “perfect”They are “perfect”No “perfect” measurements; always error; No “perfect” measurements; always error;

never exact never exact

A Very Useful TechniqueA Very Useful Technique

Dimensional Analysis (aka “Factor Dimensional Analysis (aka “Factor Labeling”)Labeling”)Converting a Measurement from One Unit to Converting a Measurement from One Unit to

AnotherAnother““Cutting to the Chase” of a Proportion Cutting to the Chase” of a Proportion

ProblemProblemm Unit 1 x Unit 2/Unit 1 = n Unit 2m Unit 1 x Unit 2/Unit 1 = n Unit 2Problem to Try – How many pounds is 583 Problem to Try – How many pounds is 583

grams?grams?