Measurement

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Measurement
I cut it twice and its still too short.

• At lunch time, sit in your parked car with
  sunglasses on and point a hair dryer at passing
  cars.
• See if they slow down.

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Today .

• Online Presentation by moderators
• Major assignment
• Please refer to Key Elements
• Reference Article Making Connections Teaching
  and The Human Brain Renate and Geoffrey Caine
  (Preservice Web Site Course Resources / Course
  Assignments)

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Authentic Mathematics
The Train Wheel Problem
Add 1 2 3 4 .. 499 500
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Major Assignment

• Reference Page 44 Course Outline and handout
  from 1st class
• Due last class (by February 16, 2004)
• Groups of 3 or 4 from J-I 1,3, 4, 5, 6, 8
• Please choose one grade and one section strand.
• Refer to the set of specific expectations from OME

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Planning A Curriculum Unit

• Choose strand and group of specific expectations
  (backward design)
• Identify the resources that you have available
  (software / manipulatives / print / people)
• Create a timeline / calendar
• A culminating activity?
• Evaluation and assessment

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Using Backward Design to Plan A Unit

• Learning Goals What are the key understandings
  that we want the students to have? What are the
  learning goals at the end of the unit?
• Strategies What teaching and learning strategies
  will promote interest, understanding and
  excellence in all categories?
• Assessment What is acceptable evidence that the
  students have achieved the learning goals?

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Problem Of The Day
How Can This Be True?
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Measure the Tim Hortons coffee cup

• Think attribute
• Think compare unknown to known
• Think estimation

A Key Consideration

• Spatial Reasoning

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Development Stages .
1. Qualitative General Comparisons Bigger
cookie Taller building Heavier box Slower
car Longer room Colder day
2. Quantitative A Need For Units A Known to An
Unknown (length, volume, speed, heat,) Can take
on many different values with different units
They must be measured.
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What Can Be Measured?

• Dimensional Space (1D / 2D / 3D)
• Mass / Weight
• Time
• Combinations
• Speed or Velocity kph, mph, kps
• Density mass per unit of volume

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Process
Direct
Indirect

• Units of measure have the same attribute
• Length of your desk
• Rulers, yardsticks, metre sticks have the
  attribute of length

• Need for instruments to translate evidence
• Temperature of room, time left for class
• Thermometer, clock

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Precision
Refers to the care taken to measure
Refers to units of measure cm more accurate than
metres
Accuracy

• Choose the unit that is most appropriate to the
  task.
• Length of gold jewelry chain.
• Area of this room
• Contents of a cereal box

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span
stone
rod
peck
cubit
barleycorn
jill
jack
grain
carat
pail
hand
fathom
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Teaching Cornerstones

• Participation (concrete material) is essential
• Non-standard units / explore ? standardization
• Lead to sub-units for precision
• Their world ? authentic measurement
• Frequent estimation activity

Measurement Activity Sequence Measurement Activity Sequence Measurement Activity Sequence
Comparisons Direct Indirect
Use of Units Nonstandard Standard Units
Use of Instruments Nonstandard Student Made Standard Units Conventional
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• The Prefixes
• Sub-Units milli / centi / deci
• Combined Units deka / hecto / kilo

System International (SI)

• The Base Units
• Metre linear
• Gram mass
• Litre - volume

In the USA, Thomas Jefferson recommended the
Metric System in the early 1800 it was made
legal in 1866. Hmmmm.
T1
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Measure 1 Dimensional Space

• Linear (line) / distance / dimension
• Straight or curved
• Tools and instruments
• Activities ..
• Make measuring tools ? compare to commercial
• Measure objects with tools after estimation
• Find objects with given values (infers
  estimation)
• Optical illusions (fun addition)

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0 1 2 3 4 5 6 7 8 9 10 11 12
Correct Responses on a standardized test Grade 4
24 Grade 8 62
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Measure 2 Dimensional Space Polygons (poly
?many gons ? sides)

• Creates regions
• May be regular
• May be irregular
• Leads to measurement of two attributes
• Distance around / boundary PERIMETER
• Enclosed surface / what you paint AREA

T2
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Interpretation of Area
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New Units for 2D Space?
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Geoboards

• Exploration
• Set a perimeter ? find
• as many different areas that
• can be enclosed.
• Try It Perimeter 14 units
• What different polygons (area)
• can be made?
• b. Set an area ? find as many
• different shapes (perimeters)
• that can be generated.
• Try It Area 12 units 2
• What different polygons (area)
• can be made?

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Looking for Shortcuts
5 cm



3 cm
3 cm
5 cm
A l x w
P2 x (lw)
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If the corner isnt square
A b x h
A 1/2 x b x h
Work From What The Student Already Knows
T3
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The Circle (A Special Ed Polygon)
Perimeter ? Circumference
Area
radius
diameter
p
A p r2
C pd
C 2pr
T4
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p r2 ? ------------------ p r round cake r2
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Measure 3 Dimensional Space Polyhedrons

• Model building ? key element
• Need for a new unit (3D) ? What packs together
  in space and leaves no gaps?

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Regular / Consistent Space
V Area of one face x 3rd dimension
A Add common multiple areas
T5
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Combinations of Regular Polyhedrons
Model Building with Centicubes
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TABS
A software tool that bridges 2D and 3D space.
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Measuring Mass
Its a comparison thing.
Would this thing work in the cargo bay of
the Space Shuttle?
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Volume A Fluid Connection
100 cc from Syringe To Graduated Cylinder
100 ml
100 g
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