Transcript Math Across the Curriculum: Geometry and

Math Across the Curriculum:
Geometry and Measurement
Paraprofessional Training
August 24th – August 28th
Naming and Describing 2D Shapes
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Regular or
irregular?
The number of
sides
The number of
angles
The size of the
angles
Naming and Describing 3D Shapes
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The number of
edges
The number of
vertices
The number of
faces
The shape of the
faces
Angles
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All angles have a vertex
360° forms a full circle
180° forms a straight line
90° forms a right angle or the angle
formed by two perpendicular lines
The angles of a triangle add up to 180°
The angles of a quadrilateral always
add up to 360°
Name the angles (in degrees°)
Activity Cards
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Use the pattern blocks to fill in the
activity cards.
Discuss what mathematical concepts
or understanding are being developed
by doing activities like these.
Assign one person to share out one
purpose or value found in doing these.
Tessellations
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Tessellations are defined as “tiling”
with shapes that cover the plane in a
regularly repeating pattern without
gaps or overlaps
Example:
Tessellation Assignments
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“Odd” Tables
Work together to
create a regular
tessellation using
three blocks that
are different
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“Even” Tables
Work together to
create a regular
tessellation using
four blocks that are
different
Use extra time to explore a bit with finding one and two block tessellations.
Fun to create and color…
Gallery Walk and Break
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Which shapes seem to fit together
easily and which shapes do not seem
to fit together with the others?
Which shapes fit together to make a
pattern using only one block?
Which shapes fit together to make a
pattern using two blocks?
Hexagon Cookie Game
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This game can be
found in our
Investigations at
grade 3 but is
appropriate for all
ages working with
fractional amounts.
Modifying the game
a bit to fit the
materials we have…
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1: one whole
cookie (hexagon)
2: one half of a
cookie
3: one third of a
cookie
6: one sixth of a
cookie
4: roll again
5: lose a turn
Trading is allowed…
M
M
M
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M
Coordinate Geometry
(x,y)
(-x,y)
x
(-x,-y)
(x,-y)
y
Pi
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3.14
3.14159265358979
323846264338327
950288419716939
937510582097494
459230781640628
620899862803482
534211706
Pi (π)
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C = πd
Cherry pie delicious!
C = Circumference of the circle
d = the diameter of the circle
So how could I determine the value of
π with my students?
Measurement Pre-test
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A traditional unit of distance called a “hand” is equal
to one half of a foot? T or F
The formula for converting Celsius to Fahrenheit is
roughly x2 plus 32°? T or F
A ton of bricks weighs more than a ton of feathers.
T or F
A 12oz can of soda weighs 12 ounces. T or F
Peter picked two gallons of pickled peppers.T or F
The inch was created to avoid using fractional parts
of a foot.
T or F
Would you ever ask an 8 year old…
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1÷¼?
How about one dollar divided into
quarters?
3÷½?
How many half-hour shows can you
watch in 3 hours?
2 ÷ 1/12 ?
How many inches are in 2 feet?
Flip and Multiply
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1 ÷ ¼ (just flip and multiply!)
¼ or “1 over 4” becomes “4 over 1”
which equals 4
Now just multiply… 1 x 4
So 1 ÷ ¼ = 1 x 4 because both
produce a value of 4 and 4 = 4
Does this make sense?
Same numeric value, but…
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1÷¼=1x4
One dollar divided into quarters (1/4)
produces 4 quarters
One dollar multiply by 4 produces 4
dollars
3÷½=3x2
2 ÷ 1/12 = 2 x 12
Let’s try one…
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3÷¼=?
Try explaining it with money…
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Try explaining it with clocks…
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twelve quarters
Twelve 15 minute sessions
Try explaining it with rulers…
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Twelve 3 inch sections
Let’s try a harder one…
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2 ÷ 2/3
Two divided by two thirds
Money?
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Clocks?
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Money doesn’t work well with thirds
Three 40 minute session
Rulers?
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Three 8 inch sections
One more…
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1½÷¼
One and one-half divided by one fourth
Money?
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Clocks?
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6 quarters
Six 15 minute sessions
Rulers?
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Six three inch sections
Money
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Good for exploring with…
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Fourths (quarters)
Tenths (dime $0.10 or 0.1)
Twentieths (nickel)
Hundredths (penny $0.01)
Havles ? (half – dollar)
Clocks
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Good for exploring with…
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Halves (half hour – 30 minutes)
Fourths (quarter of an hour - 15 minutes)
Thirds (20 minutes)
Sixths (10 minutes)
Twelvths (5 minutes)
Fifths (12 minutes)
Tenths (6 minutes)
Rulers or “one foot”
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Good for exploring with…
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Halves (6 inches)
Thirds (4 inches)
Fourths (3 inches)
Twelvths (one inch)
Metric system
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Good for exploring with our base ten
system…
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1 kilogram = 1,000 grams
10 kilograms = 10,000 grams
100 kilograms = 100,000 grams
1 centimeter = 0.01 meters
10 centimeters = 0.1 meters
100 centimeters = 1 meter
Back Cover of Notebook
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