miles of tiles
DESCRIPTION
Miles of Tiles. The Exhibit. Miles of Tiles. The Exhibit. Miles of Tiles. The Exhibit. Miles of Tiles. The Exhibit. Miles of Tiles. The Exhibit. Math. Geometry + Nature. Math. Geometry + Nature. Why do bees use hexagons?. Is there something special about them?. Math. - PowerPoint PPT PresentationTRANSCRIPT
Miles of TilesThe Exhibit
Miles of TilesThe Exhibit
Miles of TilesThe Exhibit
Miles of TilesThe Exhibit
Miles of TilesThe Exhibit
MathGeometry +
Nature
MathGeometry +
NatureWhy do bees use hexagons?
Is there something special about them?
MathGeometry +
NatureLet’s compare what we calculated
P = 12A = 9
P = 12A = 10.38
P = 12A = 11.47
MathGeometry +
NatureA circle yields the greatest
interior space for the smallest
perimeter of any shape!
P = 12A = 11.47
MathGeometry +
Nature
P = 12A = 10.38
Hexagons yields the greatest
interior space for the smallest
perimeter of any shape that
tessellates!
Lesson IdeasGrade 3
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbersFraction Fracture
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
Fracture - break into pieces
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
Fractions - break into pieces using
numbers
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
4 = 1 1 1 1
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
4 = 1 1 1 1¼ means you have one of the four 1s
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
You have one of
the four squares
Lesson IdeasGrade 3Develop
Understanding of
fractions as numbers
Tiles provide a concrete example of the abstract concept of fractions
Lesson IdeasGrade 3
Understand the concepts of
area and relate it to
multiplication and addition
Lesson IdeasGrade 3
Area relationship to multiplication &
addition
Lesson IdeasGrade 3
Area relationship to multiplication &
addition
Lesson IdeasGrade 3
Area relationship to multiplication &
addition1 1
11
Lesson IdeasGrade 3
Area relationship to multiplication &
addition2
2
Lesson IdeasGrade 3
Area relationship to multiplication &
addition2
2 2 x 2 = 4
Lesson IdeasGrade 3
Area relationship to multiplication &
addition2 x 2 = 4
Area of this square is 4
Lesson IdeasGrade 4
Lesson IdeasGrade 4
Understanding fraction equivalence
Lesson IdeasGrade 4
Understanding fraction equivalence
Lesson IdeasGrade 4
Understanding fraction equivalence
Lesson IdeasGrade 4
Understanding fraction equivalence4/16 =
1/4
Lesson IdeasGrade 4
Understanding decimal notation for
fractions
Lesson IdeasGrade 4
Understanding decimal notation for
fractions¼ spoken as “one quarter”
Lesson IdeasGrade 4
Understanding decimal notation for
fractionsWith money ¼ of
a dollar is one quarte
r
Lesson IdeasGrade 4
Understanding decimal notation for
fractionsOne quarter
is twenty-
five cents
25¢
Lesson IdeasGrade 4
Understanding decimal notation for
fractionsTwenty-five
cents is written
as
25¢
.25
Lesson IdeasGrade 4
Understanding decimal notation for
fractions.25
.25.2
5.25$1
Lesson IdeasGrade 5
Understanding concepts of volume
Lesson IdeasGrade 5
Understanding concepts of volumeStart
with simple shapes
Lesson IdeasGrade 5
Understanding concepts of volumeStack the
physical shapes on the board
Lesson IdeasGrade 5
Understanding concepts of volumeExplain
that the volume for all simple
shapes is area x height
Lesson IdeasGrade 5
Understanding concepts of volumeExplain
that the volume for all simple
shapes is area x height
Lesson IdeasGrade 5
Understanding concepts of volumeExplain
that the volume for all simple
shapes is area x height
Lesson IdeasGrade 5
Understanding concepts of volumeExplain
that the volume for all simple
shapes is area x height
Lesson IdeasGrade 5
Understanding concepts of volumeCompare
volumes to
illustrate the bee’s
use of hexagon
s
Lesson IdeasGrade 6
Solve real-world problems involving
area
Lesson IdeasGrade 6
Solve real-world problems involving
areaYou are installing new tiling on
your bathroom floor
Lesson IdeasGrade 6
Solve real-world problems involving
area
Lesson IdeasGrade 6
Solve real-world problems involving
area
Lesson IdeasGrade 6
Solve real-world problems involving
areaNo bathroom is an exact multiple of
the size of tile chosen
Lesson IdeasGrade 6
Solve real-world problems involving
areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x
5”
Lesson IdeasGrade 6
Solve real-world problems involving
areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x
5”How many tiles are
needed?
Lesson IdeasGrade 6
Solve real-world problems involving
areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x
5”Remember to convert feet to
inches!
Lesson IdeasGrade 6
Solve real-world problems involving
areaRemember to convert feet to
inches!
Lesson IdeasGrade 6
Solve real-world problems involving
areaRemember to convert feet to
inches!NASA's Climate Orbiter lost
September 23, 1999 (CNN) -- NASA lost a $125 million Mars orbiter because a Lockheed Martin team used English measurement while the NASA team used the metric system.
Lesson IdeasGrade 6
Solve real-world problems involving
areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x
5”Remember to convert feet to
inches!
Lesson IdeasGrade 6
Solve real-world problems involving
areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x
5”How many tiles must be cut?
Lesson IdeasGrade 6
Solve real-world problems involving
areaWhat if the tiles are a different shape?
Lesson IdeasGrade 6
Solve real-world problems involving
area
Lesson IdeasGrade 7
Investigate chance processes
Lesson IdeasGrade 7
Investigate chance processes4 different
colored monkeys live on
monkey island.
Lesson IdeasGrade 7
Investigate chance processesOne of
them walks up to you
begging for a
banana.
Lesson IdeasGrade 7
Investigate chance processesWhat is
the probability that it is yellow?
?
Lesson IdeasGrade 7
Investigate chance processesHave a
student stand with their back
to the board.
Hand them one of the
four monkeys.
Lesson IdeasGrade 7
Investigate chance processes6 different
colored monkeys live on
monkey island…
Lesson IdeasGrade 8
Solve real-world problems involving
volume
Lesson IdeasGrade 8
Solve real-world problems involving
volumeCalculate the
volume of a milk carton
Lesson IdeasGrade 8
Solve real-world problems involving
volumeCalculate the
volume of a milk carton
Lesson IdeasGrade 8
Solve real-world problems involving
volumeBreak it down into
basic shapes that are easy to
calculate
Lesson IdeasGrade 8
Solve real-world problems involving
volumeBreak it down into
basic shapes that are easy to
calculate
Lesson IdeasGrade 8
Solve real-world problems involving
volumeBreak it down into
basic shapes that are easy to
calculate
Lesson IdeasGrade 8
Understand and apply Pythagorean
Theorem
Area = ½ b x h2 2
2
Lesson IdeasGrade 8
A = ½ b x h2 2
2
Lesson IdeasGrade 8
A = ½ b x h2 21 1
Lesson IdeasGrade 8
A = ½ b x h21
h
Lesson IdeasGrade 8
A = ½ b x h21
h
Determin
e the value of “h”
Lesson IdeasGrade 8
a2 + b2 = c2
21
h
Determin
e the value of “h”
Lesson IdeasGrade 8
12 + h2 = 22
21
h
Determin
e the value of “h”
Lesson IdeasGrade 8
1 + h2 = 421
h
Determin
e the value of “h”
Lesson IdeasGrade 8
h2 = 321
h
Determin
e the value of “h”
Lesson IdeasGrade 8
h2 = 321
h
Determin
e the value of “h”
Lesson IdeasGrade 8
h = 321
h
Determin
e the value of “h”
Lesson IdeasGrade 8
h ≈ 1.73 21
h ≈ 1.73
Determin
e the value of “h”
Lesson IdeasGrade 8
A = ½ b x h
1 1h
Now we can
calculate the area
of one equilat
eral triangl
e
Lesson IdeasGrade 8
A = 1 x 1.73
1 1h
Now we can
calculate the area
of one equilat
eral triangl
e
Lesson IdeasGrade 8
A = 1.73The area
of one equilat
eral triangl
e is 1.73
1.73
Lesson IdeasGrade 8
Lesson IdeasGeometry
Lesson IdeasNumbers &
Quantity
Lesson IdeasNumbers &
QuantityIn real world problems, the answers are usually not
numbers but quantities:
numbers with units, which
involves measurement.
Lesson IdeasNumbers &
QuantityMeasure the actual shapes at
the exhibit. Printed paper rulers can be provided to students.
Lesson IdeasNumbers &
QuantityMeasure lengths, widths, & diameters. Calculate areas, circumferences, & volumes
Lesson IdeasAlgebra
Lesson IdeasAlgebra
An expression uses symbols that represent numbers, arithmetic operations, and exponents.
Lesson IdeasAlgebra
Formulas for AreaTriangle =
½ b x h
Lesson IdeasAlgebra
Formulas for AreaCircle = ∏ r2
Lesson IdeasAlgebra
Pythagorean Theorema2 + b2 = c2
Lesson IdeasAlgebra
Volume FormulasVolume =
Area x height
Lesson IdeasStatistics & Probability
Lesson IdeasStatistics & ProbabilityWhat is
the probability that it is yellow?
?
Lesson IdeasStatistics & ProbabilityA yellow
and a red monkey get
married and have a
baby monkey.
Punnett Squares
Lesson IdeasStatistics & ProbabilityWhat is the
probability that the
baby is red.
Punnett Squares
Y r
r YY rr
r Yr rr
Lesson IdeasFunctions
Lesson IdeasFunctions
Functions describe situations where
one quantity determines another.
Lesson IdeasFunctions
Plot the curve that shows the area of shapes with the
same circumference as the number of sides of the shape
increases.
Lesson IdeasFunctions
Area
# side
s
Lesson IdeasModeling
Lesson IdeasModeling
Lesson IdeasModeling
?
Lesson IdeasModeling
Choosing and using appropriate
mathematics and statistics to analyze empirical situations
