miles of tiles the exhibit miles of tiles the exhibit

http://www.youtube.com/watch?v=htrYdrGbkSQ

http://www.youtube.com/watch?v=htrYdrGbkSQ

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 numbers

Fraction Fracture


Understanding of


Fracture - break into pieces


Understanding of


Fractions - break into pieces using

numbers


Understanding of


4 = 1 1 1 1


Understanding of


4 = 1 1 1 1¼ means you have one of the four 1s


Understanding of


You have one of

the four squares


Understanding of


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


addition1 1

11

Lesson IdeasGrade 3


addition2

2

Lesson IdeasGrade 3


addition2

2 2 x 2 = 4

Lesson IdeasGrade 3


addition2 x 2 = 4

Area of this square is 4

Lesson IdeasGrade 4

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


fractions¼ spoken as “one quarter”

Lesson IdeasGrade 4


fractionsWith money ¼ of

a dollar is one quarte

r

Lesson IdeasGrade 4


fractionsOne quarter

is twenty-

five cents

25¢

Lesson IdeasGrade 4


fractionsTwenty-five

cents is written

as

25¢

.25

Lesson IdeasGrade 4


fractions.25

.25.2

5.25

$1

Lesson IdeasGrade 5

Understanding concepts of volume

Lesson IdeasGrade 5


Start with

simple shapes

Lesson IdeasGrade 5


Stack 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 volumeCompare

volumes to

illustrate the bee’s

use of hexagon

s

Lesson IdeasGrade 6

Solve real-world problems involving

area

Lesson IdeasGrade 6


areaYou are installing new tiling on

your bathroom floor

Lesson IdeasGrade 6


area

Lesson IdeasGrade 6


areaNo bathroom is an exact multiple of

the size of tile chosen

Lesson IdeasGrade 6


areaLet’s say the bathroom is 9’ x 9’and each tile is 5” x

5”

Lesson IdeasGrade 6



5”How many tiles are

needed?

Lesson IdeasGrade 6



5”Remember to convert feet to

inches!

Lesson IdeasGrade 6


areaRemember to convert feet to

inches!

Lesson IdeasGrade 6


areaRemember to convert feet to

inches!

NASA's Climate Orbiter lostSeptember 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



5”Remember to convert feet to

inches!

Lesson IdeasGrade 6



5”How many tiles must be cut?

Lesson IdeasGrade 6


areaWhat if the tiles are a different shape?

Lesson IdeasGrade 6


area

Lesson IdeasGrade 7

Investigate chance processes

Lesson IdeasGrade 7


4 different colored

monkeys live on

monkey island.

Lesson IdeasGrade 7


One of them

walks up to you

begging for a

banana.

Lesson IdeasGrade 7


What 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


6 different colored

monkeys live on

monkey island…

Lesson IdeasGrade 8


volume

Lesson IdeasGrade 8


volumeCalculate

the volume of

a milk carton

Lesson IdeasGrade 8


volumeBreak it

down into basic

shapes that are easy to

calculate

Lesson IdeasGrade 8

Understand and apply Pythagorean

Theorem

Area = ½ b x h

2 2

2

Lesson IdeasGrade 8

A = ½ b x h

2 2

2

Lesson IdeasGrade 8

A = ½ b x h

2 2

1 1

Lesson IdeasGrade 8

A = ½ b x h

2

1

h

Lesson IdeasGrade 8

A = ½ b x h

2

1

h

Determin

e the value of “h”

Lesson IdeasGrade 8

a2 + b2 = c2

2

1

h

Determin


Lesson IdeasGrade 8

12 + h2 = 22

2

1

h

Determin


Lesson IdeasGrade 8

1 + h2 = 4

2

1

h

Determin


Lesson IdeasGrade 8

h2 = 3

2

1

h

Determin


Lesson IdeasGrade 8

h = 3

2

1

h

Determin


Lesson IdeasGrade 8

h ≈ 1.73

2

1

h ≈ 1.73

Determin


Lesson IdeasGrade 8

A = ½ b x h

1 1

h

Now we can

calculate the area

of one equilat

eral triangl

e

Lesson IdeasGrade 8

A = 1 x 1.73

1 1

h

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


QuantityIn real world problems, the answers are usually not

numbers but quantities:

numbers with units, which

involves measurement.


QuantityMeasure the actual shapes at

the exhibit. Printed paper rulers can be provided to students.


Quantity

Measure 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 Area

Triangle = ½ b x h

Lesson IdeasAlgebra

Formulas for Area

Circle = ∏ r2

Lesson IdeasAlgebra

Pythagorean Theorema2 + b2 = c2

Lesson IdeasAlgebra

Volume FormulasVolume =

Area x height

Lesson IdeasStatistics & Probability


What is the

probability that it is yellow?

?


A yellow and a red

monkey get married

and have a baby

monkey.

Punnett Squares


What is the probability

that the baby is red.

Punnett Squares

Y r

r YY rr

r Yr rr

Lesson IdeasFunctions


Functions describe situations where

one quantity determines another.


Plot the curve that shows the area of shapes with the

same circumference as the number of sides of the shape

increases.


Area

# side

s

Lesson IdeasModeling


?


Choosing and using appropriate

mathematics and statistics to analyze empirical situations

miles of tiles the exhibit miles of tiles the exhibit

Documents

quarter lesson ideasgrade

pieces lesson ideasgrade

numbers lesson ideasgrade

board lesson ideasgrade

squares lesson ideasgrade

understanding offractions

area relationship

decimal notation