thou shall love math ii - seminar presentation
DESCRIPTION
- a seminar presentation in Mathematical Investigation and ModelingTRANSCRIPT
PP
uzzling
atterns
PROBLEM SOVING
TOXIC
it is a higher order cognitive process that requires the modulation and control of more routine or fundamental skills
PROBLEM SOLVING
a process that provides the content in which concepts and skills can be learned.
Goals when teaching Problem Solving
Improve our pupils’ willingness to try problems and improve their perseverance when solving problems.
Make pupils aware of the problem solving strategies.
Make pupils aware that many problems can be solved in more than one way.
Improve pupils’ abilities to select appropriate solution strategies.
Improve pupils’ abilities to get more correct answers to problem.
Here are some of the Problem
Solving Strategies!
Making a Picture
Working Backward
Intelligent Guessing and Testing
Finding a Pattern
Considering Extremes
Organizing Data
Using a Computer or Calculator
Using Logical Reasoning
Solving a simpler Analogous Problem
Accounting for all Possibilities
Adopting a Different Point of View
Pattern
Blocks
Pattern
Blocks
The purpose of this activity is to recognize, describe, construct and extend geometric patterns and provide visual support for extending number sequences.
What are Pattern Blocks?
PATTERN BLOCKSPattern Blocks are type
of mathematical manipulative developed
in the sixties by the Elementary Science
Studies.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling. They allow students to see how shapes
can be decomposed into other shapes and introduce them to tiling.
They help students to see visual support on extending number sequences.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
ANIMALS
FLOWERS
Boats & Ships
Rockets & Planes
Cars
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
Find a pattern in the following sequence of figures and use your tiles to construct and sketch the fifth and sixth figures.
1
2
34
1
2
34
5th & 6th Figure
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
Fifth Figure
9 tiles
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
Sixth Figure
11 tiles
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
Figure 1Figure 2
Figure 6Figure 5
Figure 4Figure 3
Figure Number of Tiles123456
135
7911
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
tn = t1 + (n-1) dWhere:
tn = last term (nth term)
t1 = first number in the sequence
n = number of term
d = common difference
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.1, 3, 5, 7, 9, 11
Given:
t1 = 1
d = 2
Find the general formula for the nth term:
tn = 2n - 1
Formula for the nth term:
Figure Number of Tiles123456
135
7911
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.•Number of tiles
for the 20th figure39
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.•Number of tiles
for the 100th figure199
Tower of
Hanoi
Tower of
Hanoi
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
TOWER OF HANOI
The Tower of Hanoi, also called Tower of Brahma, is a mathematical game or puzzle.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
It consists of three rods and a number of disks of different sizes which can slide onto any rod. The disks should be in ascending order of size on one rod, the smallest at the top.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
I’m Edouard Lucas and I invented the Tower of Hanoi in
1883.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
The objective of the puzzle is to move the entire stack
to another rod.
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
Rules of the Game:
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
No. of Disks No. of Moves12345678
137
1531
63??
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
1, 3, 7, 15, 31, 63 n = number of terms
21 = 222 = 423 = 824 = 1625 = 3226 = 64
2n Formula
- 1 = 1 - 1 = 3- 1 = 7- 1 = 15- 1 = 31- 1 = 63
2n Formula- 1
2n - 1
Formula
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.
No. of Disks No. of Moves1 12 33 74 155 316 6378
127255
They allow students to see how shapes can be decomposed into other shapes and introduce them to tiling.T.H.GENIU
S
T.H.GENIU
S