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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