The sequence of exercises through which the child is introduced to the group operations with the Golden Beads Math operations include addition, multiplication, subtraction, and division. All these operations require full understanding of quantities on a concrete level before moving to the abstract level of performing these operations mentally. So the first exercise introduced to the child to prepare him for these operations; is the “Number Rods”. The ten number rods are graduated in length from 4 inches length for the shortest one, to 40 inches length for the longest one. The different four inch sections are alternately colored red and blue and can be counted on each rod. So , each rod consists of distinct countable units, united together to represent a number. This overcomes the difficulty of adding one unit after another in a sum total. “The fact that a group is enlarged through the addition of a unit, and that this increasing must be considered; constitutes the chief obstacle for the children of three and a half to four, in learning how to count.” Maria Montessori, The Discovery of the Child, page 263 Several activities are done with the number rods. All of them are activities of moving and joining. One time the child builds them next to each other starting with the shortest and ending with the longest, and another time, he builds them on top of each other. All this joining and moving is an introduction to arithmetic. Then the “Sand Paper Numerals” are introduced to the child, to teach him their names and how to write them. Later on the child learns to match the card to the corresponding rod, which “forms the basis for a lengthy task which a child can continue by himself. The sums of the rods can be written so that they correspond to the numbers.” Maria Montessori, The Discovery of the Child, page 265 Two other objects are used to help the child begin arithmetic; The “Spindle Box”, and “The Cards and Counters”. ”The Spindle Box” attains three main objectives. It gives a child a concept of numerical groups , and at the same time; it fixes before his eyes the succession of numerals, and finally he is introduced to the “Zero”. In this activity; the child reads a number on the wall of a compartment, and then he groups the corresponding number of spindles in his hand, then he places them in the compartment. “Cards and Counters” accomplish another two objectives. It shows that the child has understood the order of the numbers, and that he recognizes the figures representing the numbers. Moreover; it is by this activity that the child realizes the difference between odd and even numbers. By then; the foundation for counting and arithmetical operations is laid.
Till now, the child is working with numbers not more than ten. “Number Games” are then played to make sure that the child deeply understands the quantities and the written symbols of numbers from 1 to 10, and to make sure that he really understands the concept of “Zero”. When this understanding is shown; the child is introduced to the “Decimal System”. First the child is taught “The Names of The Power of Ten” through the bead material. By the power of ten, we mean the unit, ten, hundred and thousand. For this lesson; the teacher uses one single bead to represent the “Unit”, ten beads wired together in the form of a bar to represent the “ Ten”, ten of the ten bars wired beside each other forming a square of hundred beads to represent the “Hundred”, and finally, ten hundreds wired on top of each others forming a cube of thousand beads to represent the “Thousand”. The teacher introduces these names with a three period name lesson, and to make him understand this on a more concrete level; “The Counting Through” activity is introduced. He would see how repeating a digit 10 times makes it become another digit. He will see hoe ten units make a ten, ten tens make a hundred, and ten hundreds make a thousand. This is...
...SEQUENCE
* In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, a sequence can be defined...
...Anatolia College 
Mathematics HL investigation

The Fibonacci sequence 
Christos Vassos

Introduction
In this investigation we are going to examine the Fibonacci sequence and investigate some of its aspects by forming conjectures and trying to prove them. Finally, we are going to reach a conclusion about the conjectures we have previously established.
Segment 1: The Fibonacci sequence
The Fibonacci sequence...
...Sequence of Operations (Gas Furnace)
Natural Draft Furnace
24 volts is always present to the thermostat R terminal.
1. When the thermostat closes its switch to call for heat, 24 volts is sent out of the thermostat on the W terminal.
2. This 24 volts goes back into the furnace, then typically through 1 or 2 safety devices to the gas valve.
3. If the standing pilot is lit. The gas valve opens, and the gas to the burners is then ignited...
...Exercise 1 page 224
a. Using Maximax, the worst payoffs for the alternatives are as follws:
Do nothing: $60 thousands
Expand: $80 thousands
Subcontract: $70 thousands
Hence, since $80 thousands is the best, choose to expand the firms using the maximax strategy
b. Using Maximin
Do nothing: $50 thousands
Expand: $20 thousands
Subcontract: $40 thousands
Hence, since $50 thousands is the best, choose to do nothing using the maximin strategy
c. Using Laplace...
...Through the Eyes of a Child
Why are some people judgmental towards others? Whether we judge on race, gender, or something as simple as age, judging not only causes anguish but can leave emotional scars people never recover from. Racism is one of the most common of judgmental forms still seen today in our society. Although today we do not find racism as prominent as back in the 1920s and 1930s. When reading the story “The Angel of the Candy Counter” written by...
...Exercise on group behavior
1. Based on knowledge from your company group relate to and explain the 5stage group development model and the punctuated equilibrium model (both very important for exam.
Group analysis based on 5stage model:
* Forming. Firs task was to find out people with the same level of motivation, expectations and similar point of view through the vision of business idea. After...
...Which social groups are marginalized, excluded or silenced within the text?
Social groups are significant in Golding’s novel “Lord of the Flies”, as they exhibit and accompany the development of a group of British schoolboys, which socially deteriorates into savagery, splitting into certain social subgroups.
In a context shaped by the world wars and the resulting communal imbalance, perhaps creating or...
...
A Child development through parenting
Parenting or child rearing is a process of support a child physical, mental, emotional, social and intellectual development through childhood to adulthood. Every person in the world neither gets parenting nor gives parenting to others. Parenting is not something that you only can get from your parents. People can get parenting from their siblings, teachers...
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