Mathematical Investigation
In this report we were asked a number of questions about the solving
of magic squares. The final goal was to fill a magic square in
correctly. The information I was given was about the history of magic
squares and information on how they work. I did not need any extra
information.
Investigation:
What I had to do for this investigation was to fill in a magic square
correctly. I chose to do this by answering the questions given to me
and using my answers to those questions to fill in the magic square. I
did this the way I chose to do it.
Results:
1. The central cell is the only one that touches all the other cells.
Therefore, it is crucial to find the number to place in this cell.
Could you choose any of the numbers to place in this cell? Ask
yourself, could the number 7 be placed in this cell, or the number 1?
Thin about the reasons for your answers and explain them thoroughly.
You can not put just any number in the central cell of the magic
square because the number has number has to be able to be added to 9
without a repeated number and it has to be added to all other numbers
without crossing the “15” limit. The number 7 could not be placed in
the middle cell because you can only get 3 equations that equal 15
using 7. The problem here is that you need at least 4 solutions: 2
diagonally, 1 horizontally and 1 vertically. The same counts for all
other numbers except for 5. Therefore, the number that should be in
the center cell is 5.
2. There may possibly be restricted on where some of the other umbers
can be placed. The number 9 is the largest to be placed. Could 9 be
placed corner cell? If not, where could it be placed? Think about it
and explain your answer as clear as possible.
The number 9 could not be placed in a corner cell because 9+8= 17 and
On the second day of class, the Professor Judit Kerekes developed a short chart of the Xmania system and briefly explained how students would experience a number problem. Professor Kerekes invented letters to name the quantities such as “A” for one box, “B” for two boxes. “C” is for three boxes, “D” is for four boxes and “E” is for five boxes. This chart confused me because I wasn’t too familiar with this system. One thing that generated a lot of excitement for me was when she used huge foam blocks shaped as dice. A student threw two blocks across the room and identified the symbol “0”, “A”, “B”, “C”, “D”, and “E.” To everyone’s amazement, we had fun practicing the Xmania system and learned as each table took turns trying to work out problems.
The task consists of generating a program which asks the user 10 mathematical questions. Using in each case any two numbers and addition, subtraction or multiplication. The finale score out of 10 should also be outputted at the end.
From that fundamental step, many cultures have built their own number systems, usually as a written language with similar conventions. The Babylonians, the Mayans, and the people of India, for example, indented essentially the same way of writing large numbers as a sequence of digits that we use, although they lived far apart in space and time (155).
x 3, 4 x 4 x 4, 5 x 5 x 5, 6 x 6 x 6, 7 x 7 x 7, 8 x 8 x 8, 9 x 9 x 9)
numbers 1 to 9 and 0, and the words yes and no. A smaller board, shaped like a
People use numbers whenever they do math. Yet, do they know that each number in the number system has its own unique trait? Numbers such as 4 and 9 are considered square numbers because 2 times 2 is 4, and 3 times 3 is 9. There also prime numbers. Prime numbers are numbers that have exactly two divisors. The number one is not included because it only has one divisor, itself. The smallest prime number is two, then three, then five, and so on. This list goes on forever and the largest known primes are called Mersenne primes. A Mersenne prime is written in the form of 2p-1. So far, the largest known Mersenne prime is 225,964,951-1, which is the 42nd Mersenne prime. This prime number has 7,816,230 digits!
Sophocles wrote the classic tragedy Antigone in 496-406 BC this play dramatizes the conflict between self-morality versus human law by representing each conflict by two characters; Antigone and Creon. In this play Antigone decides to bury her brother Polyneices regardless of the king Creon’s decree. After Antigone is caught Creon decides that the punishment of death will be enforced. This sets of a chain reaction of conflicts between Antigone and Creon, both filled with pride and will. The chorus states that the gods vigorously punish the proud, yet punishment brings wisdom. ( )
The research our experiment was founded on was that carried out by Taylor and Faust (1952). They carried out an experiment on 105 student’s, which was designed in the method of the game ‘twenty questions’. The students were split into teams of one member, two members and four members. They were then told that the experimenter would keep an object in mind whether it is animal vegetable or mineral was also stated, and they were then allowed 20 questions and guesses to reveal the identity of the object. In there experiment they found that the group of two members performed better than the group of four members in terms of how many guesses and questions it took them and how long it took them to deduce the identity of the object. However Taylor and Faust found that the efficiency did not differ in any significant way.
I am going to begin by investigating a square with a side length of 10
Text Box: Using the same method: (3 x 7) – (1 x 9) 21 - 9 = 12 Answer = 12
Countless time teachers encounter students that struggle with mathematical concepts trough elementary grades. Often, the struggle stems from the inability to comprehend the mathematical concept of place value. “Understanding our place value system is an essential foundation for all computations with whole numbers” (Burns, 2010, p. 20). Students that recognize the composition of the numbers have more flexibility in mathematical computation. “Not only does the base-ten system allow us to express arbitrarily large numbers and arbitrarily small numbers, but it also enables us to quickly compare numbers and assess the ballpark size of a number” (Beckmann, 2014a, p. 1). Addressing student misconceptions should be part of every lesson. If a student perpetuates place value misconceptions they will not be able to fully recognize and explain other mathematical ideas. In this paper, I will analyze some misconceptions relating place value and suggest some strategies to help students understand the concept of place value.
entered one at a time and their volume was computed in order to add to
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
A decimal integer constant is made up of digits 0 to 9 in any combination. The first digit should not be zero.
To the future researchers, using this study it would be helpful for them to formulate new actions and information and make it as one of their sources with regard to solving a word problem.