Importance Of Oral And Written Names For Numbers

Importance Of Oral And Written Names For Numbers
Oral and Written Names for Numbers: This section is focusing on connecting oral and written names
for numbers with base–ten concepts by using groups of tens or hundreds for counting. It is essential
to remember that saying and writing numbers are conventions instead of concepts, and students are
learning this by being told instead problem–based activities. It is especially important to remember
that these conventions or patterns may be different for English Langauage Learners.
Two–Digit Number Names: For two–digit numbers, it is best to start with base ten materials and
language, because when they go to writing it will be easier to transfer, otherwise they may write 52
as 502 because of how it said. It is much easier to go from base ten language to the standard
language.
Three–Digit Number Names: As the numbers increase in size, there tends to be an increase in
mistakes, but to avoid mistakes, it is essential that you vary use of base–ten language and standard
language. It is also helpful to only change one place value at a time. Another way to help students is
to show them counterexamples and then have them correct the example. Numbers with no tens
usually leads to major confusion, and this is where base–ten language will help, but avoid calling
zero a placeholder because it does contain value.
Written Symbols: When starting to teach the students on how to write the names out, there are
Place–Value mats and Place–Value Cards. These two methods are more effective when
... Get more on HelpWriting.net ...

Identifying Error Patterns Of Computation
Identifying Error Patterns in Computation
According to Ashlock, not only do students need to understand computations of arithmetic, but also
need to have computational fluency, in other words, conceptual understanding. As stated in
Principles and Standards for School Mathematics: Knowing basic number combinations – the
single–digit addition and multiplication pairs and their counterparts for subtraction and division – is
essential. Equally essential is computational fluency – having and using efficient and accurate
methods for computing.
The following examples demonstrate fictitious students and the common error patterns they exhibit
along with the suggested instruction on how to teach the students to correct the errors. In the first ...
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To verify that Albert multiplied correctly, have him use a calculator to compute each partial product,
making sure the correct values are multiplied; for 52 × 312, multiply 50 × 312 then 2 × 312. If
needed, provide instruction to Albert to ensure he knows how to operate the calculator.
To further emphasize multiplication for one place value at a time, teacher Albert to apply a paper
mask. The composition of the mask consists of a piece of with a hole in the middle allowing the
student to view the multiplier as multiplying the entire multiplicand. Once the completion of the
multiplication of the units (ones) digits, move the mask to the left to allow the visibly of only the
tens digit. This process continues until each place value has been multiplied to the multiplicand.
Continue to remind Albert to complete the multiplication problem with each digit and placement of
each digit in the appropriate place value.
The second error pattern shows Rosanne making errors starting with the incorrect place value in a
long division problem. Although, Rosanne demonstrates understanding her multiplication facts, her
errors show a misconception of where to start dividing the divisor into the dividend as shown in the
examples below.
Rosanna
By estimating the quotient before computing it, allows Rosanna to determine if her answer is
reasonable. Once Rosanna estimates and computes the answer for a

Identify His Strengths and Error Pattern
Identify his strengths and error pattern. Describe why you think that way. He is excellent in his
addition skills. He understands how to add numbers together, but he is just confused about this set
up of addition. His error pattern is that if he has a two digit number in the first column he will put
both numbers in the answer instead of the number in the ones place. For example, in the first
problem he adds 6 + 7 correctly (13) but he puts both the ones and the tens in the answer. Then he
brings down the 1 instead of what it should have been 1 + 1 (2) to make the answer 23. He follows
this same pattern in problems 4, 5, 7, and 8 as well. In the third problem he adds the tens digits first
3 + 8 (11) and puts one 1 in the answer and the other 1 over the ones place. Then adds 5 + 1 + 1 (7)
instead of adding 5 + 1 (6) and 3 + 8 (11) making the answer 116. He follows this pattern with
number six too.
2)How would you respond to John? Design a mathematics activity to use with this child in
addressing his errors. In your intervention, use concrete materials such as base–ten blocks including
a place value chart. Briefly describe what questions you would use in accordance with the activity. I
would tell him that he is on the right track with his addition skills! There is a common error that he
keeps making, but we can work on it and easily fix it! I would provide a lot of practice for him to
correct this error. I believe in one problem he added from the tens place before

Place Value And Decision-Making Model
Introduction This report is about place value and how it should be approached based on the
interview style diagnostic observations of year six student 'Ariel' and her knowledge and
understanding of place value, including her ability to correctly use it with mathematical operations.
The aim was to diagnose areas that required learning and offered improvement opportunities. The
aim was to then support this with the development of a teaching plan. This was achieved by
instructional activities through a series of tutoring sessions that worked towards refining her areas of
knowledge and improvement, and then extend on those ideas. After completing the diagnostic test,
the areas Ariel struggled most with were multiplicative thinking, partitioning, ... Show more content
on Helpwriting.net ...
They are selected to support and enhance the lesson objective (Reys et al., 2012, p. 43). There are
ungrouped materials that can be formed in to groups, for example, single beads or straws or
anything that can be bundled into groups of say,10, or another amount. There are also pre–grouped
materials that are already bundled to represent an amount. The use of 'manipulative' materials can be
useful visual aids and assist children grasp concepts with a hands on approach, making it easier for a
teacher to observe what a child is doing rather than thinking (Marshall & Swan,

Evaluation of Various Numerical Methods for Option Pricing...
In finance, a derivative is a financial instrument whose value is derived from one or more
underlying assets. An option is a contract which gives the owner the right, but not the obligation, to
buy or sell the asset at a specified strike price at the specified date. The derivative itself is just a
contract between two or more parties. Its value is determined by fluctuations in the value of the
underlying asset. This price is chosen so that the value of the contract to both sides is zero at the
outset, which means that the price is fair, so neither party is taking advantage of the other. Hence,
numerical methods are needed for pricing options in cases where analytic solutions are either
unavailable or not easily computable. The subject of ... Show more content on Helpwriting.net ...
This method is widely used as it is able to handle a variety of conditions. Finite difference methods
were first applied to option pricing by Eduardo Schwartz in1977. In general, finite difference
methods are used to price options by approximating the differential equation that describes how the
option price moves over time by a set of difference equations. This method arises since the option
value can be modeled by partial differential equations, such as the Black–Scholes PDE. This
approach has the same level of complexity tree methods. The application of Monte Carlo method to
option pricing was by Phelim Boyle in 1977. In terms of theory, Monte Carlo valuation relies on risk
neutral valuation. The technique is to generate several thousand possible random price paths for the
underlying asset and via simulation, and to calculate the average payoff of each path. This approach
is particularly useful in the valuation of options with complicated features, which would be difficult
to value through straightforward Black–Scholes style or tree model. ( reference [3] Valuation of
Options)
Each of these methods has its own advantages and disadvantages. The comparison of accuracy and
consistence are presented and suitable method for each situation is discussed.
Then the report briefly goes through some exotic options and implements the numerical solutions
with binomial tree method. These options, includes American option which can be exercised any
time before the

Math
IPPR #: EDUC 530 Lesson Plan: Place Value, Integer, Computation
|Teacher Candidate: |Course: EDUC 530 |
|LESSON PREPARATION [before the lesson] |
|Topic: Place Value, Integer, Computation |Concept: Regrouping during multiplication of two–digit
numbers without |
| |decimals |
|Subject: Mathematics ... Show more content on Helpwriting.net ...
|
|Three ESL students– Reduce wordings on number labels and instead use digits to encourage ease of
understanding |
|Three students with ADD– Give students with attention disorder fewer problems to solve |
|One student with visual difficulty– Incorporation of visual enhancements such as pictures |
|Materials/Equipment: |
|Paper and pencils for students |
|Math handbook |
|Chart |
|Flash Cards |
|Computer with internet

How To Write A Class Observation Paper
2–28–17: Today I observed her during her recess. I usually don't go outside with them but today I
went just to observe her. She hangs out with 3 of the other girls from my class. She seems to be
outgoing and a bit of a ruff player. They started to play tag and she was just like the rest of the girls
running and screaming and playing. She seems to get along with everybody she seems to be friendly
and loves to play outside. When going back into the classroom she was walking in the back of the
line, which is rare for her. She was being a bit more loud this day then before. Watching her outside
and being more interactive with other students seems to bring her joyful side out.
3–7–17: Today I was working with her during silent reading. Every Tuesday ... Show more content
on Helpwriting.net ...
This was phase one for her error pattern. If you look at her answer she can do the correct expanded
form for the numbers that are given to her. For example on one question she had to expanded 205
she wrote 200 + 20+ 5, she couldn't read the number. Then when asked to write 500 + 5 in standard
form, she wrote 500 +5 and 200 +5. This was problem one to her error pattern she can't put them in
the correct form. She doesn't know her place values correctly for example for the question on here
she answered that 6 was not in the tens place in the number 472. Then she answer the correct answer
was 70.
Assessment sample 2: This assessment is a pre–assessment given to her that has to deal with
addition and subtraction with and without regrouping. This was were I got her problem from in the
two problems she actually tired to do for the first one she had the problem 78 + 21 she got to the
expanded form correctly some how. The numbers came out incorrect, and then she was subtracting
when she should have to be adding. For the second problem she was doing the same thing and for
some odd reason when she was trying to borrow from another number she would put

The Importance Of Student Achievement
Student achievement is a multi–faceted concept and does not look the same for every student. At the
core of student achievement are comprehension and connection. Students must be able to understand
and contextualize instructional material to foster comprehension. Equal to comprehension is the
ability of students to connect with the material and make relevant associations between concepts and
skills for application. The intention of instruction based on prioritizing and unwrapping standards
helps educators to define the instructional pathway that best supports the standard and facilitates
student learning. Learning pathways align essential objectives, activities and resources to outline
progress within a standard. Learning pathways detail the skills students need to acquire for
demonstrating comprehension and mastery, which constitute achievement. Additionally, learning
pathways present an interpretive value for gauging student understanding and performance.
Gutierrez explains that learning pathways "must have strategic opportunities to build in prior
knowledge, reflection, and application" (Gutierrez, 2017, para 8). Gutierrez further positions that
"learning pathways are intended to be flexible, multidisciplinary, and increasingly personalized"
(Gutierrez, 2017, para 8). Without properly considering and using learning pathways, students are
not provided opportunities to connect content with comprehension and skill. Effective learning
pathways scaffold on what students

Analysis Of Ryan 's ' The Flies '
Similar to a circle, Ryan 's face is rounded just enough for his Aunt to love it. Despite a chubby face
and fingers, his body is small. Fragile. In the six years of his life he has come to enjoy learning new
concepts. He understands that to draw a house he must start with a square base. A roof is nothing
more than a triangle on top. Add two squares for Windows and a rectangle for a door and Ryan has
drawn a squiggly lined house. Red. Yellow. Green. One plus two equals three. Ryan understands
these concepts, because they 're easy to control. Understanding becomes hard when the shapes are
replaced by feelings, and the colors and numbers are replaced by people. Why is it hard to be
understanding towards one another? How come it is difficult to put myself into someone else 's
shoes and say they had every right to mock me. Could it be because I am too simpleminded to
understand? Or, is it because I am too unwilling to let myself be carried away by someone else 's
life. If they refuse to accept my world, then why should I try to understand theirs? It 's that kind of
thinking that keeps me from truly enjoying life. When I fail to see the rough aspects in others lives,
it not only makes them, but also me, feel frustrated as well. I know how it feels to be unheard. I
know how it feels to have someone watch me talk, but ignore my words; like I wasn 't there to begin
with. Who am I if my peers are willing to treat my voice as if it was nothing more than a gust of air?
I crash

Why I Learned Mathematics For Teaching Mathematics
Introduction This report follows the progress of an eight year old, grade three child's progress,
through a mathematical diagnostic assessment pertaining specifically to number placement, and
proceeds through the relevant stages of mathematical learning, mapping the strategic points
involved in teaching mathematics whilst following the progress of the child, and the areas with
which they required improvement. The partitioned focus, of this report is on specific areas such as
the mechanics of learning numbers specifically, counting and the developmental appropriate
learning stages of a neurotypical child. Succeeding the initial factual proponent of the report (Part
A), is an account of the experience of tutoring (Part B) the grade three child, whom shall be known
as "Boris" (a neighbours child). A permission slip was attained a copy of which may be found within
the appendices. This portion of the report will explain any errors Boris made, why Boris made those
errors, and what was done to rectify them. Pictorial evidence of the tutoring sessions may be found
within the body of the Part B text. Part A Rationale In order to teach well, there must be an
observance of the student, and how that student may best learn. The commonsense within the points,
which make up the components of the "professional judgement circle (Department of Education,
(DoEWA) 2013. p. 2.)" describe well the necessary stages for the development of student learning,
as opposed to teacher teaching and a

Length and Savings Account Essay examples
1. If 5 times the value of a number is increased by 3, the result is 28. What is the number?
5x+3=28
5x=25 x=5 The answer is 5
2. If 4 times the reciprocal of a number is 3 more than 5/2 times the reciprocal of that number, find
the number.
4*(1/x)=(5/2)*(1/x)+3
4/x=(5/2x)+3
(8/2x)=(5/2x)+3
(8/2x)–(5/2x)=3
(3/2x)=3
x=1/2
The answer would be x=1/2
3. John had $30,000 to invest. He invested part of this money in bonds paying 12% annual simple
interest and the rest of the money in a savings account giving 4% annual interest. At the end of the
year, he received $2,400 as extra income. How much money did John place in each investment?
.4x+.12(30000–x)=2400
.04x+.12(30000)–.12x=2400
.04x+3600–.12x=2400
.12x–.04x+3600=2400 ... Show more content on Helpwriting.net ...
The length of a rectangular field is 50 feet less than its width. If the perimeter of the field is 840 feet,
find the length of the field
2x+2y=840
2(y–50)+2y=840
2y–100+2y=840
4y=940 y=235 x=235–50 x=185 The length of the field would be 185Ft.
11. Alan participated in a car race in which he had to cover a distance of at least 50 kilometers. He
had fuel in his car for a maximum distance of 53 kilometers. If the distance is given by , where t is
the time in hours, find the minimum and maximum number of hours for which Alan can drive his
car. for at least 50 km s (t)=3t+47 s (t) =50
50=3t+47
3t=3 t=1 hour for a maximum of 53 km s(t)=53 53=3t+47
3t=6
t=2 hours
The minimum number of hours which Alan can drive is 1 hour. the maximum Alan can drive is

2hours.
12. in a 2–digit number, the number in the unit's place is 4 more than the number in the ten's place.
If the digits of the number are reversed, the new number is 6 more than thrice the original number.
Find the original number.
13.
x= units digit y=tens digit
10x+y=3(10y+x)+6
7x–29y=6
7(y+4)–29y=6
7y+28–29y=6
–22y=–22
y=1
Therefore x=5
Therefore the original number is

The Effect Of Chewing Gum On Cognitive Processing
Some reports have suggested that chewing gum might improve the performance in memory task,
although other studies have not confirmed this effect of chewing. Little is known about the brain
activity and the task performance while chewing gum. Near–infrared spectroscopy is a
spectroscopic method that uses the near infrared region of the electromagnetic spectrum(what does
this mean). Put in my own words, describe what it means.Near–infrared spectroscopy is a useful tool
for investigating brain function and can measure brain activity during bodily movements. Wadi et
al.'s purpose of the study was to "clarify the effects of chewing gum on cognitive processing during
and after chewing gum, using NIRS–based measurement of cerebral hemodynamic response." They
investigated the effect of chewing on the hemodynamic changes in this brain region, using NIRS
(Hoshi et al., 2000), and the performance of subjects in a short–term memory task involving serial
recall of random eight–digit numbers. The study asked for 30 healthy volunteers(is this enough to
make conclusive) with no history of neurological, psychiatric, temporomandibular joint disorders.
The volunteers were asked to recall random eight digit numbers. They sat in a dimly lit room in
front of a PC monitor and the a series of 8 digit numbers flashed on the screen for two seconds.
They were then told to type out the numbers and the PC proceeded to flash a new 8 digit number
when they had finished typing the previous number. The

Personal Narrative: My Life In Our Town By Thornton Wilder
In order for you to get to know me, I need to introduce you to someone else, or rather, something
else. Belleaire Circle. Belleaire is a brick street in downtown Orlando, one that could have been
plucked from Thornton Wilder's first act of "Our Town" and placed in 2015. These people have
impacted my life and each house represents a chapter of my story. This quaint street lined with
massive oaks, Belleaire Circle, is the street that built me. If you step outside my house and look
across the road, your eyes will be drawn to a beautiful two–story home. This house began shaping
me long before I moved here. This is my mother's childhood home and where my grandparents still
live today. Other than my parents, no one has impacted me more than they have. Whether it was
lively discussions about current events, earning money by pulling weeds in their yard, or all–family
Thanksgiving Day prayer times, my grandparents have been constants for me. Our relationship
would not be what it ... Show more content on Helpwriting.net ...
His house is an entertainment haven and home to many strategic board games and thrilling, late–
night movies. But my uncle also struggles with depression. It changes him from the fun–loving man
everyone enjoys being with to a guy that cannot get out of bed. This situation has helped me
understand that life is complicated and sometimes you simply press on, clinging to those who love
you. My best friend for most of my childhood lives on Belleaire as well. Since we were babies we
have vacationed together, attended the same school, played sports together. Practically inseparable.
But, high school has been different. Our paths rarely cross. It is weird how much high school can
alter relationships. At one corner of Belleaire is the home of my little league baseball coach. More
than any lessons about how to hold the bat or lay a bunt, he taught me to never make excuses. That
lesson will stay with me

Math Evistigetion Project
NINETUPLES CABUGCABUG NATIONAL HIGH SCHOOL President Roxas, Capiz S.Y. 2012–
2013 Researcher: Mizraim Tirol Ruan Cyrrene Vallejera Ma. Krizza Vergara Mrs. Roselyn Palorma
Adviser NINETUPLES I. Introduction : A mathematical investigation is defined as a collection of
worthwhile problem–solving tasks that has multi–dimensional content, is an open–minded,
permitting several acceptable solutions and is often embedded in a focus question. In addition, a
mathematical investigation involves a number of processes, which includes –––– researching
outside sources to gather information, collecting data through such means as surveying, observing or
measuring, collaborating with each team member taking specific jobs ... Show more content on
Helpwriting.net ...
III. Conjectures Conjecture #1 A number is a multiple of 9 if the sum of the digit is divisible by nine.
Testing/verifying conjecture #1 This Conjecture #1 is applicable to the big numbers that are higher
than 9. For example: 26,847= 2+6+8+4+7=27 27÷9=3 As given iin the example given, 26,847. We
added 2,6,8,4and 7 to get the sum, 27 which is a perfect number. Perfect numbers are numbers that
are equal to the sum of their proper factors. And we divided 27 by 9 so we get 3. Since the quotient
is a whole number it is a multiple of 9. We know that 27 is a multiple of 9 because when we count..
9 18 27 The sum of the given example "26,847" 36 So as shown in the figure above 27is a multiple
of 9. Now single digits are not applicaple to this conjecture for example 1,2,3,4,5,6,7 and 8. Since
they are single digit there is no other numbers or digits that can be added to them. Conjecture #2 The
tens digit increases by 1 while the ones digit decrease by 1. Testing/verifying conjecture #2
9,18,27,36,45,54,63,72,81,90,99 –For the tens digit it started from 0,1,2,3,4,5,6,7,8,9 and it is
increasing by 1. While in the ones place it is decreasing by 1 like 9,8,7,6,5,4,3,2,1. Conjecture#3
The reverseof the given digit but still have a multiple of 9. Testing/Verifying Conjecture#3 Example:
–317 x 9 = 2853 is a multiple of 9 which is equal to 317. When you reverse 2853 to 3582

Essay on You Never Thought You Had to Think to Count
You Never Thought You Had to Think to Count
It was after taking the 2nd MOEMS (Math Olympiad Elementary and Middle School) that I heard
this phrase from my school's math coach. We had sat and taken this test for 26 minutes, and then
afterwards ALWAYS talked about the problems. It came up when looking at a problem that went
somewhat like this: 'Each student in an art class is given 48 cubes that measure 1cm x 1cm x 1cm.
No students make the same design. What is the largest possible amount of students in that class?' I
was so close! I answered eight, when in fact, the answer was nine! Everything was right about my
strategy, thinking, and what I did, but I had missed one of the figures. That is what I am getting to;
that is what makes it so ... Show more content on Helpwriting.net ...
Did I miss one? Did I count one twice? All the things that go through your head... 'But, but, but, bu–'
one might think. There is algebra, and calculus, and... and... and...! Yes, but there is also counting in
other base systems. Ever heard of that? This is page 10 of this chapter! You can count in any base
system at all. Almost everyone uses base system ten. Hypothetically speaking, if you were to say 'I
want to count in base system three!' You tell you friend you are going to count to seven so they
know when to start the race. The number seven in base system three is twenty–one. So you would
count like this: '1, 2, 10, 11, 12, 20, 21!' When you are about to say three, the tens digit goes up one.
The only possible units digits when counting in base three are 0, 1, and 2. Here is how you figure it
out using a quick shortcut. Three goes into seven twice (2_) with one remainder, so it turns into 21.
It seems pretty simple, but in reality, it is not.
Counting began with the simple action of putting marks on a bone. "Numbers, and counting, began
about 4,000 BC in Sumeria one of the earliest civilizations." Also, algorithm I guess you could say;
started with chickens...? Well, not really. "Their method of counting began as a series of tokens. [...]
If a man had five chickens he was given five tokens. When he traded or killed one of his chickens,
one of his tokens was removed." It also seems like the people who

Justifications : Warm Up : Shared Book Essay
Justifications: Warm–up: Shared Book Description: Justification: The warm up for this lesson is
reading a book called, "Earth Day – hooray!" I chose to incorporate reading as a math warm–up
because it is an effective way to explore mathematical concepts, which are both engaging and
informative for the students. Integrating elements of literature into the lesson supports problem
solving and allows students to be fully immersed in the story, solving themselves the mathematical
issues that the characters fall into. Ministry of Education, 2016, endorses this idea stating that
applying visual elements of picture books aid in illustrating mathematical concepts, which are
difficult to teach with other resources, or challenging for students to comprehend. This particular
book introduces properties of place value, discussing the idea that 10 tens is equal to 1 one hundred,
which all groups need assisting with. Picture books contextualize mathematical ideas in meaningful
ways for students, while creating stories, which are relatable and spark curiosity and enthusiasm
(McGrath, 2014). McGrath further explains that learners will respond positively when stories are not
written with the intention of teaching children mathematics and will be more receptive to learning
the math message, if the thinking is second nature. As the cappuccinos are learning about place
value this warm–up is a great launching point for furthering exploring this concept and prompts
ideas for discussion and

Essay About My Math Teaching Experience
My math teaching experience went with students who are in third grade. In my group I had four
students, where was one ELL student. They were struggling in math as per their teacher, especially
in subtracting big numbers with zeroes. I had to reteach subtraction, three or two digit number, as
needed, from three digit number. And concentrate on subtractions from zeroes. Everything started
great, the kids were exiting, as of they are going out of the room. We sat down in the hall and it was
not comfortable.The kids were sitting near the wall, I was sitting in front of them in the middle of
the walking area. As of kids were sitting on the floor and me too, we were several times distracted
by other kids or adults, who was walking through the hall, it was always disturbing us. I started my
lesson with math solving problem and my students easy were able to figure out what operation that
needs to do. They all said subtraction. I said great. Then, I asked them to solve this problem
independently. Student 1, was just sitting, Student 2 used her fingers to count, Student 3 did very
fast, but not correctly and Student 4 just copied that incorrect answer. Then, I asked to share their
answers. Student 3 raised her hand and said, it was easy, we have 0–9, will be 9. Then 0–5, will be
5. Then 4–2 will be 2. So, the answer is 259. From this answer I understood, that my students
understand that ones must be under one, and tens under tens, hundred under hundred, but students

The Correlation Between Digit Ratio
The correlation between digit ratio (2D:4D) and the ability in dart throwing in both males and
females
Paria Rahmannejadi
500632950
Section 12
TA: Romeo
Dr. Koprivnikar
Submitted by: Feb.16.2015
BLG144
I understand that it is a violation of the Academic Code of Conduct to copy answers or text from
another student, either verbatim or in substance (i.e. to use another student's answers but rephrase in
my own words). I also understand that it is a violation of the Academic Code of Conduct to share
my answers or text with another student in a way that facilitates copying of my answers. Such
violations could result in a charge of Academic Misconduct. In submitting this assignment for a
grade, I am declaring that the work presented is my own original work, other than the data in the
figures that were provided by my instructor
Introduction
Genetics is the study of the biological process of heredity from parents to their offspring. Every
offspring receives a specific gene, which is located in the chromosomes, from their parents, and
these genes express specific trait.(Dr Ananya Mandal, MD ,2013). These traits may be either
physical and observable traits or behavioral traits. Furthermore, traits are subdivided in to two sets
of groups, Autosomal and sex linked traits. Autosomal traits are known as the traits that are not
dependable of sex of the individual and are same in both females and males however; sexed linked
traits are ones that are directly

Informative Statement Of Gatorade
Message: When you drink the sports drink called Gatorade, you will obtain the energy to perform
exceptionally well in athletic sports, without sacrificing any good nutrition since the beverage is low
calories.
Audience: Any athlete who is looking for a form of hydration before, during, or after their
workout/game.
Conditional Form: If you drink Gatorade, then you will have the energy and stamina to succeed in
any fitness activity in a low amount of calories.
Converse: If you have the energy and stamina to succeed in any fitness activity while taking in a low
amount of calories, then you drink Gatorade.
Inverse: If you don't drink Gatorade, then you will not have the energy and stamina to succeed in
any fitness activity with a low amount of calories.
Contrapositive: If you don't have the energy and stamina to succeed in any fitness activity while
intaking a low amount of calories, then you don't drink Gatorade.
Conditional: False, Gatorade will give you enough electrolytes to boost your performance, but not to
the point where it can give a whole new level of skill. Gatorade is more of just a slightly better
"fuel" to the human body, not exactly an enhancer like it advertises. Other sports drinks can contain
little to no calories, as well.
Converse: False, you can simply be a fit person or have great skill at a certain sport to possess the
conditions necessary to find achievement in any type of exercise, with other foods or drinks fueling
your energy.
Inverse: False, there are countless other forms of hydration, most commonly water, that can provide
energy to the human body while only having few calories. Multiple professional athletes today don't
drink Gatorade.
Contrapositive: False, although Gatorade does provide somewhat better hydration than water, but
that's not what this advertisements states. People who do not have the ability to train or compete
well in certain athletics, it could possibly be due to just having general health problems or finding

difficulty in executing the movements necessary to perform sufficiently in that activity. Taking in
less calories from Gatorade doesn't really affect this process, either.
Gatorade's message in this advertisement and many of their others I feel are

Math Observation
In the beginning of my observations the students in the classroom had been practicing their addition
and subtraction in a one digit numbers. However, as the year went on my cooperating teacher started
to get her students to be solving two–digit addition and subtractions problems. Before she started
with two–digit she wanted to be certain that her students felt confident along with concrete
knowledge and examples in their one digit equations because if not, they would fall apart for two
digit equations. My teacher had opened with two–digit addition, by developing knowledge on base
ten blocks for approximately two weeks, then progressed her students to the standard algorithm. My
classroom is set up for their numeracy portion of the class that ... Show more content on
Helpwriting.net ...
My student at the beginning of two–digit addition struggled with being organized in his base ten
block drawings and would get the answer wrong because he would circle 11 ones instead of 10.
When he got the opportunity to work with the actual base ten blocks he had a strong concept of
regrouping. Before the lesson my cooperating teacher taught them how to do the standard algorithm,
which my case study student took to excellent. During the process of the standard algorithm I asked
him to walk me through what he was doing and the process. He explained that he carried the one
over because it was making a new ten and then counted twenty plus thirty plus ten instead of 1 plus
two plus three, which I felt like the was understanding the place value. I thought during the lesson if
my student was advancing ways to challenge him on this assignment would be to have him add
three two digit numbers or have him add one two digit and one three digit number. Then if I felt like
my student was starting to struggle I could have his partner help him solve the process, bring out the
base ten blocks, or have him just add one two digit and one digit numbers until he got the concept

Using Adaptive Response Surface Regression
3 Methodology
The developed optimisation routine makes use of adaptive response surface regression to use a
limited initial amount of FE models to feed an optimisation routine which is specifically designed
for general thermal problems where parameters linked to the general heat equation can be optimised
or estimated using experimental input data. The algorithm uses a pan and zoom function to move
through the design space and delivers faster predictions with fewer iterations than standard updating
routines [35, 41].
3.1 Adaptive response surface method
The adaptive response surface optimisation routine is used to optimise numerical models with a lot
of data points and the time reducing by the algorithm increases as the number of parameters rises
[40]. The routine is designed to handle multiple–output time series data [35]. The optimisation
procedure can be divided into following steps:
1. Starting reference simulation points are ran and a correct object function is built of the difference
between the FE model and the target value (experiment or validation model).
2. The FE model is replaced by a meta–model of response surfaces to decrease the optimisation time
but remains an accurate approximation.
3. The optimisation routine is run on a specific object function. It is possible to use multiple
objective functions or build an objective function related to multiple outputs.
4. The estimated parameter values are used as input parameters for a new FE model that corrects the

Thinking, Fractions And Decimals
Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires
teachers to have a true understanding of the concepts and best ways to develop students
understanding. It is also vital that teachers understand the importance of conceptual understanding
and the success this often provides for many students opposed to just being taught the procedures
(Reys et al., ch. 12.1). It will be further looked at the important factors to remember when
developing a solid conceptual understanding and connection to multiplicative thinking, fractions and
decimals.
When teaching mathematical concepts it is important to look at the big ideas that will follow in
order to prevent misconceptions and slower transformation ... Show more content on
Helpwriting.net ...
C., 2015, p. 3).
Symbolic representation using base–ten and expanded algorithms is a way to show students the
written connection to the visual models used. The partial–products algorithm is a more detailed
step–by–step process and therefore more advisable to avoid errors in students learning to grasp the
procedure (Reys ch.11.4). This process allows students to visualise the distributive property more
easily. However, the standard multiplication algorithm is quicker and acceptable for students, if the
teacher feels they have complete understanding of the steps in the partial–products algorithm.
Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended
on(Reys et al. ch. 11.4). In addition, multiples of 10 give students the knowledge that all digits move
left one place and an additional place hundreths. This concept can be used to introduce the decimal
place which is also moving place each time something is multiplied by tens. Exposing students to a
range of examples which displays patterns that occur when multiplying by tens and hundreths will
generate meaning of digits moving place (Reys et al., ch. 11.4).
Visual models known as arrays or grids can be introduced early to assist students thinking by
providing a visual representation when going from adding to multiplying. In addition, arrays are a
great

Simulation: Questions And Answers
05 – PERMUTATIONS AND COMBINATIONS
( Answers at the end of all questions )
Page 1
(1)
If the letters of the word SACHIN are arranged in all possible ways and these words are written out
as in dictionary, then the word 'SACHIN' appears at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d )
602 [ AIEEE 2005 ]
(2)
The value of
50
C4 +
55
r =1
∑
6
56
–r C 3
is
( a ) 55 C 4
(b)

C3
( c ) 56 C 3
(d)
56
C4
[ AIEEE 2005 ]
(3)
How many ways are here to arrange the letters in the word GARDEN with the vowels in
alphabetical order ? ( a ) 120 ( b ) 240 ( c ) 360 (d ) 480 [ AIEEE 2004 ]
(4)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is
empty is (a) 5 ( b ) 21 (c) 3
8
( d ) 8 ... Show more content on Helpwriting.net ...
 !   2  [ C 0 2 – 2C 12 + 3C 2 2 – ... + ( – 1 )n ( n + 1 ) C n 2 ], n! where n is an even
positive integer, is equal to (a) 0 (b) (–1) ( e ) none of these n/2 (n + 1)
(c) (–1) (n + 2)
n
(d) (–1) n [ IIT 1986 ]
n
( 23 )
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First
the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select the
chairs from amongst the remaining. The number of possible arrangements is (a)
6
C3 × C2
4

(b)
4
P2 × P3
4
(c)
4
C2 × P3
4
( d ) none of these
[ IIT 1982 ]
( 24 ) Ten different letters of an alphabet are given. Words with five letters are formed from these
given letters. Then, the number of words which have at least one letter repeated is ( a ) 69,760 ( b )
30,240 ( c ) 99,748
5
( d ) none of these
[ IIT 1980 ]
( 25 ) The value of the expression (a)
47 C 5
47
C4 + (c)
j=1
∑
52 – j C 3
is equal to [ IIT 1980 ]
( b ) 52 C 5

52 C
4
( d ) none of these
( 26 ) n Cr – 1 = 36 n C r = 84 and n Cr + 1 = 126 , then r is (a) 1 (b) 2 (c) 3 ( d ) none of these [ IIT
1979 ]
( 27 )
There are 27 points in a plane. 5, 10 and 15 points are collinear on distinct lines. By joining

Multiplication Of Urdhva Tiryabhyam Sutra
Urdhva Tiryakbhyam Sutra is a general multiplication formula applicable to all cases of
multiplication. It literally means "Vertically and crosswise". It is based on a novel concept through
which the generation of all partial products can be done with the concurrent addition of these partial
products. Power dissipation which results in higher device operating temperatures. Therefore it is
time, space and power efficient. It is demonstrated that this architecture is quite efficient in terms of
silicon area/speed. Now let us take two three digit decimal numbers and understand the Urdhva
technique. Let the first number be "123" and the second the number be "456".
Step 1: Initially the unit's digit numbers are multiplied and the unit's digit of the product that is 8 is
kept as the unit's digit of the result, the ... Show more content on Helpwriting.net ...
2. Let us consider the multiplication of two decimal numbers (5498 × 2314). The conventional
methods already know to us will require 16 multiplications and 15 additions. The numbers to be
multiplied are written on two consecutive sides of the square as shown in the figure. The square is
divided into rows and columns where each row/column corresponds to one of the digit of either a
multiplier or a multiplicand. Thus, each digit of the multiplier has a small box common to a digit of
the multiplicand. These small boxes are partitioned into two halves by the crosswise lines. Each
digit of the multiplier is then independently multiplied with every digit of the multiplicand and the
two–digit product is written in the common box. All the digits lying on a crosswise dotted line are
added to the previous carry. The least significant digit of the obtained number acts as the result digit
and the rest as the carry for the next step. Carry for the first step (i.e., the dotted line on the extreme
right side) is taken to be

Wk6AssgnNixL
Latin American Subtraction Algorithm
Lisa Nix
Walden University
Dr. Mary Robinson, Instructor
MATH–6562G–1, Base Ten Number System & Operation: Addition/Subtraction
October 21, 2013
Latin American Subtraction Algorithm The Latin American subtraction algorithm is based on the
fact that the difference between the two numbers does not change while adding the same amount to
the minuend and subtrahend (Indiana University Southeast, n.d.). This algorithm appears to be one
that requires precision to detail as it is different from the traditional subtraction algorithm the
majority of students have been taught. Regardless of teacher preference, providing students with
various strategies allows them to experience the diversity in problem ... Show more content on
Helpwriting.net ...
A: Exemplary Work
A = 4.00; A– = 3.75
All of the previous, in addition to the following:
B: Graduate Level Work
B+ = 3.50; B = 3.00;
B– = 2.75
All of the previous, in addition to the following:
C: Minimal Work
C+ = 2.50; C = 2.00;
C– = 1.75
F: Work Submitted but Unacceptable
F = 1.00
Adherence to Assignment Expectations
The extent to which work meets the assigned criteria.
Assignment exceeds expectations, integrating additional material and/or information.
Assignment

Questions On Learning And Teaching
Task #4: Mathematics Learning & Teaching
Competency 662.1.4: Aligning Learning Activities to National Standards
Competency 662.1.5: Standards and Best Practices in Teaching and Learning
Competency 662.1.7: Differentiated Instruction
Jennifer Moore
Western Governor's University
Part A: The "Equivalent Fractions and Decimals Lesson Plan" is aligned to NCTM's content and
process standards. The content standard that this lesson is addressing is numbers and operations.
This entire lesson is about students using fractions and decimals to solve problems. This lesson also
has several process standards addressed in the lesson plan. One of the process standards used in this
lesson is Connections. Throughout this ... Show more content on Helpwriting.net ...
"The Show or the Ad" activity has students using word problems that talk about television programs
and commercials. The teacher has made the students connect that math is even in the TV shows that
they watch. The teacher then makes it even more the students own connections by allowing them to
be creative and writing their own word problem about TV and commercials. The teacher also uses
these types of problems on the summative assessment. The teacher uses connections even in the
homework that is assigned to the students. The teacher assigns students to watch their favorite
television show, and as they watch the show to record how many minutes the commercials are. All
of this shows the students understanding of the concept while allowing the students to relate this to
something they enjoy. The one NCTM process standard that I would add to this lesson plan would
be the reasoning and proof standard. This is the only standard that is rarely used in this lesson plan.
"The Reasoning and Proof standard emphasizes the logical thinking that helps us decide if and why
our answers make sense" (Walle, p. 5). This lesson needs to allow students to justify the reason for
their answers. This lesson only has them justifying their answers on one question, throughout the
entire lesson. I would add more to the questions than just the answers. One part of this lesson I
would change to incorporate the reasoning and proof standard is on the "The Show or the

The Student That I Have Been Working With Over The Past...
The student that I have been working with over the past six weeks is Brad Concordia. Brad attends
Shiloh Hills Elementary School in the rural area of the Wilson School District. Brad is a first–grade
student in Mrs. Detwiler's classroom who suffers from brain damage and unfortunately he's dealt
with it since he was born. Brad is an energetic, positive kid who loves to tell stories and talk about
Pokémon. He does not act up in class and he tends to be very polite and well behaved. Whenever the
teacher gives him an activity to do he tries his very best to accomplish it without the help of an aid,
but most times he is left with no choice due to his condition.
A couple of Brad's strengths include being able to count dots 1–34 without any issues, and he is able
to comprehend the number of dots he counted and write it down for the answer. For basic numbers
such as 1–10, he is able to do it fully on his on and get all of the digits correct. For numbers greater
than 10, he is dependent on the help of one of the other teachers. His main weakness in math is his
lack of ability to do problems on his own. He relies on counting dots to add up the numbers and my
goal for him is for him to be able to see a number and know how much it is "worth" rather than
using dots to count. After talking with Mrs. Detwiler, we discussed a plan to help Brad comprehend
single digits numbers using his number line. Brad has been very positive toward this intervention
and he is eager to work

A Scheme Of The Department Of Education
Part A: Scheme of work
The basis of this essay will discuss at a scheme within mathematics. Per the Department of
Education (DfE) (2013) "mathematics is a creative and highly interconnected disciplines that have
been developed over centuries......... It is essential to everyday life, critical to science, technology
and engineering, and necessary for financial literacy and most forms of employment." The substance
of maths is divided into five reasons; significance it has in everyday life, its use within other
curricular areas, the pupil can develop intellectually, pupil's enjoyment of learning and has a
distinctive place in pupil's human knowledge and culture (Haylock & Manning 2014). The scheme
is based on six lessons it will consider EAL learners, ability based differentiation, assessment and
motivation. The second section of the essay will explore further in to motivation and how and why
this is important to the teacher, pupils, classroom for effective learning of the subject. It will then
look at the consider the implications within the class and to personal development as a teacher.
The scheme is based on a year 2 class, looking at place value through partitioning, one more, one
less and ten more, ten less. I have chosen this due to it being the key focus within the curriculum for
key stage 1 learners. The aim by the completion of Key stage 1 stands that pupils have a strong
understanding, confidence and mental fluency with whole numbers, counting and place value (DfE,

Questions On Grasp Problem Solving Method
GRASP Problem Solving Method
Given – You need to figure out the important information in the question.
Required – What do I have to do to answer the question?
Application – What is my plan to solve the question?
Solve – Use your plan to solve the problem.
Paraphrase – Write a couple of sentences about your answer and how you found it.
Example: Shane is setting up for his birthday party. There are 50 people coming to the party. If each
table holds 6 people, how many table does he need?
Given –1 table = 6 people 2 tables = 10 people 3 tables = 14 people
Required – We need to find out how many table he needs.
Application – We could use –repeated addition –make a chart –draw pictures –make a graph
Solve – Use a chart
# of tables # of people
1 6
2 10
3 14
4 18
5 22
6 26
7 30
8 34
9 38
10 42
11 46
12 50
Paraphrase – we found out that Shane needs 12 tables for 50 people. We know this because we made
a chart and increased the chart until we reached 50 people and see how many tables are needed.

BEDMAS
BEDMAS is an acronym for the order of operations used to solve a math equation that has more
than 1 operation.
A math equation is a math sentence (e.g. 2 + 2 = 4).
BEDMAS tells us the order we need to use to complete the operations in an equation.
Brackets
Exponent
Division
Multiplication
Addition
Subtraction

Ancient China Research Paper
In 1,500 bc, the mathematicians of China were using numbers. Long before the people of India
invented the number zero, Chinese people were using base ten counting systems. The base ten
method they used is different than the one we use today, using ancient Chinese math, the number
465 would be written as four one hundred markers, six ten markers, and five one markers. They
were also advanced in geometry, this was proved in 600 BC, when the Tangram was invented. The
Tangram is an amazing math game, that allows you to explore geometry to huge extents. This essay
tells the fascinating story of how the game is played, how it was used, and how it became known to
the western world. China is often thought of as one of the wealthiest countries in ... Show more
content on Helpwriting.net ...
In ancient times, believe it or not, they were used to tell stories. The pictures made by Tangrams can
be put in order to make a scene. You can arrange the shapes in any way, and trace the picture onto
paper, and make a new figure. The traced pictures can look just like comics. You actually can think
of Tangrams as the comic books of the ancient world. Quite truly, you can make any story, from
superheroes to mathematics. This is actually quite important, creating a story using geometric shapes
can actually improve your skills in geometry. That probably explains why they were so popular in
China. "Scholars and artists thrown together are often annoyed at the puzzle of where they differ.
Both work from knowledge; but I suspect they differ most importantly in the way their knowledge is
come by. Scholars get theirs with conscientious thoroughness along projected lines of logic; poets
theirs cavalierly and as it happens in and out of books. They stick to nothing deliberately, but let
what will stick to them like burrs where they walk in the fields." –Robert Frost. This quote
highlights the fact that both scholars and artists take an interest in Tangrams. "Tangrams are a great
thing to incorporate into the mathematics classroom because they are fun, interesting, and

Diagnosis Of Attention Deficit Hyperactivity Disorder
Assessment 1 Specific Difficulty in the Number Strand Chloe has a difficulty in completing vertical
subtraction algorithms, particularly when there is a zero in the minuend. Learner Profile Chloe is an
11 year and 10 months old girl who lives on Sydney's North Shore with her mother, father and two
younger brothers. Her first language is English and she is currently in Year 7 at a comprehensive
systemic girls Catholic high school located in Chatswood. Chloe excels at Dance and Music, and
has been a member of the Australian Girls Choir for four years. She has a history of ongoing
difficulties with Maths. Chloe was born with Morning Glory Anomaly in her left eye; a congenital
condition that results in the failure of the optic nerve to fully develop. In late 2015, her left retina
completely detached resulting in almost total blindness. Her visual acuity is normal in the right eye.
Chloe has a diagnosis of Attention Deficit Hyperactivity Disorder (predominantly inattentive),
clinically significant levels of anxiety and a specific learning disorder with impairment in written
expression. Her ADHD is managed through a low chemical diet and she is not medicated. Chloe's
most recent review of cognitive and learning abilities was completed in early 2014. The key findings
include stronger verbal intellectual skills (average) than non–verbal intellectual skills (low average);
the abstract reasoning that is needed for many maths tasks. Whilst her working memory and
processing speed

Examples Of Josephus Problem
The next base the essay will explore is base 3 also known as ternary, this is the base that was used in
the original Josephus problem. By exploring this base and a few more bases, I will find a pattern and
derive an equation to solve Josephus problem with any number of people in any number base.
Josephus problem in base 3 is when each person kills the person who sits two seats away from him
and the following diagram will demonstrate how it happens, the numbers on the inside show the
order of the people that are gone which will make it easier to follow.
Figure 7 An example of how Josephus problem works in base 3 with 12 people
I will now create the same table as I did for the problem in a binary form.
Table 3 Analyzing the Josephus problem in base 3 when 1≤n≤12
Number of people
()
Order in which people are gone
The winning number
1
1
1
2
1,2
2
3
3,1,2
2
4
3, ... Show more content on Helpwriting.net ...
Applying the equation to Josephus problem, to find we have to find as . We know how to solve as
there are only 2 people and starts meaning he has to skip and therefore dies first and wins. Now we
know that , we can see from the table above the answer is correct however we have to do it once
more to find .
We can always consider position and we have to repeat the equation until getting to the required
number. This solution can be very frustrating as you must do the same thing over and over, however
it can be programmed very easily and save a lot of time.
This method is the third and the last method to solve the Josephus problem, it is the most useful

method as it works for all bases however it is the most complicated one. In order to compare
between this method and the other two methods, we first have to write the equation in base

Place Value
The ability to make sense of numbers is necessary in order to solve a wide range of mathematical
problems, both in further education and every day life. A teachers understanding of place value and
the base–ten system is paramount for developing a student's ability to confidently approach number
operations. To underpin and guide a student's knowledge of place value, clear insight into what a
student knows about the concept, is pertinent to the continuation of learning and building of
understanding.
Rationale
Educators must draw upon their professional judgement to make astute teaching and learning
decisions, to extend a student's learning of place value and the base–ten system. Effective teachers
will; implement well–planned mathematical activities to help engage learning, use observation and
focused question to see where support is needed, and provide opportunities for growth and
understanding of place value (Department Of Education Western Australia [DOEWA], 2013). One–
on–one interviews are an invaluable diagnostic assessment strategy that unravels, not only the ...
Show more content on Helpwriting.net ...
The essence of understanding place value, is not only knowing the values of the numbers depending
on their position, but being able to rename their values in order to problem solve (NSW
Government, 2015). For example, the number 345 could be written as 34 tens and 5 ones, 345 ones
or 3450 tenths (National Council for Curriculum and Assessment [2015], 2015). The most
significant aspect is being able to comprehend that whilst there may be different ways to write the
number, it still has the same value. The Australian Curriculum recognises this importance for more
complex learning in; algebra, fractions, decimals and multiplicative thinking (Commonwealth Of
Australian, 2009). Without this knowledge, problem solving becomes limited, resulting in confusion
and

The Military Sector Of The Marine Corps
We are losing some of our best Machinists and Welders after their first enlistment due to the
lucrative options available in the civilian sector and the lack of opportunities to display their
innovative nature in the Marine Corps. An additive and subtractive fabricator in the trenches would
serve to be an asset to commanders, because he/she will not be limited by technology or lack of
expertise. Both of these specialties present an opportunity to exploit manufacturing capabilities.
After all, exploitation is a human endeavor and until unmanned technologies take over completely,
is it not the Marines using the technologies that are the assets? In the civilian sector, experience is
often necessary in most fields; however, machining and ... Show more content on Helpwriting.net ...
Thus, the opportunities to exploit machining and welding capabilities disappear along with the
opportunities to pass down their knowledge and skills through guidance and mentoring.
Interestingly enough the current manpower structure places these two MOS' side by side in every
ESB, Maintenance battalion and Ground Ordnance Vehicle Battalions. In an effort to challenge the
status quo and to continue on with the Commandant guidance; what benefits could arise if these two
specialties are aligned together and be allowed to merge at the fifteen year mark?
These two specialties share similar skills in terms of fabrication and metallurgy, including a
thorough understanding of the physical and mechanical properties of metals. They both have a
strong understanding of structural design and manufacturing regardless of material. And one
particular aspect that is often overlooked is the ability to be critical thinkers, as this is inherent with
artistic creation (White, Robinson 2001). Additionally, all the processes used in machining and
welding require a level of critical thinking and creativity in order to maximize efforts and resources.
The current employment of these two specialties is minimal while in garrison; however, while
forward deployed, these specialties become an integral part of combat innovation. Their creativity
and ingenuity have made a significant impact in the

Description And Description Of A Calculator
<!DOCTYPE html> CALCULATOR body{ margin: 0px; padding:0px; } main section{margin:
20px;} #calc_body, #calc_header{ background–color: #BFBABE;} main section table {padding:
20px; border–radius: 10px; border–spacing:0px; border–collapse:collapse;} table, th, td
{display:inline–block; padding:0;float:left;} #heading{ text–align: center; font–size:23pt; color:
black; font–weight:bold; text–transform: uppercase;} main section table tr td button{ height: 70px;
display:block; width: 90px; font–size: 22pt; border:0; } .longbutton{ height: 70px; width: 180px;
margin: 0; text–transform: uppercase; font–size: 22pt;} main section table tr td button:hover{
background–color: #E990C0; font–weight: bold; } #display {width: 540px; height: 80px;
background–color: #B0EEDB; font–size: 25pt; border:none; outline:none; text–align:right; margin–
bottom:15px;} #expr{ width: 540px; height: 80px; background–color: #B0EEDB; font–size: 13pt;
border:none; outline:none; } #Trig{font–size: 26pt;} .orangebuttons{ background–color:#F99B58; }
.orangebuttons:hover{ background–color:#FBB888;} .operators{ background–color:#7B8EF8;}
.operators:hover{ background–color:#B6C0FA;} #equalsign{ background–color:#343436;
color:white;} #equalsign:hover{ background–color:#959699;} Calculator log2 Rads

Math Reflection
Part 1– Effective Teaching of Mathematics After taking this course I have personally learned so
much about mathematics and effective ways on how to teach certain topics in my future classroom. I
believe that this course was taught in a way for me to advocate for how I teach myself mathematics.
When I knew I was taking this class I was very nervous at first. Mathematics is not my strongest
subject so automatically I felt as though this class was going to be a long struggle for me. Once I
had a couple class periods I grew more and more comfortable with the math we were learning. I
learned to teach math to myself again. I had to teach myself math concepts that I learned way back
in elementary school that I completely forgot how to do. In this class we learned a lot about how
elementary math is done now a days. Also how now a days there is more than just using the
traditional algorithm to solve equations.
I have learned math along with my students at my placement. At my placement I observed my
students using the basic operations with distributive property, partial quotients with division and
much more. One of the really cool things I learned from my placement students is the box method
which is done with multiplication. I at first thought it would be like lattice but it's not. For example
say if you had the numbers 56 and 6, you would draw a rectangle box and split it in the middle.
Then you would write 50 in the first column on top and then 6 next to it. The number that goes on
the other side is 6. So then you would multiply 50 and 6 to get 300 in the first box. After you would
do 6 times 6 with the other box which is 36. Once you have those two numbers you add them
together to get the answer. I was never taught to solve multiplication that way so that was something
with mathematics that I learned along with my students. I do believe that thoughtful listening is one
of the most effective qualities of a good teacher. I practiced this thoughtful listening when I listened
to other people participate and show their work in class. I also practiced this thoughtful listening
when I taught my unit lesson on math word problems. I took the time while teaching my lessons to
listen to every student explain how they got

Fpga Based Implementation Of Digit Recognition
FPGA BASED IMPLEMENTATION OF DIGIT RECOGNITION Under Supervision of : Dr. Pavan
Chakaraborty. Group members: IEC2012015 IEC2012028 IEC2012041 IEC2012089 IEC2012090
Table of Contents About platforms used: 4 Xilinx ISE: 4 Web Edition: 4 MATLAB: [matlab] 4
Feature extraction: 5 Algorithm speed up using FPGA implementation: 6 [parallization abitlity of
NN] 6 Conclusion 7 Result: [Verilog outputs] 4 References 7 About platforms used: Xilinx ISE:
"Xilinx ISE[xilinx] (Integrated Software Environment) is a software tool produced by Xilinx for
synthesis and analysis of HDL designs, enabling the developer to synthesize ("compile") their
designs, perform timing analysis, examine RTL diagrams, simulate a design 's reaction to ... Show
more content on Helpwriting.net ...
More than a million engineers and scientists in industry and academia use MATLAB, the language
of technical computing. [3]" Feature extraction: The method of feature extraction is based on the
spatial distribution of the black and white pixels in the image space. We are assuming that the
difference of distribution of pixels for each digit are sufficient enough to classify them. All of
extracted features are integer and could be implemented with only add and subtract operation on
FPGA [4]. We divide the image into multiple horizontal and vertical sections and the analysis of
accuracies can be done using this table. [insert the table of trade off] It can be observed that as we
are increasing the number of sections, the accuracy is also increasing. Taking consideration of
efficient use of hardware resources four horizontal and four vertical sections can be chosen safely.
[figure showing 8 blocks] To count the number of pixels in each section 8 binary ripple Algorithm
speed up using FPGA implementation: [parallization abitlity of NN] Conclusion For the
implementation

Lesson Reflection Paper
At the beginning of the Kindergarten class the class did their normal routine of calendar time. The
teacher tells them to go to the carpet for calendar time and that gets them on task. They count the
number of days they have been in school out–loud. They also count the days with straws and put
them in a ones, tens, or hundreds pocket. The students also keep record of the number of days they
have been in school with change. They count out change to the number of days they have been in
school. They say how much each coin is worth and who is on it. Lastly, they add a gumball to their
jar of gumballs and say how many they have in total. This is a normal everyday morning routine that
involves math. TMPs 3 and 6 are used for this routine and SMPs 4, 6, and 8 are used during this
time. This activity takes around thirty minutes everyday. I think doing this everyday has really
benefited the students. A student found a dime outside and he brought it to me. He knew it was a
dime, how much it was worth, and even the president that is on the dime SMP 6. I observed a forty–
five minute second grade lesson using the Invagations program. The lesson was called how many
stickers how much money (cents). The lesson began with the students coming to the carpet and
reviewing the value of coins. After that the students were shown stickers in a base ten blocks format.
They were told to come up with an answer of the total number of sticks and write it on their white
boards SMP 7. Then they were

Mathematics : A Scheme Within Mathematics
The basis of this essay will discuss at a scheme within mathematics. Per the Department of
Education (DfE) (2013) "mathematics is a creative and highly interconnected disciplines that have
been developed over centuries......... It is essential to everyday life, critical to science, technology
and engineering, and necessary for financial literacy and most forms of employment." The substance
of maths is divided into five reasons; significance it has in everyday life, its use within other
curricular areas, the pupil can develop intellectually, pupil's enjoyment of learning and has a
distinctive place in pupil's human knowledge and culture (Haylock & Manning 2014). The scheme
is based on six lessons it will consider EAL learners, ability based differentiation, assessment and
motivation. The second section of the essay will explore further in to motivation and how and why
this is important to the teacher, pupils, classroom for effective learning of the subject. It will then
look at the consider the implications within the class and to personal development as a teacher.
The scheme is based on a year 2 class, looking at place value through partitioning, one more, one
less and ten more, ten less. I have chosen this due to it being the key focus within the curriculum for
key stage 1 learners. The aim by the completion of Key stage 1 stands that pupils have a strong
understanding, confidence and mental fluency with whole numbers, counting and place value (DfE,
2013). Moreover, place value

Importance Of Oral And Written Names For Numbers

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