Final Thoughts ( Book )

Final Thoughts ( Book )
Ellyce Uy
44755122
MATH335 201
*300+ words
Final Thoughts (Whole Book) This book is not like any other, and as a whole had four main impacts on me. First it taught me about the complexity of
elementary mathematics and not to underestimate it. Secondly, it taught me about the consequences becoming overly dependent on mathematical aids
(leading to doing and not understanding). Thirdly, it taught me the reasons behind why we do certain mathematical procedures. Lastly it gave me tips
for future teaching and parenting.
One of the main themes in this book is challenging the notion of how simple it is to teach elementary kids. In fact it is profound. Often times,
professional mathematicians are so enveloped in their complex and high–level ... Show more content on Helpwriting.net ...
This reminds us not to underestimate and overlook elementary mathematics that appears basic. Mathematical diversions, therefore, cannot be taught
without the students' understanding of the basic mathematical foundations. It is like learning to play an instrument; one must know the basics before
being able to play a piece.
Learning about the long and tiresome process of transforming ordinary fractions into decimal fractions has made me realize how much I had taken for
granted using calculator for the past decade. There are downsides to relying more on the calculator than relying on "old–fashioned" mind. "Patterns as
Aids" becomes a problem when a student follows rules without understanding and calculates large numbers mentally using tricks but fails to understand
the purpose of the processes or steps. Therefore it is better to understand less but thoroughly, than to be an expert in memorizing tricks and rules
without any understanding. Principles must be taken apart, and each ingredient learned and taught individually. When something sounds hard or
difficult, it usually means we did not break the problem into portions. Often I take for granted and overlooked simple aspects of math that I
automatically perform. This book also mentions the importance of using word
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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

Research Paper On Sonic Waves
Whether or not you realize it, there is energy all around us. This energy changes and influences the way the world works. When someone tells you to
think of energy, the first thing that likely comes to mind is electricity or heat, as that is what we commonly see and hear about. If you are asked to think
of a powerful kind of energy, you may think of radiation or fire, as they can kill people and destroy forests. Although these may be the most obvious
kinds of energy, there is another kind of energy that can be both more helpful and more dangerous; shock waves. These waves surround us, yet we have
only just began to explore their many uses. Shock waves can be used by animals and humans for both utility and offense.
Shock waves, also called ... Show more content on Helpwriting.net ...
A rumor that almost everyone has heard of or seen at one point is an opera singer breaking glass with nothing but their voice. Although it seems like an
awesome power, it is sadly less than real. The idea is that the performer would sing at the objects resonant frequency loud enough to shatter the glass.
Resonant frequency is the frequency that an object vibrates at when hit. When a sound at an object's resonant frequency is played, it causes the object to
vibrate. Ideally, the glass would shatter because it vibrates itself to pieces (Schrock, 2007). In theory it is possible, but a human cannot create enough
volume without machinery to shatter glass unless it is the finest, most fragile crystal. Normal glass is simply too

The Effect of Schema on Memory
The Effect of a Schema on Memory
Psychology MSc, University of Hertfordshire
Abstract
Schema Theory is a principle in which cognitive processes are influenced by social and cultural factors. According to schema theory the knowledge we
have stored in our memory is reorganised into a set of schemas which is based upon our general knowledge and our previous experience. Experiments
have proved that despite seeing and interacting with an object almost every day, our ability to remember said object is greatly influenced by the
schemas we already have. This experiment will be conducted in an almost identical way to that of French and Richards and look at the effect of
schemas on memory. It was predicted that participants use their previous ... Show more content on Helpwriting.net ...
This experiment will be conducted in an almost identical way to French and Richards experiment and look to determine the effect of schemas on
memory. It was predicted that like French and Richards experiment the participants use their previous knowledge of Roman numerals to mistakenly
draw the clock.
Method
Participants
The participants in this experiment were recruited through opportunistic sampling, the class members of a Psychology Masters Course in Hertfordshire
University. The class was made up of both male and female students of a variety of ages.
Design
This experiment used between–participants, experimental design as all the participants were in three separate conditions which were then compared.
The Independent Variable in this experiment was the different condition, whether they were in the surprise memory condition, the forewarned memory
condition or the copy condition. The Dependent Variable is the extent to which they could correctly recall/copy the clock.
Apparatus
This experiment used an instruction sheet which indicated the relevant instructions for each condition. (This is included in Appendix 1). The experiment
also used an identical clock for all the conditions with roman numerals depicting the numbers, where four was shown as IIII. (This is included in
Appendix 2). The rest of the apparatus included paper, pens and a stop watch.
Procedure
In this experiment the participants were split up into three conditions. The

Cardinality in Blind Children
Aim, objective and Hypothesis
The current study set out to explore the generalisability of counting behaviour and the understanding of the cardinal principle in blind children. To date,
research in this area has focused mainly on typically developing children. Some researchers have undertaken studies in the atypical population;
however, this is limited to disorders such as Down syndrome (Caycho, Gunn & Siegal, 1991), mental retardation (Baroody, 1986) and severe learning
difficulties (Porter, 1998). Therefore, children with visual impairment have not been given much attention in this field of research.
The aim of the first experiment will be to observe whether children are able to count objects with varying degree of manipulation and mode of input, to
assert the numerosity of the count. These entail counting objects than can and cannot be separated from those that have been counted, as well as the
counting of sounds. The second experiment is designed to confirm the findings of experiment one; hence, children who understood the cardinal
principle will be able to detect error made by others in counting. A further aim of the study will be to investigate whether smaller number words are
acquired before larger ones, as it is the case in typically developing children. The researcher hypothesised that blind children's development will be
slightly delayed in the younger age group, but will not show significant differences in the older age group when compared to typically

Kitten Angels Monologue
Kitten Angels I remember when two of my kittens died in my hands, one recently and one when I was almost nine. I remember their names, Midnight is
the one that died recently, Pudge is the one that died when I was almost nine. They were born sickly when they were born. I miss them so much, but I
know they are angels now. They fly with everyone I lost whom are in heaven. Half of the people don't go to heaven, but the ones that do have earned
their wings. But all animals go to heaven. I hope to join them one day. I cannot wait to see everyone again. But I'm not rushing my death. I want to live
life to the fullest. I want to become a veterinarian to help and save animals, even if I have to put the animals down, it'll stop the suffering and pain the ...
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I remember having a kitten in a coma, she had no name, but she was a pretty black color with a little bit of white on her chest. I remember having two
cats that ran away, Simba and Icy, I don't know how old icy was, but simba was two to three years old. I miss those two cats, I wonder how simba is
doing. I hope he's well, I understand if he died, his name should've been Scar, that's what my big sister, Amy said. I miss the cats that ran away. But it's
okay, I understand the good lord calls everyone home. Only if heaven wasn't so far away, I would go visit my family and the kittens I lost. I'd go see my
ancestors and my family members on my momma's and my daddy's sides. I'd see my pap–paw again. He died in 2006, right after hurricane Katrina, on
the eighth of December, fourteen days before my birthday. I really miss him. If only he were still alive. I hear my family comes from royalty. I wonder
if that's true, they say we are royalty from England. I don't know if that's true. I loved my kittens

Scram Jet Essay
The SCRAMJET, simply abbreviated from Supersonic Combustion Ramjet, is the latest evolution of the jet engine family. NASA made the news with
each test of the X–43A scramjet craft, so I set about to discover why this type of jet engine should garner so much scientific attention. Turbojet The
most basic jet engine is the turbojet. As soon as the air enters the front of the engine, the blades of the compressor, compresses the air before funneling
it into the combustion chamber. During the compression, not only is the density of the air increased by compressing it in a confined chamber, but the
temperature of the air also increases as the air molecules of squeezed closer together. The resulting air that emerges into the ... Show more content on
Helpwriting.net ...
Turboprop The turboprop (turbo propeller) engine combines the simple propeller engine with that of the turbojet. In this case, in addition to driving the
compressor, the turbine also drives a propeller. The propeller provides thrust like a normal propeller (the wedge shape of the blades pushes the air
back), in addition to the thrust produced by the turbojet part of the engine. Ramjet The ramjet engine is a much simpler construction than either the
propeller or turbojet engine. Unlike these the other engines that require moving parts (propeller, compressor, turbine, shaft, etc), the ramjet consists
basically of a tube that scoops the air into the combustion chamber where it is mixed with fuel and ignited, and exhausts the hot gasses through the
necked down exhaust nozzle. Because of the high speeds of operation, instead of compressing the air, the chamber of the ramjet actually expands and
thereby slows the air to subsonic speeds for the combustion process. The force of the incoming air forces the combustion to be kept behind the inlet.
Because of this fact, the engine cannot be operated at subsonic velocities (Velocities below Mach 1 – One time the speed of sound or roughly 740 mph
at standard temperature and pressure). Hence another engine has to accelerate the plane to the point where the ramjet can function. On the other hand,
because of its simplistic construction, the ramjet engine can

Sonic Monologue
Scourage's POV I mind as well stay in this damn jail for the rest of my days. Things just aren't the same anymore. So what if I lost my temper and was
about to go ape shit on the rest of my crew? All's I wanted to was get back at sonic and those damn freedom fighters and now here I am, barely feeling
like myself let alone an anti–sonic in jail without any of my other team mates. "this straight up sucks!" I said punching my hand into the wall. When I
did get here it was to look for sonic, but instead I found shadow. I didn't mind picking a fight with that dude, I'd figure I'd give him a run for his money,
but even in my super form I lost, and it felt like it didn't take much either. "at least I don't get bullied around here..." I said to myself, ... Show more
content on Helpwriting.net ...
Knuckles! What are you doing up?" eggman said to knuckles. "I couldn't get any sleep, and now, I'm going to destroy you're robots and be known as a
village hero." Knuckles said with a pose and fireworks going off in the background. "seriously? fireworks? No one gives my entrance fireworks!"
Knuckles continued to battle the robots, but eggman refused to give up. "luckily, I have other robots, that have already made it to your friends house."
"oh no you don't!" said knuckles. He quickly headed to the homes of his friends. They were begin carried out by the robots. Knuckles picked them up
and put them down somewhere else and destroyed the robots. He then went inside to do the same, only to find them watching tv. "all right, this is my
favorite show! Pass the popcorn!" he then sat down with them and watched some tv. One show later Knuckles destroyed the robots and sent eggman
flying, literally. "seriously, one does not simply get a giant slingshot–" and he flew off.
"nooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
he

The Development Of Children 's Education
5–7 years:
This age group of children will have to go through a transition from nursery to school; reception year, (where practitioners still follow EYFS) and then
children move on to key stage one, (where teachers follow the National Curriculum Key Stage 1). Children's education is still based on play, however
now children have a lot more of adult–led activities in which they learn to concentrate for longer periods of time. The environment in schools that
surrounds children is more complex because the children get to learn more, therefore some displays might contain bigger amount of more complex
mathematical language than we can find in a nursery setting. As children go into key stage 1, it isn't the only environmental look that changes, the
equipment is also more complex and advanced because it is aimed for children that are now at a higher stage of mathematical development. As I
discussed earlier– Early Years Foundation Stage changes and becomes the National Curriculum Key Stage 1; the system changes a little bit and instead
of 'carpet time' that children used to have in the nursery becomes a 'lesson'. Some children in reception might still work on their emergent mathematics.
However, as they move up to Key Stage 1, children begin to learn a lot more complex mathematics and it is not longer emergent because they have
passed this stage which should be fully achieved by now...
Children who did not go to the nursery might find it harder to learn in school and achieve their

Examples Of Focus Observation
Part A: Focused Observation
1. Student# 1 Lou (typical)
Context
I observed Lou for about twenty minutes on Monday, March 13th, 2017 and about forty–five minutes on Thursday March 16th, 2017. On Monday, Lou
was involved in a lot of different activities with her classmates because it was play time. When I first walked into the classroom she was playing with
the dollhouse with two other classmates. As I was sitting at the table with Sam to find out what she was making Lou told me about the new student they
have in the classroom, her name, and how she is unable to speak English, but can understand it. After Lou told me about the new student she started
playing cars with her. On Thursday, I came to observe Lou and Sam play the math game and complete the math worksheets I brought with me. Before
they could participate in the activities I brought they had to ... Show more content on Helpwriting.net ...
On Monday, when I came into the classroom, I sat with Sam so I could observe what she was doing and still be able to look across the room and
observe Lou. For majority of my visit on Monday, Sam created a picture using glue, paper, and green and gold shamrocks. On Thursday, Sam was
engaged in clean up and after clean up, Sam and Lou joined me to do the math activities I brought. Both days seemed to be a typical day.
Preparations
For both students, I prepared for this observation by researching the Ohio standards made for pre–school children in math and social emotional
development. I then printed work sheets and a math matching game age appropriate for Sam and Lou to complete.
Social and Emotional development standards (www.education.ohio.gov)
Recognize and identify own emotions and emotions of others
Communicate a range of emotions and socially accepted ways
Identify the diversity in human characteristics and how people are similar and

Mathematics Of The Math For Educators
The fraction lesson that we worked on in class has given me a deeper understanding of fractions that I did not have before. Fractions have never been a
topic of math that I have took a liking to. They have intimidated me for as long as I can remember. I did not imagine in my wildest dreams that there
was going to come a day that I could understand fractions. Being enrolled in the math for educators course has contributed significally to this newfound
understanding. This class has taught me a lot of valuable knowledge on how you can make fractions easy and at the same time fun for yourself and the
students you are trying to teach. I learned that fractions can estimated, they could either be close to almost nothing or zero, close to one–half, close to
one, and more than one. Based on that conclusion, students can easily figure out which fractions are bigger, smaller or equal to each other. There was an
example provided in class that talked about Irene eating pizza everyday and having to frequently call in to tell her doctor how much she had eaten that
day. Irene figured out that instead of telling him the exact amount, she would give him an estimate. There was a magnetic circle on the board with
removal able pieces, from here Dr. Math took away and added pieces in multiple ways and would ask if it was close to nothing, close to 0, close to ½,
or close to 1. This helped me visualize and understand what she was trying to teach us on a deeper level. We also learned that when

Fawn-M Research Paper
Fawn–M Fawn has a proficient understanding of topics covered in term three. Fawn has a strong understanding of operations with fraction involving
like denominators. She was also successful in our money unit and understands operations including currency. Good work Fawn! It would benefit Fawn
to practice basic subtraction, addition, multiplication, and division facts during summer. A guide on some practice games has been sent home with the
report card! Feather–M Feather has had a great term three! She comes to class prepared and ready to learn. She has been completing her work ahead of
other classmates and receives free time to read. It has been great to see Feather improve this term. Keep it up! Titus–M Titus has a proficient
understanding

Hieroglyphics and History of Mathematics
Hieroglyphics deal a lot with the history of math, because it was one of the earliest of maths. The ancient Egyptians were the first civilization to
practice the scientific arts. It is said that the Egyptians introduced the earliest fully–developed base 10 numeration systems at least as early as 2700 B.C.
The word chemistry is derived from the word Alchemy which is the ancient name for Egypt. It was between the third and first millennia B.C. It later
then died in 400 AD. This was first used as legal matters such as commerce, education, literature, and science. This type of math was mostly used by
Egyptians, but there numbering was different than ours today. Instead of them using numbers they would use pictures to illustrate the numbers.
It is said that hieroglyphics were created by the Egyptian god Thoth. He is said to be the god of the moon, magic, and writing. Hieroglyph comes from
the root word hieros which is Greek meaning sacred, and the root word glypho which means inscription. Hieroglyphs were first used by Clement of
Alexandria.
It was first used in ancient Egypt, as a decimal numbering system. But the decimal was non–positional; it could deal with numbers of great scale.
Egyptian used this method mostly in medicine and geometry. The earliest known examples of hieroglyphs in Egypt have been dated to 3,400 BC. The
latest date in hieroglyphs was made on the gate post of a temple at Philae in 396 AD. The Egyptians were really involved in medicine and applied

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

Essay on Supersonic Flight
In 1943, Theodor Von Karman, in response to a request by US Air Force headquarters, claimed that the realization of a supersonic aircraft would have
been doable using the right technology and tools. The fear of breaking the "sound barrier" was finally removed in 1947, when the Captain Yaeger flew
the Bell X–1 at a speed slightly above Mach 1 for few seconds, producing the famous and long–awaited sonic boom (caused by an impulsive pressure
change created by the sonic waves detaching from the aircraft), music for the scientists attending that historical moment, but current nightmare for the
21st Century supersonic vehicles' designers [8].
Since the first wind tunnel investigations on high speed flow over a stationary airfoil (1918), it was ... Show more content on Helpwriting.net ...
The B–58 itself showed to the world that the possibility of a civilian SST was at least worthy of accurate investigation and capital investments.
Although the large bomber implemented the supersonic efficient area–ruling design first introduced by Whitcomb (mid 1950s [1]) and therefore it
could deliver a nuclear payload cruising at Mach 2 for about two hours, the light and thin wings, designed for high altitude flight and inefficient close to
the ground at subsonic speed, highlighted a new set of primary technical challenges to be addressed by a commercial SST: the realization satisfactory
structural design, the optimization of the wing aerodynamics for subsonic flow, and related to the last point, the improvement of takeoff and landing
performance. A deadly crash at 1961 Paris air show summed up all the concerns about safety issues related to a not optimal overall design [4].
Three civilian SST programs started in the 1960s: the successful Anglo–French Concorde, the somewhat failed Russian TU–144 and the short ten year
long attempt of the USA SST, all belonging to the category of what today is referred as "first generation" supersonic transport.
Politics played a big role in the development of a SST in the post–WWI years. European countries were looking for a way to challenge America's
leading position in civil aviation. In particular, British and French governments, moved by

Essay Significance of the Number 3 in Fairy Tales
Significance of the Number 3 in Fairy Tales
Numbers do not exist. They are creations of the mind, existing only in the realm of understanding. No one has ever touched a number, nor would it be
possible to do so. You may sketch a symbol on a paper that represents a number, but that symbol is not the number itself. A number is just understood.
Nevertheless, numbers hold symbolic meaning. Have you ever asked yourself serious questions about the significance, implications, and roles of
numbers? For example, "Why does the number ten denote a change to double digits?" "Is zero a number or a non–number?" Or, the matter this paper
will address: "Why does the number three hold an understood and symbolic importance?"
My interest ... Show more content on Helpwriting.net ...
Therefore, I offer what I call the Utility–Based Approach, which attempts to explain the prominence of "three" by noting its usefulness in telling fairy
tales. Indeed, the Utility–Based Approach proposes that "three," being the smallest possible number that denotes a group, is a useful entity when
recalling a tale whose audience is assumed to either (1) desire mental relaxation, or (2) lack advanced/complex mental capabilities.
Background/Historical Context
"Three" has a logical reason for its important role throughout history. It is not merely the number that happens to fall between two and four. "Three" is
the union of oneness and duality. It is the first number that is a combination of various previous numbers (assuming, as most societies have done, that
zero is not a number). One and two are special as they are representations of 'oneness' and 'otherness', but three starts the procession of all other
numbers to follow (the set of numbers, 3 ––> infinity, that can be the sum of a variety of previous numbers) (Symbolism). Whether this is realized
consciously or subconsciously, it is an undeniable truth that seems hard to avoid. Indeed, this idea could be what gave rise to the spiritual significance
of "three."
"Three" has always played an important part in the Judeo/Christian beliefs, as Ken Bassett outlines in his Pastor Note No. 138. First, and probably most

Charles Galton 's Theory Of Differential Psychology
Francis Galton was born into a wealthy quaker family, their fortune coming from his banker father. Of course, his mother wasn 't a nobody; she was the
daughter of the Erasmus Darwin, a man of many things, one of which was medicine. At an early age, Francis was expected to become a doctor by his
father, which didn 't leave him with much of a choice, since his father could cut him off at any time. So he went to Trinity and studied medicine and
mathematics, until he had a nervous breakdown from the pressure at 21. Fortunately, his dad died soon after, leaving him with a lot of money to do
whatever he wanted and no need to go into a field that he didn 't want to do. Galton was one of the first experimental psychologists and the founder of
Differential psychology. It is the study of characteristic differences and variations of groups or individuals, especially through the use of analytic
techniques and statistical methods. He was most known for his work in intelligence. He believed that aspects of human nature could be measured
scientifically. Galton tried to measure intelligence through reaction time tests. For example, the faster someone could register and identify a sound, the
more intelligent that person was. Galton believed that intelligence as well as some physical and mental characteristics of humans were inherited and
biologically based. Based on studies of prominent individuals and their family trees, he concluded that intellectual ability is inherited the same

Multiscale Modeling Of A Gas Separation Device
Multiscale modeling of a gas separation device based on e ect of thermal transpiration in the membrane
Vasily Kosyanchuka,b,, Valery Kovaleva,b, Artem Yakunchikova,b aLaboratory of Nanomechanics, Institute of Mechanics, Lomonosov Moscow
State
University, Michurinskyi aven. 1, 119192, Moscow, Russian Federation bDepartment of Mechanics and Mathematics, M.V. Lomonosov Moscow State
University,
Leninskie Gory 1, 119991, Moscow, Russian Federation
Abstract
This article studies a novel approach to improve membrane separation e– ciency { application of external physical in uence (temperature di erence
across the membrane). Oppositely directed pressure and temperature gradients in membrane establish a molecular exchange ow when two components
of the binary gas mixture ow in the opposite directions through the membrane. The model of gas separator based on this e ect is studied numerically at
di erent scales. At microscale (in membrane channels) solution of the linearized Boltz– mann equation is used. At macroscale (external part of the
device) the system of Navier–Stokes equations for two–component gas mixture is solved using nite volume method adopted for low Mach number
limit. Dependence of device e– ciency on all of the de ning parameters is studied and comparison with previous numerical simulation of the device
is made. The key feature of the device is that it can produce output gas with any purity up to 100% with temperature di er– ence of only 30K applied
to the sides of

How We Broke The Sound Barrier
How We Broke the Sound Barrier
Submitted by
Joshua Reichler
In partial fulfillment of the requirements of AES2050 – Aerospace History
To
Instructor: William C. Hoffman
Metro State University Denver
On
25th of September, 2016 Instructor Comments: Abstract
For humans to go faster than they have ever gone before they had to research many different things spend both money and time to finally reach this
goal and this paper will take you through that process of research done for that goal to be reached. With the possibility of faster flight people will
always want to see how fast they can push the aircraft they design. The development and research that went into the aircrafts that helped break the
sound barrier, took a long time and many people co–operation. But after many years of research and testing with several different types of aircrafts they
were able to succeed in producing an aircraft that could surpass the sound barrier and bring us into a new era of flight. The ideas on how to get an
aircraft up to the speed and the designs of many researcher had to come together in order for this feat to be accomplished. From the engineering stages
of the project to the research on how the air around the aircraft will react to an object moving through it to at such high speeds and the equipment that
needed to be made that can used during the flight all had to be crated for this to work (John D. Anderson, Jr. (2001, 1) Research in Supersonic Flight
and the Breaking of the Sound

Essay About A Lesson
The report analyses concepts taught in two lessons and links them to proficiency strands, contents descriptions, elaborations, general capabilities and
cross–curriculum priorities outlined in the Australian Curriculum. Furthermore, the report explores three best teaching practices commonly used in the
classroom and examines the benefits to students learning. Finally, a detailed lesson outline will be created.
The first lesson ('Christie') observes Christie Kawalsky at Saint Albans East Primary School teaching fractions to a Year 3/4 class (Australian Institute
for Teaching and School Leadership [AITSL] (Producer), n.d.–a). Christie demonstrates how teachers use concrete resources during explicit numeracy
lessons. Christie demonstrates ... Show more content on Helpwriting.net ...
Most importantly, Christie meets Curriculum standard 1.3 as she selects and uses resources and strategies appropriate to the strength and needs of her
diverse students.
The second lesson, ('Kelly') shows Kelly Rhinehart exploring addition and multiplication with a Year 5 class at Humpty Doo Primary (AITSL, n.d.–b).
Kelly focuses on students learning mental computation skills and developing automaticity through the use of open–ended eliciting. Kelly uses eliciting
to encourage students to investigate different strategies to solve math problems and explain the process they used to find solutions, which not only
empowers students to take control over their learning and engage them in the learning activities but also reflects proficiency strand reasoning.
Furthermore, Kelly teaches students to recognise and use patterns and relationships when developing strategies, which reflect the general numeracy
capabilities (ACARA, n.d.–c). Kelly starts the lesson with a warm–up activity of playing a dice game to learn nines timetable, which reflects content
description and elaborations of ACMNA098, as students learn to identify, describe and solve multiples using number sequences (ACARA, n.d.–c,

2d and 3d Method of Characteristics for Nozzle Design
Applied Physics Laboratory
RTDC–TPS–48 I
Laurel MD 207236099
Y
2D and 3D Method of Characteristic Tools for
Complex Nozzle Development
Final Report
Tharen Rice
June 3 0,2003
Prepared under Grant No. NAG3–2460, Design of Exhaust Nozzle for the RBCC– GTX
Concept, with the NASA Glenn Research Center
THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY
Johns Hopkins Road, Laurel, Maryland 20723–6099
1
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Applied PhytiCS Laboratory
RTDC–TPS–48 1
Laurel M D 207236(199
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Table of Contents
1 .0
Purpose ..................................................................................................................
2.0 ... Show more content on Helpwriting.net ...
4.2
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File Input/Output......................................................................................
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Grid Setup ................................................................................................
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Surface Fit ................................................................................................
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Initial Plane Properties .............................................................................
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Calculate Nozzle Button and Progress Indicators ....................................
4.2.6
Print Output Parameters ...........................................................................
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2D and 3D MOC Tool Verification ......................................................................
2D MOC Tool Verification ...............................................................................
5.1
3D MOC Tool Verification ..............................................................................
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References

Article Analysis: 'Representations In Teaching And...
The article, Representations in Teaching and Learning Fractions, explains the concept of teaching and learning fractions using representations. One of
the Common Core Concepts that is supported in this article is CCSS.Math.Content.3.NF.A.2: Understand a fraction as a number on the number line;
represent fractions on a number line diagram (Grade 3). Watanabe talks about using linear model to represent fractions. The article discuss about how
number lines do not help children comprehend fraction as numbers but only makes sense to those who already know fractions. Watanabe says that some
teachers think that number lines are useful tools to teach children relationships between whole numbers and fractions. The manipulatives that are
discussed ... Show more content on Helpwriting.net ...
Model is the instructional materials while representation refers both to process and to produce. I always thought these two terms were synonymous. I
learned that the difference between the comparison method and part–whole method is the relationship between the whole and fraction part. The whole
part method is the fractional part embedded in the whole while the comparison method is the whole and the fractional part are constructed separately
(p.459). I learned that we should write out the fraction words rather than the numbers because it is more consistent. For example, we should write 1–
half instead of 1/2. By writing the words instead of numbers, it helps children identify the fraction units.
This article would be appropriate for third teachers as well as other elementary teachers because Watanabe mentioned about how fraction is one of the
challenging topics for elementary children. Elementary is when the children starts to learn fractions. The article talks about whether these tools or
methods are helpful to students who are beginning to learn fractions. Watanabe comments that number lines are often used in primary grades. The
article mentions that children should understand fractions as numbers before going

Statment of Intents for MS Program in Aeronautical and...
Statement of Intent a part of the application for MS program in Aeronautical and Astronautical Engineering He had a suspicion of plausible answers;
they were so often wrong. – Arthur C. Clarke, Rendezvous with Rama. I believe that the above words of sci–fi writer Arthur Clarke have multiple
connotations – to life, human nature or science. Or even computational studies. Higher ideologies aside, I am certain that I had always possessed a
predilection towards fields that involved a scientific mindset – fields that required great humility along with the obvious and much needed eagerness to
learn. If mere fascination for all things that flew wasn't enough, the child in me always dreamt of doing a space–walk someday. Like for any ... Show
more content on Helpwriting.net ...
I had great interest in the subject Heat and Mass Transfer as well, which was compulsory. 4th semester had also given me the choice of taking up the
elective subject Introduction to Aircraft Industry and Aircraft Systems which I readily took up. With the help of a great and experienced faculty, that
subject provided me a brilliant know–how of the happenings in the aviation industry and also provided me a grasp of the basics of flight along with the
control systems that aid. During the summer that followed the end of third year, I was selected as a trainee in one of the best labs in the country – The
Advanced Systems Laboratory (ASL) at the Defence Research and Development Labs, Hyderabad. This was the programme that had changed my
mindset for the better and gave the required direction. Apart from witnessing at a yard's length the manufacture and fabrication of parts that made the
Agni missile, I learnt, what was then, a very surprising thing to me– the right computational methods and simulation meant everything for the success
of this nationwide defense project. This is where I grew to finally understand that mere fascination is not enough. Rather than fascinate me, I must say
that my time as a trainee there had humbled me. Computational methods, for the lack of perfect analytical solutions, were the key to designing any
engineering product, for which safety and cost effectiveness are critically important. I

Essay On Ello
Step 14: Draw place–value blocks
Tell students, another way we can solve this is drawing place–value blocks. Tel students a line will represent a tens rod and a unit cube will be
represented by an X. (Draw and label on ELMO for students to see)
Model how to represent 39 with place–value blocks.
Draw the three long lines on ELMO to represent the three equal rows that Nelly wants to use to divide her 39 stickers.
Inside each line start to draw one vertical line to represent a tens rod, then draw 3 X's per line to represent 3 unit cubes.
Each row should have one line (tens rod) and 3 X's (three unit cubes).
Ask students how many place–value blocks do we have per row? (13)
You can draw place–value blocks to help you solve division problems whenever you don't have place–value blocks to help you solve a problem. ...
Show more content on Helpwriting.net ...
Step 16: Write an equation
Now that we have modeled division with place–value blocks and drawings lets come up with an equation.
Write on ELMO:
Step 17: Introduce mnemonic: Does McDonalds Sell Cheeseburgers?
Explain to students the mnemonic Does McDonalds Sell Cheese Burgers? will help them remember the steps for division
Write down these steps next to the division equation on the ELMO and go over each one with students o D– Divide (÷) o M– Multiply (x) o S– Subtract
(–) o C– Check () o B– Bring down ()
Provide handout to students for them to glue in their math

The Importance Of Reducing The Intensity Of A Sonic Boom
Shawn Merrick–Miller Ryan Cilsick Science Research 12/20/16
The importance of reducing the intensity of a sonic boom is essential to making supersonic flight a possibility for passenger aircraft over land.
Currently, supersonic flight over land in the US is prohibited by the FAA due to the annoyance associated with the sonicboom to people (observers) on
the ground. The advancement of sonic boom reduction could lead to the advancement in the way we travel around the world with amazing speeds.
Speeds up to mach 3.3 at 88,000ft (That 's nearly 17 miles!) can be achieved in an SR–71 Blackbird, that keep in mind, it was made and introduced in
1966. 50 years later, we have the ability to transport people vast distances and at high speeds safely, but we don't. Why not? Getting up to speed is not
the issue in this circumstance, the issue is doing it quietly. It can be said that this problem can be eliminated by making a suborbital transport aircraft,
which could be very beneficial, but will still create a sonic boom, and will still, annoy people. At a higher price. Supersonic flight was pioneered by the
air force in 1947, when Chuck Yeager became the first man to break the sound barrier. Shortly after, supersonic aircraft research was started.
Supersonic cruising aircraft did not begin until the mid–1950 's. Research on such aircraft had its origins in the United States in the work which was
begun in 1954 or 1955 in support of the Air Force XB–70

What Is Relative Absolute Unfairness?
To figure the Hamilton Method first thing you need to do is come up with a standard divisor. This is determined by dividing the total population of all
the states by the number of seats available. In the example given there are 5321, 88 people divided by 100 seats.
Divisor = __Total Population = D 532188 = 5321.88 Number of Seats 100 Now you take the number and divide it by the population of each state. This
is what they determine the Standard Quota.
State Population = Standard Quota 5321.88 Using the Hamilton Method you have to round down to the nearest whole number. If you round up you will
come out with more seats per state than are available. For the additional seats left over, they are given out based on the decimal going from largest to
the smallest, but every state no matter how small must have a Representative. Because we ended up ... Show more content on Helpwriting.net ...
The absolute unfairness is the difference between the average numbers of people per representative in each state, i.e... the difference in average
constituencies (Apportionment Practice Hamilton, 2015). Relative unfairness is a better measure of unfairness because it takes into account the size of
the population of the states. It is calculated as follows.
Relative Unfairness = Absolute Unfairness/ Smaller Average Constituency of the two states (Apportionment Practice Hamilton, 2015).
State 3 has the highest constituency of 5486.44, state 4 has the lowest constituency of 369. I would subtract the two. 5486.44 369____ = Absolute
Unfairness value of 5117.44 5117.44 The relative unfairness is completed by dividing the absolute unfairness by the smallest constituency, so it would
be. 5117.44 = 13.87 Relative Unfairness.

Accounting Standards And The Codification System
DATE: January 19, 2016
TO: Chris Yost, CPA
FROM: Holly Thobe, Junior Accountant
SUBJECT: Using the Accounting Standards Codification
All Staff Accountants must learn how to research GAAP accounting standards using FASB's accounting standards Codification system. The purpose of
this memo is to provide instructions on how to research the accounting standards using the new Codification system. Users will discover how to
research the accounting standards using the Codification system, explore the updated revenue recognition standards, and learn how to access updates
from the system.
FASB Accounting Standards Codification
The FASB Codification database is easy to use when researching the accounting standards once the basics are fully understood. The FASB Codification
database can be accessed by logging in at http://aaahq.org/ascLogin.cfm and using the following codes (case sensitive): Username – AAA51207
Password – HFdU64n
The Codification uses a hierarchy to organize its subject matter. Area is the largest collection, and then comes topic, subtopic and section. Each topic,
subtopic and section is identified with a number and a title. The numbers provide a simple way to find specific accounting guidance. A three–digit
number and a title identify topics. The first digit of the numerical identifier resembles the area of the topic. Subtopics are either exclusive or shared.
Exclusive subtopics have unique content and shared subtopics have common content. To identify

Roman Numerals
Roman numerals originated in ancient Rome. It lasted from 8th century BC to 2nd century AD. When the Romans became industrious in trade and
commerce, they soon realized that they needed a method of counting, assuming all they had at that time were fingers to count on. So they developed a
system based on their hands.
An I, based on one finger, was used to represent the number one, II, two fingers, for the number two, and III, three fingers, for the number three.
The numeral for the number five, V, came from the v that your hand makes between the thumb and fore finger. IV was used for the number four by
subtracting the first letter, I from V. The numeral X, or ten, came from using two hands. The numbers were made by joining

Kidwatching Project Analysis
For the Kidwatching Project Part 1, I found myself interviewing a few students on the concept of multiplication and division. According to Merriam–
Webster Dictionary, multiplication is defined as the process of adding a number to itself a certain number of times: the act or process of multiplying
numbers. Merriam–Webster Dictionary also defines Division to be the act or process of dividing something into parts: the way that something is
divided (Merriam–Webster, 2015). Multiplication and Division is a subject that many different students in early ages can grasp or struggle with because
the concept of using different ways to approach these particular problems. Many kindergarten children can solve simple multiplication and division
problems

Evaluating Janet's Vocabulary
Reason for Referral and My Suggestions Janet is experiencing academic difficulty in mathematics and timed tasks, however her language skills
(vocabulary and comprehension) appear to be strong, yet her parents feel it would be best to evaluate Janet in order to draw on her strengths and help
pin point her limitations. As the psychologist that will be evaluating Janet, I will be administering the following tests:
Wechsler Intelligence Scale for Children– IV (WISC–IV) o Consists of 15 subtests, 10 of which are designated as core subtest used in the computation
of composite scores and full Scale IQ, and five of which are designated as supplemental (Gregory, 2010, p.172).
Wechsler Individual Achievement Test –II (WIAT–III) o Consists ... Show more content on Helpwriting.net ...
My reasoning for using this theory over another would be the architectural system (hardware) refers to biologically based properties necessary for
information processing, such as memory span and speed of encoding/decoding information (Gregory, 2010,, p.154). Memory span and speed of
decoding is very important when dealing with mathematical work such as how remember our multiplication table, which some individuals remember
by using mnemonic techniques while still others struggle. According to Gregory (2010), individuals who are able to use the metacognition approach to
learning tend to have higher performance levels than those individuals that do not use the metacognition approach. Two Other Theories of Intelligence
in Comparison Gardner's original Theory of Multiple Intelligences consists of three components, seven intelligences, and eight supporting criteria of
what comprises an intelligence. The Three Components include: a definition of intelligence, a challenge to the notion of a general intelligence (g),
and a challenge to the conviction that g can be reliably measured. (Helding,

Nt1110 Unit 7
So what we need to do is convert each number into binary and then use the number defined by the subnet mask to pick out the nth most significant bits
and then convert the number back to decimal, followed by checking that number against the provided table.
135.46.63.10. In binary this is 10000111.00101110.00111111.00001010. The 135.46 preface points us to one of the Interfaces on the table, which both
have a subnet mask of /22. The 22 MSB's of the binary are 10000111.00101110.00111100.00000000. Back to decimal, this is 135.46.60.0, which
matches Interface 1, so it is routed there.
135.46.57.14 in binary is 10000111.00101110.00111001.00001110. Again the prefix points us to one of the Interfaces, so we take the 22 MSB's, or
10000111.00101110.00111000.00000000. Back to decimal, this is 135.46.56.0, which points to Interface 0, so that's where it is routed.
135.46.52.2. In binary this is 10000111.00101110.00110100.00000010. Again, we are looking at one of the Interfaces, so we take the 22 MSB's, which
... Show more content on Helpwriting.net ...
Give one reason why PPP uses byte stuffing instead of bit stuffing? Tanenbaum(2011) states that the primary reason behind this is that PPP is byte–
oriented. While HDLC is still in use to a limited extent, it was created before the Internet as part of the OSI model. The internet itself is byte–oriented,
so it follows that PPP (as a protocol designed for the internet) would use byte stuffing instead of bit stuffing.
References
Tanenbaum, A. S., Wetherall, D. (2011). Computer networks (5th

Different Visual Illustrations in Perception Essay
Different Visual Illustrations in Perception How can visual illusions illustrate top down processes in perception? Contrast this with a visual illusion that
can be explained through bottom up processes.
Text Box:
Figure 1 Muller Lyer illusion
There are many suggestions to explain how visual illusions can be perceived. These suggestions include physical illusions, bottom up illusions and top
down illusions. An example of a physical illusion is ... Show more content on Helpwriting.net ...
In this illusion the lines in both A and B are the same length however the arrows pointing inwards in A make the line appear longer than when the
arrows point outwards as in B. Gregory explained this illusion in 1970 by suggesting that the lines are perceived as being three dimensional rather than
two–dimensional. This is shown in figure 2 where A is shown as the inside of the room and B shown as the outside. By perceiving the objects in this
way A becomes further away than B. However given that the lines are of the same size by applying the principle of size constancy it can be concluded
that A is perceived as being longer than B. For this to be perceived knowledge about what the outside and inside of a building looks like must be taken
into account. This therefore shows how prior knowledge is used when the image is perceived and so shows how the Muller Lyer illusion is perceived
through top down processing.
Similarly the Â'Necker CubeÂ' illusion (figure 3) can also be explained through top down processing. In this illusion the cube flips between two
different interpretations of the picture whereby one of the faces of the cube can appear to be at the front of the cube but also can appear to be at the back
of the cube. Work carried out by Wheatstone

Mathematics Of Creative Writing : Exposing The Invisible Tool
Mathematical Proportions in Creative Writing: Exposing the Invisible Tool
In the academic world, creative writing and mathematical proportions are often considered to be located at opposite ends of the spectrum, but they are
not as different as they seem. Authors often need to carefully plan and divide their story to create an end result that is a balance between exposition and
dialogue, romance and action, or tragedy and comedy. That is where mathematical proportions come in–ratio and fractions in particular. Every author
uses ratio and fractions, whether they know it or not, and the proper use of them determines the quality of their writing. Who would read a book that's
70% exposition or 100% dialogue? Therefore, in this essay I will ... Show more content on Helpwriting.net ...
Fractions can also be used to represent ratios or even division equations and all rational numbers. While fractions come in many different forms such as
mixed numbers, improper, vulgar and proper fractions, the function of a fraction is generally the same–to represent parts of a whole. To simplify the
matter further–if you can solve a division problem, then you are able to use fractions. In fact, you use fractions all the time without a hint of doubt. For
instance, when we tell the time, use or recipe or figure out the price of an object after a sale–it is all fractions. We use them every day, but why? What is
the inclination to measure ingredients in halves, quarters and two–thirds? Why do we reflexively say Half past 3 when telling the time? It is all
because parts of a whole are far more common than complete collectives of any one thing. So let us take a step back and analyze a fraction: 2/5. 2 is
considered the numerator, and 5 is the denominator. 5 would be the whole–for instance, there are 5 stuffed bears in total. But then 2 is the amount we
have from the whole–as in, we only have 2 of the 5 stuffed bears. A slightly more challenging problem would be saying that a $50 shirt is ½ price. To
solve this, we would simply convert 50 into an improper fraction (a fraction in which the numerator is larger than the denominator), 50/1 and multiply it
by ½. This would result in the improper fraction, 50/2. You would then simplify

Reflection Of A Interview With The Algebra Interview...
For the student interview, I interviewed a 9th–grade boy and used the Algebra Interview questions. When we started the interview the boy was very
apprehensive. I assured him it was not a test, and not much writing was required. He slowly started to relax. I read the first question (1a) out loud and
had barely finished when he gave me the answer. His mental math was in high gear despite his initial apprehension. I proceeded to the next question
(1b) with the same result. He provided an answer quickly to this question as well. I was beginning to wonder if this was going to be too easy for him, so
I asked him to write down and explain his thinking so I could understand how he got the answers. For number (1a), he explained that he multiplied 6 by
3 because Alice ate 6 ounces of cake and she grew 3 feet for each ounce of cake that she ate. He then added the product of 36 to her original height of 4
and came up with the answer of 40 feet. For (1b), he modeled a different approach where he started with 16 feet and subtracted 4 increments of 3 until
he arrived at Alice's original height of 4 feet. He told me that he knew that he needed to get to the base height, and that is why he used subtraction. He
did it in increments of 3 as he knew that Alice grew 3 feet/ounce of cake. For question (2) he again used mental math and came to the conclusion that it
was 4 feet/ounce of water. His rationale was the same as for (1b), to get back down to the base height. At this point, it

Surface Pressure Measurements on an Aerofoil in Transonic...
DEN 302 Applied Aerodynamics
SURFACE PRESSURE MEASUREMENTS ON AN AEROFOIL IN TRANSONIC FLOW
Abstract
The objective of this exercise is to measure the pressure distribution across the surface on an aerofoil in a wind tunnel. The aerofoil is tested under
several different Mach numbers from subsonic to supercritical. The purpose of measuring the pressure distributions is to assess the validity of the
Prandtl–Glauert law and to discuss the changing chracteristics of the flow as the Mach number increases from subsonic to transonic.
As a result of the experiment and computation of data, the aerofoil was found to have a critical Mach number of M=0.732. Below this freestream Mach
number the Prandtl–Glauert law predicted results very ... Show more content on Helpwriting.net ...
However it is deemed reasonably accurate for cases such as this in which thin aerofoils are tested at small incidence. The law does not hold in super–
critical flow when local regions of supersonic flow and shockwaves appear.
The value of the critical pressure coefficient, Cp*, according to local sonic conditions is calculated by:
Cp*=10.7M∞25+M∞263.5–1forγ=7/5 (6)
The co–ordinates for the NACA 0012 section are as follows:
Figure 1–Co–ordinates for aerofoil (Motallebi, 2012)
Results
Given atmospheric conditions of:
Patm=30.65 in–Hg
Tatm=21°C
The following results were achieved:
Figure 2–Pressure coefficient vs x/c for M=0.83566
Figure 8–Cp* and Cpminvs Mach Number
From figure 7 the critical Mach number is

Common Sense Abbreviations
The common sense approach to abbreviations should apply to PSI reports as well. Of course one can abbreviate suffixes (Dr. Mr., etc.), words like rd.
(road) st. (street) and ave. (avenue). Agency names could be spelled out completely and followed in parenthesis, i.e. State Bureau of Investigation
(SBI). Beyond these, I see no reason to include abbreviations to the point that they are even a topic of discussion. Probation officers are not really
relaying a personal opinion in the PSI. They present documented and measurable progress of the individual under supervision. The officer might have
assigned a rating for the offender based on their behavior during an interview, such as level of remorse on a Likert scale. The recommendations

Characteristic Studies Of Supersonic Diffuser With Various...
Characteristic studies of supersonic diffuser with various ramp design and optimization of ramp profile
Objective:
The main idea behind the proposed project is to decrease the pressure loss at the supersonic diffusers with the help of varying the conventional ramp
design. Three different ramp profiles (Sharp edged conic section, Blunted conic section and Ogive conic section) are optimized for the particular inlet
Mach number. The efficient design for the supersonic compression process is to be obtained from the experimental analysis.
Introduction:
Designing supersonic diffusers requires more concentration than the subsonic diffusers, which is mainly due to the formation of shockwaves. In this
scenario, the ramp (a part of the supersonic ... Show more content on Helpwriting.net ...
They are: o Ramp body, o Fore body of subsonic diffuser, o Rear body of subsonic diffuser.
 Ramp body:
The ramp body is the component to create shock waves. The ramp body has a collar for mounting purpose along the axis of the diffuser.
 Fore body of the subsonic diffuser:
The fore body has the cowl lip section which generates the normal shock waves. The fore body has the ports across its walls to measure the static
pressure inside the diffuser section.
 Rear body of the subsonic diffuser:
The rear body which is very helpful for stream lining the flow flied from the diffuser. The collars of the all components are connected together which
provides the whole setup of the supersonic diffuser.
The mounting system is also to be designed very carefully, to facilitate testing of the model in the laboratory, using open test jet facility.
Methodology:
 Design a conical nozzle for the desired exit Mach number.
 Optimally design a fore body and rear body (cowl) of the diffuser.
 Analyse the preliminary design with the help of an analysis software (ANSYS).
 Optimize the design further depending upon the CFD results.
 Fabricate the nozzle and the diffuser along with the mounting system.
 Carry out experimental work using the Open jet facility available in the Aerodynamics laboratory, Department of Aerospace Engineering, Madras
Institute of Technology.
Implementation:
The project is to be implemented in three phases:
 Phase I: Preliminary

The Learning Objective Of The Lesson Comparing Fractions
Activity 1: Comparing Fractions (October 12, 2016) The learning objective of the lesson Comparing Fractions was to demonstrate to students that
fractions are everywhere we go and the importance of being able to identify fractions with greater or less value when comparing fractions.
Engage
During this activity students were very engaged, they created their own figures using the pattern blocks. Below there are some of the examples of the
figures that students come up with (see fig.12). After creating these figures, they realized that they could have use tringles to make their figures
instead of the different shapes. So, I ask them Could you show me how this could work? Some students started to make the same figures but this time
only using tringles. However, I noticed that David, one of the students was not doing the same as his classmates. Instead, he was writing a key, he wrote
how many triangles were in a Hexagon, a rhombus, and in a trapezoid. Then he said I think that I need 21 triangles. I thought that was very
impressive for him to completely do something different than his classmates. Then, I saw the opportunity to allow him to continue with the lesson while
the others were still figuring out how many triangles were needed to create the same figure. After everyone was done with counting how many triangles
were needed for their figures, I asked them to create fractions to represent the different shapes in their figures. In order for students to see from an

Integrated 1 And Macdougall Littel Algebra Summary
Review of Standards of Text
Amanda E.L. Kent
Chico State University, Chico
November 18, 2014
Professor Matthews
Author Note
Review of Sequences in CPM Common Core Integrated 1 and MacDougal Littel Algebra 2
The introduction and understanding of sequences, arithmetic and geometric in 8th grade was reviewed for content and standards in CPM CC Integrated
1 and MacDougall Littel Algebra 2. Sequences are defined as an ordered list of numbers that are in a specific pattern. Arithmetic Sequences are an
ordered list of numbers where the difference between successive numbers is a constant value. Geometric sequences are an ordered list of numbers
where the successive numbers differ by a common ratio.
Sequences in California ... Show more content on Helpwriting.net ...
Make sense of problems and persevere in solving them. In each section 5.2.1–5.2.3 the students are required to make sense as a group and persevere in
solving the problems. Example of the practice is seen in 5.2.1 5–42, 5.2.2 5–59, and 5.2.3 5–74. Each problem in this text is recommended that the
students work in groups and there are no formulas, or rules given until the students have reasoned out the problem and solved as a group. By having the
student reason and understand, then persevere, the student gains an understanding of the concept in sequences rather that the rule. Given that many of
the lesson plans are built around the students making sense of conceptual problems this practice seems to be the focus of the sections. Used beyond
moderately, it is the stepping stone to the

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