Naplan Test Paper

Naplan Test Paper
Introduction
I was quite confident in completeing the compulsory NAPLAN Year 9 questions, I have a high level of understanding in the three numeracy strands
("Numeracy," 2016) covered in the test and the questions that were selected cover the range of topics. The NAPLAN test is a compulsory test that
enables the assessment of students from years three to nine, which provides statistical analysis to ensure the students are meeting the relevant
educational outcomes for their year.
Question 1
My confidence in completing this question was quite high, as the cubes are clearly visible and the top view, or plan view is identifiable by the white
top section of each cube, with the sides being grey or shadowed to show a diferent side in a three dimensional drawing ("Isometric ... Show more
content on Helpwriting.net ...
Another way would be to find the difference between the pre 3d ticket and after as followed.
To calculate the mean involve adding all the costs up before the 3d movie ($41) and dividing them by the total number of tickets (4) which equals
$10.25, using the same steps to find the mean after the 3d movie is $75/ 5 movies = $15 a difference of $4.75.
To find the range the numbers need to be aligned numerically, 8, 10, 10, 13, Subtract 8 from 13 leaves the range of 5, if the 3d movie ticket price is
added into the list 8, 10, 10, 13, 34, subtract 8 from 34 leaving the range after the 3d movie of 26.
Again to find the median it is essential to align the numbers numerically, 8, 10, 10, 13 is and equal number therfore we must use addition to calculate
the two middle numbers (10+10) and divide this by two, (10+10)2 which equals $10 if the 3d movie ticked is added into the equation 8, 10, 10, 13,
34 the median is still
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Age Group Justification Paper
Age Group Justification
According to Piaget's theory of cognitive development, 4th graders between the ages of 9 and 10 are primed to begin exercising more complex logical
conceptualizations of knowledge. To illustrate, one of his basic assumptions includes the idea that by this age group–– they should be able to generate
(construct) and analyze patterns (Ormrod, 2017, 29). This is evidenced as their thought processes are organized into larger systems of mental processes
and operations that allow them to conceptualize information in more logical or "adult–like" manner. Furthermore, the content presented in this lesson
is appropriate for this age group of students by virtue of the idea that though they are not keen to the purposes of double–digit multiplication in real life
/authentic settings –– they are starting to mature and will be more eager/ready to learn more advanced concepts (Ormrod, 2017, 31). Finally, we
perused the Georgia State Standards of Excellence's guide for instruction in fourth grade. Our lesson was based upon the following two standards:
MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for
the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
MGSE3.NBT.5 Multiply a whole number of up to four digits by one–digit whole number, and multiply by two–digit numbers, using strategies based on
place value and

Kayleigh Poudrier, Jakara Small. 05/02/2017. Ma112-002.
Kayleigh Poudrier, Jakara Small
05/02/2017
MA112–002
Dear Ms. Politis,
Upon observing your class, we have learned a lot about the methods you utilize in order to help the students with mathematics and about how the
students learn. Observing your class was both an honor and a learning opportunity for us, as you are an important, and well–respected faculty member in
the school system. However, while we appreciate your goals and tactics to make learning mathematics easier for the students, we have discovered some
flaws in the use of mnemonics, rules, and tricks for helping students understand the subject material.
Procedural knowledge involves working out a procedure, but the students may not understand the reasoning behind a procedure. ... Show more content
on Helpwriting.net ...
Mnemonics can be detrimental in the sense that they often prevent students from truly understanding what it is they are learning. Instead of learning
math, they are just learning a process.
There are many tips and tricks that have an "expiration date"(Bush and Dougherty, 2014), or are unable to be utilized by the students in more than
one situation. One of the tricks that does not carry through to every situation is having students use keywords to solve word problems. Now, while
finding key words in a word problem can make it easier to identify what the problem is asking in some instances, they can also mislead the student.
The keywords that students are taught to look for can be misleading because in different circumstances, these words can be used to mean different
things. If a student is only able to associate one word with one meaning, they could be missing the overall conflict of the world problem and complete
the wrong operation in order to solve it. The trouble with teaching students to only identify key words in the problem without regarding the other
terms comes when there are multistep word problems. While there may be a familiar key word in there, the student may be missing another step that
is needed to reach the answer that is not given away by a keyword, or the student may not fully read the problem in order to

Use Of The Abacus Script By Leiden Huber And Denise Tran
How to Use the Abacus Script
Created By: Leiden Huber and Denise Tran
Leiden: Hi. Today we are going to show you how to use the abacus and tell you a couple background details about it too.
Denise: The abacus is also known as the "saunpan" (calculating pan) and was created by a mathematician named Cheng Dawei. He created it during
the Ming Dynasty which was in reign from 1368–1644 B.C. and is known as the Fifth Invention of China. The Chinese abacus is very similar to the
Roman abacus and was thought to be influenced by it.
Leiden: The typical abacus is about 20 centimeters high and comes in varying widths depending on how many rods it has (usually has 7 or more
rods). Its beads are usually rounded and made of hardwood making them able to last for a long time. Lastly, the most important fact to know about
the abacus is that is has 2 beads in the in the upper deck which have a value of 5 and 5 beads in the lower deck which each have a value of 1.
Denise: The bars outside of our abacus is called the frame and the bar separating the top and bottom row is called the beam. Each section is also
called a deck. These are very important terms to know when talking about the abacus.
Leiden: Now you know some facts about the abacus' history; next we'll show you now to do basic calculations using the abacus. The first form of
calculation I will show you how to do is adding on the abacus. This one is very basic and you should be able to do it in no time. Before you start your
addition

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 Describe How You Demonstrated Respect For And...
Describe any changes in the lesson plan and the reasons for those changes.
[ The lesson plan was cut short due to a two hour snow delay, this change forced the lesson plan time to be shorter than expected. Due to this change, I
decreased the amount of whole group instruction. I made this adjustment because I wanted to offer students as much peer discussion and social learning
as possible within the time offered. ]
2. N/A for Educ 364
3.Promoting a Positive Learning Environment
a.Describe how you demonstrated respect for and rapport with all learners.
[ During the lesson, I always address the focus learner by his first name, Peter. When he would get through parts of the lesson, I would tell him that he
was doing a good job and that he could move onto the next activity when he was done. I introduce the lesson to the entire class by stating the
expectations, the activities, and materials used. During the lesson, I observed that Peter was very comfortable with both myself and his peers, this
observation can be determined when Peter completes a problem on the board during the ... Show more content on Helpwriting.net ...
This allows the student to become increasingly engaged and motivated in the class. Peter is engaged during peer discussion and classroom discussion.
Peter is not a 'leader' among the group; however, he did participate to complete a multiplication problem in front of the class. During this volunteer
time, Peter was aided by his peer, Michael to further his understanding of repeated addition. It has also been discovered throughout the school year that
Peter is a hands on learner; the manipulatives present in the lesson keep Peter more engaged and increase his learning outcomes. Peter was able to
complete the multiplication problem 10x3 on the board using the area model format; this displays that Peter understands the method of breaking
numbers into equal groups.

The Teacher Had Put On Board
''Slightly and squeaky!" The door to the classroom flew open as I burst into the room and sat in my usual seat. This was the day I was going to
learn how to do polynomial long division. "Good morning." The professor said, as she walked into the classroom. Almost every one of the students
had at least a pencil and notebook copying notes that the teacher had put on the board. After writing the notes down, I said to myself let me try to do
one of the problems that the teacher had put on board. Surprisingly, I could not start the problem because I did not even understand the first step.
Therefore I stopped and wait on the professor.
After the teacher did the first problem, but she did not do or put all the steps on the board, she skipped some of it. She said "you guys should have
known how to do this stuff already. This is not elementary or grade school, so I am not going to do or write every little step. Without paying close
attention and understand every single steps and everything she was saying. The first thing I did was, I immediately started the next one. I started good.
I did the first step which was the division part. Where I had to change the way the problem was writing and to look at that first number of the guy that
I was going to divide into. I got stuck in the middle of step number two which was the multiplication part. In the multiplication step, I had to multiply
the divisor with the quotient. However, I did not know if I had to put the answer right under the

My Reflection Of Mathematics : My Experience In Mathematics
Mathematics has been my favorite subject since I was 12 years old. It all began when I was 9 years old, back in Mexico. As any child, I struggled a
lot with math, I did not know how to multiply in my 3rd of school, in fact, I did not learn the multiplication table during that time. I struggled with
subtractions and additions as well. That was not bad at all, I really love that at that time I was having troubles with math. As a big sister's must have,
my big sister, who was really good at mathematics, helped me with math problems, homework and anything related to math, I felt lucky, not for her
helping me, but for me sharing time with her, when that happened she tied to teach me how to solve more advanced math problem. At a very young
age, I learned that math was not only a subject to struggle with in school, but it was logic, all those problems presented in my math class were some
kind related to real life problems. When I understood that, I become more efficient at math, I was able to present a math problem in as many ways as I
could, I saw mathematics more familiarly.
Time passed, my sister left the small town where we lived to go to the city to follow her dreams and achieve a career, I thanked my her for those
advises in math, and promised I would be just like her. Though, I thought I was not that great at math, not that low, but at least I could "understand" it.
In no time, I became a 8th grader, or a "1st secondary grader" how it is known in Mexico. My math teacher was

Higher Order Essay
Higher Order Thinking and Diverse Learners
Grand Canyon University: Secondary Methods and Data–Driven Pedagogy
April Smith
GCU: SED–444
August 25, 2013
Grand Canyon University: Secondary Methods and Data–Driven Pedagogy
April Smith
GCU: SED–444
August 25, 2013
This unit is designed for students in beginning Algebra classes. It is an introduction to the basic functions of algebra including the definition of an
equation, using basic mathematical skills to solve equations, and applying equations to problem solving.
South Carolina Standard 8–3: Through the process standards students will demonstrate an understanding of equations, ... Show more content on
Helpwriting.net ...
Algebraic Equation Unit Plan | Knowledge| Comprehension| Application| Analysis| Synthesis| Evaluation| Algebraic Equations| State the definition of
an Algebraic Equation? Explain how to identify an Algebraic Equation?| Describe the parts of an Algebraic Equation including variables, like terms,
and coefficients.| Apply labels to the parts of equations and illustrate knowledge of like terms.| Classify problems as Algebraic Expressions or
Algebraic Equations. | As a group create sample problems and then share with the class the results.| Students will complete a group quiz and label each
part of an equation. They will also explain the difference between an expression and equation.| Algebraic Equations using Addition and Subtraction|
Students will tell how addition and subtraction can be applied to solving an equation?| Students will restate the steps involved to solve an equation
using addition and subtraction.| Students will practice solving equations using addition and subtraction.| As a group students will compare their results
in their practice problems and create questions for discussion.| With a partner, students will compose equations and exchange with another group. |
Students will evaluate another group's equations and share with the class their results.|

Hill Cipher
CioheWednesday, April 13, 2016
University of Botswana
ISS 334 LAB 2 ASSIGNMENT
Ndlovu.I 200902852
Ndlovu.I
ISS 334 Lab 2 Assignment
Page 1 of 27
Wednesday, April 13, 2016
Contents
1.
Hill Cipher Description .......................................................................................................................... 3
2.
Question ................................................................................................................................................ 3
3.
Implementation .................................................................................................................................... 3
3.1.

Hill Cipher Encryption and ... Show more content on Helpwriting.net ...
Step 3 is the same as Step 2 but using a different matrix multiplication to find the key. All the programs have written in java using Dr. Java.
Ndlovu.I
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3.1. Hill Cipher Encryption and Decryption
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3.1.1. Part 1
Class Basic the class has the indexOfChar and indexAtChar method.
The first method matches characters of a string to the alphabet and returns a numeric value, the second method is used to return a char which is located
at the position int pos.
Class Hill has an object basic of the class basic so as to access the methods from the basic class, this is done later on in the program.
Class Hill also contains method Hill, this ensures that the matrix we are using is a 2X2 matrix, that's why the variable block=2.
The method reads the key matrix. The user will enter in the first number and press "enter" and do this until the fourth number is entered. The
assumption is that we are using a 2x2 matrix as the key size.
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3.1.2. Part 2
The method KeyInverse also reads 4 integers which are stored to the double array Key[][] and uses them for the decryption key.
The method encryptBlock is

Thinking, Fractions And Decimals Are Extremely Important...
Multiplicative thinking, fractions and decimals are extremely important areas of mathematics children are required to develop. The concepts within
these three areas are related and it is critical for educators to support these relationships in the classroom. Multiplicative thinking involves recall of basic
facts, the relationship between multiplication and division and underpins the development of fractions. Comprehension of fractions includes the
division of objects, fractions as numbers, the multiple ways equal fractions can be represented, as well as being represented as decimals. Place value
is a very important underpinning concept of decimals. Place value aids the ability to read, write and work with decimals. There are a number of
difficulties children can come across when developing these concepts and relationships. With a vast mathematical content knowledge and pedagogical
content knowledge educators can provide effective instruction to help children over come their difficulties. Developing a deep understanding of
multiplicative thinking, fractions and decimals will assist children in later mathematics.
To become a multiplicative thinker the ability to recall basic multiplication facts and understanding of the relationship between multiplication and
division must be developed. If children do not develop the ability to recall basic multiplication facts they can be in danger of developing negative
feelings towards mathematics and becoming withdrawn (Booker, Bond,

Design Of The Games For Primary School Children
CHAPTER 3: DESIGN
In this chapter, we describe the design of the games for the project which covers the interfaces and structures of the game, the components and the
technical details of the game using flowcharts to describe the various processes of the game. Also, the purpose of the game and how the purpose can
be achieved are discussed here. These are presented under the following sub headings:
1.How are the games structured?
2.How are the games built?
3.What are the purposes of the games?
4.How can the purposes of the games be achieved?
5.How can the games be tested?
These questions tend to address how the games are built towards achieving its purposes. The questions are addressed as follows:
3.1How are the games structured?
The ... Show more content on Helpwriting.net ...
The player would then receive the final inspiring comment. From here the player would be prompted to either exit the game or start again.
The benefits of starting again cannot be overemphasised as the player tends to master the game thereby mastering the subject the game is built to
teach. To begin with, the game has to get a start menu so that the player would not be thrown straight into playing the game. The Menu would then
link to the different games which the player would have to choose from. The levels of the game and the process of winning in all the games are the
same. It involves the player doing the right thing as required and moving on to the next level till the game is completed. 3.1.1 The Main Menu
Each game begins with a Graphical User Interface that shows the Main Menu of the game which ensures that the players do not just start playing the
game as soon as the program is loaded. This acts as the control panel for the game allowing the player to access all the features of the game like
choosing the game to play, getting instructions on how to play the game or closing the entire program. The Main Menu contains buttons that leads the
player to either choose a game which links the user to the Game Menu showing the game and links to playing the game. The Main Menu contains a
Help button that links the player to instructions of how to play the game. The Main Menu also contains the

I Am A Math Lesson Essay
For my second lesson, I decided to conduct a math lesson as I had never conducted a math lesson in an elementary classroom let alone a 3rd grade
classroom. I discussed with my CT what math concept I could teach that pertained to one of the 3rd grade standards. My CT told me that I could
introduce the new concept of area to the class on the Friday that I was supposed to teach my lesson. I knew that that introducing a new topic on a
Friday in an elementary classroom was not ideal as the majority of teachers that I have observed in the past usually wrap up their week's lessons on
Friday. The Friday I was conducting my lesson was also a shorten day due to Fall Break, so I thought the students would show some off task behavior
for the early release day. These circumstances made me think hard about how I was going to introduce the concept of area to the students in an
effective way. I knew that I needed to have a lesson that included an exploratory hands– on activity to keep the students engaged and wanting to learn.
Therefore, I decided to use cheese crackers as manipulatives to represent square units. The students were to first guess what the area of the different
shapes in a worksheet packet were and then they were to use the crackers to figure out the actually area of the different shapes. I had been grading the
students' weekly math quizzes that pertained to arrays and multiplication a couple of weeks prior to my lesson which helped me presses the students'
knowledge on

Basic Math Facts On Math
MichalczukвЂџs (2007) understood basic math facts to be an important skill for students to succeed in math. Michalczuk (2007) generalized students
who could answer single–digit, 0 – 9, multiplication problems (2 times 3, or 5 times 7, etc.) "Within three seconds will do well at math and those that
answer in less than one second will do excellent at math" (p. 1). Perso (2007) has defined the "looking back–to–basics" as a need to teach and focus on
the basic arithmetic skills needed as a skill for higher level mathematics learning.
In addition, Hersh (2009) stated that skills in general are more important than ever because they allow students to further their learning as well as make
judgments about the meaning, adequacy, and accuracy of the overall content. Clavel (2003) stated if students wanted to engage and be successful in
higher–order mathematical thinking skills, mastery of the multiplication table was critical. Henry and Brown (2008) reported "students who learn to use
derived–fact strategies in concert with memorization are more likely to develop mathematical proficiency than those students who have memorized the
facts without supplementary strategies" (p. 172).
Wallace and Gurganus (2005) identified students who mastered the multiplication facts, not only acquired a more positive attitude to mathematics
learning, but they also developed an overall positive mathematics experience. Basic math fact fluency provided the necessary foundation to succeed in
higher level

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 ... Show more content on Helpwriting.net ...
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 Г— 312, multiply 50 Г— 312 then 2 Г— 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

The Distributive Property of Algebraic Expressions
The Distributive property of Algebraic expressions
Janet Mency
MAT 221
Instructor: Amy Glidewell
January 25, 2014
Completing algebra problems can be difficult if you don't understand the properties of real numbers. There are several properties in algebra dealing
with both integers and real numbers; one that will be the focus of this report will be the distributive property. We use this property when we are
combining addition and multiplication in an algebraic expression. Let's say that you are presented with the expression 6x(2 + y) = 9x + 5xy, now with
this problem the order of operation would have you to add the terms in parenthesis first, by using the distributive property it allows to simplify the
problem by multiplying all ... Show more content on Helpwriting.net ...
0.015m+17.6m+1.15n+0.072nCombine the like terms by adding coefficients.
17.615m+1.222nThe expression with decimals simplified notice that we completed we completed each one by using the same concept.
In conclusion we have learn about some of the basic pre–algebra properties of real numbers. We have discussed the how important of knowing what
each property allows you to do. Not knowing about the properties of real numbers would be like, just looking at a bunch of numbers and letters. So
understanding them helps you to know and understand how algebra works. Reading and applying these properties have helped me to understand
algebra a little bit better. We only talked about three of the properties, which are commutative, associative and distributive properties. These properties
are some of the basics in pre–algebra that I liked and that helped me to be able to simplify expression in algebra. When it's all said and done it really
all boils down to one thing completing algebra problems can be difficult if you don't understand the properties of real

Effects Of Positive Reinforcement
Question:
How will positive reinforcement affect speed and accuracy on a timed multiplication test?
Purpose:
To determine whether positive reinforcement has a bigger effect on speed or accuracy, and to what degree.
Research:
When I took AP Psychology last year, I learned that positive reinforcement will reinforce someone's behavior by making them associate the behavior
with a positive stimulus. In my experience, rushing through things usually causes me to have a faster time, but a lower score. In a study published
February of 1990, it was stated that "teachers' systematic use of certain categories of verbal statements, such as praise and reprimands, can have a
positive impact on student behavior, achievement, or both." This seems to indicate that positive reinforcement and encouragement may have an effect
on the achievement of students. However I was unable to find a study comparing the accuracy and speed of participants in a study, and so I will have
to make a few assumptions of my own based on previous knowledge in order to form a hypothesis.
Hypothesis:
If people are given positive reinforcement on a timed multiplication test, then their overall speed will increase, while their overall accuracy will
decrease.
Materials:
Pen, Pencil, Eraser, and Marking Pen/Marker
Stopwatch (Including those found on smartphones)
3 randomly generated multiplication sheets of times tables between 2 and 12 (All participants get the exact same 3 sheets) [the first sheet is 25

The Planned Supports, Including Allowing Peter To Have
The planned supports, including allowing Peter to have more time to solve problems, work with a general education peer (this peer should be a trusted
individual that we know Peter will work well and effectively with), and the visual manipulatives, align with the learning goal by having a visual
learning tool that allows the students to use equal groups and repeated addition to understand that concept of multiplication. Peter will be supplied with
a list of activity instructions, and will be supplied with a math addition fact table to assist him (this list will include information that the class has
previously discussed during class) with repeated addition.]
c. List any special accommodations or modifications in the learning environment, ... Show more content on Helpwriting.net ...
The magnet board and dots allow the students to interpret problems as the total number of objects in different groups; for example, 5x7 is interpreted
as 5 groups of 7 objects each. The math fact table, supplied to Peter, will help build connection between prior learning that is essential for the lesson;
furthermore, repetition of concepts over the course of the day will be supplied to the student. For example, the skills practiced will be extended into the
other courses throughout the day (i.e. english, science, etc.) ]
2. Knowledge of Focus Learner to Inform Teaching of the Learning Segment
For each of the categories listed below (2a–d), describe what you know about the focus learner's strengths and challenges as related to the lesson
objective(s) of the learning segment. Cite evidence of what the learner knows, what s/he can do, and what s/he is learning to do in relation to the
learning goal and any relevant planned supports.
Refer to baseline data obtained prior to the beginning of the learning segment.
a. Prior learning and experiences, including prerequisite knowledge and skills related to the lesson objective(s)
[ Prerequisite skills that students must master include single and multi–digit addition, the ability to separate objects into equal groups (grouping skills),
and the ability to effectively "skip count" with different numbers.

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 standardmultiplication
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

Learning Objective Assessment
The learning objective for question number 1 was, "to correctly write the expanded form of a 4– digit number." Most of the students understood this
concept, but didn't read the direction in full to understand that they were supposed to define expanded form, and then show an example. Students lost
one point for not defining, giving the class average for question 1 a 66%. Only one student lost 2 points on the question, half are almost approaching
the objective, and the other half are meeting the objective. The next objective was, "to accurately solve multi step equations using 4 different
methods." This was a difficult question for the class. The average for this question was 54%. Four students are below the objective, one in the middle,
and... Show more content on Helpwriting.net ...
I feel it was crucial for me to learn about the Common Core, especially since it has changed since I've been a student. It was also good for me to learn
about the many components involved with each math objective. This wasn't an easy assignment, but it wasn't extremely difficult. I felt it was time
consuming, and detailed. I learned that formative assessment is extremely helpful in the classroom because you can see how well your students can
apply what they have learned in your class. I learned a lot about the processes that students go through when taking a formative assessment. For
example, in the text it discuses procedural knowledge as, "knowledge that is needed to carry out an action or solve a problem," (McMillian, James H.
(2014). Classroom assessment: Principles and practice for effective standards– based Instruction (6th ed). Boston, MA: Pearson). I also saw through out
this assessment the students were having a hard time with simply identifying or repeating the needed steps, (McMillian, 2014). Another important
aspect of teaching with assessments is that its crucial to show, and tell the students what is expected of them in regards to showing work, and what
objectives will be on the test. I can remember being in school, and having a test on some material that I wasn't told would be on the test, and how
angry I felt. I will always ensure my criteria are clearly articulated. In this formative assessment project I learned that assessments are essential ways
for teachers to evaluate their students, and also a good way to self reflect on your own lessons. In the "Assessment, Decision Making, and Learning
Targets" lecture, I learned that assessments are a great way of knowing where the students are, and where you want them to be with knowledge and
skills, (Heilbroner, 2016). I also learned that its ultimately a professional judgment, and includes a variety of valid methods. I enjoyed

I Want To Become A Teacher
I want to become a teacher because I would love to give back to the village who helped raise me, be a mentor to my students, help students to learn
and truly understand Science Technology Engineering and Mathematics also known as STEM and the careers associated with it. People in my
community have helped me get to where I am today. With my mom being a single parent to two kids and maintaining a full time job was not easy,
she relied on extended family when needed. For example, when I was in Kindergarten my Grandfather would always talk to me about money
management. The basics of budgeting of how a person can have fifty dollars to spend, but they want to purchases six items for ten dollars each. I
was able to do this by adding ten dollars, six times then subtracting this by fifty dollars to see that there was ten dollars left. He did not like my
method of reasoning so he taught me how to multiply six times ten dollars and to subtract fifty dollars from this answer. I remember asking him what is
multiplication, and within two weeks I not only knew how to multiply, when to multiply, but I learned my multiplication facts one through twelve.
Multiplication is very hard for most second graders, let alone a kindergarteners. One lesson I learned from that day forward it does not matter how
young a person is or the time frame they have to learn it in they can do it. I have applied this same rule time and time again for the past fifteen years.
Without this lesson, I am

Disadvantage Of Vedic Multiplier
Abstract–Theperformance of system is directly proportional to throughput of the multiplierhence multipliers are effective in many applications. The
system depended throughput of multiplier and a system became slow therefore we need to design high performance multiplier. In this paper we
implement The Vedic Multiplier and the Reversible Logic Gates and Accumulate Unit (MAC) UrdhavaTriyagbhayam sutra for design of Vedic
multiplier and the adder design is done by using reversible logic gate. Reversible logics are also the fundamental requirement for the emerging field of
Quantum computing. . The analyses result shows that our multiplier is faster than conventional multiplier and compares delay required for multiplier
operation and also compare... Show more content on Helpwriting.net ...
VEDIC MULTIPLIER
The Vedic mathematics applicable over complex calculation, it reduces the typical calculation into a very simple one. This is so because the Vedic
formulae are claimed to be based on the natural principles on which the human mind works. Vedic Mathematics is a methodology of arithmetic rules
that allow more efficient speed implementation. It also provides some effective algorithms which can be applied to various branches of engineering
such as computing.
1)UrdhvaTiryakbhyam Sutra
The Vedic multiplier is depends on the "UrdhvaTiryagbhyam" sutra (algorithm). These Sutras have been traditionally used for themultiplication of two
numbers in the decimal number system. In this work, we apply the same ideas to the binary number system to make the proposed algorithm
compatible with the digital hardware. It 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. The algorithm can be generalized for n x n bit number. Since the partial products and their sums are calculated in parallel, the
multiplier is independent of the clock frequency of the processor. Due to its regular structure, it can be easily layout in microprocessors and
designers can easily circumvent these problems to avoid catastrophic device failures. The processing power of multiplier can easily be increased by
increasing the input and output data bus widths since it has a quite a regular structure. Due to its regular structure, it can be easily layout in a silicon
chip. The Multiplier based on this sutra has the advantage that as the number of bits increases, gate delay and area increases very slowly as compared
to other conventional

My Goals And Dedication Of Dedication
When people hear dedication, they may think about relationships or a job. Dedication means something different to all of us. To me, dedication is
more general. It is chasing a dream or goal relentlessly yet selflessly. It has shaped me into the person I am today. Dedication emerged in me when
I first started school and competing in athletics, and it has led me to every major achievement. Twelve years after dedication started to model me
into who I am today, I realized it was shaping my life when I became a National Merit Scholar and placed eighth at state wrestling, both in February
of 2016. I looked back to all the times where dedication is all that kept me on the track of achieving my goals and where dedication paid off. I
didn't choose to value dedication; external factors grew it up inside of me. Every youth soccer league practice and game, every wrestling practice and
tournament, and every class I had were factors in the development of dedication. It's clear what made me become so dedicated. The question to ask
myself is why these experiences instilled dedication in me. The first place to look is wrestling. It's a sport that can build or destroy character. Wrestling
builds confidence. This confidence can grow or shrink depending on the outcome of competition. Some people become overconfident and others settle
into the perfect amount of confidence. I believe I fall into the latter group. Practice can grow humility and dedication by fighting through

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
2. Let us consider the multiplication of two decimal numbers (5498 Г— 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

Pt1420 Unit 4 Research Paper
Algebra 2 Unit 1 Option 3: Systems/Matrices Poster Super Long And Complicated Matrix Problem Digital Representation of Matrixes Matrix
Multiplication Mathematical Multiplication [3 –2] [2 8] [5 –6] x [4 1] How To Work The Problem First multiply the top two numbers from the first
Matrix to the top left and bottom left numbers from the second Matrix. Multiply the top two numbers of the first Matrix again to the top right and
bottom right numbers of the second Matrix. Do the same process only with the bottom two numbers of the first Matrix. Mathematical Work Of The
Problem 3 x 2 + –2 x 4 + 3 x 8 + –2 x 1= 6 –8 +24 –2= 20 5 x 2 + –6 x 4 + 5 x 8 + –6 x 1= 10 –24 + 40 –6= 20 20 + 20 = 40 Matrix Division/Inverse
Mathematical

Mygraphy Of A Teacher Autobiography
My Teacher Autobiography
Since I can remember I have always wanted to be a teacher. You can say I come from a family of teachers because several of my family members
are teachers. I enjoy helping others and I love working with children. I dream of becoming a middle school English teacher in spite of people
telling me I will have a difficult time with the children from that age group. I have had many role models throughout my life and they have all
impacted my life in their own way. My biggest role models have been my 8th grade math teacher Ms. Gurrola, my maternal grandfather, Higinio, and
my 8th grade Language Arts teacher, Ms. Cordova. All of these individuals in their own way have had a significant impact on my life and are part of
the reason why I choose to become a teacher. By learning about these people that have meant so much to me you can learn a lot me as a person and
how I will be as teacher.
One of the most memorable and favorite teachers I have had is my eighth–grade math teacher Ms. Gurrola. Although she wasn't my favorite teacher at
the time, today is she is one of my most significant roles models and inspirations for becoming a teacher. Being a new member of the bilingual
program at my school, Ms. Gurrola's math class was one of the most challenging because I had never taken a math class in Spanish before and
although Spanish is my first language the terminology was new to me. To me, Ms. Gurrola was a great teacher in spite of her strict rules and at
times unpleasant attitude. She knew her subject matter very well and was always open to helping her students whenever possible. She had a strong
accent that made it evident that she was bilingual and that English was not her first language. It was rumored that she had come to the United
States from Mexico with a convent of nuns but left and became a teacher. I did not realize her value as a teacher until one day that I stayed after
school with her to finish an exam for her class. I was upset with her over something that happened the previous day in class and I gave her a little bit
of attitude that day yet when I went to her class after school it seemed as if nothing had ever happened. She was helpful and very nice to me. After I
finished the exam

The Problem Of Mental Multiplication
Mental Multiplication
The United States of America is one of the countries with the highest education standards; where most of the best universities worldwide are located.
However, the dependency on technology is becoming an issue that can impact future generations on the primary and secondary education. One
dependency in particular is the calculator, a device with a visual display use to perform mathematical calculations. The mathematic departments of
elementary and high school centers allow the use of such device in order to solve calculations in an easy and fast way; although, they do not realize
how a calculator is taking away the basic ability to think logically from their students. Additionally, students also have to face the change... Show more
As it is known, multiplication is only a simplified version of addition; adding a number a fixed number of times. Therefore, first it is fundamental to
have a satisfactory background in addition in order to dominate multiplication, including all the rules and properties such us the commutative,
associative, and distributive properties. Another important knowledge is to learn the multiplication table from 0 to 12 at the top of our head. Finally,
it is also recommended to keep in mind certain properties of multiplication but especially know the property that specifies the interaction between odd
and even numbers. When an even number with an odd one or two even numbers are multiplied, the result will always be an even number; however,
when two odd numbers are multiplied, the answer will be an odd number. It is essential to know such property because every time we have to
multiply and look at the numbers we are multiplying; one will have a better idea of what the result is going to be.
Once the preparation is completed, one can start practicing some tricks to get results without the need to use a calculator. Personally, I found seven
efficient cases that involve multiplying large numbers.
The first case, is known as the benefit of the distributive property, or applying the distributive property to one's benefit. It is better to use this case
when one is multiplying a big number with a one–digit

Understanding Students ' Responses From The Australian...
1.0 Introduction Educators are required to interpret students' responses to mathematical questions. The purpose of this report was to provide an
opportunity to examine the step by step approach to answering problems, interrogate the results and recognise mathematical concepts. There are six
questions in total from the Australian Curriculum Assessment Reporting Authority [ACARA], (2012) NAPLAN year nine numeracy non–calculator
test. The six questions mentioned in the report are question 12, 14, 16, 18, 22 and 23. Each issue is set out in the report in numerical order with a
screen shot of the methods used to solve the question followed by a reflection. The reflection describes my feelings, confidence and approach
towards each question along with the type of mathematics used, the year level suitable for each question according to the ACARA (2015) and
alternative ideas for solving the six questions. 2.1 Question 12 Reflection Initial thoughts were I could easily solve this because I use metric units on
a regular basis for working out distances for driving and dimensions of furniture. I knew millimetres were the smallest followed by centimetres, metres
and kilometres the largest (Lakin, 2011). That did not mean that kilometre was the answer. I understood that converting the units would help solve the
question but could not remember how to do conversions. Once I refreshed my knowledge as discussed before step 1 of figure 1, I

Understanding The Concept Of Division
The purpose of this lesson is to introduce the students to the concept of division. This will be somewhat of a review for the students who have had
practice with division in past grade levels. It has been a long time since the students have had any practice with division, so this lesson will serve an
introduction to the meaning of division, division vocabulary, as well as its relationship to multiplication. Students will be introduced to fact families as a
way to show the connection between multiplication and division. The students will be able to see the relationship between a concept they have had a
lot of practice with (multiplication), to a concept that might be new to them (division).
Common Core State Standards:
CCSS.MATH.CONTENT.5.NBT.B.6: Find whole
–number quotients of whole numbers with up to four–digit dividends and two–digit divisors, using
strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Student Learning Objective:
Students will demonstrate an understanding of the relationship between multiplication and division through verbal and written communication.
Goals/Objectives of Lesson: What do you hope for/expect?
Before this lesson: Students will complete a written pre–assessment on division concepts using their prior knowledge.
With guidance from the teacher and class notes,

Multiplication In The Classroom
I tried something new when I was in the 1st grade. It all happened when my teacher said Hey class we are going to learn about Multiplication. I
remember when I heard that word I thought that was going to puke.
It all started the day after Martin Luther King Jr. i was going to class when my mom stopped me and gave me a hug then I walked into school looking
like a cool kid. When I got into my class my teacher made me stop outside of the door to ask me a few questions about a fight that happened a few
days ago. I told her which day was it, and she said Tuesday and today was Thursday.
When she told me it happened I was shocked like a sloth. Then when I came into the classroom I noticed that half of the class was missing. I ask the
teacher where

Disadvantages Of Multiplication In Mathematics
Based on the Council of Teacher of Mathematics,(1993) "Multiplication involves the counting of units of a size other than one." The repeated addition
definition while is a useful link between multiplication and addition is limiting if it is students' only concept of multiplication.
The meaning of the multiplication sign, "Г—", depends on the language of the speaker. In Japanese it always means "multiplied by." "3 Г— 4" and "3
times 4" mean, "Three multiplied by four," or four groups of three items. In English, however, the sign means either "times" or "multiplied by,"
where"3 times 4," denotes three groups of four items, and "three multiplied by four" means four groups of three items. Therefore, in English the sign
"Г—" has two interpretations ... Show more content on Helpwriting.net ...
Basic knowledge on numbers and Mathematical skills.
4.Pedagogical readiness is the "Students" understanding of the materials they use as they learn Mathematics.
5.Maturation readiness is the "Students" level of mental maturity (each person passes through four stages of mental maturity).
The use of games and concrete materials can aid in pupils' recognition of the importance of Mathematics and its many different real applications.
Educators views on the use of concrete materials and Manipulatives in the classroom
Manipulative materials are objects that pupils can feel, touch, handle and move. The National Council of Teacher of Mathematics( 1993), proposes that
pupils and teachers often view the use of manipulatives"as play time", but stress that using manipulatives is any excellent way to help learners make
faster connection between mathematical ideas. It is also established that learning is enhanced when pupils are exposed to concepts in varying
manipulative context. Learners who are at the concrete level deal with manipulative materials as they discover solution to problems. Many if not all
games, involve object manipulation at some

The Teacher Had Put On Board
"Slightly and squeaky!" The door to the classroom flew open as I burst into the room and sat in my usual seat. This was the day I was going to
learn how to do polynomial long division. "Good morning." The professor said, as she walked into the classroom. Almost every one of the students
had at least a pencil and notebook, copying notes that the teacher had put on the board. After writing the notes down, I said to myself, let me try to do
one of the problems that the teacher had put on board. Surprisingly, I could not start the problem because I did not even understand the first step.
Therefore, I stopped and wait for the professor.
After the teacher did the first problem, but she did not do or put all the steps on the board, she skipped some of it. She said "you guys should have
known how to do this stuff already. This is not an elementary or grade school, so I am not going to do or write every little step. Without paying close
attention and understand every single step and everything she was saying. The first thing I did was, I immediately started the next one. I started well. I
did the first step which was the division part. Where I had to change the way the problem was writing and to look at that first number of the guy that I
was going to divide into. I got stuck in the middle of step number two which was the multiplication part. In the multiplication step, I had to multiply the
divisor with the quotient. However, I did not know if I had to put the answer right under

Building Parking Lots For A Mall
Hello fellow construction workers, today we are scheduled to make parking lots for a mall. Before we sit down and do our blueprints, do you guys
know the product of 2–two digit numbers using arrays by multiplication? What examples can you name where you have seen array multiplication?
Example, Construction workers are planning to build new parking lots for a mall. There has to be a total of 3 floors. Floor 1 can fit 384 cars, Floor 2
can fit 169 cars, and Floor 3 can fit 144 cars. Show all of the array possibilities for all 3 floors. However, between each parking lot they have to be 2
inches apart. Draw 2 yellow lines to show the 2 inches. After, label each array as amultiplication problem. You will have to see what 2–two digit
numbers ... Show more content on Helpwriting.net ...
Make sure to remember your multiplication tables. Let's try to solve the construction site.
We have fifteen students in our class today, so that means we will have 5 groups of 3 people. Each group will have to come up with the best way
possible to fit all cars on floor 1, 2, and 3 in the parking lots. Now, before you construct your parking lot, you must be able to complete your
blueprints. In the blueprints, you show all the arrays for each floor that are best to be able to construct your floors. Check your blueprints with the
supervisor (teacher). However, your floors will be made out of cardboard box that can be between 12 inches to 48 inches, nothing more and nothing
less. Remember also between each parking space, they have to be 2 inches apart and to mark those inches you must draw your 2 yellow lines. Once
you are able to construct your floors you can stack them up together and tape them up so they can hold. After all of that, you are ready to turn them it.
Each group is engaged in the activity that is assigned to them. The classroom may stay quiet for a while, but you will notice their concentration on
their blueprints and on how to construct their floors. We listen closely to how they are going to build their floors, and on how they solved their word
problems. We can't wait to have their blueprints been checked by the supervisor (teacher) and to see what they are going to create based off of their

Number Grid Investigation
The Patterns, Rules and Formulae Found in a Number Grid
For this coursework I shall investigate and explain thoroughly the patterns, rules and formulae found in a number grid when placing a square at any
point in the grid, multiplying the top left and bottom right corners and the top right and bottom left corners and finding the difference. I will look at all
the variables and use systematic methods when doing this.
Suggested Variables:
Width of grid
Size of Square
$#$#1$#$# Tables
Width of Grid: Does the width of the grid make a difference to formulae? I shall keep the size of the square at a constant (2 x 2)
Width of Grid size 10)
12345678910
11121314151617181920
2122 ... Show more content on Helpwriting.net ...
Now I shall try to answer the question "does this differ with a different size grid?"
I shall try to fill the table shown underneath to get a clear view on all the data and try to see a formula from this data.
Grid Width Difference

4x410
3x39
2x28
Square size 2x2 grid width 10
12345678910
11121314151617181920
21222324252627282930
12 x 23 = 276
22 x 13 = 286
286 – 276 = 10
I shall now use letters to prove this correct
X
X+1
X+10
X+11
X(X+11) = XВІ + 11X
(X+1)(X+10) = XВІ+11x+10
(XВІ+11x+10) – (XВІ+11X) = 10
Square Size 2x2, Grid Width 9

123456789
101112131415161718
192021222324212627
11 x 21 = 231
20 x 12 = 240
240 – 231 = 9
I shall now use letters to prove this correct
X
X+1
X+9
X+10
X(X+10) = XВІ + 10X
(X+9)(X+1)=XВІ+10X+9
(XВІ+10X+9) – (XВІ+10X) = 9
Square size 2x2, Grid Width 8)
12345678
910111213

The Importance Of Multiplicative Thinking
Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following
portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that
children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and
discuss the need for succinct teaching instead of an isolated approach. Multiplicative Thinking Multiplicative thinking is imperative to a child's
understanding of important mathematical concepts and is seen as the 'big idea' in number that links multiple key ideas and strategies (Vergnaud, as
cited in Siemon, 2011). Commonly, children have a procedural based view of multiplicative thinking which can hinder progress, as opposed to a more
conceptual view which is a far better learning framework (Hurst & Hurrell, 2016). If teachers are to maximise a child's learning, they must acknowledge
this and help children maintain a conceptual understanding of multiplicative thinking and emphasise this much more so than procedural rules. Several
key ideas and strategies underpin the success of multiplicative thinking and a greater conceptual understanding. Hurst and Hurrell (2014) explain that
children need to be acutely aware of the ten times multiplicative relationship between places and how this effects many aspects of mathematics.

Standard Classroom Size Or Virtual Unlimited
UNDERSTANDING MULTIPLICATION WITH ARRAYS
LEVEL/SUBJECT
Grade 3 Math
CLASS SIZE
Standard classroom size or virtual unlimited
LESSON DESCRIPTION
Curriculum and instruction are differentiated to the needs and interests of each student and engage multiple intelligences. The lesson can be
customized and adjusted to the needs of students and teachers. The lesson is aligned with the academic standards of the National Council of Teachers
of Mathematics and Common Core.
TIME FRAME
20 min–1hour
OBJECTIVES/OUTCOMES
Student will electronically construct an array of up to 10 shapes using an interactive applet to understand and to identify the pattern that any number
multiplied by 1 equals that same number.
DIFFERENTIATION
Struggling

On Grade Level
Mastery/Extension Using an array, student will multiply 5x2 to equal 10
COMMON CORE ALIGNMENT
http://www.corestandards.org/Math/Content/3/OA/Student Target Language Levels
http://www.corestandards.org/Math/Content/3/introduction/
. . .developing understanding of the structure of rectangular arrays
Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving
equal–sized groups, arrays. . .
Represent and solve problems involving multiplication. . .
CCSS.Math.Content.3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by
using drawings and

Science Reflection
Today was Halloween, so my teacher had planned some really fun activities for the students to participate in. Before the students arrived, I talked with
Mrs. Beach about the lesson that I would be teaching in two weeks. I also helped her set up the science experiment that the students would get to
observe while they were working on another activity. When the students arrived, Mrs. Beach explained the science demonstration to the students and
asked them to develop a hypothesis of what they thought might happen to the Peep Pumpkins when she put them in hot water, cold water, club
soda, vinegar, and oil. She also asked them to predict what would happen when she put candy corn in these types of liquids. Once the students had
made their predictions, Mrs. Beach asked for some of them to share their predictions. Three boys proceeded to share their hypotheses with the class.
Mrs. Beach wanted some girls to share their hypotheses with the class, so she encouraged them by saying, "Come on girls, the boys are out doing
you by sharing their hypotheses. Let's hear from some of the girls. What do you think will happen?" Even though I probably would not say these
exact words, I really like how Mrs. Beach was encouraging the girls to share their thoughts as well. Following this exchange, Mrs. Beach proceeded to
place the candy into the cups of liquid, and then she explained the next activity, Halloween Glyphs.
I loved how prepared Mrs. Beach was for the Halloween Glyphs activity. Some of

Implement Derrick Ward's Calculator In C +)
Discrete Mathematics
SUBJECT CODE – MCA 105
PRACTICAL/RESEARCH ASSIGNMENT
OF
MCA 1st SEMESTER
(MORNING)
SUBMITTED TO SUBMITTED BY
Mr. Somendra Aman Sharma
(Asst. Professor) MCA 1'st SHIFT BATCH– 2015–2018
INDEX
S No.
Contents
Page No.
1.
Derrick Ward'sCalculator in C++
3–8
2.
Sudoku in C++
9–16

3.
Conclusion
17
4.
Plagiarism Report
18
Q1 Implement Derrick Ward's Calculator.
#include
#include
#include ... Show more content on Helpwriting.net ...
#include void main()
{
long double a, b; char ch, ar; do { clrscr(); cout<< " *WELCOME TO NANU'S CALCULATOR* "; cout<< " This is a Calculator containing the
following functions : Addition, Subtraction, Multiplication, Division, Percentage, Power "; cout<< " Type [+] for Addition, [–] for Subtraction, [*] for
Multiplication, [/] for Division, [%] for Percentage, [^] for Power "; cout<< " Enter Function To use = "; cin>> ch; cout<< (char)7; cout<< endl; //For
Addition If (ch=='+') { clrscr(); cout<< "You are using Addition

Implementation Of 8x8 Modified Booth Multiplier With Hpm...
Figure 3.6: Implementation of 8x8 Modified Booth Multiplier with HPM Reduction Method [4]
The Figure.3.6 shows the implementation 8x8 modified booth multiplier using High Performance Multiplier (HPM) reduction method [4]. The
modified booth algorithm is a predominant high performance multiplier which has low number of partial products row. The generation of these partial
products is quite complex to implement in hardware. So in this work has used a straight forward way of implementing a Signed and Unsigned
Multiplication using Baugh–Wooley Algorithm with HPM reduction tree method. Baugh–Wooley Multiplier with HPM reduction tree is discussed in
Chapter Six.
CHAPTER FOUR: LOW–POWER DESIGN
4.1 Introduction:
In earlier stages of VLSI circuit design the emphasis is on Area and Speed optimization giving concerns to Packaging and Efficient designing. As the
technology scales down according to predictions of Moor's Law, it is advent that the CMOS dimensions have been scaled down drastically. But due to
increase in use of Portable Devices Such as Cellphones, Laptops, Personal Health Monitoring systems, there has been a demand of higher battery life
for Portable devices. Whereas big data centers which contains large set of circuits consumes tremendous power and dissipates large amount of heat
which incurs huge cost to maintain. The solution for these problems is to design circuits which consume low power which give rise to the concept of
Low–Power VLSI designing.
As this

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