The document summarizes a classroom observation of a Grade 8 mathematics lesson on rational algebraic expressions. The lesson included reviewing the previous concept, defining key terms like rational and polynomial, providing examples of rational algebraic expressions, and activities for students to practice identifying rational expressions and determining excluded values. The lesson objectives were for students to be able to identify, evaluate, and relate rational algebraic expressions to real-life situations by the end of the class.
Algebraic Expression and Expansion.pptxMisbahSadia1
Algebraic expressions are fundamental mathematical constructs that play a crucial role in representing and solving a wide range of mathematical and real-world problems. They are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions are a bridge between the abstract world of mathematics and the practical world of problem-solving.
Key components of an algebraic expression:
Variables: These are symbols (usually letters) that represent unknown values or quantities. Common variables include "x," "y," and "z." Variables allow us to generalize mathematical relationships and solve problems with unknowns.
Constants: These are fixed numerical values that do not change within the expression. Examples include numbers like 2, 5, π (pi), or any other specific constant value.
Mathematical Operations: Algebraic expressions include operations like addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^ or **). These operations define how the variables and constants interact within the expression.
Coefficients: Coefficients are the numerical values that multiply variables. For example, in the expression 3x, 3 is the coefficient of the variable x.
Algebraic expressions can take various forms, from simple linear expressions like 2x + 3 to more complex ones like (x^2 - 4)(x + 1). They are used in a wide range of mathematical contexts, including equations, inequalities, and functions.
Expansion of Algebraic Expressions:
Expanding an algebraic expression involves simplifying it by removing parentheses and combining like terms. This process is essential for solving equations, simplifying complex expressions, and gaining a better understanding of the underlying mathematical relationships.
Here's how to expand algebraic expressions:
Distribute: When an expression contains parentheses, you distribute each term within the parentheses to every term outside the parentheses using the appropriate mathematical operation (usually multiplication or addition).
Example: To expand 2(x + 3), you distribute the 2 to both terms inside the parentheses: 2x + 6.
Combine Like Terms: After distributing and simplifying, you look for like terms (terms with the same variable(s) and exponent(s)) and combine them.
Example: In the expression 3x + 2x, you combine the like terms to get 5x.
Remove Parentheses: If there are nested parentheses, continue to distribute and simplify until no parentheses remain.
Expanding algebraic expressions is a crucial step in solving equations and simplifying complex expressions. It allows mathematicians and scientists to manipulate and analyze mathematical relationships efficiently, making it an essential tool in various fields, including physics, engineering, and computer science.
Un grupo de variables representadas por letras junto con un conjunto de números combinados con operaciones de suma, resta, multiplicación, división, potencia o extracción de raíces es llamado una expresión algebraica. Las expresiones algebraicas nos permiten, por ejemplo, hallar áreas y volúmenes
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Algebraic Expression and Expansion.pptxMisbahSadia1
Algebraic expressions are fundamental mathematical constructs that play a crucial role in representing and solving a wide range of mathematical and real-world problems. They are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions are a bridge between the abstract world of mathematics and the practical world of problem-solving.
Key components of an algebraic expression:
Variables: These are symbols (usually letters) that represent unknown values or quantities. Common variables include "x," "y," and "z." Variables allow us to generalize mathematical relationships and solve problems with unknowns.
Constants: These are fixed numerical values that do not change within the expression. Examples include numbers like 2, 5, π (pi), or any other specific constant value.
Mathematical Operations: Algebraic expressions include operations like addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^ or **). These operations define how the variables and constants interact within the expression.
Coefficients: Coefficients are the numerical values that multiply variables. For example, in the expression 3x, 3 is the coefficient of the variable x.
Algebraic expressions can take various forms, from simple linear expressions like 2x + 3 to more complex ones like (x^2 - 4)(x + 1). They are used in a wide range of mathematical contexts, including equations, inequalities, and functions.
Expansion of Algebraic Expressions:
Expanding an algebraic expression involves simplifying it by removing parentheses and combining like terms. This process is essential for solving equations, simplifying complex expressions, and gaining a better understanding of the underlying mathematical relationships.
Here's how to expand algebraic expressions:
Distribute: When an expression contains parentheses, you distribute each term within the parentheses to every term outside the parentheses using the appropriate mathematical operation (usually multiplication or addition).
Example: To expand 2(x + 3), you distribute the 2 to both terms inside the parentheses: 2x + 6.
Combine Like Terms: After distributing and simplifying, you look for like terms (terms with the same variable(s) and exponent(s)) and combine them.
Example: In the expression 3x + 2x, you combine the like terms to get 5x.
Remove Parentheses: If there are nested parentheses, continue to distribute and simplify until no parentheses remain.
Expanding algebraic expressions is a crucial step in solving equations and simplifying complex expressions. It allows mathematicians and scientists to manipulate and analyze mathematical relationships efficiently, making it an essential tool in various fields, including physics, engineering, and computer science.
Un grupo de variables representadas por letras junto con un conjunto de números combinados con operaciones de suma, resta, multiplicación, división, potencia o extracción de raíces es llamado una expresión algebraica. Las expresiones algebraicas nos permiten, por ejemplo, hallar áreas y volúmenes
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
3. Raise your hand if you want to
answer
Participate actively in our class
discussion/group work
Observe and listen carefully
Be Respectful on one another
Encourage each other to do the
task
4. ll. Reviewing previous lesson or
presenting the new lesson
B. Review/Recall on the
previous lesson
How will you know that the
expression is a rational algebraic
expression?
6. Activity A. MATCH IT TO ME
Match the verbal phrases in
column A to the corresponding
mathematical phrases in column B.
A.Verbal Phrase
1. The sum of a number n and nine
2. The product of p and the number
eight
3. The ratio of distance (d) and time
(t)
7. 4. The difference of a number x and
twenty-one
5. The cube root of a number y
decrease by five
9. Activity B: Identifying Polynomials
Identify whether the expression is
a polynomial or not?
a. 3
𝒚 − 𝟓
b. x – 21
c. n + 9
d. d
t
e. 𝒏 + 𝟐𝟏
f. 8p
10. C. Review/Recall on the
previous lesson
Questions:
1. What must be considered in
translating verbal phrases to
mathematical phrases?
2. Will you consider these mathematical
phrases as polynomials?
3. Were you able to identify each
expression?
11. Questions:
4. How did you classify a polynomial
from not a polynomial?
5. How will you describe a polynomial?
12. : Illustrating Rational Algebraic
Expression
O B J E C T I V E S
(ESABLISHING A PURPOSE FOR THE LESSON)
At the end of the session, the learners will be able to...
1. Identify rational algebraic expressions;
2. Evaluate rational algebraic expressios; and
3. Relate rational algebraic expressions in real-life
situations.
13. Activity 2 (Presenting examples)
Rational Algebraic Expressions
Identify whether the expression is a
rational or not?
1.) __6__
x – 3
2.) 3x-√𝒚
5 𝒙
15. Definition of terms:
Rational → a number, quantity or
expression
Expression → numbers, symbols and
operation grouped together.
Numerator → is the part of a fraction above the
line, which signifies the number to be
divided by another number below the line.
Denominator → the number below the line in a
common fraction; a divisor.
16. Undefined → a term that is mathematically
inexpressible, or without meaning.
Anything divided by zero is considered
undefined by the rules of mathematics.
18. All of the expressions are rational
algebraic expressions since these contain
polynomial expressions in both numerator
and denominator, respectively.
Here’s a useful checklist in identifying
whether the expression is rational
algebraic expression:
• The expression must be in fraction form.
19. • The expression must have in its
numerator and denominator a constant, a
variable, or a combination of both, that
are polynomial expressions.
• The expression must not have a negative
exponent in the variable/s in both
numerator and denominator.
20. → Recall that the rational algebraic
expression is a fraction containing
polynomials in both numerator and
denominator, provided that the
denominator must not equal to zero.
The denominator cannot be equal to
Zero because a division of 0 is undefined
or meaningless.
21. In rational algebraic expressions, you
need to to pay attention to what values of
the variables that will make the
denominator equal to zero. These values
are called excluded values.
How are you going to determine the
excluded value/s in a rational algebraic
expression?
22. (Developing mastery leads to formative)
Example: 1. Determine the value of x for
which the expression _7_ is undefined.
x+2
Solution: x+2 = 0 Checking: x+2 =0
x+2-2 =0-2 -2+2= 0
x = -2 0 = 0
If the denominator is equal to zero
(excluded value/s), then the expression is
said to be undefined.
23. Example: 2. The area of a rectangle is
(x²–121) square units while its width
measures (x+11) units. Illustrate a rational
algebraic expression in finding the length
of the rectangle.
Recall that the formula in finding the
length given the area and the width of the
rectangle is length = Areaofrectangle
width
24. Solution: Substituting the area and the
width of the rectangle,
length = Areaofrectangle = x² - 121
width x + 11
Then the length of the rectangle can be
illustrated as x² - 121 , so x+11 =0
x + 11 x+11-11=0-11
x = -11
25. (Finding Practical application of concepts)
Activity 1. Classify the different
expressions as to which set of expressions
they belong. Write the expression in the
appropriate column.
Activity 2. Determine the excluded value/s
that will make the given expression
undefined.
26. CRITERIA Outstanding 4 Satisfactory 3
Developing
2
Beginning
1
Mathematical
reasoning
Explanation shows
thorough reasoning
and insightful
justifications.
Explana-tion shows
substantial
reasoning
Explanation shows
gaps in reasoning.
Explana-tion shows
illogical reasoning.
Accuracy
All computa-tions
are correct and
shown in detail.
All computa-tions
are correct.
Most of the
computa-tions are
correct.
Some of the
computa-tions are
correct.
Presentation The present-ation
is delivered in a
very convincing
manner.
Appropriate and
creative visual
materials used.
The present-ation
is delivered in a
clear manner.
Appro-priate visual
materials used.
The present-ation
is delivered in a
disorganized
manner. Some
visual materials
used.
The present-ation
is delivered in a
clear manner. It
does not use any
visual materials.
