This document contains a math teacher's notes for a lesson on determining if expressions are equivalent. It includes examples of checking expressions using different values for variables and discussing why using at least two values is needed to determine equivalence. Students are instructed to work in groups on practice problems and turn in their work for credit. The lesson emphasizes that plugging in one value alone is not sufficient to determine if expressions are equivalent.
This document is a teacher's notes for a lesson on writing and solving two-step equations from word problems. It includes sample math problems, permission slips due for a math competition, and word problems to write as two-step equations with boxes to fill in for the variable. The lesson covers reviewing mistakes, practicing sample equations, and an upcoming homework assignment and exam.
This document is the 2012-2013 school calendar for Umble ISD. It shows the monthly calendars for the school year with dates for holidays, breaks, the first and last day of each semester. There are a total of 177 instructional days for students and 187 days for teachers. The first semester runs from August 27 to December 21, 2012 and the second semester runs from January 7 to June 7, 2013. Several professional development and planning days are included for teachers during the school year.
The document discusses 3 instrumental values - logical values, broad-minded values, and honest values - that are important for critical thinking. It argues that these values can help make our beliefs stronger, understand other perspectives, and be happy and trustworthy. While learning these values takes work, with role models, family, professors and a healthy lifestyle people can stand the test of time using these values even when choices are difficult. The values can be tested throughout life and appreciated by family, work, ourselves, and community.
The document is a lesson plan on representing areas of rectangles. It includes instructions for students to complete warm-up problems, discuss expressing quantities with algebra, and model adding and subtracting polynomial expressions using algebra tiles. Students are asked to derive an equation for the original square area and notice the relationship to the new rectangle area. They are then asked to write the equation for the new rectangle area.
The document provides biographical details about the early life of Muhammad, the prophet of Islam:
- Muhammad was born in 570 AD in Mecca and became an orphan as a child, being raised by his grandfather and uncle. As a young adult, he worked as a merchant and married Khadijah.
- In 610 AD, while meditating in a cave, Muhammad began receiving revelations from God that became verses of the Quran. He began preaching monotheism, rejecting traditional Meccan polytheism.
- Persecuted by the Quraysh tribe, Muhammad and his followers migrated to Medina in 622 AD, establishing the first Muslim community. From there, Muhammad consolidated
The document is a notebook for a lesson on representing the areas of rectangles. It includes examples of expressing the length and width of squares and rectangles in terms of variables and arithmetic operations. Students are asked to analyze patterns involving how changing the length and width of an original square affects its area and the area of the resulting rectangle. The lesson also covers using algebra tiles to model adding and subtracting polynomials.
The document outlines 3 instrumental values - logical values, broad-minded values, and honest values - that are important for critical thinking. It argues that these values can help one understand their own beliefs, respect others' perspectives, and be happy and trustworthy. Examples are provided for how each value can be applied. The document also notes that these values can be learned through role models, family, professors, and community support services. Overall, the values are presented as mental tools that can help one make wise decisions and stand the test of time.
The document provides instructions for students to interpret equivalent expressions. It tells students to take out homework and a red pen to solve equations for variables. It also assigns additional practice problems from their ACE workbook and instructs them to label their classwork paper with their name, date, and "Equivalent Expressions" title.
This document is a teacher's notes for a lesson on writing and solving two-step equations from word problems. It includes sample math problems, permission slips due for a math competition, and word problems to write as two-step equations with boxes to fill in for the variable. The lesson covers reviewing mistakes, practicing sample equations, and an upcoming homework assignment and exam.
This document is the 2012-2013 school calendar for Umble ISD. It shows the monthly calendars for the school year with dates for holidays, breaks, the first and last day of each semester. There are a total of 177 instructional days for students and 187 days for teachers. The first semester runs from August 27 to December 21, 2012 and the second semester runs from January 7 to June 7, 2013. Several professional development and planning days are included for teachers during the school year.
The document discusses 3 instrumental values - logical values, broad-minded values, and honest values - that are important for critical thinking. It argues that these values can help make our beliefs stronger, understand other perspectives, and be happy and trustworthy. While learning these values takes work, with role models, family, professors and a healthy lifestyle people can stand the test of time using these values even when choices are difficult. The values can be tested throughout life and appreciated by family, work, ourselves, and community.
The document is a lesson plan on representing areas of rectangles. It includes instructions for students to complete warm-up problems, discuss expressing quantities with algebra, and model adding and subtracting polynomial expressions using algebra tiles. Students are asked to derive an equation for the original square area and notice the relationship to the new rectangle area. They are then asked to write the equation for the new rectangle area.
The document provides biographical details about the early life of Muhammad, the prophet of Islam:
- Muhammad was born in 570 AD in Mecca and became an orphan as a child, being raised by his grandfather and uncle. As a young adult, he worked as a merchant and married Khadijah.
- In 610 AD, while meditating in a cave, Muhammad began receiving revelations from God that became verses of the Quran. He began preaching monotheism, rejecting traditional Meccan polytheism.
- Persecuted by the Quraysh tribe, Muhammad and his followers migrated to Medina in 622 AD, establishing the first Muslim community. From there, Muhammad consolidated
The document is a notebook for a lesson on representing the areas of rectangles. It includes examples of expressing the length and width of squares and rectangles in terms of variables and arithmetic operations. Students are asked to analyze patterns involving how changing the length and width of an original square affects its area and the area of the resulting rectangle. The lesson also covers using algebra tiles to model adding and subtracting polynomials.
The document outlines 3 instrumental values - logical values, broad-minded values, and honest values - that are important for critical thinking. It argues that these values can help one understand their own beliefs, respect others' perspectives, and be happy and trustworthy. Examples are provided for how each value can be applied. The document also notes that these values can be learned through role models, family, professors, and community support services. Overall, the values are presented as mental tools that can help one make wise decisions and stand the test of time.
The document provides instructions for students to interpret equivalent expressions. It tells students to take out homework and a red pen to solve equations for variables. It also assigns additional practice problems from their ACE workbook and instructs them to label their classwork paper with their name, date, and "Equivalent Expressions" title.
The document contains multiple choice, true/false, and completion questions about the periodic table and properties of elements. It covers topics like Mendeleev's creation of the periodic table based on atomic mass, use of atomic number to organize the table, predicting properties from an element's location, groups having similar properties, atomic structure, states of matter, and nuclear fusion in stars.
Linear Equations and Graphs_Lesson 1_Slope and Rate of Changemrstrementozzi
1. The document provides examples of how to calculate rate of change and slope from tables, graphs, and two points. It explains that rate of change is the change in the dependent variable over the change in the independent variable, while slope is the rate of change between any two points on a line.
2. Examples are given for finding constant and non-constant rates of change from tables, as well as how to determine if a set of data has a constant rate of change. Graphs are used to demonstrate horizontal, vertical, and standard linear slopes.
3. Calculating slope from two points on a graph or when given two point coordinates is demonstrated. Special cases for horizontal and vertical lines are explained.
1. The document provides steps for factoring polynomials, simplifying binomials, multiplying monomials and binomials, finding areas of rectangles with variable sides, naming polynomials, and other algebra concepts. It includes examples and explanations for each topic.
2. Methods are given for factoring polynomials by finding the greatest common factor or using the difference of squares formula. Binomials should be squared by writing them twice and using FOIL, not squaring individual terms.
3. To multiply a monomial by a polynomial, the term outside is distributed to each term inside. FOIL is used to multiply binomials. Perimeters can be found by doubling the total length and width given in an area formula.
This document provides instructions on how to multiply binomials. It explains that to multiply two binomials, you multiply each term in one binomial by each term in the other binomial and circle like terms to combine them. It provides examples of multiplying (x + 7)(x + 2) as (x^2 + 2x + 7x + 14) and simplifying to (x^2 + 9x + 14). It then provides exercises for students to practice multiplying different binomial expressions.
The document provides instructions on multiplying polynomials. It discusses multiplying monomials by polynomials by distributing the monomial. It also covers multiplying binomials using the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms. Finally, it addresses multiplying binomials by polynomials with more than two terms, which does not use FOIL but instead distributes the binomial to every term. Examples and practice problems are provided for each type of polynomial multiplication.
The document discusses finding the square of a binomial expression. It explains that to find the square of (a + b), the expression is (a + b)(a + b), not (a + b)2. Using FOIL or the distributive property, the square of (a + b) is a2 + 2ab + b2. Similarly, the square of (a - b) is a2 - 2ab + b2. The document provides examples of expanding squared binomial expressions and warns students not to make mistakes like (x + 6)2 = x2 + 36.
Challenge 11 multiplying differences of squaresmrstrementozzi
The document discusses differences of squares, which is when two binomial expressions with the same terms are multiplied but one pair of terms is added and the other is subtracted. This results in the expanded form being the first term squared minus the second term squared. It provides examples of expanding expressions using FOIL and the distributive property, including recognizing that (x+2)(x-2) is a difference of squares. It then has practice problems for the reader to expand additional expressions using this concept.
El documento proporciona 24 ejercicios de álgebra que involucran la aplicación de la propiedad distributiva para simplificar expresiones. Los ejercicios piden factorizar términos entre paréntesis y distribuirlos a los términos adyacentes para simplificar las expresiones dadas.
November 26, 2012: Polynomials (SmartBoard Note)mrstrementozzi
This document contains notes and exercises on polynomials from a math class. It instructs students to complete problems 1-13 on a worksheet about adding and subtracting polynomials. It defines the degree of a polynomial and has students find the degree of example polynomials. It also demonstrates adding and subtracting polynomials using algebra tiles to model the expressions.
The document contains multiple choice, true/false, and completion questions about the periodic table and properties of elements. It covers topics like Mendeleev's creation of the periodic table based on atomic mass, use of atomic number to organize the table, predicting properties from an element's location, groups having similar properties, atomic structure, states of matter, and nuclear fusion in stars.
Linear Equations and Graphs_Lesson 1_Slope and Rate of Changemrstrementozzi
1. The document provides examples of how to calculate rate of change and slope from tables, graphs, and two points. It explains that rate of change is the change in the dependent variable over the change in the independent variable, while slope is the rate of change between any two points on a line.
2. Examples are given for finding constant and non-constant rates of change from tables, as well as how to determine if a set of data has a constant rate of change. Graphs are used to demonstrate horizontal, vertical, and standard linear slopes.
3. Calculating slope from two points on a graph or when given two point coordinates is demonstrated. Special cases for horizontal and vertical lines are explained.
1. The document provides steps for factoring polynomials, simplifying binomials, multiplying monomials and binomials, finding areas of rectangles with variable sides, naming polynomials, and other algebra concepts. It includes examples and explanations for each topic.
2. Methods are given for factoring polynomials by finding the greatest common factor or using the difference of squares formula. Binomials should be squared by writing them twice and using FOIL, not squaring individual terms.
3. To multiply a monomial by a polynomial, the term outside is distributed to each term inside. FOIL is used to multiply binomials. Perimeters can be found by doubling the total length and width given in an area formula.
This document provides instructions on how to multiply binomials. It explains that to multiply two binomials, you multiply each term in one binomial by each term in the other binomial and circle like terms to combine them. It provides examples of multiplying (x + 7)(x + 2) as (x^2 + 2x + 7x + 14) and simplifying to (x^2 + 9x + 14). It then provides exercises for students to practice multiplying different binomial expressions.
The document provides instructions on multiplying polynomials. It discusses multiplying monomials by polynomials by distributing the monomial. It also covers multiplying binomials using the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms. Finally, it addresses multiplying binomials by polynomials with more than two terms, which does not use FOIL but instead distributes the binomial to every term. Examples and practice problems are provided for each type of polynomial multiplication.
The document discusses finding the square of a binomial expression. It explains that to find the square of (a + b), the expression is (a + b)(a + b), not (a + b)2. Using FOIL or the distributive property, the square of (a + b) is a2 + 2ab + b2. Similarly, the square of (a - b) is a2 - 2ab + b2. The document provides examples of expanding squared binomial expressions and warns students not to make mistakes like (x + 6)2 = x2 + 36.
Challenge 11 multiplying differences of squaresmrstrementozzi
The document discusses differences of squares, which is when two binomial expressions with the same terms are multiplied but one pair of terms is added and the other is subtracted. This results in the expanded form being the first term squared minus the second term squared. It provides examples of expanding expressions using FOIL and the distributive property, including recognizing that (x+2)(x-2) is a difference of squares. It then has practice problems for the reader to expand additional expressions using this concept.
El documento proporciona 24 ejercicios de álgebra que involucran la aplicación de la propiedad distributiva para simplificar expresiones. Los ejercicios piden factorizar términos entre paréntesis y distribuirlos a los términos adyacentes para simplificar las expresiones dadas.
November 26, 2012: Polynomials (SmartBoard Note)mrstrementozzi
This document contains notes and exercises on polynomials from a math class. It instructs students to complete problems 1-13 on a worksheet about adding and subtracting polynomials. It defines the degree of a polynomial and has students find the degree of example polynomials. It also demonstrates adding and subtracting polynomials using algebra tiles to model the expressions.
3. 3. Determining Equivalence.notebook February 06, 2013
Happy Wednesday!
Today's warmup is Mental Math #15.
When you are finished, please take out your homework
and a red pen.
Solve each equation or inequality for the variable:
1) 2x + 2 > 4
2) 2(x + 2) 3x > 2
3) 5(x 3) + 4 =
4) 3(c+4) 2 > 7
5) 9 = 8 + [ 3 (2x + 4)] 6x
3
5. 3. Determining Equivalence.notebook February 06, 2013
While I check in your work, please continue
working on the following ACE problems:
Page 15: 1012
Page 16: 1823, 2532, 4649
Label the paper you use with your name,
date, and "Classwork" and title it
"Equivalent Expressions". You may use the
same paper as yesterday.
5
14. 3. Determining Equivalence.notebook February 06, 2013
Key Question: Is plugging in one value to
both expressions good enough to determine
equivalency?
Let's try 2x + 1 and x + 2. Evaluate for x = 1.
Are the expressions equivalent?
14
15. 3. Determining Equivalence.notebook February 06, 2013
Key Question: Is plugging in one value to both
expressions good enough to determine equivalency?
Let's try 2x + 1 and x + 2 again. This time
evaluate for x = 3.
Are the expressions equivalent?
15
16. 3. Determining Equivalence.notebook February 06, 2013
Key Question: Is plugging in one value to both expressions
good enough to determine equivalency?
This time we'll use y = 4(x + 2) 4 and
y = 4(x + 1). Evaluate for x = 1 and x = 2
Are the expressions equivalent?
Do you need at least two values to produce
the same answer to confirm that expressions
are equivalent?
16
17. 3. Determining Equivalence.notebook February 06, 2013
Why are two values for x
y = 4(x + 2) 4
good enough to determine
equivalent expressions?
y = 4(x + 1)
17
20. 3. Determining Equivalence.notebook February 06, 2013
Group Work: Problem 1.4 AE
Write neatly and show your
work; this will be turned in for
credit.
No more than two people per
group.
Groups not working will be split
up and work alone.
20