...Equations and Inequalities Unit Overview Investigating patterns is a good foundation for studying Algebra 1. You will begin this unit by analyzing, describing, and generalizing patterns using tables, expressions, graphs, and words. You will then write and solve equations and inequalities in mathematical and real-world problems. Key Terms As you study this unit, add these and other terms to your math notebook. Include in your notes your prior knowledge of each word, as well as your experiences in using the word in different mathematical examples. If needed, ask for help in pronouncing new words and add information on pronunciation to your math notebook. It is important that you learn new terms and use them correctly in your class discussions and in your problem solutions. © 2014 College Board. All rights reserved. Academic Vocabulary • consecutive Math Terms • sequence • common difference • expression • variable • equilateral • equation • solution • formula • literal equation • compound inequality • conjunction • disjunction • absolute value • absolute value notation • absolute value equation • absolute value inequality ESSENTIAL QUESTIONS How can you represent patterns from everyday life by using tables, expressions, and graphs? How can you write and solve equations and inequalities? EMBEDDED ASSESSMENTS These assessments, following Activities 2 and 4, will give you an opportunity to demonstrate what you have learned...
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... - ‘What the French call ‘laïcité’ is a matter which concerns the separation of religion and state. In England, this issue is not taken as seriously as in France.’ a good deal of… (beaucoup) ALTERNATIVE EXPRESSIONS - a large amount of - a considerable number of - a significant amount of - a great deal of (more emphatic) NB- You can mix the phrases: ‘a large number of’/ ‘a considerable amount’/ a good amount of Fierce (féroce/passionné) heated lively vivid to give a series of… (donner plusieurs/une serie de) - Professor Clark will give a series of lectures - The Cinematheque plans to show a series of films by the Lumiere brothers - The police made a series of arrests in connection with a drugs cartel - The government has announced a series of initiatives to encourage reading among 6-12 year-olds NB- Dans les phrases en-dessus, le verbe ‘give’ est remplace par un autre verbe ‘show’/ ‘make’/ ‘announce’ selon l’action- verifies toujours le meilleur verbe pour l’action. ALTERNATIVE EXPRESSIONS to give a number of to give a succession of Strategy… Indefensible… ‘The policy of taxing poor people more than rich people is indefensible.’ ‘The policy of making children under the age of 16 work full-time is indefensible.’ ALTERNATIVE EXPRESSIONS unacceptable- unjustifiable- ‘Paying workers less than they need to survive is unjustifiable’ cannot be justified- off the charts- (really high/ unprecedented) -‘The level of...
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...between man and man. Every work of art causes the receiver to enter into a certain kind of relationship both with him who produced, or is producing, the art, and with all those who, simultaneously, previously, or subsequently, receive the same artistic impression. Speech, transmitting the thoughts and experiences of men, serves as a means of union among them, and art acts in a similar manner. The peculiarity of this latter means of intercourse, distinguishing it from intercourse by means of words, consists in this, that whereas by words a man transmits his thoughts to another, by means of art he transmits his feelings. The activity of art is based on the fact that a man, receiving through his sense of hearing or sight another man’s expression of feeling, is capable of experiencing the emotion which moved the man who expressed it. To take the simplest example; one man laughs, and another who hears becomes merry; or a man weeps, and another who hears feels sorrow. A man is excited or irritated, and another man seeing him comes to a similar state of mind. By his movements or by the sounds of his voice, a man expresses courage and determination or sadness and calmness, and this state of mind passes on to others. A man suffers, expressing his sufferings by groans and spasms, and this suffering transmits itself to other people; a man expresses his feeling of admiration, devotion, fear, respect, or love to certain objects, persons, or phenomena, and others are infected by the same...
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...Jordan Hodge Josh Lane English111 1-11-15 “Cuss Time” 1. I feel as though McCorkle began with her father story to reflect on what this story is going to be about, and summing up the main points. 2. Because when her son writes fiction, fiction is known to be false so I feel as though her son was freely to express everything necessary to what he wants to talk about. © 3. ( E) The word captured is referred to the meaning taking something in your possession controlled by force. The girl was angry and frustrated, instead of taking the frustration else where it was already lead on. 4. (P) The word Gestapo is being identified as a word much more than an actual person, defining what is acceptable and what is not. 5. Cussing make one better by growing up with the idea of the cussing instead of “soap licking” witch was mentioned in the text. You have to be a certain legal age to be engaged in “cuss time”. 6. (T) No, cussing is not the only way we can express individuality, by limiting or denying freedom of speech and expression people take away a lot of potential of what they do have. 7. (B) The family’s feelings described in the last sentence was just very blunt and realistic about the situation, expressing your feelings in a fiction novel calls for using your freedom and using it wisely. 8. (H) It adds to the understatement of freedom because why be embarrassed, because having freedom is not being scared to hold back or withdraw information that’s...
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...does George Saunders’ short story addresses that people can choose symbolic ways to express their feelings? ) In his short story, George Saunders’ addresses that people can choose symbolic ways to express their feelings by giving real life examples from the story’s main character, veteran father of the family. He sees the pole as his expression of his feelings. He decorates it on veteran days, people’s death, basically, on every important events. The medals he hangs on the pole, shows us that he is a veteran and it is known that veterans are usually have hard time expressing their emotions or feelings. This is why he chooses a “ different “ way of expressing his feelings and emotions. Narrator says, “The pole was Dad’s one concession to glee.” ( pg 29 “ Sticks”, Tenth of December) which tells us the importance of this pole to the Father. When he died, his children sold the house to a young couple and they threw the pole away. One’s most important or valuable thing might not have any meaning for the others. The pole was his everything, his mirror of his emotions. He chose the pole to talk and explain himself to the world. His way of expression was may be different then other people but it was the best way for...
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...assigned You Tube video titled, “History Channel Secrets of Body Language” it was encouraged to look beyond words because body language tells it all. Big ideas highlighted in the video stressed this point. The video states body movement composes ninety-three percent of communication and only seven percent of communication derives from words. The video expressed a walk can convey power or a simple gesture can hide a lie, meaning body language can betray us. It was also expressed in the video that when a person is under public pressure and scrutiny while speaking their gestures, facial expressions and body movements, even subtle movements can be used to persuade mass communication. This response can establish power in unconventional manners without people being directly aware. The main points of the video highlighted that communication is conveyed through body movements, facial expression and their raising or lowering of their voice to undercover hidden secret messages. In reflecting on how this relates to my personal life. I have experienced the need to maintain a stoic disposition while working with clients. My body language remained focused and constant as I knew it the impact it could have on clients and people with whom I engage. I also watched this dynamic unfold in the courtroom and in trial hearing, attorneys had to demonstrate little or no reaction to verdicts pertaining to criminal or civil matters. When talking to clients and taking their interrogatories or...
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...text and web, T-Mobile also has a plan for 30 dollars a month for 1,500 talk and text minutes. After you go through your allotted 1,500 talk and text time was up, the cost skyrockets up to 10 cents a minute. 10 cents a minute comes out to 6.00 per hour, I thought in my head. I decided that instead of jumping into a decision about phone plans, that I should first go home and do the math. I wanted to figure out which plan was going to be the most cost effective, and which plan would suite my needs the best. 2. Explain all needs (e.g., financial, non-financial, situational) of the hypothetical consumer. The needs include many different factors: • The first and most important factor how much do you use your phone? The breaking point on the problem today is 200 talk or text above the 1500 minute plan and I will be paying less up front but more on the back end which is no good. If I chose the 1500 minute plan, I will not want to be going over the 1500 minutes as then the cost would go up to 10 cents a minute or 6.00 per hour. • Is this replacing a work or office phone? If I am going to use this phone for several purposes it is more valuable to me and it is easier to justify higher costs. • What should I do right now if I am unsure but need a phone? I would say the best starting point unless I use my phone all the time is to try out the 30 dollar a month plan. Saving 20 dollars right off the bat and then closely monitoring your minutes over the next couple...
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...using. 1) Budget: a) What integer would represent their total initial budget? 60,000 + 75,000 + 30,000 = 165,000 b) Thirty-five percent of this budget will be used for renting space and paying the utilities. Another twenty-five percent will go toward buying bakery equipment and finally another five percent will be used to purchase initial ingredients. Write an algebraic expression that indicates how much money will be spent on renting space, utilities, equipment and supplies. 0.3560,000+75,000+30,000+0.2560,000+75,000+30,000+0.0560,000+75,000+30,000= c) Write an algebraic equation to show how the total budget is being used. Use x for the remaining funds. Next solve this equation for the remaining funds. 0.35 * 165,000+0.25 * 165,000+0.05 *165,000=x 2) Baking: 0.25 x 165,000 = 41,250 a) You have decided to make two sizes of cupcakes, regular and mini. The regular pans hold 12 cupcakes and the mini pans hold 18. If your oven will hold 6 regular pans and 4 mini pans at the same time, how many cupcakes will you be able to bake at one...
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...structure lets the value of a variable or an expression determine which path of execution the program will take. It’s a multiple alternative decision structure that allows you to test the value of a variable or an expression and then use that value to determin which statement to execute. 2. The AND operator takes two Boolean expressions as operands and creates a compound Boolean expression that is true only when both expressions are true. True AND True = True 3. The OR operator takes two Boolean expressions as operands and creates a compound Boolean expression that is true when either of the sub expressions is true. True OR False = True 4. The NOT operator is a unary operator that takes a Boolean expression as its operand an reverses its logical value. The Not operator reverses the truth of its operand. If it is applied to an expression that is true the operator returns false. If it is applied to an expression that is false it returns True. Not true = False, Not false = True 5. Flow chart 6. And, Or , Not 7. And, Or, Not 8. And, OR, Not 9. > greater than, < less than, >= greater than or equal to, <= less than or equal to, == equal to, != not equal to 10. Case structure has a diamond at the top and branches down into different parallelograms. 11. A repetition structure causes a statement or set of statements to execute repeatedly. 12. A condition-controlled loop uses a true/false condition to control the number of times that it repeats, a count-controlled loop...
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...Final Exam Guide Boolean Expressions and Relational Operators – Named after English mathematician George Boole. In 1800s Boole invented a system of mathematics in which the abstract concepts of true and false can be used in computations. If-Then statement is formed with a relational operator, which determines whether a specific relationship exists between two values. (>) Greater than operator. (==) Equal to operator. (<) Less than operator. (>=) Greater than or equal to. (<=) Less than or equal to. (!=) Not equal to. The case structure is a multiple alternative decision structure. It allows you to test the value of a variable or an expression and then use that value to determine which statement or set of statements to execute. The testExpression is usually a variable, but in many languages it can also be anything that gives a value (such as a math expression). Short-Circuit Evaluation – In many languages both the AND and OR operators perform short-circuit evaluation. If the expression on the left side of the AND operator is false, the expression on the right side will not be checked. Because the compound expression will be false if only one of the sub-expressions is false, it would waste CPU time to check the remaining expression. So, when the AND operator finds that the expression on its left is false, it short-circuits and does not evaluate the expression on its right. With the OR operator if the expression on the left side of the OR...
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...teaching strategy could be one small component of the unit. There may not be enough instructional time to utilize every strategy in the curriculum guide. The 2007 Mississippi Mathematics Framework Revised includes the Depthof-Knowledge (DOK) level for each objective. As closely as possible, each strategy addresses the DOK level specified for that objective or a higher level. Suggestions or techniques for increasing the level of thinking may be included in the strategy(ies). In addition, the process strands (problem solving, communication, connections, reasoning and proof, and representation) are included in the strategies. The purpose of the suggested teaching strategies is to assist school districts and teachers in the development of possible methods of organizing the competencies and objectives to be taught. Since the competencies and objectives require multiple assessment methods, some assessment ideas may be included in the strategy. October 2007 2007 Mississippi Mathematics Framework Revised Strategies Comp. 1 2 Obj. a g Suggested Teaching Strategies Give students an algebraic expression such as 3x + 2y2. Ask them to create as many different algebraic expressions that can be simplified to the given expression. Some possible expressions might be: 1) 2x + 2(x + y2) – x; 2) 4(x – ay) + 2y(2a + y) – x; or 3) 3(x + y2) – y2. Have students share their expressions as others check to be sure that it can be simplified...
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...theme of the play was about the influence of greed and prejudice in Cuban society in the 1860’s. The play also expressed the problems concerning race, ethnicity, and social class that were prevalent during this time period. There were many different aspects of the play that made the theme more visible to a spectator. Some of the positive aspects of the play included: the acting, the costumes, and the storyline. Although the play had many advantages, there were also disadvantages about the play. Some of the disadvantages were the staging and the acting. The actresses and actors chosen for this play did a wonderful job at portraying their characters. My favorite character to watch during the play was La Senora Condesa, who was played by Gabrielle Bailes. Gabrielle did phenomenal job acting like a snooty and upper class woman. Some of the things she did well were her facial expressions, vocal choice, and body movements. Gabrielle’s facial expressions represented every emotion her character was experiencing in each scene. For example, when she found out her son Carlos, who was played by Jordon Webb, was in love with Julia the expression on her face was anger and disgust. Gabrielle also looked pretentious because she raised her head high, and she had a pinch expression on her face throughout the play. Another thing that Gabrielle did well was her vocal choice. She sounded exactly like a proper women from the 1800s. She had a soft voice, but she was loud enough for everyone in...
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...= 12 Base = b = 20 Area = ½ × b × h = ½ × 20 × 12 = 120 Volume of Rectangular Figures The volume of a rectangular prism is the length on the side times the width times the height. Example: What is the volume of the rectangular prism with the dimension shown below? Use the formula for the volume of a cylinder as shown below. Volume= (2) (5) (3) = 30 Area of Irregular Figures Without symmetry, even shape, formal arrangement It may seem easy to find the area of a rectangle, but what if the figure has more than 4 sides? . The area of the first rectangle is 72 square centimeters and the area of the second rectangle is 50 square centimeters. Together there are 72 + 50 = 122 square centimeters. Therefore, the area of the entire figure is 122 square centimeters. Surface Area of Rectangular Figures Surface area is the sum of the areas of all the surfaces of a 3 – Dimensional figure. 7 m 7 m 1 m 1 m 12m 12m S.A. = 2(1 x 7 + 12 x 7 + 12 x 1) S.A. = 2 (7 + 84 + 12) S.A. = 2 (103) S.A. = 206 Determining if two ratios are proportion If the product of the means equals the product of the extremes, then the two ratios form a true proportion. In less methyl way, cross multiply and if you get the same number both times, it is a true proportion. The top number of one ratio times the bottom number of the other. Example 5 x 18 = 90 10 x 8 = 80 not proportion. For 8/24 and 10/30 8 x 30 = 240 and 24 x 10 = 240 is proportional ...
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...A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable but they can have two three or more variables. Knowing the formula and how to use and brake down polynomial can help us in our everyday lives. It can help you figure out how much interest you can accrue from a deposit or investment that you made with a given interest rate. Let’s take a closer look at an equation that deals with polynomials. “P dollars is invested at annual interest rate r for 1 year. If the interest is compounded annually then the polynomial P(1 + r)2 represents the value of the investment after 1year” (Dugopolski, 2012). P(1 + r/2)2 Original expression P(1 + r/2)(1 + r/2) Simplify the expression by using foil this means multiply first outer, Inner, last P(1+ r/2 + r/2 + r2/4) Combine the like terms P(1 + 2(r/2) + r2/4) Distribute P across the trinomial P + Pr + Pr2/4 Put all variables in descending order Now let’s try our formula with a given set of numerical information P=200 r =10% interest rate .10 as a decimal. P + Pr + Pr2/4 expanded formula 200 + 2/4(200)(.10) + 200(.10)2 substitute values into formula 200 + 10 + 200(.01) multiply 200 + 10 + 2 ...
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...Appendix C Starting a Business Starting your own business can be exciting and daunting at the same time. Businesses use math when managing finances, determining production levels, designing products and packaging, and monitoring labor. A bakery can be a highly profitable and rewarding business. During this activity, you will apply the skills from Ch. 1 & 2 to navigate some of the issues facing bakery owners. Application Practice Answer the following questions. Use Equation Editor when writing mathematical expressions or equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. 1. You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an $80,000 loan from your family and a $38,250 small business loan. These loans must be repaid in full within 10 years. a) What integer would represent your total budget? The integer is 118,250 b) Twenty-five percent of your budget will be used to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve. .25(118,250)=u c) How much money will rent and utilities cost? Explain how you arrived at this answer. I solved this problem by converting 25% into a decimal and multiplying it by the total loan amount. d) Suppose an...
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