PoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey)


 Baldric Berry
 1 years ago
 Views:
Transcription
1 PoWTER Problem Packet A Phoney Deal? (Author: Peggy McCloskey) 1. The Problem: A Phoney Deal? [Problem #3280] With cell phones being so common these days, the phone companies are all competing to earn business by offering various calling plans. One of them, Horizon, offers 700 minutes of calls per month for $45.99, and additional minutes are charged at 6 cents per minute. Another company, Stingular, offers 700 minutes for $29.99 per month, and additional minutes are 35 cents each. 1. For each plan, write an expression that represents the total cost per month in terms of the number of additional minutes used. 2. For how many total minutes of calls per month is Horizon's plan a better deal? Extra: A third company, Dash, offers a plan that costs $49 for 500 minutes, and extra minutes are 2 cents each. For how many total minutes of calls per month is the Dash plan the best deal of the three? Note: This problem, A PhoneyDeal?, is one of many from the Math Drexel's Problems of the Week Library. Are you interested in having access to more and also the many teacher resources that the Math Forum provides? View information about the different levels of membership including a free Trial Account from this page: 2. About the Problem A Phoney Deal can be found in the Math Forum Problems of the Week Library. Many students today possess a cell phone and know about cell phone usage. The problem is slightly outdated since now all sorts of plans exist for cellular phones, individual and family plans along with the fees for texting, downloads, and web usage. In the middle school classroom we start with the basics and then we can assign others independent research on the cost today for using the phones and the services they enjoy. There are a variety of places where one can insert the challenge posed by this problem into the middle school and algebra 1 curriculum. In the 6 th grade curriculum students write stories for graphs and draw graphs for stories. Eliminate the two questions and have students draw three graphs to represent all three companies. These stories can lead to a discussion on the horizontal segment and why we call that a constant function. Although slope is not introduced in your curriculum, a discussion on which segment is steeper and A Phoney Deal? 1
2 why, can lead to some critical thinking among students. It is a good exercise then to work with the labels on the x and yaxis and put the first two companies on a single axis. Compare and contrast discussions can begin. The children could be introduced to the questions to write the expression for the pricing of each phone plan and to find the number of minutes for Horizon to be the better plan. I would not expect them to solve algebraically but the students are capable of evaluating the expressions and creating in/out tables. In PreAlgebra or Algebra class the problem can be used in the curriculum when writing and evaluating expressions, equations and inequalities. This problem demonstrates the effect of different slopes. In an Algebra class one might insert this problem into the lessons on systems of equations or inequalities and look for an algebraic solution to this system of equations. The primary goal for introducing this problem can be aligned to the algebra standard for 6 th 8th grade students published by NCTM: Represent situations using algebraic symbols; Analyze situations using algebraic symbols. You would hope that the translation of this problem would lead to expressions for the cost of each company as asked for in question number 1. Question number 2 is asking to compare these expressions to find when one company offers the better deal. The extra includes a third company with different constraints. You would hope younger students could construct tables to solve the problem and that prealgebra and algebra students would write equations or inequalities to solve a system. The NTCM algebra standard is expanded for 9 th 12 th grade to include fluent solving of systems of equations or inequalities. Asking students to submit a written explanation to the Math Forum allows them to work on the NCTM communication standard. Working in groups, and or class room discussion will also increase the student s ability to communicate with peers and teachers. NCTM standard of representation and problem solving can be aligned as this problem will lead to extensions in representing the given functions using graphs and or spreadsheet models. Or as in the case of 6 th graders the story and graph can lead to the representation in algebraic symbols. Recently, the Math Forum has encouraged children to solve this problem using technology by listing the problem in the tpows (technology problems). Published Geometer s Sketch pad activities has a similar problem listed in a unit on matching graphs with a story. The NCTM curriculum standard on problem solving encourages the use of problems that will lead to building math knowledge. Another extension building on this problem would be to discuss domain intervals and piece wise functions. A Phoney Deal? 2
3 3. Common Misconceptions Assigning and labeling of variables and expressions. This student did a wonderful job in communicating the labels for the variables and correctly simplified the equation labeled cost per month for two companies. The equations did lead to the correct answer since the bill for Horizon was less than Singular when the total minutes was over 756 minutes. The student solved problem #2 by setting up an inequality. The solution is greater than The process of rounding up means the student should use this symbol 756. The student knew this since the statement reads 756 minutes per month or more. Horizon is the better deal. To emphasize that the cost given is only when the usage is over 700 minutes wonder what is the cost for Horizon, Singular and Dash if one only used 100 minutes. Two of the equations would yield a negative value. Wonder what the cost would be if the students evaluate the equations using x as 500 minutes in the first two companies. What the student A Phoney Deal? 3
4 needed to label y was the cost per month when the total minutes was over 700 minutes for Horizon and Singular. The misconception follows for the extra that is not written correctly. The student also needs to change.2 to.02. I might wonder how the student would now label the cost for Dash. Then I might wonder how one can compare cost and minutes. I wonder what the cost for Dash is for 500 minutes to make sure the equation is correct. Here we need to lead the student and most likely the entire class to discover an equation to compare. Wondering what the cost of Dash is at 700 minutes might help. These wonderings should lead the student to discover a new equation for the cost of Dash when the total usage is over 700 minutes. In the student presentations we will discover the solution to the extra. Interpreting the Solution to answer the question Again labeling m = the total minutes talked, hurt the student when checking the answer. The student was aware when checking the answer that the answer did not correspond. Wonder why she thought there was a typo. Wonder if there is another label for m. If m is labeled minutes over 700 wonder what the total minutes would be. The student did solve the equation correctly. This student found when the two bills would be equal. In solving this problems we will see that some used the logic of finding when the cost were equal an equation; while others looked for the solution when one bill was less than the other bill. Labels and making sure one answers the question are important skills for the middle school child to develop. You can point out the skill of eliminating decimals was used correctly, the expressions for more than 700 are correct and the solution is correct. The reporting of the answer does not match the question. The question was for the total minutes talked not the minutes over 700. A Phoney Deal? 4
5 Equations or a Label Here we have a student who used an expression for a label. The expression for cost is x. This is the cost when total minutes is 700 +x. These two expressions are not equal. When solving the student used substitution to make the cost are equal and was able to solve the equation correctly because the two expression in the equation were both cost. The solution does not answer the question since the reported response should be the expression 700 +x. Assuming the companies charge per minute only not part of a minute the answer should be rounded up. This student found the number of minutes over 700 to make the two cost equivalent. A Phoney Deal? 5
6 4. Sample Student Solutions Trial and Error: Using minutes over 700 The student answered question 2 correctly and the expressions for Horizon and Singular are correct if labeled total cost for usage over 700 minutes. Labeling would make the solution easier for peers to follow. This student did not show how the solution was derived. There is a magnitude error in the solution. Since the check for 5.51 did not work it appears the student decided to use trial and error method. The solution is discovered in the table when the cost for 56 extra minutes makes Horizon a better deal than Singular. Encourage the student to revise and add labels. Encourage all students to verify their work. The student reports the answer using total minutes which is correct. A Phoney Deal? 6
7 Trial and Error: Equations for total minutes. A Phoney Deal? 7
8 The solution above uses the total minutes for the variable t and reports the cost at the end of month using the expression (t700). The labeling is correct and the evaluating at 800, 750, 753, and 755 show that the student was looking for a time when Horizon was less than Singular. Remind students that this equation for C is correct only when the usage is over 700. We need to begin to suggest that for the first 700 minutes there is another equation. Be sure to point out the reasoning why the student did not need to verify that 756 was the solution to the problem. Wonder if everyone follows that line of reasoning. A Phoney Deal? 8
9 XY Chart Here the student uses an XY chart to demonstrate the formula. The student mentions graphing. I would wonder if they graphed and if they used the table function for the figures published above. Writing mathematics and formatting work is hard for the students but the software and tools are improving each year. I might use this solution to review for students how one can insert charts so that there is no fear of someone wondering what, 8 = means. Also if students are going to use the technology available to them we can show them how to insert graphs and images to enhance their communication of mathematics. We know the student knows the x is minutes over 700 from his last paragraph. Wonder how his graph would show the cost for a 100 minutes or any value less than 700. This will set the stage for new learning on piecewise functions. A Phoney Deal? 9
10 Graphing These two students told us they solved the problem by graphing. Finding the intersection point is the correct process. But even using technology the process of communication needs to improve. The same misconceptions occur. Labeling the variable and the equations are important pieces of communicating thinking. The class now knows that the equations given are for minutes over 700 and over 500 for the third company. We can wonder on the graph the same as we did for the trial and error solutions. What is the cost for 100 minutes of usage? Is there away to combine the two pieces of the billing process in a graph? The first student reports the correct solution whereas the second student report the overage minutes. Finding the intersection is a way to solve systems of equations so it is important to present this method. This is the correct theory but now in our presentation we need to start the questioning about the third company Dash. The reported price increases after 500 minutes. Wonder what the cost of all three companies is at 557 and 575 minutes, at 757 and 775 minutes. If x = the extra minutes would you use the same x for the given minutes for all three companies? We will address this issue after we present the algebraic solutions. Algebraic solutions: x= total minutes, solve an inequality A Phoney Deal? 10
11 Algebra x= extra minutes, solve an equality. Here we have two concise simple algebraic solutions. In the first one the student gives the expressions representing the cost in terms of total minutes. We now know it is the cost when usage is over 700 minutes. The student sets up an inequality. The verb to use would be 756 minutes or more is when Horizon is better than Singular. In the second example the student lets x equal the extra minutes and solves an equation. Note that the student uses cents to eliminate the decimals in the original expressions. The student solves an equation looking for the number of minutes where the cost would be equal then reasons that Horizon is cheaper for usage of 756 or more. Both students used the substitution method correctly. Algebraic differences This student uses a different approach. The expressions are given for the first two companies. The student tells us the difference in cost and the difference in the extra cost per minute. I would wonder if he could revise this work and include the sentences showing the differences and quotients mentioned. The quotient of and.29 gives the number of minutes for the two plans to be equal. Rounding up he found that at 756 minutes Horizon became a better deal. Although we are not shown the cost of the third A Phoney Deal? 11
12 company nor the work this student solved the extra and tell us even more than asked for. Dash was better than Singular when the total is 770 minutes and Dash is a better plan than Horizon when total minutes used in 876. In order to see if the class understands this line of reasoning, I might wonder aloud for the class what was the total cost for Dash, what was the result of Dash Horizon, Dash Singular, Extra cost of Dash extra cost of Horizon, Extra of Dash Extra of Singular. Does a negative value mean anything or are we looking for the absolute value of the difference? The author and the class might need support for finding the expressions that gave 770 minutes and 876 minutes above. Ask students to verify that these values are correct. Wonder what happened with the student who graphed the three expression and found 57 and 75 as the intersection using x as the extra minutes. The first wonderings concerning the extra came up in the graphing example. We raised a few questions. We now know there are two expressions one can use in solving these problems. Let x = extra minutes and the cost of Dash over 500 minutes is.02x +49. Let x = total time and the expression is.02(x500) The expressions change depending on the variable label. The extra was solved above using differences but the student did not communicate his ideas clearly enough for the peers. The last presentation creates another equation for dash so that it can be compared with the other two companies using x as the same total. If x = extra minuets 50 extra minutes would be a total of 750 for Horizon and for Singular but for Dash x= 50 is a total of 550; that is why we see conflicting solutions in the extras presented above and the graphing. Had the student written the expressions using x as total minutes the answers would be the same. Here is an approach to the Extra: A Phoney Deal? 12
13 The extra poses a problem since the price changes after 500 minutes. So our student finds the cost of Dash when the total time was 700. Using the expression now of m and setting up the equations the solutions tells us when Dash is equal to Horizon and when Dash is equal to Singular. I would wonder with this student if statements could be made when each company is the better deal. I would wonder if the students could revise the compound inequality. The student is correct that Dash is the better deal for 876 minutes or more. Presentation order I would present the student solutions as presented above. Trial and error is a method all should be able to follow and use. I want to stress the two different expressions depending on the label given to the variable. I want to stress the two strategies. Setting up an equation and reasoning from the equality point to report the answer as greater than or equal to the solution is one strategy. The other is setting up the inequality and reporting the answer as such. Trial and Error leads naturally to a XY chart or in out table understandable by younger students. The XY table then leads to graphs. Although the graphing students both used x as the extra minutes and neither produced the graphs, I want to present graphing as a valid method and use this as jumping off point for extending this problem to graphing, piece wise functions and spreadsheet representations. It is important that students see various models of the same data. Algebra students know how to solve a system and substitution is a method of choice. The examples given use the different expressions and one solves equations while the other thinks in terms of inequalities. Finding the differences was a different and accurate way to reason. The extra is a challenge for all. 5. Extensions According to NCTM standard on problem solving good problems lead students to build new mathematical knowledge. The NCTM standard on representation encourages students to select, apply and translate among mathematical representations to solve problems. This problem needs to be modeled by graphing and spreadsheet. This problem can build new knowledge on graphing piece wise functions and discussion on domain intervals. Using the constant price and then using the expressions written by the students for the cost for 500 and 700 minutes or more respectively they can produce this model using a A Phoney Deal? 13
14 spreadsheet. From the spreadsheet data students can answers the questions. The yellow shows the better deal total min total min Horizon Singular Dash Horizon Singular Dash The spreadsheet will produce the following model. Even younger students can visualize the constant function and then the change in steepness. Discussion for the younger child can be on what the horizontal segment represents and what does the differences in the steepness signify? Wondering for the algebra students could include wondering about the equation of the constant functions. A Phoney Deal? 14
15 Wonder what is the domain for the constant function. What is the domain for the functions that show a constant rate of change. Wonder if they can make any changes to the functions they used for total monthly bill. I would also wonder if this model could be produced by the handheld. Discussion on piece wise functions could be discussed and modeled. Fig. 1 Fig.2 Fig.3 Figures 1 can model the intersection of Horizon and Singular. Figure 2 shows all functions and figure 3 zooms in on the intersection found by graphing. Once students discover reporting total cost with respect to the domain we can graph piece wise functions by adding the interval to the expression. A Geometer s Sketchpad model could be created with the younger students asking them to find the significance of point A, B, and C. A Phoney Deal? 15
16 Hopefully one can see the many uses of having students grapple with this Math Forum problem. The primary goals of writing expressions and finding a solution can be achieved by trial and error, graphing, or the substitution method of solving a system. If you re lucky someone might use another line of reasoning as the student who reasoned using the differences in price and the fees for the extra usage. Giving students challenging problems to wonder about, and formulate a written response will increase their mathematical skills, analytic thinking and reasoning ability. Having them produced a written response can enhance the discussion for all on the different approaches to label and solve. The problem leaves open the door to introducing other topics to challenge or enrich and other models to represent the data. Since cell phones are dear to the heart of the preteens and teenagers you might even expand the problem to compare the plans offered today. This problem will engage all and all can be encouraged to find a solution through the wonderings of the teachers and peers. A Phoney Deal? 16
High School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
More informationHigh School Algebra Reasoning with Equations and Inequalities Solve systems of equations.
Performance Assessment Task Graphs (2006) Grade 9 This task challenges a student to use knowledge of graphs and their significant features to identify the linear equations for various lines. A student
More informationMathematics Curriculum Guide Precalculus 201516. Page 1 of 12
Mathematics Curriculum Guide Precalculus 201516 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing
More informationGrade Level Year Total Points Core Points % At Standard 9 2003 10 5 7 %
Performance Assessment Task Number Towers Grade 9 The task challenges a student to demonstrate understanding of the concepts of algebraic properties and representations. A student must make sense of the
More informationLinear Equations. 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber
Linear Equations 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI 83
More informationGRADE 8 MATH: TALK AND TEXT PLANS
GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculumembedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems
More informationLines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan
Lines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan I. Topic: SlopeIntercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
More informationHigh School Algebra Reasoning with Equations and Inequalities Solve equations and inequalities in one variable.
Performance Assessment Task Quadratic (2009) Grade 9 The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations
More informationLesson 4: Solving and Graphing Linear Equations
Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A2M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,
More informationGeometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.
Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find
More informationPA Common Core Standards Standards for Mathematical Practice Grade Level Emphasis*
Habits of Mind of a Productive Thinker Make sense of problems and persevere in solving them. Attend to precision. PA Common Core Standards The Pennsylvania Common Core Standards cannot be viewed and addressed
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationThe program also provides supplemental modules on topics in geometry and probability and statistics.
Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students
More informationGraphic Designing with Transformed Functions
Math Objectives Students will be able to identify a restricted domain interval and use function translations and dilations to choose and position a portion of the graph accurately in the plane to match
More informationPerformance Assessment Task Which Shape? Grade 3. Common Core State Standards Math  Content Standards
Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to
More informationhttp://www.aleks.com Access Code: RVAE4EGKVN Financial Aid Code: 6A9DBDEE3B74F5157304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More informationPerformance Assessment Task Bikes and Trikes Grade 4. Common Core State Standards Math  Content Standards
Performance Assessment Task Bikes and Trikes Grade 4 The task challenges a student to demonstrate understanding of concepts involved in multiplication. A student must make sense of equal sized groups of
More informationTotal Student Count: 3170. Grade 8 2005 pg. 2
Grade 8 2005 pg. 1 Total Student Count: 3170 Grade 8 2005 pg. 2 8 th grade Task 1 Pen Pal Student Task Core Idea 3 Algebra and Functions Core Idea 2 Mathematical Reasoning Convert cake baking temperatures
More informationTask: Will and Latisha s Tile Problem Algebra I
Tennessee Department of Education Task: Will and Latisha s Tile Problem Algebra I In math class, Will and Latisha were challenged to create their own pattern with tiles. Latisha built the first three arrangements
More informationThe Distributive Property
The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationAnswers Teacher Copy. Systems of Linear Equations Monetary Systems Overload. Activity 3. Solving Systems of Two Equations in Two Variables
of 26 8/20/2014 2:00 PM Answers Teacher Copy Activity 3 Lesson 31 Systems of Linear Equations Monetary Systems Overload Solving Systems of Two Equations in Two Variables Plan Pacing: 1 class period Chunking
More informationTYPES OF NUMBERS. Example 2. Example 1. Problems. Answers
TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationNumber and Numeracy SE/TE: 43, 49, 140145, 367369, 457, 459, 479
Ohio Proficiency Test for Mathematics, New Graduation Test, (Grade 10) Mathematics Competencies Competency in mathematics includes understanding of mathematical concepts, facility with mathematical skills,
More informationUNIT PLAN: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
UNIT PLAN: EXPONENTIAL AND LOGARITHMIC FUNCTIONS Summary: This unit plan covers the basics of exponential and logarithmic functions in about 6 days of class. It is intended for an Algebra II class. The
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE:  Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationMAT 116. Algebra 1A. Version 5 12/15/07 MAT 116
 MAT 116 Algebra 1A Version 5 12/15/07 MAT 116 Program Council The Academic Program Councils for each college oversee the design and development of all University of Phoenix curricula. Council members
More informationTennessee Department of Education. Task: Sally s Car Loan
Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was $15,. She made a down payment of $43. She financed the remaining amount
More informationLyman Memorial High School. PreCalculus Prerequisite Packet. Name:
Lyman Memorial High School PreCalculus Prerequisite Packet Name: Dear PreCalculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These
More informationPerformance Based Learning and Assessment Task
Performance Based Learning and Assessment Task Staircases and Ramps I. ASSESSSMENT TASK OVERVIEW & PURPOSE: The students will use slope to describe the characteristics of ramps versus the stairs between
More informationStudent Activity: To investigate an ESB bill
Student Activity: To investigate an ESB bill Use in connection with the interactive file, ESB Bill, on the Student s CD. 1. What are the 2 main costs that contribute to your ESB bill? 2. a. Complete the
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours Essential Question: LESSON 2 Absolute Value Equations and Inequalities How do you
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationF.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions
F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed
More informationPythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom
Pythagorean Theorem Differentiated Instruction for Use in an Inclusion Classroom Grade Level: Seven Time Span: Four Days Tools: Calculators, The Proofs of Pythagoras, GSP, Internet Colleen Parker Objectives
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationTImath.com Algebra 1. Absolutely!
Absolutely! ID: 8791 Time required 45 minutes Activity Overview In this activity, students first solve linear absolute value equations in a single variable using the definition of absolute value to write
More informationGraphing Parabolas With Microsoft Excel
Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1100 Overview: This unit models realworld situations by using one and twovariable linear equations. This unit will further expand upon pervious
More informationMTH124: Honors Algebra I
MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,
More informationBig Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit
Big Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit Big Ideas Graphs are a way of organizing data and they appear in newspapers, magazines, on the Internet and other places in everyday
More informationAccommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego
Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 67 Grade: 8th Number of Students: 25 Date: May 1213, 2011 Goal: Students will
More informationAlgebra II Unit Number 4
Title Polynomial Functions, Expressions, and Equations Big Ideas/Enduring Understandings Applying the processes of solving equations and simplifying expressions to problems with variables of varying degrees.
More information2. THE xy PLANE 7 C7
2. THE xy PLANE 2.1. The Real Line When we plot quantities on a graph we can plot not only integer values like 1, 2 and 3 but also fractions, like 3½ or 4¾. In fact we can, in principle, plot any real
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationEvaluation Tool for Assessment Instrument Quality
REPRODUCIBLE Figure 4.4: Evaluation Tool for Assessment Instrument Quality Assessment indicators Description of Level 1 of the Indicator Are Not Present Limited of This Indicator Are Present Substantially
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationhttps://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...
of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach BellRinger Activity Students
More informationFinancial Literacy in Grade 11 Mathematics Understanding Annuities
Grade 11 Mathematics Functions (MCR3U) Connections to Financial Literacy Students are building their understanding of financial literacy by solving problems related to annuities. Students set up a hypothetical
More informationOperations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. MP.
Performance Assessment Task Incredible Equations Grade 2 The task challenges a student to demonstrate understanding of concepts involved in addition and subtraction. A student must be able to understand
More informationWhat to Expect on the Compass
What to Expect on the Compass What is the Compass? COMPASS is a set of untimed computer adaptive tests created by the American College Test (ACT) Program. Because COMPASS tests are "computer adaptive,"
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationMATH THAT MAKES ENTS
The Bureau of Labor statistics share this data to describe the difference in earnings and unemployment rates by the amount of education attained. (1) Take a look at this table, describe what you notice
More informationPolynomials and Factoring. Unit Lesson Plan
Polynomials and Factoring Unit Lesson Plan By: David Harris University of North Carolina Chapel Hill Math 410 Dr. Thomas, M D. 2 Abstract This paper will discuss, and give, lesson plans for all the topics
More informationSupport for Student Literacy
Support for Student Literacy Introduction In today s schools, many students struggle with English language literacy. Some students grow up speaking, reading and/or writing other languages before being
More informationSolving Quadratic & Higher Degree Inequalities
Ch. 8 Solving Quadratic & Higher Degree Inequalities We solve quadratic and higher degree inequalities very much like we solve quadratic and higher degree equations. One method we often use to solve quadratic
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationYou might be surprised to know that the word Tshirt wasn t really used until
Hot Shirts Using Tables, Graphs, and Equations, Part 2 Learning Goals In this lesson, you will: Use different methods to represent a problem situation. Estimate values of expressions that involve decimals.
More informationALGEBRA I (Common Core)
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................
More informationPerformance Assessment Task Gym Grade 6. Common Core State Standards Math  Content Standards
Performance Assessment Task Gym Grade 6 This task challenges a student to use rules to calculate and compare the costs of memberships. Students must be able to work with the idea of breakeven point to
More informationPreAP Algebra 2 Lesson 17 Graphing Absolute Value Functions
Lesson 17 Graphing Absolute Value Functions Name Objectives: In this activity, students will relate the piecewise function to the graph of the absolute value function and continue their development of
More informationPowerTeaching i3: Algebra I Mathematics
PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationBalanced Assessment Test Algebra 2008
Balanced Assessment Test Algebra 2008 Core Idea Task Score Representations Expressions This task asks students find algebraic expressions for area and perimeter of parallelograms and trapezoids. Successful
More information1.7 Graphs of Functions
64 Relations and Functions 1.7 Graphs of Functions In Section 1.4 we defined a function as a special type of relation; one in which each xcoordinate was matched with only one ycoordinate. We spent most
More informationClovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
More informationInteger Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.
More informationAdministrative  Master Syllabus COVER SHEET
Administrative  Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for
More informationStandards for Mathematical Practice: Commentary and Elaborations for 6 8
Standards for Mathematical Practice: Commentary and Elaborations for 6 8 c Illustrative Mathematics 6 May 2014 Suggested citation: Illustrative Mathematics. (2014, May 6). Standards for Mathematical Practice:
More informationTeacher: Maple So School: Herron High School. Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles
Teacher: Maple So School: Herron High School Name of Lesson: Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles Subject/ Course: Mathematics, Algebra I Grade Level: 9 th
More information1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
More informationTennessee Department of Education
Tennessee Department of Education Task: Pool Patio Problem Algebra I A hotel is remodeling their grounds and plans to improve the area around a 20 foot by 40 foot rectangular pool. The owner wants to use
More informationNumbers Plus Preschool Mathematics Curriculum: Teacher s Manual
Number and operations involves understanding whole numbers and realizing that numbers represent quantity. It includes learning number words and symbols, counting, comparing and ordering quantities, composing
More informationAlgebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test
Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action
More informationAbsolute Value of Reasoning
About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationA + dvancer College Readiness Online Alignment to Florida PERT
A + dvancer College Readiness Online Alignment to Florida PERT Area Objective ID Topic Subject Activity Mathematics Math MPRC1 Equations: Solve linear in one variable College ReadinessArithmetic Solving
More informationUnit 1: Place value and operations with whole numbers and decimals
Unit 1: Place value and operations with whole numbers and decimals Content Area: Mathematics Course(s): Generic Course Time Period: 1st Marking Period Length: 10 Weeks Status: Published Unit Overview Students
More informationData Analysis, Statistics, and Probability
Chapter 6 Data Analysis, Statistics, and Probability Content Strand Description Questions in this content strand assessed students skills in collecting, organizing, reading, representing, and interpreting
More informationConnections Across Strands Provides a sampling of connections that can be made across strands, using the theme (integers) as an organizer.
Overview Context Connections Positions integers in a larger context and shows connections to everyday situations, careers, and tasks. Identifies relevant manipulatives, technology, and webbased resources
More informationPrentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1
STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason
More informationHigh School Student Project: AppleWorks or MS Office Investing in the Stock Market
High School Student Project: AppleWorks or MS Office Investing in the Stock Market The Unit of Practice Invitation How can we give students an opportunity to apply the knowledge they ve gained from their
More informationDELAWARE MATHEMATICS CONTENT STANDARDS GRADES 910. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))
Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 910) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS
More informationINTRODUCTION CONTENTS
INTRODUCTION Algebra for All and No Child Left Behind are phrases in the education community that suggest, and in many cases require, action. They give impetus for mathematics teachers at all levels to
More informationLife Insurance Modelling: Notes for teachers. Overview
Life Insurance Modelling: Notes for teachers In this mathematics activity, students model the following situation: An investment fund is set up Investors pay a set amount at the beginning of 20 years.
More informationMathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight
Mathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight Contents by Grade Level: Overview of Exam Grade Level Results Cut Score and Grade History
More informationA synonym is a word that has the same or almost the same definition of
SlopeIntercept Form Determining the Rate of Change and yintercept Learning Goals In this lesson, you will: Graph lines using the slope and yintercept. Calculate the yintercept of a line when given
More informationBasic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.
Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:
More informationYears after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540
To complete this technology assignment, you should already have created a scatter plot for your data on your calculator and/or in Excel. You could do this with any two columns of data, but for demonstration
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More information1. At what interest rate, compounded monthly, would you need to invest your money so that you have at least $5,000 accumulated in 4 years?
Suppose your grandparents offer you $3,500 as a graduation gift. However, you will receive the gift only if you agree to invest the money for at least 4 years. At that time, you hope to purchase a new
More informationUnit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:
Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning
More informationRadius, Diameter, Circumference, π, Geometer s Sketchpad, and You! T. Scott Edge
TMME,Vol.1, no.1,p.9 Radius, Diameter, Circumference, π, Geometer s Sketchpad, and You! T. Scott Edge Introduction I truly believe learning mathematics can be a fun experience for children of all ages.
More informationTeaching Algebra with The Geometer s Sketchpad
Teaching Algebra with The Geometer s Sketchpad COURSE DESCRIPTION UCB Extension X305.5 Education (2 semester units) This is a professionallevel, moderated, online course in the use of The Geometer s Sketchpad
More information