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# Production of Algebraic Expressions

## Production of Algebraic Expressions

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1. Candy Boxes - This class centers on the possible amounts of= candies two children, John and Maria, have. They each have the same, unspe= cified number of candies inside their own candy box. John has, in addition,= one extra candy and Maria has three extra candies. What are the possible t= otal candies they might have?
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3. Comparison Problems & Tables - This class will be used to= review concepts and representations as applied to the solution of verbal c= omparison problems and to work on function tables.
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5. Dinner Tables II - Students work with a function relat= ing the number of tables (in a straight line) to the number of available se= ats. One table seats 4, two tables seat 6, three tables seat 8....
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7. Functions - Earning Money - The students will= create tables and equations from given stories. The functions are additive= and multiplicative.
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9. Functions II - The students will use three functions that = are represented as a sequence of patterns and create a sequence of hops on = the number line, a data table, and an algebraic expression to express the f= unctions.
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11. Guess my Rule - Multiplicative Tables - Two children create secret rules for transforming input numbers. The= teacher uses a doubling or tripling rule.
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13. Guess my Rule - Tables - Two children create sec= ret rules for transforming input numbers. The teacher uses a doubling rule.=
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15. Multiple Number Lines - Students continue to lear= n that two partial changes that start at different points on the number lin= e are equivalent. At the end, they will work with notation for variables (N= + 5 - 3 or N + 2).
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17. N-Number Line I - Students work with the table they bui= lt in the previous class for multiple number lines, focusing on the notatio= n for variables (N + 5 - 3 or N + 2).
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19. N-Number Line II - Students use the N-Number line to m= ake generalizations about an unknown amount of money in a piggy bank.
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21. Number Line - Locations - Students place themse= lves at points on the number line. Main contexts: stairs, age, money, tempe= rature, and pure number.
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23. Number Line Shortcuts - The students will use a n= umber line to see how two addends or subtrahends are equivalent to one sing= le change once combined.
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25. Piggy Banks - The whole lesson revolves around a multipart = story problem involving changes in two quantities over several days of a we= ek. The initial quantities are equal yet unknown. Then transformations are = applied to the quantities. Students are asked to compare the quantities thr= oughout the week even though only their relative relationship can be determ= ined.
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27. Three Heights - In this class we will explore: (a) How th= e children deal with comparisons, (b) How they draw inferences from compari= sons, and (c) How they represent comparisons between three unknown amounts.=
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1. Evaluation Problem - Students will be given a proble= m that asks about the amount of money each person has, based on the amount = in a piggy bank. They will be given one graph and asked to draw the second = graph.
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3. Multiplicative Candy Boxes I - This class = centers on the possible amounts of candies two children, Juan and Marcia, h= ave. Juan has a box of candy and Marcia has twice as much candy. What are t= he possible amounts of candies they might have?
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5. Multiplicative Candy Boxes II - This clas= s is a continuation of the Multiplicative Candy Boxes I lesson. It centers = on the possible amounts of candies two children, Juan and Marcia, have. Jua= n has a box of candy and Marcia has twice as much candy. What are the possi= ble amounts of candies they might have?
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7. The Better Paying Job I - Children work on a pr= oblem about rate of pay per hour of work. They compare ratios (dollars earn= ed per hour of work) and discuss and plot points in a Cartesian plane.
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9. The Better Paying Job II - Children work on a = problem about rate of pay per hour of work. They compare ratios (dollars ea= rned per hour of work) and discuss and plot points in a Cartesian plane.=20
10. Three Heights Review - In this class we will explo= re: (a) How children deal with comparisons, (b) How they draw inferences fr= om comparisons, and (c) How they represent comparisons between three unknow= n amounts.
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12. Wallet Problem I - Students compare the amounts of mon= ey two students have. The amounts are described relationally but not throug= h precise dollar amounts.
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14. Wallet Problem II - Students will be given a wallet p= roblem. They will be asked to compare the amounts of money two students hav= e. The amounts are described relationally but not through precise dollar am= ounts.
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16. Wallet Problem III - Students will continue working = with the wallet problem. They will be shown a graph for Mike's amounts and = asked to (a) determine whether it represents Robin's or Mike's money and (b= ) to predict where the line for Mike would fall. Later they will plot Mike'= s amounts and will discuss why the lines cross.
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1. Ar= cade - Students are told a story about two children, each of w= hom has a certain amount of money, but only one of whom has an amount known= to us. After a series of events they happen to end up with the same amount= of money.
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3. Enacting and Solving Equations - Student= s enact and discuss a situation where two children have amounts of candies.= Some of the candies are visible, others are inside opaque tubes or boxes. = After considering multiple possibilities they are told that the children ha= ve the same amount of candies. The situation corresponds to the equation 3x= + y + 6 =3D x + y + 20, where x is the amount of candies per tube and y is= the amount of candies per box. Students will be asked to discuss and to re= present the situation, to solve the equation that corresponds to the situat= ion, and to solve other written equations with similar structure.
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5. Equations and Graphs - Students will further compa= re two linear functions in the context of evaluating two plans for shovelin= g snow. One plan has two parts: a basic charge plus a charge based on the n= umber of square meters cleared. The other plan has no basic charge; it only= charges according to the number of square meters cleared. However the per-= meter charge is higher than in the other plan. Students are asked to determ= ine the circumstances in which the bill from each plan would be the same. T= hey then examine the graph of the two functions and discuss how equations a= nd inequalities relate to the graph.
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7. Fifth Grade Assessment I - This assessment wil= l focus on writing equations to solve verbal problems and on solving equati= ons using syntactic rules. It is intended as a diagnostic tool to assist te= achers in planning future activities.
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9. Fifth Grade Assessment I Review - This = lesson will focus on reviewing the recent in-class assessment, on writing e= quations for word problems, and on solving equations.
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11. Fifth Grade Assessment II - This assessment w= ill focus on writing equations to solve verbal problems and on solving equa= tions using the syntactic rules of algebra.
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13. Fifth Grade Assessment III - This assessment= will focus on writing equations to solve verbal problems and on solving eq= uations using the syntactic rules of algebra.
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15. Phone Plans - Students will compare two linear functions in= the context of evaluating phone plans. One plan has two parts: a basic cha= rge plus a charge based upon the number of minutes used. The other plan has= no basic charge; it only charges according to the minutes used. However th= e per-minute charge is higher than in the other plan. Students are asked to= determine the circumstances in which the monthly bill from each plan would= be the same. They then examine the graph of the two functions and discuss = how equations and inequalities relate to the graph.
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17. Review on Graphs and Equations - In this= lesson, the students will solve individually or in small groups the set of= problems. For each problem, the teacher will lead a discussion based on th= e students' work (the teacher should identify strong and weak points in the= students' work). The class is organized around four main problems. Within = each problem students will answer different questions.
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19. Solving Equations with One Variable= - Students work on a story about two children who each have a certain amou= nt of money. The amount of one of the children is known but the other is no= t. After a sequence of transformations they end with the same amount of mon= ey. Students will be led to solve for the starting value by relating the eq= uation to the events in the story. After that, they will be asked to solve = another similar problem.
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21. Train Crash - Students will compare two linear functions re= presented in a graph. They reason about the problem using (a) the word prob= lem and two diagrams; (b) a graph of position vs. time; (c) a table of valu= es (d) making expressions for each position function; and (e) solving the e= quation algebraically.
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23. Wallet Review Problem - This activity is a review= of the Wallet Problem done in fourth grade. It is intended to introduce ne= w students to some of the concepts we have covered and to refresh the memor= ies of our old students. Students compare the amounts of money two students= have. The amounts are described relationally but not through specific doll= ar amounts.
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