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**Recipes that Exchange**- The lesson focuses on a f= unction that multiplies input by two but also changes the ingredient to ano= ther type of ingredient. =20
**Rules and Formulas**- Students are given a rule and a= data table supposedly generated according to the rule. Students evaluate w= hether: (1) the proper rule has been applied and (2) the result is correct.= =20
**Starting With A Rule**- Students focus on whether g= iven outputs are consistent with a given rule. =20
**Times Two**- The lesson focuses on a function that multiplies = the input by two. New notations are introduced. =20

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**Comparing Strips of Unmeasured Lengths I**- The class is the first of a series that will focus directly up= on the algebraic representation of measurements and their multiplicative re= lations. Children are asked to compare the lengths of strips, to describe t= he relationships between them in multiple ways, and to demonstrate that the= relationships they represent are true. =20
**Comparing Strips of Unmeasured Lengths II<= /a>**- The class is the second of the "Strips of Unmeasured Lengths= " series that will focus directly upon the algebraic representation of meas= urements and their multiplicative relations. Children are asked to compare = the lengths of strips, to use algebraic notation to describe the relationsh= ips between them, and to demonstrate that the relationships they represent = are true. =20
**Comparing Strips of Unmeasured Lengths II= I**- This is the third lesson in the "Strips of Unmeasured Leng= ths" series that focuses directly upon the algebraic representation of meas= urements and their multiplicative relations. We will work with the relation= ship B =3D 3S, focusing on equations and their verbal descriptions and on t= rue and false equations and statements. =20
**Fourth Grade Assessment I**- This is a written= assessment where children will interpret and determine the truth or falseh= ood of equations and statements that describe comparisons between quantitie= s. =20
**Fourth Grade Assessment I Review**- Chi= ldren discuss responses to problems where they interpret and determine the = truth or falsehood of equations and of statements that describe comparisons= between quantities. =20
**Fourth Grade Assessment II**- This is a writt= en assessment where children will interpret and determine the truth or fals= ehood of equations and of statements that describe comparisons between quan= tities. =20
**Fourth Grade Assessment III**- This is a wri= tten assessment where children will be asked to interpret graphs and to int= erpret and determine the truth or falsehood of equations and statements tha= t describe comparisons between quantities. =20
**Three to One**- Children discuss and produce verbal and mat= hematical statements on the proportion, S:L :: 1:3, that is, on the functio= n f( x ) =3D 3x and on its inverse f^{-1}( x ) =3D 1/3 x =20
**Two Phone Plans I**- Students compare two phone plans,= one of which has a lower rate, but a monthly basic charge; the other has a= higher rate but no basic charge. =20
**Two Phone Plans II**- Students will work on the compa= rison between two phone plans (also used in the lesson "Two Phone Plans I")= , one of which has a lower rate, but a monthly basic charge, the other has = a higher rate but no basic charge. =20
**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. =20

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**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. =20
**Equations in Groups**- Students first discuss equali= ty situations and how equal changes on both sides of the equality do not ch= ange the equality or the solution to the equation. In a second activity, A = pair of students begins with a solved equation (e.g. N =3D 4) and passes th= e equation to their neighbor; the neighbor operates equally on each side of= the equation and passes the equations to the following neighbor. They cont= inue this process until the series of equations return to the first two stu= dents who, then, check whether the solution still holds. They also check th= e logic and correctness of their colleagues operations on the initial equat= ion. =20
**Equations in Groups II**- A student (or a pair of= students) begins with a solved equation (e.g. N =3D 4) and pass(es) the eq= uation to neighbor (or pair of neighbors); the neighbor(s) operate(s) equal= ly on each side of the equation. And so on, around the table. There should = be at least three students or pair of students at each table. When the seri= es of equations returns to the first students, each student (or pair of stu= dents) check whether the solution still holds for the solution they had pro= posed at the beginning. They also check the logic and correctness of the ch= anges implemented by their classmates. =20
**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. =20
**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. =20
**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. =20
**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. =20
**Solving Equations I**- Students will be asked to use= the syntactic rules of algebra to solve equations with variables on both s= ides of the equals sign. =20

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**Graphing Equations**- Students will practice moving b= etween graphs and equations of functions, as well as identifying the y-inte= rcept and slope. =20
**Relating Graphs and E= quations - Linear and Quadratic Functions**- Students will gene= rate graphs from given equations and equations from given graphs. =20
**What Will Happen**- Students will work with equations o= f functions (both linear and non-linear) to find the y-intercept without gr= aphing. =20
**Who Shares My Function? - Linear with All Representations**- S= tudents will work in groups after finding other students who have the same = linear function represented by a story, a table, a graph, or an equation. T= hey will attempt to explain and discuss why the different representations r= efer to the same function. =20
**Who Shares My Function? - Linear with Graphs, Tables, and Equations - Students will make groups by finding other students who have the s= ame linear function, as shown in representations of graphs, tables, or equa= tions. They will then generate a story to go with the function.****Who Shares My Function? - Linear with Negative and Fractional Slope - Students will find other functions that are the same as theirs, st= arting from a table, a graph, or an equation. Once they have identified the= same function represented in a different way, they will create a story tha= t describes all of the different representations of the same function.****Who Shares My Function? - Quadratics**- Students will make gro= ups by finding other students who have the same quadratic or linear functio= n in different representations. =20