Each of our activities is designed to be flexible and self-conta= ined. Please feel free to use any of the activities as the basis of your te= aching or as supplementary materials.

=20You do not need to do more than one of the activities in order for them = to be useful. However, we have listed them here in the approximate order th= at we have used them with students. This may be helpful for teachers lookin= g for a series of activities.

=20Please explore our categorizations by activity type, process, and math c= oncept if you are looking for something specific!

=20- =20
**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. =20
**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. =20
**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. =20
**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
**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
**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
**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
**Solving Equations II**- Students will be asked to r= epresent and solve verbal problems requiring algebra and to use the syntact= ic rules of algebra to solve equations with variables on both sides of the = equals sign. =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
**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. =20
**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. =20
**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. =20
**Elapsed Time**- A variant of the train crash problem is use= d to address questions about elapsed time. The task is to determine where a= train is, given a certain time. =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
**Varying Rates of Change**- Students will compare= three functions, two of which are nonlinear, that tell the story of three = cousins who all save $1,000 in one year. One saves a lot the first day and = less and less each day as time goes on; one saves very little the first day= and more and more each day throughout the year; the last cousin saves the = same amount each day. Students will be asked to predict the shape of the gr= aph for each function and, later, to look at and describe graphs of all thr= ee cousins' savings. =20
**Basic Function Shapes**- In this lesson, the stude= nts will (a) discuss, represent, and solve a verbal problem involving the c= hoice between two functions; (b) choose, among 8 basic graphs (7 distinct s= hapes), the one that matches specific situations; and (c) write stories to = match a specific graph shape. =20
**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. =20