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
**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? =20
**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? =20
**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
**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
**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
**Consistency**- Children choose pairs of numbers that maintai= n the relationship of 1 to 3 that is given in a statement, and they explain= why they believe the relationship is maintained. =20
**Cartesian Candy Bars I**- We compare ratios of va= rious ordered pairs in a Cartesian grid. The initial discussion concerns th= e space as a whole; the task will focus on selected points and on the ratio= of the dependent variable to the independent variable. =20
**Cartesian Candy Bars II**- Children work on shar= ing different amounts of candy bars among different numbers of people. They= compare ratios (candy bars per person) and plot points in a Cartesian grid= . =20
**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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**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**Graphing Halves and Doubles**- Children work= on a problem about distance and time and compare two rates: half a meter p= er second and two meters per second. =20
**Graphing Thirds and Triples**- Children work= on a problem about distance and time and compare two rates: one third of a= meter per second and three meters per second. =20
**Varying Speed**- Children are asked to tell a story about = a trip depicted through a graph that has varying slopes/speeds. =20
**Varying Velocity**- Children are asked to tell a story = about a trip depicted through a graph that has varying slopes/velocities.=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
**Graphing A Story**- A trip is described in miles, hours= , and miles/hr. Students produce a graph from the description. They then pr= oduce a table from the graph and answer questions about the trip. =20
**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. =20
**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. =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
**Equations and Inequalities**- Students will w= ork with equations and inequalities, first with simple ones and later with = comparisons of two functions. The Wallet Problem, introduced in a previous = lesson, will provide the background context. =20
**Intervals**- Students reason about graphs showing growth over = time. They compare heights of children and heights of two animals at differ= ent time intervals. =20
**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. =20
**Running Race I**- Compare a race between two students: on= e who runs at a constant pace, the other who tires out as the race proceeds= . =20
**Running Race II**- Compare a race between two students: = one who runs at a constant pace and one who changes pace as the race procee= ds. =20
**Fourth Grade Assessment IV**- This is a writt= en assessment where children will compare two students. One of the students= ' speed can be represented linearly while the other's speed is represented = by a non-linear graph. =20
**Swimming Pools I**- Compare how two swimming pools fill= up with water over several hours. =20
**Swimming Pools II**- Students will examine the rate of= pools filling over several hours. =20
**Comparing Functions**- This lesson is split into two= days. In the first class, the students will analyze eight basic graph shap= es and will represent and solve a verbal problem involving the choice betwe= en two functions. In the second one they will be asked to choose, among the= eight basic graph shapes, the ones that matches specific situations. =
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**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
**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. =20