- =20
**Comparing Graphs**- Students are given an hourly rate o= f pay and infer coordinates for (h, $) over a range of hours. They produce = a table and a graph of work-pay. Then they produce another graph for anothe= r rate of pay and discuss differences in time and pay. =20
**How Many Points?**- Students work with: (a) a context =E2=80= =94 distance as a function of time; (b) generating coordinates. =20
**Human Graph I**- Students plot themselves on a Cartesian p= lane. Each student will get a large card with a place for an ordered pair: = (x, y), where x refers to hours worked, and y refers to amount earned. The = students must name the coordinate pair for the point they themselves are st= anding on. =20
**Human Graph II**- Students graph the functions k x 2 $/h = and k x 3 $/h. The idea is to show that for each linear function the points= fall onto a straight line. =20
**Maps to Graphs**- Students will be given two linear dista= nce-time graphs and asked to tell a story about each graph and to compare t= hem. They will later explore comparisons between points in each line. =
=20
**Rates vs Totals**- Students compare points on an hours/p= ay Cartesian space. The main challenge lies in recognizing that, although o= ne student earned more, the other student was paid better, that is, at a hi= gher rate of pay. They must indicate the difference in pay and the differen= ces in amount worked. =20

- =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
**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. =
=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
**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
**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
**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
**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
**Swimming Pools I**- Compare how two swimming pools fill= up with water over several hours. =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. =
=20
**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**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
**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

- =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
**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
**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
**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
**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
**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

- =20
**Area of a Square as a Function**- Student= s will develop a quadratic equation to represent the area of a square. =
=20
**Biggest Output**- Students will decide on what linear and= quadratic functions will result in the greatest output, starting from an a= lgebraic expression, and using tables and graphs to help them make these de= cisions. =20
**Box of Clay Activity**- Students will compare two c= ubic functions based on the context of the volumes of a box of clay. =
=20
**Candy Experiment**- Students will create their own data= to construct a graph and equation of negative and fractional slope. =
=20
**Compare and Contrast**- Students will identify the = y-intercept and slope using equations and then use that data to create corr= esponding tables and graphs. =20
**Coupon Activity**- Students will create graphs, tables a= nd equations to explain their stories and look at how a graph changes depen= ding on the y-intercept. =20
**Curves in a Cubic**- Students will explore different k= inds of cubic functions through graphs and tables. =20
**Function Challenges - 20 Questions**-= Students will compete in a game to generate equations for functions that m= eet certain criteria, as given by the instructor. =20
**Graphing Equations**- Students will practice moving b= etween graphs and equations of functions, as well as identifying the y-inte= rcept and slope. =20
**Graphing Equations - Nonlinear Functions**- Students write equations for three graphs and examine their sl= opes by comparing and contrasting the graphs. Students also look at the sam= e functions graphed on differently scaled coordinate planes. =20
**Guess My Rule - Linear**- Students will try to de= termine the equation to match their partner's created graph and work togeth= er to correct their own mistakes. =20
**Guess My Rule - Non-Linear**- Students will p= roduce algebraic expressions starting from non-linear graphs produced by ot= her students in the class. =20
**It Depends**- Students will think about how we can show a dep= endent relationship between two quantities, using a variety of representati= ons. =20
**Jason's Tree House**- Students will extract data fr= om a story and use tables and graphs to answers questions about proposed sc= enarios. =20
**Lotto Winnings**- Students will generate a graph for a no= nlinear function, point by point, in order to realize that there are differ= ent types of functions that they might not know about yet. =20
**Relating Graphs and E= quations - Linear and Quadratic Functions**- Students will gene= rate graphs from given equations and equations from given graphs. =20
**= x2 and x**- Students will look at x squared and x as functions,= and for which values of x one function value is greater than the other.=20