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**Candy Boxes**- This class centers on the possible amounts of candies two children, John and Maria, have. They each have the same, unspecified 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 total candies they might have?**Comparing Different Functions**- The students will discuss, represent, and solve a verbal problem involving the choice between two functions.**Comparing Graphs**- Students are given an hourly rate of 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 another rate of pay and discuss differences in time and pay.**Comparison Problems & Tables**- This class will be used to review concepts and representations as applied to the solution of verbal comparison problems and to work on function tables.**Dinner Tables I**- Students work with a function relating number of tables to the number of available seats. One table seats 4, two tables seat 8, three tables seat 12....**Dinner Tables II**- Students work with a function relating the number of tables (in a straight line) to the number of available seats. One table seats 4, two tables seat 6, three tables seat 8....**Dots Problem**- We present to the students a problem dealing with a growing pattern over time. To begin, there is one dot. With each passing minute four more dots are drawn around the previous dot(s).**Formulas and Stories**- The students will be required to work with the relation between different mathematical expressions (formulas) and stories.**Functioning Together**- Students work together to develop multiple representations of a function. The students split up into groups of three with each student having a separate responsibility. When all the input values have been used up, the students are asked to, together, make up a story that describes their function.**Functions - Earning Money**- The students will create tables and equations from given stories. The functions are additive and multiplicative.**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 functions.**Functions from Tables**- Students work with a function, beginning with a table and then a formula, to generate ordered pairs that follow the rule of the function.**Guess my Rule - Multiplicative Tables**- Two children create secret rules for transforming input numbers. The teacher uses a doubling or tripling rule.**Guess my Rule - Tables**- Two children create secret rules for transforming input numbers. The teacher uses a doubling rule.**How Many Points?**- Students work with: (a) a context — distance as a function of time; (b) generating coordinates.**Human Graph I**- Students plot themselves on a Cartesian plane. 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 standing on.**Multiple Number Lines**- Students continue to learn that two partial changes that start at different points on the number line are equivalent. At the end, they will work with notation for variables (N + 5 - 3 or N + 2).**N-Number Line II**- Students use the N-Number line to make generalizations about an unknown amount of money in a piggy bank.**Piggy Banks**- The whole lesson revolves around a multipart story problem involving changes in two quantities over several days of a week. The initial quantities are equal yet unknown. Then transformations are applied to the quantities. Students are asked to compare the quantities throughout the week even though only their relative relationship can be determined.**Recipes that Exchange**- The lesson focuses on a function that multiplies input by two but also changes the ingredient to another type of ingredient.**Rules and Formulas**- Students are given a rule and a data table supposedly generated according to the rule. Students evaluate whether: (1) the proper rule has been applied and (2) the result is correct.**Starting With A Rule**- Students focus on whether given outputs are consistent with a given rule.**Three Heights**- In this class we will explore: (a) How the children deal with comparisons, (b) How they draw inferences from comparisons, and (c) How they represent comparisons between three unknown amounts.**Times Two**- The lesson focuses on a function that multiplies the input by two. New notations are introduced.

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