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  • Interpretation of Tables
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Interpretation of Tables

Third Grade Lessons
  1. Comparing Different Functions - The students will discuss, represent, and solve a verbal problem involving the choice between two functions.
  2. 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.
  3. Guess my Rule - Multiplicative Tables - Two children create secret rules for transforming input numbers. The teacher uses a doubling or tripling rule.
  4. Guess my Rule - Tables - Two children create secret rules for transforming input numbers. The teacher uses a doubling rule.
  5. N-Number Line I - Students work with the table they built in the previous class for multiple number lines, focusing on the notation for variables (N + 5 - 3 or N + 2).
  6. 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.
  7. Starting With A Rule - Students focus on whether given outputs are consistent with a given rule.
Fourth Grade Lessons
  1. Comparing Functions - This lesson is split into two days. In the first class, the students will analyze eight basic graph shapes and will represent and solve a verbal problem involving the choice between two functions. In the second one they will be asked to choose, among the eight basic graph shapes, the ones that matches specific situations.
  2. Consistency - Children choose pairs of numbers that maintain the relationship of 1 to 3 that is given in a statement, and they explain why they believe the relationship is maintained.
  3. Evaluation Problem - Students will be given a problem 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.
  4. The Better Paying Job I - Children work on a problem about rate of pay per hour of work. They compare ratios (dollars earned per hour of work) and discuss and plot points in a Cartesian plane.
  5. The Better Paying Job II - Children work on a problem about rate of pay per hour of work. They compare ratios (dollars earned per hour of work) and discuss and plot points in a Cartesian plane.
  6. 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.
Fifth Grade Lessons
  1. Fifth Grade Assessment III - This assessment will focus on writing equations to solve verbal problems and on solving equations using the syntactic rules of algebra.
  2. Wallet Review Problem - This activity is a review of the Wallet Problem done in fourth grade. It is intended to introduce new students to some of the concepts we have covered and to refresh the memories of our old students. Students compare the amounts of money two students have. The amounts are described relationally but not through specific dollar amounts.
Middle School Lessons
  1. Who Shares My Function? - Linear with All Representations - Students 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. They will attempt to explain and discuss why the different representations refer to the same function.
  2. Who Shares My Function? - Linear with Graphs, Tables, and Equations - Students will make groups by finding other students who have the same linear function, as shown in representations of graphs, tables, or equations. They will then generate a story to go with the function.
  3. Who Shares My Function? - Linear with Negative and Fractional Slope - Students will find other functions that are the same as theirs, starting 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 that describes all of the different representations of the same function.
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