## Interpretation of Algebraic Expressions

###### Third Grade Lessons

**Formulas and Stories**- The students will be required to work with the relation between different mathematical expressions (formulas) and stories.**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.**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.**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.**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.

###### Fourth Grade Lessons

**Equations and Inequalities**- Students will work 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.**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.**Two Phone Plans II**- Students will work on the comparison 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.**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

**Elapsed Time**- A variant of the train crash problem is used to address questions about elapsed time. The task is to determine where a train is, given a certain time.**Fifth Grade Assessment I**- This assessment will focus on writing equations to solve verbal problems and on solving equations using syntactic rules. It is intended as a diagnostic tool to assist teachers in planning future activities.**Fifth Grade Assessment II**- This assessment will focus on writing equations to solve verbal problems and on solving equations using the syntactic rules of algebra.**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 the 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.