## Number Lines

###### Third Grade Lessons

**All Things Being Equal II**- The equals sign signifies that amounts on each side are the same. The students will use Unifix blocks and the corresponding equations to represent equalities between additive amounts.**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 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.**Guess my Rule - Multiplicative Tables**- Two children create secret rules for transforming input numbers. The teacher uses a doubling or tripling rule.**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.**Linear vs Quadratic Functions**- The students will use two functions (a linear and a quadratic) that are represented as a sequence of patterns and create a sequence of hops on the number line and an algebraic expression to express the functions.**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 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).**N-Number Line II**- Students use the N-Number line to make generalizations about an unknown amount of money in a piggy bank.**Number Line - Locations**- Students place themselves at points on the number line. Main contexts: stairs, age, money, temperature, and pure number.**Number Line Shortcuts**- The students will use a number line to see how two addends or subtrahends are equivalent to one single change once combined.**Partial and Total Changes**- Students learn that two partial changes are equivalent to a single total change. On the number line, this corresponds to the idea of a shortcut. Three notations are emphasized: words, number lines with hopping arrows, and numerical expressions.**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.**Times Two**- The lesson focuses on a function that multiplies the input by two. New notations are introduced.

###### 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.