## Ratios

###### Fourth Grades

**Cartesian Candy Bars I**- We compare ratios of various ordered pairs in a Cartesian grid. The initial discussion concerns the space as a whole; the task will focus on selected points and on the ratio of the dependent variable to the independent variable.**Cartesian Candy Bars II**- Children work on sharing different amounts of candy bars among different numbers of people. They compare ratios (candy bars per person) and plot points in a Cartesian grid.**Comparing Strips of Unmeasured Lengths I**- The class is the first of a series that will focus directly upon the algebraic representation of measurements and their multiplicative relations. Children are asked to compare the lengths of strips, to describe the relationships between them in multiple ways, and to demonstrate that the relationships they represent are true.**Comparing Strips of Unmeasured Lengths II**- The class is the second of the "Strips of Unmeasured Lengths" series that will focus directly upon the algebraic representation of measurements and their multiplicative relations. Children are asked to compare the lengths of strips, to use algebraic notation to describe the relationships between them, and to demonstrate that the relationships they represent are true.**Comparing Strips of Unmeasured Lengths III**- This is the third lesson in the "Strips of Unmeasured Lengths" series that focuses directly upon the algebraic representation of measurements and their multiplicative relations. We will work with the relationship B = 3S, focusing on equations and their verbal descriptions and on true and false equations and statements.**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.**Fourth Grade Assessment I**- This is a written assessment where children will interpret and determine the truth or falsehood of equations and statements that describe comparisons between quantities.**Fourth Grade Assessment I Review**- Children discuss responses to problems where they interpret and determine the truth or falsehood of equations and of statements that describe comparisons between quantities.**Fourth Grade Assessment II**- This is a written assessment where children will interpret and determine the truth or falsehood of equations and of statements that describe comparisons between quantities.**Fourth Grade Assessment III**- This is a written assessment where children will be asked to interpret graphs and to interpret and determine the truth or falsehood of equations and statements that describe comparisons between quantities.**Graphing Halves and Doubles**- Children work on a problem about distance and time and compare two rates: half a meter per second and two meters per second.**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.**Multiplicative Candy Boxes I**- This class centers on the possible amounts of candies two children, Juan and Marcia, have. Juan has a box of candy and Marcia has twice as much candy. What are the possible amounts of candies they might have?**Multiplicative Candy Boxes II**- This class is a continuation of the Multiplicative Candy Boxes I lesson. It centers on the possible amounts of candies two children, Juan and Marcia, have. Juan has a box of candy and Marcia has twice as much candy. What are the possible amounts of candies they might have?**Swimming Pools II**- Students will examine the rate of pools filling over several hours.**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.**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.**Three to One**- Children discuss and produce verbal and mathematical statements on the proportion, S:L :: 1:3, that is, on the function f( x ) = 3x and on its inverse f^{-1}( x ) = 1/3 x**Varying Speed**- Children are asked to tell a story about a trip depicted through a graph that has varying slopes/speeds.**Varying Velocity**- Children are asked to tell a story about a trip depicted through a graph that has varying slopes/velocities.