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  • Describing Magnitudes
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Describing Magnitudes

Third Grade Lessons
  1. Comparing Discrete Quantities - Students compare amounts of tokens and unknown amounts of discrete quantities. In both cases they are guided to adopt line segments to represent discrete amounts and the differences between them. They are also asked to discuss composition of measures: "the difference plus the smaller amount is equal to the larger amount" and, "the larger amount minus the difference is equal to the smaller amount".
  2. Comparing Heights I - Students compare the heights of two children, measure, compare, and represent one's own height in relation to a peer's height, and focus on the differences between heights.
  3. Comparisons - Comparisons and comparison operators: =, ≠, <, >.
  4. Comparisons and Attributes - Work with comparisons and comparison operators (=, ≠, <, >).
  5. Heights as Functions - In this class children will work on the functional representation of two unknown heights and on the composition of the shorter height plus the difference between the heights as equal to the second height.
  6. 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.
Fourth Grade Lessons
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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?
  10. 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
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