Fraction+Model


 * Fraction Model**



This resource enables students to see the connection between fractions, decimals, and percents. Students are able to use alter the numerator and denominator of a fraction and transform the representation to a decimal, percent, or mixed number. Students also have the potential to save numbers in a chart on the left with the purpose of comparing stored numbers. This applet relies on the use of multiple representations and student centered learning to further student understanding of numbers of various forms.


 * Grade Level:** 7-9
 * PSSM Content Standard:** Algebra
 * Math Content:** Fractions, Decimals, Percents

Evaluation & Annotations

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 * ** Which standard? **
 * **Understand Numbers**
 * Understand Operations
 * Compute Fluently || * || //Rationale//: This fraction model focuses on understanding the different types of numbers. Two sliding bars at the bottom of the applet allow students to alter the numerator and denominator of a fraction. While there a finite amount of choices there are enough options to support an understanding of the various forms of numbers. Once the numerator and denominator are selected, the number will also be displayed as a mixed number, decimal, and percent. The resource will also display the number visually using pies, boxes, sets, or squares. Students can use this applet to learn about various forms of numbers and to study through anticipating the various forms of a number prior to selected a new numerator and denominator. This applet can also be used to compare numbers by storing different numbers in a table to compare them. ||
 * ** What mathematical content is being learned (or intended to be learned)? **
 * **Whole numbers**
 * Place value
 * **Fractions**
 * Addition
 * Subtraction
 * Multiplication
 * Division || * || //Rationale//: This fraction model is designed to demonstrate to students the relationships between fractions, mixed numbers, decimals, and percents. There is no addition, subtraction, multiplication or division involved in the resource. ||
 * ** Is the focus on instrumental or relational understanding? **
 * instrumental understanding (carrying out procedures)
 * **relational understanding (understanding the meaning of mathematical words and symbols; connections among ideas)** || * || //Rationale//: This resource focuses on relational understanding. The purpose is for students to gain a deep understanding of the different forms of numbers. Through the visual representations, students are able to better understand the relationship between a numerator and denominator. Through the table students are able to test conjectures about increasing and decreasing a numerator and denominator and its result on the number. This fraction model also allows students to test how to transition between decimals, fractions, mixed numbers, and percents. It is important to note that this resource has the potential to create student exploration and understanding of numbers, yet there is no direct rules or concepts explained by the applet, leaving students to determine the relationships between the numbers. ||
 * ** What role does technology play? ** || * || //Response//: The technology plays the role of calculator and visual aide. Once students select the numerator and denominator, the resource automatically calculates the mixed number, percent, decimal, and visual representation. This allows student to test conjectures about numbers, while being provided with multiple representations of an array of numbers. ||
 * ** What instructional function(s) does the resource serve? **
 * **practice (i.e., practicing skills or knowledge already learned)**
 * direct instruction/explanation (i.e., explaining or presenting content to students)
 * **learning through exploration (i.e., provides context in which students can see new relationships; come to new understandings)** || * || //Rationale:// This resource allows students to explore the relationship between the numerator and denominator of a fraction by test what happens to the number as one or the other increases through the visual representations. With the direction from a teacher students can also explore the relationships between fractions, mixed numbers, percents, and decimals. This fraction model also has the potential to be used for practice. Students can attempt to find different forms of a given fraction by hand prior to input into the applet//,// and then compare their results with the correct response. ||
 * ** What kinds of representations of the mathematics are used? **
 * **symbolic (i.e., numerals, symbols)**
 * graphical (i.e., standard graphical notation such as Cartesian (X-Y) coordinate system, bar graph, pie chart)
 * **visual/spatial (e.g., circles or squares with lines to show fractions)**
 * **concrete or real-world objects (e.g., images of base-10 blocks, puppies, or jars)**
 * dynamic (mathematical ideas represented through motion or sound) || * || //Rationale//: This resource displays numbers in the symbolic form (as fractions, mixed numbers, decimals, and percents) as well as through visuals representations (length, areas, regions, and sets) of real world objects. ||