Free+Ride


 * Free Ride **



The applet revolves around understanding how to add and subtract fractions in a real world situation. Students are pedaling a bicycle with the task of stopping on a number of different flags, each positioned on the number line. To land exactly on a flag the bike must move a specified distance. Students determine the distance by manipulating the bicycle gears. The ratio of the front gear to the back gear is the fraction with which the bicycle will move. The settings can be changed so that the flags are on fractions with different denominators or the same denominator. In both cases students need to be able to recognize the distance the bicycle needs to travel (by subtracting fractions), and determine the how to select the correct gear (often requiring students to recognize equivalent fractions).


 * Grade Level:** 7-9


 * PSSM Content Standard:** Algebra


 * Math Content:** Fractions

Evaluation & Annotations

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 * ** Which standard? **
 * **Understand Numbers**
 * **Understand Operations**
 * **Compute Fluently** || * || //Rationale//: This resource enables students to see fractions place on the number line, to practice adding and subtracting fractions, and to understand the reasoning behind adding and subtraction through a real world application. ||
 * ** What mathematical content is being learned (or intended to be learned)? **


 * **Whole numbers**
 * Place value
 * **Fractions**
 * **Addition**
 * **Subtraction**
 * Multiplication
 * Division || * || //Rationale//: Fractions are the main form of number focused on in this applet, yet there are periodically whole numbers in which the bicycle needs to move. Addition and subtraction are the two operations with which the resource is focus. Students need to subtract the number where the flag lies by the current position of the bicycle to determine how far the bicycle will move. Addition arises when the bicycle move and when students wish to check their decision. ||
 * ** 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 is a combination of instrumental and relational understanding. Students are expected to carry out the procedures of adding and subtracting fractions to determine the distance the bicycle needs to travel. There is also a strong relational understanding being built through this applet. At the same time students are able to visually understand the importance of equivalent fractions are they balance the gears, which reduce to the distance that needs to be traveled. Furthermore, the position of the flags on the number line demonstrates to students the relationship between fractions with different denominators. ||
 * ** What role does technology play? ** || * || //Response//: Technology is at the center of this resource. The technology allows for the number line to progress backwards and forwards as the bicycle moves. Students are able to receive immediate feedback as to whether their gears were correct but the motion of the bicycle. The technology also allows for several different "routes" with varying difficulty. ||
 * ** 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 applet can be used for practice as students select a bicycle route and attempt to add and subtract (when pedaling backwards) fractions to land on the designated flags. This would benefit students who already have an understanding of adding and subtracting fractions and of equivalent fractions. This resource can also be used for exploring. The "free ride" feature allows for students to select gears and track where the bicycle lands without the sounds and flogs of the other versions. This allows students to understand that a gear ratio of 20/30 will move the bicycle 2/3. Students can also explore adding and subtracting fractions and verify their answers with "free ride". ||
 * ** 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//: Real world objects are the focus of this resource. The number line and bicycle allow for students to grasp the importance of adding, subtracting, and recognizing equivalent fractions. The real world application will surely engage students. ||