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** The Golf Range Applet ****According to most mathematics curriculum standards, students are expected to solve realistic problems when studying most topics. Instead of giving students practice word problems, they should be able to use technology to learn how to solve applied problems. On explorelearning.com, they provide useful gizmos/interactive applets for students to explore mathematics. On the website, applets are organized by grade (3rd-12th) and are also orgranized by state curriculums; students and teachers could access a gizmo according to the standard they are learning. These gizmos are available for anyone with either a 5 minute free trial or a 30-day free access trial. However for a long term use, a license is required for purchase. ** **The Golf Range applet is one of the many gizmos available on the website. One of the main audiences this targets are students in various Pre-calculus classes who are learning about vectors. When students are learning about vectors, they are required by most curriculums to be able to apply their knowledge of vectors to solving realistic problems. This applet allows students to see if they can make a hole in one by adjusting several features that can affect the motion of the golf ball. This fun applet can be appear to be just a fun game for students to compete to see who can get the first hole in one. However, with the given features, students can study the effects of changing the angle, velocity (both of its vector componets), atmospheric air, gravity, and other factors to effect the motion of the golf ball. The buttons and sliders are easy to use and are very self-explanatory. After attempting a swing, students can use the refresh button to try again, but can use the options of showing paths to recall back to previous paths. If students want to know if they get a hole in one, they can use the sound option at the bottom-right button of the screen in which it lets you know, enthusiastically, whether they got a hole in one or not. ** **Students have the option of showing a grid, paths and vector velocitys to observe the magnitude and direction of the motion of the ball. In the gizmo, learning materials are supplied that include an exploration guide for students to explore subjects such as maximum distance, hang time, and projectile motion while using the applet (See Activity section on this page for more details). ** This is what to expect the applet to look like in the gizmo. Click on image to go to the applet on explorelearning.com! Back to top

 According to the Common Core/Common Core-GPS and GPS Standards for Mathematics, the content associated with the Golf Range Applet can be useful for Pre-calculus, Accelerated Math III, and Math IV students. All of these courses require students to understand vectors and are also required to use vectors to solve realistic problems. The Common core standards are more specific about what type of realistic problems they want students to master whereas the GPS is more general with what they expect students to be able to perform. Common Core specifically wants to students to solve problems involving velocity with vectors which is a main component of the applet. Students are able to master the standard of solving realistic problems using vectors by exploring the applet in a fun, but enriching manner. Also students who are learning to create equations and determine expressions/steps for calculation from a context will have practice within the learning materials of the applet. However, the main focus of the learning materials include higher thinking knowledge and connections with context outside of mathematics. With the gizmo and the activities provided through an exploration guide, students will be able to solve problems using technology and make connections to other disciplines outside of mathematics.
 * Standards: **

__**Common Core: **__
 * Mathematical Standards: **
 * N.VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors. **

A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

__**GPS: **__ MM4A10. Students will understand and use vectors. d. Use vectors to solve realistic problems.

1. Make sense of problems and persevere in solving them. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">2. Reason abstractly and quantatively. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">5. Use appropriate tools strategically.
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 140%;">Process Standards: **
 * __<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Common Core: __**

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">MA3P1. Students will solve problems (using appropriate technology). <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">MM4P3. Students will communicate mathematically. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">MM4P4. Students will make connections among mathematical ideas and to other <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">disciplines. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">c. Recognize and apply mathematics in contexts outside of mathematics.
 * __<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">GPS: __**

<span style="font-family: Tahoma,Geneva,sans-serif;">Represent and model with vector quantities. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
 * __<span style="font-family: Tahoma,Geneva,sans-serif;">Other Standards focusing on vectors: __**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Common Core GPS: **

<span style="font-family: Tahoma,Geneva,sans-serif;">Perform operations on vectors. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.4 (+) Add and subtract vectors. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.4a (+) Add vectors end‐to‐end, component‐wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.4b (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.4c (+) Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.5 (+) Multiply a vector by a scalar. <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.5a (+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component‐wise, e.g., as c(vx, vy) = (cvx, cvy). <span style="font-family: Tahoma,Geneva,sans-serif;">MCC9‐12.N.VM.5b (+) Compute the magnitude of a scalar multiple cv using ||cv||, <span style="font-family: Tahoma,Geneva,sans-serif;">|c|v. Compute the direction of cv knowing that when |c|v is 0, the direction of cv is either along v (for c > 0) or against v (for c <0).

<span style="font-family: Tahoma,Geneva,sans-serif;">MA3A10. Students will understand and use vectors. <span style="font-family: Tahoma,Geneva,sans-serif;">a. Represent vectors algebraically and geometrically. <span style="font-family: Tahoma,Geneva,sans-serif;">b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction. <span style="font-family: Tahoma,Geneva,sans-serif;">c. Add and subtract vectors and compute scalar multiples of vectors.
 * __<span style="font-family: Tahoma,Geneva,sans-serif;">GPS: __**

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<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 23px; line-height: 35px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 23px; line-height: 35px;">**Activities with the Golf Range Applet** <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">The gizmo on explorelearning.com includes learning material and teacher preparation guide for the students to use to learn how to use the applet and includes learning activities for the students to work through. For this specific gizmo, it includes an exploration guide with four main activities.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">The first activity is a warm-up activity for students to discuss some basics of golf and the physics of golf: __<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Basic Golfing Knowledge Activity __ <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">1.) You are in a contest with your friends to see who can drive a golf ball the farthest. Should you hit a “line drive” (low to the ground) or a shot with a very high angle? Explain. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">2.) Golf drives travel much farther than Major League home runs. Why might this be? <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">-Before asking these questions, in the teacher preparation guide, it suggests that you engage students by <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">-Also in the guide, it includes directions and questions to help students become familiar with the applet. This activity has them figuring out how to receive a hole in one.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">There are three main activities that ask students to think deeper and outside of mathematics to answer the questions. The activities are labeled A, B, and C. The activity that includes material and content that correlates best to the common core and GPS standards is activity B. It explores the physics of the projectile motion of the golf ball in which it investigates the velocity of the ball. When the ball's velocity is changed by the student, the projectile motion of the ball and where it lands changes. The activity investigates and discusses the velocity of the ball and how velocity is represented by a vector with its two components: horizontal component & vertical component. As you can see in the image below, as the ball travels the velocity vector is shown where the red vector is the horizontal component and the blue vector is the vertical component <span style="font-family: Tahoma,Geneva,sans-serif;">.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">The rest of the activities included in the exploration guide explore maximum distance, hang time, acceleration, and gravity. Teachers have options on what activities they would like to investigate depending on their standards and what knowledge they want to assess their students. With vectors, activity b would be the best activity.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">However if teachers would like to use **Activity A** to investigate maximum distance, in the applet, students will be asked to form a hypothesis of how far the ball could go with varying angles and with extra natural factors being changed (Air atmosphere versus none).



The last activity, **Activity C**, goes deeper into topics outside of mathematics and has more of a physics focus. If teachers really wanted to challenge their students, and educate them a bit further than what is required then they could partake in this investigation activity on hang-time. During this activity, students will be able to use some of the advanced features that include varying the height of the golfer from the ground and gravitational acceleration.



<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Teachers may use the guides and follow it thoroughly, or they can tweak the material. Some teachers may want to focus more on the mathematics in their investigations and do more with the first part of activity b about the vector components of the velocity of the golf ball. <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">Also to extend their knowledge, they may want to challenge students and ask about some other factors that can affect the projectile motion of the golf ball that we can observe using this applet.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">All of the exploration guide and learning materials for these activities can be found at the tab at the top left corner of the [|gizmo] that says [|learning materials].

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<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 23px; text-align: left;"> **<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 23px;">Critique of the Golf Range Applet: ** //**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">How well does it work? **// <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; text-align: left;"> The Golf range applet on explorelearning.com works extremely well and at a quick pace. However, before using the applet or any other applet on the website, the computer must be up to date on their programs. Just in case you can't find out what software on your computer needs to be updated, explorelearning.com had a [|feature] that will instruct you if your computer is able to access the gizmo. Also at the bottom of the main screen, it shows you that you should get Adobe Flash Player and Adobe Shockwave Player before using the gizmos.

//**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Are the written materials well organized and useful? **//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">For this activity, the learning materials are well organized and written according to the topic being explored. There are plenty of options through the three activities for students I think they could have incorporated more material for vectors into some of the activities, but it is always useful to explore other topics outside of the main curriculum. Some of the sections could have left out some details that students could conjecture or investigate themselves. For example, in the activity B, it informs students exactly how velocity is an example of a vector quantity without giving a chance for them to explore that fact using the options and features on the applet.

//**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">What are the purposes and goals for using this technology? Does the technology reach this goal? **//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">The main purpose of using this applet is to give students an example of applying their mathematical knowledge on a subject such as vectors being taught in the classroom to a real life scenario such as motion of a golf ball through the air. Instead of just letting students practice word problems, this gives them an interactive to solve problems. The varying choices on the features of the applet gives them the freedom to change features based on what they want to study about the golf ball motion. Therefore I think this technology reaches its goal and the goals of the curriculum standards of using technology to solve real world problems involving vectors.

//**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Is the technology relatively easy to learn how to use? **//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">This technology is very easy for any student to use. Before reading the learning materials, I was playing with all the different features and sliders on the applet without looking at a set of directions. Also the applet labels everything precisely which helps the ease of using the gizmo. Students will become very addicted to wanting to adjust the settings until they get their first hole in one!

//**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Does this technology enhance or extend the teaching and learning process for the **// //**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">intended mathematics concepts? How and why? **//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">I think the purpose of this applet to help students solve real world related problems using golfing as a their real world situation for the various problems that could be asked. This activity provides an extension to learning vectors in a more applied approach whereas they are probably use to working with vector algebra and computation. Teaching students the applications of vectors will enhance their conceptual knowledge of how vectors are represented realistically. Also this golf range applet is a great introductory activity to introducing students to the many applications of vectors and it prepares students for subjects in physics where this section of mathematics has several connections to this mathematical topic. However, I do not think it could help in enhancing a lot of material discussed within the unit on vectors unless the teacher adds extensions to the learning materials to construct it that way. //**<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 130%;">Would you recommend this product for purchase to a school? Why or why not? **//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">If I was only going to use this particular applet and none of the others, I would have only ordered to the 30 day free trial and used a username that all of my students can have access to for that time period. However if I was teaching a class where a lot of the applets and learning materials were effective for a majority of the standards, than I think it would be worth spending the money, because it would give students more of an opportunity to learn the mathematics using efficient and engaging technology applets. After exploring with the basic golf range applet, a majority of these applets would be easy to use and effective for enhancing critical thinking and mathematical learning. Back to top

 **References** The Common Core State Standards Initiative (2011). // Common core state standards for mathematics //. Retrieved from []

English Language Schools (2009). //English joke: Hole in one.// Retrieved from []

Explore Learning (n.d.). //Golf range//. Retrieved from [] Georgia Department of Education (2006). // Mathematics Georgia performance standards //. Retrieved from []

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