Technology

Build a playground 7.G.B.6 and MP4

kimberlyyounger Geometry Curriculum Aligned with CCSS-Math, ML Modeling, Technology Teaching Issues , , ,

By: Kimberly Younger, Rachel Van Kopp, Lizzie Englehart and Naomi Johnson

This lesson is focused on a 7th grade standard CCSS.Math.Content.7.G.B.6 but could be used for 6th through 8th grade depending on the application. This lesson focuses on the use of formulas to find area and problem solving of a real-world problem with the use of technology.

The prompt is “The school district is building a new playground for the new elementary school down the road. They have hired Playgrounds R’ Us to build it, but the supervisor wants to know what students would want on a playground. Create a playground with the following requirements.”

The students are building on their knowledge of area and perimeter formulas and applying it to a problem. The students are given a square footage for the playground, they must use three or more different shapes to represent their equipment, and the total square footage of the equipment must cover 30% of the playground’s area or more.

The students are given a packet which includes direction, a rough draft grid paper, final draft grid paper (submitted for approval), a screen shot of their Geogebra playground and a write up about their playground.

Below is an example of the packet students received. (link to the packet)

Below is a student’s sample playground

Rough Draft Blueprint                                Final Draft Blueprint                               Geogebra Blueprint

Table for Blueprint

Extension for “Build a Playground”:

As an extension to this lesson, students will later be able to work with 3 dimensional figures and nets to build the playground they have constructed in our lesson. This lesson emphasized finding and working with area of various geometrical figures and special reasoning. Using the knowledge, they have gained through our lesson, the students will be able to create the net that would best fit the equipment shape that they have presented to us on their “blue prints”.

In order to create the appropriate net, students will need to understand that the 3-dimensional shapes base will be the shape they have placed on their map in the lesson “Build a Playground”. This extension will cover CCSS.math.content.7.g.b.6 which states “Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.” This extension will help students make connections to the relationships between 2-dimensional figures and 3-dimensional figures, and connect the concepts of surface area and volume to real-world scenarios.

Rocket Math: 8.F.A.3, 8.F.B.5, MP4

natashasmith2 ML Functions, ML Modeling , , ,

 

 

Rocket Math

By: Natasha Smith, Mariana Rosas, Paloma Vergara, & Melisa Sanchez-Leyva

 

 

 

 

This modeling lesson is for an 8th-grade classroom and is focused on the standards CCSS.MATH.CONTENT.8.F.A.3 and CCSS.MATH.CONTENT.8.F.B.5. This lesson introduces students to the concept of nonlinear functions. In the lesson, students will be able to explore the concept of a nonlinear function and expand their knowledge of what a function can look like.

This lesson follows a similar format to Dan Meyers’ 3 Acts. Students will start by watching a video of a model rocket launch. Individually, they will quickly draw a graph of what they think the relationship between the height of the rocket and time is. Next, they will work in groups to plot the points estimating the relationship of the height of the rocket at each second. Lastly, the teacher will take them outside and launch a model rocket to prove or disprove students’ theories. The model rocket will have a Pocketlab attached to it which will provide an exact graph of the height of the rocket at each time point. Students will compare their graphs to the Pocketlab graph. We decided to launch the rocket again instead of providing students with a graph from the original launch in the final act as it adds an element of excitement to the activity and the students will enjoy going outside to watch the rocket launch.

This lesson incorporates multiple types of technology. For the video used in the lesson, teachers would achieve best results by filming their own rocket launch as they will want to use the exact same type of model rocket in both the video and the in-class launch. The video representation should be similar to this video. Students will also be using the website Desmos to graph points. Lastly, the teacher will be using a Pocketlab. The Pocketlab is a wireless sensor that can be attached to different objects and will record different types of data and output graphs. For this lesson, the Pocketlab can be attached to the model rocket and will record the height (altitude) of the rocket as time passes.

Lesson Plan and Worksheet.

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Where Do We Meet? REI

sanchezesa Common Core State Standards Mathematics, HS Algebra, HS Functions, Improve Mathematical Thinking, ML Modeling, Technology Teaching Issues , , , , , ,

screen-shot-2016-12-02-at-12-47-21-pm

WHERE DO WE MEET?

Where do we meet is an interactive activity that uses technology and mathematical concepts to create and solve real life scenarios. One of the Vernier products to compliment this lesson is the Motion Detector. This device allows for data to be collected through a calculator (or a computer software) where students can then analyze their findings. For this activity students will be able to see a real life scenario of the usage of the mathematical concept of Solving Systems of Liner Equations using a motion detector, calculator and themselves. In this activity, students will be able to part of the creation of data that will be used to create equations. Students will then take part in solving the system of equations using technology and on writing (mathematically). Students will be able to use this activity that ties to the following Common Core State Standards:

INQB.2 Collect, analyze and display data using calculators, computers, or other technical devices when available

APPD.2 Use computers, probes, and software when available to collect, display, and analyze data.

M3.2.H Formulate a question that can be answered by analyzing data, identify relevant data sources, create an appropriate data display, select appropriate statistical techniques to answer the question, report results, and draw and defend conclusions.

H.A.REI.1– Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

H.A.REI.2– Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

H.A.REI.5– Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

H.A.REI.6– Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

vernieractivity-wheredowemeet

Using Geogebra to Show Triangle Congruences HSG.CO.B.8

massed Common Core State Standards Mathematics, Technology Teaching Issues ,

This lesson is for teachers to use technology to invoke a thoughtful and engaging classroom experience with their students. It is designed to show concretely through Geogebra all of the triangle congruences and all of the combinations that don’t work. This is a fantastic way for a teacher to show this to their students because it is difficult on a white board or with pen and paper to prove to the students that these congruences work. The most insightful part of this lesson is where the combinations that don’t work are shown to the students and the students can see on the screen why.

Geogebra is an excellent source that teachers can use which can incorporate visual understanding of many geometry lessons. It is a completely free computer application which can be downloaded here: https://www.geogebra.org/download. This application specifically allows a person to manipulate different points, lines, angles, and other things in ways that a pencil and paper cannot. For this lesson specifically, it works fantastically because of the free motion that the program gives you.

Common Core State Standard:

HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Lesson plan: technology-lesson-plan_triangle-congruencies

Attached worksheet: http://cdn.kutasoftware.com/Worksheets/Geo/4-SSS%20SAS%20ASA%20and%20AAS%20Congruence.pdf

Velocity Test: Interpreting Velocity Graphs HSF.IF.C.7

massed Common Core State Standards Mathematics, HS Functions, HS Modeling, Technology Teaching Issues , , ,

Figure from experiment 12 from Real-World Math with Vernier

Students are notoriously difficult for teachers to engage in a lesson. With Vernier, teachers are able to use lessons on quick notice that involve technology and student attention. With technology, students become excited about something different in the classroom and are therefore more attentive. With Vernier, there are numerous different technologies with hundreds of ideas for lessons (not exclusive to math if you are a science teacher-or if you are a math teacher wanting to introduce some science into your lesson!). The product used in this lesson is the Motion Detector, which can be acquired through https://www.vernier.com/products/sensors/motion-detectors/md-btd/. This sensor is designed to collect data from the distance between the sensor and what it is pointing at. There are Image result for speednumerous more lessons involving it, and is especially useful for any movement-based projects/lessons that a teacher plans to do.

 

This specific lesson deals with velocity. Students are assigned to record their distance and time with the Motion Detector. After they have that, they are to formulate a graph based on that data of their motion and compare/contrast that graph to the graph that the motion detector collected from their motion.

CCSS.MATH.CONTENT.HSF.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

CCSS.MATH.CONTENT.HSF.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Lesson: velocity-test-interpreting-velocity-graphs

Resources from vernier.com

Modeling a Digital and Global Age Learning Environment

yinglingk Geometry Teaching Issues, ML Modeling, Technology Teaching Issues , , ,

Modeling a Digital and Global Age Learning Environment

 

Over the past decade our world has become increasingly more dependent on technology. Some school districts have made an effort to bring more technology into every classroom, but it is time for teachers to include technological tools in each of their lessons to assist each of their students’ needs. There are tools that can be used in the classroom such as clickers, smartboards, and document cameras. There are also so many web based resources that teachers can use in the classroom and that students can use at home, given they have internet access. Teachers need to take the time to be trained in technological tools that can improve their students’ learning environment and many will quickly find that these tools assist many of their teaching strategies.

Class Website

             A class website is a great communication tool for teachers, their students, and the students’ parents. My website includes a unit calendar that includes daily homework and quiz/test dates. Parents and students can check the website each evening to make sure all homework is being completed and to be made aware of future assignments. My website also includes links to online textbooks, helpful math websites and websites that provide fun games for extending each of my students’ mathematical skills. Many schools have web address set up for each teacher or more personalized websites can be created on KompoZer which is available for free download.

Math is Fun

Math is Fun is a resource website that makes learning mathematics fun and easy. The site covers k-12 curriculum and provides definitions and procedures for solving all types of math problems. This is a great review website as well as a resource for double checking equations and methods for solving problems you are not 100% comfortable with. This online website can help students complete their homework if they forget any needed equations and it can also help parents help their children. It is no secret that many parents have difficulty helping with their child’s math homework past the elementary years; this website will help parents quickly review some concepts and procedures and further their ability to help with homework.

Khan Academy

Khan Academy is another math resource website. This website is excellent for students who learn by example. There are 2-3 examples for each topic that begin with video instruction showing step by step procedures to solve a problem. After video examples there are practice problems that have to be correct before moving forward but also hints to help. My students love Khan Academy and many times when I know I will have a substitute I have them show the Khan Academy video as opposed to teach a lesson to my students. On my website I update the Khan Academy link to go directly to our current topic page.  This resource along with the textbook website, which also has instructional videos, is usually enough instruction for my advanced students to keep on top of work when they miss class. This allows me to not have to take time away from other students to teach students who were absent. For some of my struggling learners it is expected of them to review lessons on Khan Academy each evening because hearing the information twice greatly improves their success.

GeoGebra

When my students enter the geometry unit we spend a lot of time on laptops or in the computer lab. I have found that geometry is one of the toughest units for young middle school students to comprehend because it involves so much more than they are used to dealing with at one time. GeoGebra is a great resource for all students, but especially those who are just beginning their journey through geometry. My students use GeoGebra, which is an online resource that can help students create shapes and find their measurements. Students have difficulty with relationships between shapes and remembering differences between area and perimeter. GeoGebra helps students, especially visual learners, actually see what area means vs perimeter. I have GeoGebra linked on my class website so students can have quick access to it at home.

With an ever changing world technology allows teachers keep their lessons and students up to date with the latest mathematical tools. Providing students with the knowledge of how many resources are online and available for help with homework will make students more interested in completing their homework because going online and searching through websites is fun for young adolescents. It is important for teachers to be able to make the transition from paper and pencil, to online tools, and then back to paper and pencil. Resources such as GeoGebra are wonderful for helping students gain conceptual understanding of abstract concepts, but the procedures that are needed to solve problems without the help of technology cannot be forgotten. Students will be taught what a good digital citizen is and the importance of this will be reminded to students whenever we go online as a class. I will model each resource for my students before I expect, or encourage them to use it without my supervision. Trusting my students to make good choices usually makes them want to keep that trust and I rarely come across problems with online resources.

 

Resources

KompoZer

http://kompozer.net/

Math is Fun

https://www.mathsisfun.com/

Khan Academy https://www.khanacademy.org/

GeoGebra

https://www.geogebra.org/

Digital Citizenship

http://www.digitalcitizenship.net/Nine_Elements.html

Technological advances for the class by going online

erdmanri HS Number and Quantity, Technology Teaching Issues

The use of technology has become a growing requirement in mathematics curriculum. As technology became more used in people’s lives it was decided that technology should see more use in schools. One very useful technology that can be adapted and integrated into any mathematics class is Edmodo. Edmodo is a social media style program where teachers can set up online classes where students can join. In this online class students can post questions and receive answers to those questions by the teacher and fellow students alike. This allows students to receive more immediate feedback to questions while they are at home or away from school, instead of having to wait till the following day. Students are able to reflect on what they know by helping their fellow students, and by what they don’t know from the questions they can ask. The teacher can also have a more close interaction with each individual student who has questions, while also allowing the teacher to help expand the students learning.

Edmodo can be accessed at www.edmodo.com where the teacher can sign up for free. The teacher can create a group that their students can join by using the group code. By being connected like this it can be especially useful for CCSS N-RN.3 allowing students to explain to each other and to the teacher why the sums or products of rational or irrational numbers are rational or irrational. This technology allows the students communication to be organized and recorded so that students can review what they talked about and can verify their understanding.

Teaching a Specific CCSS for High School Students Using GeoGebra

carmonma HS Geometry, Technology Teaching Issues

Different types of technology are available these days. Students are more engaged and inclined to do work when it involves technology. Since students are surrounded by technology every day a lesson on technology would be more beneficial than a lecture. A type of technology that students will find engaging and interesting is GeoGebra. This is a free and interactive website for students to work with in geometry, for example. The link to download GeoGebra is the following:

http://www.geogebra.org/cms/en/

The following link contains tutorials on how to get started:

http://wiki.geogebra.org/en/Tutorial:Main_Page

The use of GeoGebra would be great for a lesson for high school students about circles in Geometry. The standard CCSS.Math.Content.HSG-C.A.3 states that students should be able to Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Using GeoGebra for a lesson on this could bring many benefits. To start off the lesson involves going to the computer lab, which is already exciting to students since class will be held outside the usual classroom setting. Students will feel motivated to do the work and experiment on their own.

On GeoGebra students can create, erase, and move around objects in a 2-dimensional plane to visually “prove” to themselves a property. The students’ learning will be enhanced because they will be able to move objects around by dragging them. Sometimes it is better to actually see inscribed and circumscribed circles in a triangle or a quadrilateral inscribed in a circle instead of just learning the steps to constructing them. The teacher can have students create a variety of diagrams using the “Tools” in GeoGebra. The lesson will be easier to teach since the teacher will have already caught their attention and students will feel confident and curious to learn more.

The teacher then, will be able to explain the properties of angles and how to prove them. She can refer to the work done on GeoGebra and ask students to explain their reasoning based on their experiments. Students will also be able to self-assess themselves by referring to their work done on this interactive site. Since GeoGebra is a free site, those students who need more time or want to keep “playing” with it, will be able to do so by downloading the software onto their computer. Lastly, GeoGebra is easy to use; each command has its own name such as “perpendicular bisector” or “parallel line”; thus, students know what the command will do. Therefore, teaching with technology has become easy, effective, and fun for students and teachers.