Cabri 3D Construction

I will share with you unfolding of a hexagonal pyramid cut by a plane and its construction on Cabri 3D.

The file of the Cabri:

https://drive.google.com/open?id=1FeQXjqMPF9i1a2zzf_inaTYXhaAvV0PO

Construction Video:

 https://drive.google.com/open?id=1Rz5t7wfilE4olcNkDfhdc92mBfAcZEPQ

GeoGebra

Hello,
We created a game with GeoGebra about the exponential numbers. The game is designed for 7 grade students. Generally, -1, 0, 1 confuse students in exponential numbers and it can cause some misuderstandings. The game is designed to diagnose this misconceptions and to eliminate them. Also, it provides understanding of the importance of paranthesis in exponential numbers. The content includes questions that is presented from simple to complex. After teaching the concept of exponential numbers, you can check your students' understanding with this game.
In the game,
Harry Potter and his friends lost their way. To go Hogwarts, they should use the road in the Exponential Numbers Forest. However, the forest is very dangerous and there are witches who want to catch them. To pass through the forest, they should use the road that witches set traps for them. These traps include magical questions about exponential numbers. If you answer questions correctly, you can help them to go further.

If you are curious about the game you can visit my GeoGebra book that contains 2 chapter.
First chapter presents the game and its relation to mathematics and the second is about the costruction of the game step by step.

The link of the GeoGebra Book:

https://ggbm.at/Edxn57gb

7th Grade Ratio and Proportion: An Example of Technology Integrated Classes

     

Components of the lessons:

First week: SketchUp as homework

Second week: Kahoot questions from students, Poster examining (Group work), Articulate Project, Research(Piazza)

Third week:  Individual work of research in class, Edpuzzle(competition), Kahoot.

 One week before the first class, it will be said students to construct buildings on Sketch-Up that are suitable with conditions that is given them. It will be given different conditions for each student. For example, it will be given a paper a student which is written these conditions:

•  Construct a 3D shape; 1/12 of it is red, 3/6 of it is blue, 1/4 of it includes patterns or pictures, 1/6 of it constructed from a different shape. ( Each piece should have one characteristic like only being red)

 With these conditions, the student will construct a 3D shape on Sketch-Up. After all students construct shapes with conditions that are given, they will deliver it to teacher via an e mail which is attached Google Drive link of their 3D shapes. In first class, it will be given them blank papers to write 2 questions and their answers about their shapes. For instance, questions can be like:

•      I have three red pieces in my shape. We know that 1/12 of my shape is red and 3/6 of my shape is blue. Then, how many blue pieces are there in my shape?
•      2/12 of my shape’s pieces are cubes and the other pieces are rectangular prisms. In total, it has 36 pieces, then how many rectangular prisms are there in my shape?

 It will be collected all these papers and it will be wanted their shapes’ pictures. Then, it will be prepared a Kahoot that include these questions with their pictures and it will be applied this Kahoot next week in class.

 After, they wrote questions for Kahoot, they will discuss about a Poster that is written some statistics on it.

Firstly, it will be made students groups of four. Then, it will be wanted them to discuss these questions:

1) What can be the population of the children in Turkey according to information on Poster? (Population of Turkey is 78 million)

2) What is the ratio of the number of child labor to the population of whole children?

3) How many child labors go to school and how many of them don’t go to school?

Note: They can use calculators.

 While they are discussing, it will be observed all groups, if they need, it can be given some help. After all groups discuss it 30 minutes, they will choose a group leader and each leader will tell to the class how they found answers and what their strategies were.

 In the second lesson, it will be taken all students to the Computer Lab and they will use Articulate application that is prepared for this class. In articulate, they will learn about proportions, proportional relationship in real world. They will see their tables and graphics and also proportion constant. All these issues are not explained literally, but when they use the application, they will understand internally all of them. While they are using application, it will be observed students and if there is a problem it can be given help them. After all students finish application, they will talk about new concepts like proportion, proportional relationships, and constant of variation. Also, they will examine tables and graphics in Articulate Project and students will say their ideas about tables’ and graphics’ usage in proportions.

 It will be wanted them to make a research about proportional relationships in real world and they will write their findings on Piazza. It will be important to write sources of their information and making cites. Also, they can discuss and make comments about the findings of each other.

Next week, in first class, they will start to lesson with examples in their research. It will be wanted them making their examples’ tables and graphs. Also, they will find constant of variation in their examples. They will work individually, and the teacher will be around to observe and help them while they are making this work. The following is an example of this work.

Rose can download two songs from the Internet each minute. This is shown in the table and in the graph.

Find the constant of variation.

Notice that as the number of songs increases by 2, the time in minutes increases by 1.

Constant of variation =songs per minute.

                                                      

 After the teacher makes sure all students had done it, the teacher will want each student to say what he or she has done in his or her work with 2 or three sentences.

 In the second class, it will made students groups of four and it will be showed this video that is prepared on edpuzzle. When it is came to the question marks, groups will show their answers that are written to a paper and the fastest and most correct group will win the competition. If they want to watch it again they will login the edpuzzle and they will enter this code: gabcunm

The link is: https://edpuzzle.com/join/gabcunm

Youtube address of the original video:

https://www.youtube.com/watch?v=WJipgy0vUWE&t=88s

Finally, at the end of the class, it will be applied Kahoot that is prepared with the questions that students wrote about their 3D shapes previous week.

PANTOGRAPH ON SKETCHPAD AND MATHEMATICS

i. Objectives:

M.6.1.7.2. Bir bütünün iki parçaya ayrıldığı durumlarda iki parçanın birbirine veya her bir parçanın bütüne oranını belirler, problem durumlarında oranlardan biri verildiğinde diğerini bulur.

M.6.1.7.3. Aynı veya farklı birimlerdeki iki çokluğun birbirine oranını belirler.

M.8.3.3.2. Benzer çokgenlerin benzerlik oranını belirler, bir çokgene eş ve benzer çokgenler oluşturur.

ii. Pedagogical Explanation:

My tool is a pantograph. Its working principle depends on the ratios. For example,

 You draw a segment and you put a point on it that is B. When you move the point B, point A will move too.  (In Sketchpad, when you put a point to a segment; even you make bigger the segment, the ratio of AB to BC does not change.) However, there is difference in their movement. If you move B, A will move more. When it is investigated, it is seen that the ratio of CB to CA is the same with the ratio of drawings with B to A (the ratio of one side of the little house to the same side of the big house). The pantograph works like this, too. The construction I made above is not possible in real life because when you fixed C and when you put a pencil to B, you cannot move freely as in this app because your movement capability is limited. To benefit from this ratio property, people improved the pantograph in real life.

I constructed a pantograph on Sketchpad that is similar to real life version.

 This tool can be helpful to teach the objectives of M.6.1.7.2 and M.6.1.7.3 because it works according to ratios. Students can find the ratios of FA to FB, AC to BE and FC to FE with the Measure-length and Number-calculations parts of the Sketchpad. Also, the teacher can relate the topic with pantograph by saying ‘There is interesting ratios in pantograph, can this be related with the working principle of the pantographs?’. Thus, it will be seen that the topic of ratio has relations with the real world and the topic can help making a tool that makes drawings bigger or smaller. On the other hand, this tool is very helpful for teaching the objective of M.8.3.3.2 because this tool works according to similarity principle in mathematics. While we are constructing this tool, we draw AC as parallel to BE and DC parallel to BF. At the end we see that AFC and BFE are similar triangles. Also, we see that EDC and EBF are similar triangles, too. This property of pantograph will provide students’ better understanding of similarity and similarity ratio.

iii. User Manual:

 Firstly, you can watch the video that I put on to the construction steps below and you can construct a tool that is same with my tool. You can download this construction to all computers in PC lab. For 6^th grades, all students can open on Sketchpad this construction. The teacher can start to lesson by introducing what a pantograph is. For example it can be showed a video about how it works. This can be an example of this video: https://www.youtube.com/watch?v=yZEg7cnDejM

 Then, the teacher can say ‘We will try to discover more this tool.’ Students can try in their PC whether the tool makes the thing bigger or smaller and then the teacher can say ‘How this tool can work? Let’s make some measurements.’ Students can measure the lengths of FA, FB, AC, BE, FC, FE from the measure-length part of the Sketchpad. The teacher can ask them to find the division of FA to FB, AC to BE and FC to FE with Number-calculations parts of the Sketchpad. During this the teacher can say ‘The division of one segment to other segment or the division of one part of a segment to whole segment named as ratio. We can find the ratio of various lengths.’ Also, the teacher can ask ‘Did you aware of these three ratios that we measured are equal to each other?’ and can say ‘These ratios form the base of the working principle of a pantograph.’ If it is possible students can try to improve different tools with ratios.

 On the other hand, for 8^th grades, the teacher can start to lesson with the same thing like by introducing the pantograph and watching a video. Then, they can try this tool on their computers whether it works or not. In that case, students already know what is ratio, so the teacher can say ‘Can you find the ratios of FA to FB, AC to BE and FC to FE?’ They will calculate these from Sketchpad. Also, the teacher will say in this tool it is drawn AC as parallel to BE and DC parallel to BF. Because they learnt what similarity is in the previous objective the teacher will ask ‘Which triangles can be similar here?’ After they find similar triangles, the teacher will ask ‘Do you see any relationship between the ratios of the sides of the triangles?’ We are expecting that they will say all are equal. At the end, it will be concluded as we name this common ratio as similarity ratio. Students can try to change these ratios by moving the points of B and C. They can make estimations about the magnitude of drawing. It can be asked ‘How the magnitude of drawings changes when we changed the ratio?’ The lesson can be concluded as pantographs work with this principle and in the real life it was beneficial to use pantographs in the past.

iv. Construction Steps:

 Here there is the video of construction steps of the pantograph on Sketchpad:

https://drive.google.com/file/d/1UQS5mFYps4e8aXupeJsdGNhJwSpTyjMi/view

Also, here is the file of Sketchpad : 

https://drive.google.com/open?id=1yZ246RmJO1cgU6aVEUItwZNF30wcokP2


If you want, you can draw segments of AD, BC, CE, too. And then you can hide the rays that you constructed at the beginning by right clicking on them and choosing ‘hide the ray’. Also, you can add a picture by dragging the picture to the Sketchpad screen. Then, you can put a J close to point C on CD and from the edit menu and merge option, merge the picture and J.

Second way to construct a pantograph:

Link: https://drive.google.com/open?id=1G4_8GkiHwZZC50cFbea-RrfmorO1DcVV

The steps can be listed as,

- construct segment AB.

- Construct ray CD

- Construct circles with centers C and D and radius AB.

- Construct ray CE, where E is one of the intersection points of these circles.

- Construct segment CE and segment DE.

- Construct segment EF, where F is any point past E on ray CE.

- Construct a line through point F parallel to segment DE and also construct point G where the new line and ray CD intersect.

- Construct a line through point D parallel to segment EF.

- Construct segment DH, where point H is the intersection of the lines constructed in steps 7 and 8.

- Hide the circles, lines, and rays so that your pantograph consists only of segments.

-Trace points D and G and drag point D to write something.

TELLAGAMI

 Today, I will mention an application that is beneficial in classrooms to make the lessons more enjoying and to give the chance students to use their creativity while they are developing projects with this application.

 Tellagami is a mobile application where you can speak to the stage and character by customizing and recording the characters you have created. Also, we can save it in video format. Tellagami is only available on iOS and Android operating systems. Tellagami has opened the application version for education for $ 4.99 with the apple store. When you download the training version, you can have free features that you can buy in Tellagami. Especially at pre-primary and primary education level, giving the course contents with animated videos will increase interest. You can make fun videos with EDU version for a small fee.

 With Tellagami, presentations, projects, term papers, stories, poetry, audio books, etc. events can be created. In addition, students who are afraid to speak in front of the community will be able to express themselves more easily thanks to the digital stories they create. Also, Tellagami can be used as a first step, making it easier for students to have prepared presentations in front of the class.

How can we use the Tellagami?

·        Select Character: Select your character and visualize the characteristics such as skin color, hair color, hair length, eye color, clothes just by touching the screen.

·        Choose Emotion: You choose the mood of our character who will tell you about the topic.

·        Position Character: Position the character on the scene. Rotate, zoom out, zoom in.

·        Set Background: Use the camera for scene funding, put an image, or make a drawing.

·        Make a voice recording or write a dialog: In this section you need to make a text or voice recording in which the character will sound.

·        Preview: The final stage before publishing. Watch all the work you've done up to this time.

·        Share Gami: The name of the character we made is called Gami in the Tellagami software. You are publishing and sharing your work at this stage.

 In the following links you will see some applications of Tellagami.

https://www.youtube.com/watch?v=sbG4ExNDnjE

https://www.youtube.com/watch?v=zccQ-7r3qUI

https://www.youtube.com/watch?v=8ontoZIkbKA

https://www.youtube.com/watch?v=EJrcvslIWbE

https://www.youtube.com/watch?v=vRuFSJhT9fQ&list=PLC7efp0MnLPiitC5_GIld7vg0pKOK44WR

https://www.youtube.com/watch?v=hckH-YqiZ90&index=2&list=PLqiGiE4M7XXPb6ze7cRpX7OIFV2GoxaNH

 In addition, there is a video prepared by Tellagami to teach what Tellagami is:

https://www.youtube.com/watch?v=CL5sCbD3BMg

 Also, there are some alternative programs like Goanimate, Powtoon, Morfo and Chatterpix that we can use for similar aims.

TECHNOLOGY AND TEACHING

 In that blog post, I will continue to introduce some applications or softwares that can be used in classrooms creatively.

Class dojo, is a communication application for the class. It brings together teachers, parents and students who use it to share photos, videos and messages throughout the school day.

About it: https://www.classdojo.com/tr-tr/about/

By giving badges to your students you can encourage and improve their behavior. In ClassDojo, your students become cute monsters. Therefore, you can draw the attention of the students with the rosettes and all the attentions of the students instantly with the avatars of the students. ClassDojo is a free application and has a Turkish language option. You can get the ClassDojo Teacher app for your Smartphone or a Smartboard or a computer with an internet connection.

Edpuzzle, is an application where you can edit videos using any video available on the internet, add your own voice, add voice notes, add questions for your students and check the answers given by the students, and check if you are watching the video you have created. You can upload videos that are in your computer or mobile device as well as you can create videos by adding videos from sources such as Youtube and Khan Academy.

How to use it: https://www.youtube.com/watch?v=dGK5qAe4Dck

Socrative, is a free web 2.0 tool that you can take an online test as a group, within the classroom or at your own discretion, with instant feedback on questions you prepare, you can do a questionnaire, do an online test, and share your results instantly.

More about socrative: https://www.youtube.com/watch?v=WlnI1f-Q1JM

If you wish, you can take the output of the tests you have prepared via Socrative and offer your students the opportunity to solve them in class. Tests can be organized as true-false, multiple-choice, and short-answer. Also, the application can be used in two different ways: Socratic Student and Socrative Teacher. It can be used on both Android and IOS platforms as well as on any Internet browser.

Showbie;  with Showbie, you can create your virtual classroom and quiz your students who are included in your classroom, give homework, check the homework or provide feedback. Students can respond to your assignments by drawing with a pen or writing from the keyboard. You can lock the event when you have finished your homework or quiz time, preventing you from making changes to the past event. You can send content to any class, you can also send a student within the class.

An example for its usage: https://www.youtube.com/watch?v=iHVnsnekHVI

Quizlet; if you want your students to practice the concepts they learn, you can use Ouizlet. You can prepare flash cards for your opponent. Your students will also be able to use these flash cards on their tablet computers and refresh their knowledge. When they select the space race mode, the activity becomes a competition, and from the scores on the side, the student can see their own ranking.

 All of these applications can be used in classrooms according to needs of classroom environment and topics. You can also see class examples of some applications in your area via İnternet sources.

TECHNOLOGY AND MATHEMATICS TEACHING

NCTM Position

“It is essential that teachers and students have regular access to technologies that support and advance mathematical sense making, reasoning, problem solving, and communication. Effective teachers optimize the potential of technology to develop students' understanding, stimulate their interest, and increase their proficiency in mathematics. When teachers use technology strategically, they can provide greater access to mathematics for all students.”

 As we see in the NCTM’s position, in the era of today it is necessary and essential to have regular access to technologies which are beneficial in teaching and learning.

 As teachers, which technologies can we use? In that blog post, I will mention these.

 Firstly, I want to make emphasize that in our classes we can use any technology that will contribute our teaching in a positive way that satisfies NCTM’s position. It depends on only the creativity and innovation of teachers. However, there are some softwares, applications or tools that teachers can get inspired from them.

Articulate StoryLine, is a good software to prepare interactive games, content, and quizzes. This software is like an interactive Power Point. With this software, you can teach the topic that you want to teach by preparing a content that provide instructions which they should follow to students and help learning of the topic by following these instructions. On the other hand, with this software, you can give feedbacks to students after asking some questions or giving some tasks.

Geogebra, is a dynamic mathematics software developed for better understanding of mathematics and geometry. Teachers can use GeoGebra to describe mathematical concepts, visualize them, and prepare enriched materials. Dynamic geometry software helps you to create geometric structures and other dynamic figures (eg, function graphs) using a variety of geometric tools and menu items.

Geometer’s Sketchpad, is a dynamic geometry software that is the most widely used mathematical software program in the world. For example, it can easily be shown that the sum of the interior angles will not change even if the triangle type (narrow angle, vertical, wide angle, etc.) drawn by GSP Sketchpad is changed. This allows students to make new inferences from their observations and discover their mathematical properties.

Dreamweaver, is a program for designing and coding a web page. It provides both visual design and code editing tools.

SketchUp, is a 3D Modeling software designed for architects, engineers, filmmakers, game developers, and users in almost every area where 3D modeling is required. SketchUp is also a great tool for teaching geometry. This sites can be inspiring how educators can use Sketchup: http://mathforum.org/sketchup/

 https://www.youtube.com/watch?v=_L59WF5VUP8

https://www.youtube.com/watch?v=t4FMGJQ4zfc

http://edupln.ning.com/profiles/blogs/google-sketchup-math-and-21st-century-critical-thinking