Cabri 3D

Today, I am going to share the unfolding of a hexagonal pyramid cut by a plane and its construction on Cabri 3D.

You can find the file on the link: https://drive.google.com/file/d/1GCxVd01eHO5g9nldpaavjYSklR_JBUGh/view


You can reach the video record that explains the construction step by step from the link:https://drive.google.com/file/d/1I15TbXVyqqiyw1H0PG1jK0hYKkNfMiKb/view

Typora

Hello all,
This week I want to talk about a program that I found while matching math objectives and the questions in  Meb objective tests. The program interface is very easy to use as you see below.

I think math teachers can use this program while preparing exam questions. Sometimes writing formulas or operations in word document is difficult. However, Typora has its own ways for writing simple formulas and operations signs. For example you can write formulas like,

$$F=ma$$

$$x = v \times t$$

$$c^2 = a^2 + b^2$$

$$\alpha = \beta = \gamma = \theta = \phi$$

As you see in the examples, if you start with writing double $, typora understands you will write formula after describing what you want Typora will transfer it to a mathematical language as you see in the above picture.

Two Apss Activity

      Hello, I am going to talk about an activity for your math classes that requires the use of two technological apps.

Purpose: What's the purpose of the activity? What will the participants gain as a result of it?

The main topic of the activity is fractions; students will be able to understand fraction concepts and can compare fractions through the activity. They are expected to design a dream house with given fraction restrictions.

 For example, the size of the bedroom is 1/4 of the home and the kitchen covers 1/5 of the whole house, etc. Then children sketch their homes up according to given fractions.  While doing this activity, students will gain the skills of fraction computation (mostly addition) and understanding of part/whole concepts of fractions. Also, this activity allows children to produce their own products because they can arrange the home according to their inspirations.

After the homes are sketched up, the Kahoot link will be shared with students. There will be questions about the comparisons of the sizes of rooms(fractions).

For example;

The bedroom is 1/2 of the living room. (T/F)

The kitchen is bigger than a balcony. (T/F)

Which one is bigger than the dining room? (roof= or = kitchen)

Thanks to this activity they may understand the sizes of fractions and compare them.

Tools: Which mobile applications will be used in this activity? Name tools, and include URLs.

Sketchup will be used at the beginning of the activity.

-https://www.sketchup.com/

 Kahoot

-https://kahoot.it/#/

Procedure: What will the teacher and the participants do? How will these tools be used?

The activity includes two apps to use in class.

Firstly, the fraction restrictions for dream house activity will be given by the teacher. Each room size represents a fraction. (Kitchen 1/4 of the house, living room 1/3 of the house, balcony 1/2 of the living room, and so on.)  after the given restrictions for the size of rooms, students try to sketch their home up. To sketch their homes as 3D manipulations, they need to compute fractions and make some calculations on them because they need to represent a home as 1(whole) and the rooms are parts of this whole. In this activity they are free to produce their dream house, they may sketch different combinations of rooms in 3D, they may prefer a duplex building or not.

   In the second part, the teacher prepares Kahoot questions and shares the pin with students. Then, the teacher expects that students will make comparisons by using their plan of dream houses.

The questions will be;

-The bedroom is 1/2 of the living room. (T/F)

-The kitchen is bigger than a balcony. (T/F)

-Which one is bigger than the dining room? (roof or kitchen)

-1/2 of the living room is bigger than the kitchen(T/F)

The teacher is responsible for preparing questions, helping children to make comparisons, ıf there would be some problems with the activities, a teacher should have knowledge of the use of apps and the relation between the apps and the main topic of the lesson.

Construction of 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.7.1.4.2. Birbirine oranı verilen iki çokluktan biri verildiğinde diğerini bulur.

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 which is a simple device that uses two pens to enlarge or reduce drawings and maps. It can be constructed by computer software programs (see sketchpad below) or constructed from four strips of wood, metal, or poster board.

Its working principle is related to the ratio in Mathematics.

The arms of the pantograph are hinged at points D, E, F, and H so that they move freely. Point C is the projection point and should be held fixed. As point D traces the original figure, a pencil at point G(its image) traces the enlargement. To reduce or enlarge the figure, the pencil is positioned at D, and G is moved around the boundary of the original figure. The pantograph can be changed to obtain different scale factors by adjusting the locations of points E and H. 

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The scale factor is the ratio distance from the fixed point to the drawing point distance from the fixed point to the tracing point. The mechanism of the pantograph serve to keep that ratio constant as the mechanism is rotated, expanded, and/or contracted.

** while responding to this, they can use the measure and calculate tab of the sketchpad.

This tool can be helpful to teach the objectives of M.6.1.7.2, and M.7.1.4.2 because it works according to the ratio. To give an example, for an enlargement with a scale factor of 2, point E is halfway between C and F, and point H is halfway between F and G. Students can find the ratios of FE to FC and FC to FG with the Measure-length and Number-calculations parts of the Sketchpad and see the relationship. You can give distance and ask for ratio or vice-versa to investigate the working principle of pantographs and their relation to ratio. While doing this, the teacher can ask “Do you see any ratio while enlarging or reducing your image on pantograph? Is it changing or stable?” Therefore students can make relations with pantograph and ratio. The questions may engage students in the topic and see the relationship between the images and their ratios.

Moreover, this tool is helpful for teaching the objective M.8.3.3.2 in the curriculum, since this tool also works with the similarity principle. While we are constructing this tool, we draw ED as parallel to FG and HD parallel to FE. In the end, we may not hide the segment between CG and see that ACD and HDG are similar triangles. Also, we see that HDG and FGC are similar triangles, too. This property of the pantograph will provide students’ better understanding of similarity and similarity ratio.

iii. User Manual: 

Before showing how you will use this tool, I am going to introduce you to the parts of the pantograph I created above.

PARTS:

(C) Pivot Base - To mount Pantograph to the working surface

(D) Tracing Point - To trace original

(G) Lead Holder - To draw a picture lead must be inserted in the lead holder and must be held in contact with the blank drawing paper.

(F) Balancing Pin - Must be on a working surface

(E, H) Ratio Screws - Used to set the desired ratio of enlargement or reduction.

First of all, you can watch my construction video which explains how to construct a pantograph on a sketchpad then create your own pantograph. You can download this construction to all computers in your lab for your students. https://drive.google.com/file/d/1UQS5mFYps4e8aXupeJsdGNhJwSpTyjMi/view

For 6th and 7th graders you can start by showing the working mechanism of the pantograph and ask them to measure EF, DH, FH, and ED. Then ask them to measure CE, CF, CD, CG, ED, and FG to find the constant ratio. After measuring, they will find  EF=DH and FH=ED. Also, when point D moves G moves accordingly, and CE/CF=CD/CG= ED/FG. At this point, you can say "The division of one segment to another segment or the division of one part of a segment to the whole segment called as a ratio. We can find the ratio of various lengths." Also, you can ask "Did you notice that these three ratios that we measured are equal to each other?" and  you can explain "These ratios form the base of the working principle of a pantograph, If you want to change this ratio, you can change the distance AB or move free points." For more investigations you can ask your students;

1. What happens to the scale factor for enlargement as point E is moved toward D and point H is moved toward F?

2. Where should points E and H be placed for an enlargement with a scale factor of 8?

3. What happens to the scale factor for enlargement as point E is moved toward F and point H is moved toward G?

For your 8th graders, you can create different similar triangles on pantograph with changing distance AB or moving free points..For example, triangle CED and  CFG are similar in my construction. You can start to lesson by introducing the pantograph and watching the video in this link https://www.youtube.com/watch?v=raQs62xOmXk. Then, you can want them to try the working mechanism of the pantograph on their own computers. In this step, students have already know what is ratio thus, you may ask them to find ratios. Also, you can mention a little about the construction and say EF// DH and ED//FH because it is important for the similarity. Then, you can ask them "How many different triangles do you see? " Which ones are similar to each other?" After finding similar triangles, you can ask them their strategy. It is expected that they will relate the similarity with ratio. For example,  they may say "triangle CED and  CFG are similar because the ratio of side CE to CF, ED to FG and CD to CG are the same." After that, you can call this ratio a similarity ratio.

iv. Construction Steps: 

We found 2 different ways of constructing a pantograph on a sketchpad. You can choose one of them and construct your own pantograph.

1. You can click the link and see our construction video. In this video, we vocalize the construction.

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

Here is the file of Sketchpad

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

2. You can also watch this video that we record on sketchpad as an alternative method.

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 the previous 2 steps.

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

-Tracepoints D and G and drag point D to write something.

Mathigon

Hello all,
I want to introduce you to a new application that is free and enjoyable for math learners and teachers. You can reach and login the website from this link;https://mathigon.org/courses

Students can learn from it and also it can be useful for teachers because of the good mathematical content that the website offers. Therefore, students and teachers can create accounts and reach many contents from the present mathematics curriculum. Mathigon also enables teachers to choose a chapter and create a homework assignment, or a flipped classroom setting. A teacher dashboard shows detailed analytics on students' progress and mastery.
I found it functional because, every chapter comes with a corresponding lesson plan for teachers, and Mathigon has a library of all the interactive games and components to use on a whiteboard or other platforms (e.g. Google Classroom or OneNote). In addition to chapters and dashboard, Mathigon includes enjoyable and inspiring content such as mathematical origami, a treasure hunt, puzzles, games and fun presentations.

When I logged in to that website, for example, I choose mathematical origami as a topic. Mathigon opens a new tab about the history of origami than it presented many different examples about origami. For further reading, it gave me two options (paper folding-polygons and polyhedra) If you choose any options that are interesting for you it offers more articles and related apps for you. Readers are encouraged to 'ask anything'.  The results are usually relevant and useful.  Some questions are answered with a YouTube video, others with a text response so feel free yourself and have a look at this useful app.

Tinkercad

Tinkercad is an application that I found by chance but I was really impressed and liked it after some testing.  It has tools for creating simple designs from scratch to quickly modifying existing designs. Also, It is a free online 3D design program that you can use in your web browser without downloading any software.  Math teachers can use this application for free in their lessons while teaching 3D shapes. You can sign the app from https://www.tinkercad.com/learn/ 
The app facilitates producing new shapes such as robots, homes, and whatever you want. While producing you can look at them from different sides such as the back, above, right, left, or inside, it is up to you.
The interface is easy to understand and use. Custom Shape Scripts add more flexible tools like text, shape generators, and parametrized forms. You can cut things into parts, add simple features, make holes, and combine, align, and arrange objects. If you make your designs public then other people can open their own copies of your models and you can also follow educators and students from your personal account.

Tinkercad allows users basic training after they create their own account. Also, it includes teach and learn buttons which means you can teach your students with this app. If you still have problems with using Tinkercad, you can follow the youtube training videos about tools and producing basic shapes from https://www.youtube.com/watch?v=rdqT5MyMzik .

I think Tinkercad is very useful for teaching 3D shapes. It has a colorful and simple interface that may attract students' attention. You don't need to create basic shapes, they are available on the tools bar. Therefore, students can construct their own shapes and share them. This really improves their learning and spatial visualization. 

 

You can give projects like constructing your dream item (house, car, clothe, computer) and draw it from different perspectives. Also, you can connect this app and activity with the ratio subject. Maybe you can give them a determined scale and want them to construct according to this scale. To do this they should measure real sizes of items and also use the measure tool on Tinkercad to take their ratios.

Another good feature of tinkercad that can be used for lessons is making simulations. You can create different types of simulations with Tinkercad as shown in belove.

Gimp and Pdf Exchange Viewer

Hello All,
I want to introduce you Pdf Exchange Viewer and Gimp programs. The idea of offering these two programs came to my mind when I tried to take screenshots of two pdf pages and tried to get only small piece of these pages. Many people do it with Paint and it takes time and effort as you know. However, with these two programs, it only takes 30 seconds.

For example, I have this math test and I just want to get only 8th question of this test.

,
Firstly, move the pdf file into the pdf exchange viewer, and select the screenshot tool which is in the middle of the tools bar and drag the mouse on the question which you want and select it totally
.

After that, you can send the selected piece by e-mail just one click on the tools bar also, you can print out and scan your selected object but what  would yo do, if you want to save it in the format of png file? Gimp is the second program that can help you. Open it and follow these steps
-choose files
-select create from screen
-click to export the image as tool

This is Gimp interface and it is really easy to use, you can play with image with menu bar above as you see. After saving (from files) your document as png format just like shown in below you have what you want as an image.

There are also easy ways of having image format of your screen such as screenshot tool in microsoft word that I used to prepare this page. These are not big programs or tools but they are really life saving and useful for teachers.