Mates y TIC - Maths and ICT

Actividades de Matemáticas con TIC - Math Activities with ICT - - - ( Ricardo García Mesa

Archive for the '4º ESO'

Line. slope, y-intercept, cockroaches…

Posted by ricardogm on 12th February 2019


1. In order to better fight cockroaches, we are going to usee a Geogebra file, and I hope that this way you are going to visualize the slope and the y-intercept of a line really fast. It’s going to be something like that:

With this information, we can hopefully kill more cockroaches:
Algebra vs cockroaches.

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Posted by ricardogm on 11th February 2019


It’s time to discover this classic:

(Extract from Wikipedia):  “Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by “A Square”,[1] the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella’s more enduring contribution is its examination of dimensions.[2]

Book (pdf format)

Another version.

And the movie:

You can get it as a free ebook.

Y una versión en castellano: Planilandia.

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Posted by ricardogm on 7th February 2019


0. First thing, use geogebra to correct some of the exercises from wednesday. Pay attention

17. Now we are going to  create something like this:

Send the file to me, as usual.

145. A game to practice the explicit equation (or slope-intercept) of a line. Read the instructions carefully. The aim is to kill the cockroaches with lines.

(NOTE: it’s an old game in flash, you must allow flash in the page, and maybe it will work easily in Chrome than in Firefox)

Algebra vs cockroaches

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Moving Homer with vectors

Posted by ricardogm on 31st January 2019


We are going to use vectors to create animations, similar to this applet:

Pay attention and send me the files, as usual.

The math thing we are going to use is “linear combinations of vectors“, which is simply a·u+b·v, being  u and v vectors and a and b, numbers.

1. First, an easier construction. We are going to generate something similar to this:

2. Now, the Homer thing. It’s more difficult, so you have to pay even more attention than usual Wink.

The images you need are in this folder:


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Posted by ricardogm on 28th January 2019

Basic things:

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Trigonometric ratios in every quadrant

Posted by ricardogm on 28th January 2019


We have seen this thing before:

Now we are going to work with it a little more. Go to this page.

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Trigonometric identities and homer measuring trees

Posted by ricardogm on 21st January 2019


We are going to prove these two famous trigonometic identities:

sin2(x) + cos2(x) = 1


that can be seen in this applet:​

And how to measure trees with trigonometry (we are going to do more or less the same thing):

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Goniometric circumference

Posted by ricardogm on 18th January 2019



Today we are going to create something similar to this:

The idea is to study the trigonometric ratios of angles greater than 90º.

Pay attention. Send me the file.

Now time to solve some problems in your notebook:


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Posted by ricardogm on 10th January 2019


We have some things to do:

0. Solve these problems in your notebook while I try to correct your homework. Make drawings, of course.

1 The known data for a right triangle ABC is a = 5 m and B = 41.7°. Solve the triangle.

2 The known data for a right triangle ABC is b = 3 m and B = 54.6°. Solve the triangle.

3 The known data for a right triangle ABC is a = 6 m and b = 4 m. Solve the triangle.

4 The known data for a right triangle ABC is b = 3 m and c = 5 m. Solve the triangle.

5 A tree 50 m tall casts a shadow 60 m long. Find the angle of elevation of the sun at that time.

6 An airship is flying at an altitude of 800 m when it spots a village in the distance with a depression angle of 12°. How far is the village from where the plane is flying over?

7 Find the radius of a circle knowing that a chord of 24.6 m has a corresponding arc of 70°.

8 Calculate the area of a triangular field, knowing that two of its sides measure 80 m and 130 m and between them is an angle of 70°.

9 Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of 30º and from 10 m closer the top can be seen at an angle of 60°.

10 The length of the side of a regular octagon is 12 m. Find the radii of the inscribed and circumscribed circles.

11 Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of 49 centimeters.

12 Three towns A, B and C are connected by roads which form a triangle. The distance from A to C is 6 km and from B to C, 9 km. The angle between these roads is 120°. How far are the towns A and B from each other?

And here you have the solutions..

2. More problems.

The drawing below shows nicely what we are going to do:

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Posted by ricardogm on 20th December 2018


Today class has two parts:

a) Geogebra work. Pay attention and try to create a thing similar to the one the teacher is going to show you. Send it to me.

b) Game work. Try the games 2048 and Bloxorz and send me a review. Ciao

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