First assignment

Using the properties of similar triangles, your group will measure the height of a tree in each of your school grounds and compare notes. You must use all three methods and afterwards discuss the accuracy of the 3 methods that are given with your foreign friends.

The final product for the group is a blog post here on the blog showing your calculations and your discussion.

Also each group must keep a log to show your process – what did you do? Which problems occurred? How did you overcome obstacles? And so on. This must also be shown in a blog post. You can use pictures in you post.

Method 1 – Stacking friends

Here you need a friend.
Your friend stands beside the thee.
Walk about 30 meters away from the tree.
Use your fingers to measure your friend.
How many times can your friend be put on top of himself to reach the top of the tree?
Measure your friend’s height and times it to get the height of the tree.

Method 2 – stick in hand

Find a stick that is at least the length of your arm. Hold the stick vertically in your stretched arm. The stick above your hand should have the same length as your arm. You can check it by resting the stick on your stretched arm. If the end reaches your shoulder it is right. 

Stand in front of the tree. Remember to hold the stick vertically out in front of you with your arm stretched.

Walk backwards until the tree is completely covered by the stick in the height – it should not be longer or shorter than the tree.  Look over the stick to see the treetop flush with the top of the tree and look down to see the bottom of the stick flush with the root of the tree. (See pic.)

The distance from the tree to where you are standing is now the same height as the tree. Measure the distance to get the height of the tree.

We are using to similar triangles to find the height of the tree.
On the drawing below you see the two similar triangles inside each other.  The big triangle has the sides A,B and C. The smaller triangle has the sides a, b and c. The angles in the small triangle are the same as in the bigger triangle. Therefore we know that they are similar.

The length of your arm is the same distance as the distance from your eye to where you are holding the stick. That means that the distance from your eye to the stick (a) is the same as the length of the stick (b) - a=b.
The same goes for the large triangle – A=B, because:
In two similar triangle the ratio between the sides are the same

A = B = C
a     b    c

So when a=b, then A=B. Meaning the distance from you (A) = the height of the tree (B)

Method 3 – The sun

This method is only workable when the sun is out and there has to be room around the tree so you can where the shadow is cast.

Find a stick and stick it vertically into the ground. Measure the length of the stick (p).
Measure the length of the shadow of the stick (s)
Measure the shadow of the tree (t)

The height of the tree is:

h = t x p / s

(see youtube video for explanation http://www.youtube.com/watch?v=LhEe0kB4QIs)

Goal circles, round 1, Denmark:

FYI: We now have a group on facebook called "Speaking about maths - figure it out". Make sure you get added and add the ones who are not there yet:-) This will be used for quick questions, socializing and other things that do not belong on the blog.

Vocabulary excercise in Denmark - the result; a lot of new words and expressions to be used the next two years...

Hi Lithuanians

 Hi Lithuanians,

How are you? My name is Mathias, my birthday is 30/7 and I’m 15 years old and my last name is Skovdal Hansen. I´m going at 8^th on the school called Bakkeskolen in Kolding. In my spare time I playing football in a club called KIF and work at humör and that is a clothing company and I’m also together with my friends. Freja and Thorbjørgn, that’s my Cats names. My mother and father are separate and I live 6 days with my father and 8 with my mother and her husband Carsten.    

My sister’s name is Julie and she is 12 years old and goes also at Bakkeskolen.

My mother’s name is Rikke and she is 38 years old.

My mother’s husband name is Carsten and he is 40 years old.

My father’s name is Klaus and he is 41 years old. 

I’m looking forward to meeting and working on our project.

Best wishes, Mathias.

Hello!

My name is Emilija, but friends call me Ema! I live in Prienai, but study in Birštonas at Birštonas gymnasium, because I think this school is better for me than the schools in Prienai. I'm the only child in the family and I live with my dad and grandmother.
I like music: singing,  playing the piano. I've graduated music school last year, but still i attend solo, chorus singing and piano classes!
Also I'm a scout, I've been a scout for 7 years.
In this project I'll try to improve my English and math skills.
Hope to see you soon, guys!
Best wishes

Hi Litauens my name is Konstantin and I am 14 years old. I live in Denmark in a city called Kolding. I live in a house in the area of Seest.

I have to small brothers their names are Jakob and Carl. Jakob is 8 years old and Carl is 12 years old, my mother’s name Kristina and my father’s name is Mattias. Originally I come from Copenhagen. My family and I have many friends from Copenhagen. In my spare time I’m playing games with friends and I play music in the music school in Kolding. I have a job in my spare time, and my favourite sport is skating. I skate every day to school, and also in my spare time. I skate on a skateboard called a penny board. Every second weekend I travel in a train to Germany, because my parents are divorced.

And my father lives in Germany as a minister.

Study groups

Dear all of you,

Thank you ever so much for your letters. I think everyone is excited to get to know one another. To this post I've attached the study groups for the Maths projects. I'm looking forward to working with all of you:-)

Best whishes, Thora

Study Groups

1)  Linas, Evelina, Konstantin and Jonathan

2)  Migle, Lukas, Julie K. and Louise

3)  Gabrielius, Diana, Simon, Mathias and Celina

4)  Mantas J., Simona., Malene and Maria A.

5)  Mantas G., Edvinas V., Winnie, Julie A. and Sara S

6)  Tomas, Edvinas J., Kirsten and Nicole

7)  Kostas, Monika, Christian and Natan

8)  Aiste, Emilija, Michelle, Miklas and Maria W.

9)  Erikas, Dominykas, Sarah J, and Iben

10)   Jurgita., Brigita, Nan and Mia Maja