This week in geometry one of my students is learning about the different "centers" in a triangle (orthocenter, circumcenter, incenter, etc), as well as the midsegments theorem and triangle inequalities.
To help him visualize why all of these things are true, I had him cut out an acute triangle, an obtuse triangle, and a right triangle and use these to illustrate the concepts.
For triangle inequalities, we worked with different lengths of string to see why some combination of leg lengths and some do not.
These are both quick, easy ways that help students understand beyond the words and definitions what we are talking about!

Today one of my Spanish students was learning vocabulary related to personal appearance (hair and eye color, height, etc) and had previously learned professions, so to practice all of this vocabulary, we played a couple rounds of 20 questions. We alternated
who was thinking of the person and who was guessing so that she could practice both speaking and listening as well as practice her question words! She really enjoyed this, and I have used this method in the past with students which was very successful. It's
a fun way to practice a variety of vocabulary and use imagination.

As I have mentioned in previous blog posts, I work with students of a variety of levels to improve their Spanish speaking ability. Meeting with a student twice a week can make it quite difficult to keep sessions fresh and exciting and to come up with conversational
topics that haven't previously been covered.
Today one of my more advanced students wanted to practice using the correct imperfect and preterit conjugations and so he described to me, in great detail, his favorite movie. Since most people can talk for a long time about their favorite movie, and it
is easy to prod more shy students into engaging on this topic, I thought it a great topic choice on his part and will steal this idea to use with other students.

Pretend you are Christopher Columbus, writing to the King and Queen of Spain to beg them to finance your trip to the Americas. Explain to them what you need, why it is necessary, what you hope to gain. In Spanish this requires the use of the subjunctive!
I have often struggled with finding a fun activity to get students to practice writing the subjunctive in context, and came across this idea the other day. I used it this past weekend with a student who found it a fun yet challenging task.
One piece of advice I would say is to have a mini word bank of phrases that might be useful for them, as this was the only real obstacle to my student's success!

A website I like to use with my SAT students is freerice.com. This website has a vocabulary section which asks students to pick a synonym from a list of 4. For every correct answer, the website donates 10 grains of rice to the World Hunger Programme. It's
a great way to study vocabulary and do good at the same time! You can create a profile and the website will track your progress with the vocabulary. For every 5 consecutive correct answers at a given level, the difficulty is then increased, so it is also a
good way to challenge yourself. Encourage students to look up words that they have never heard of and create a list of their own of vocab words to study.
I've found this to be much more effective than simply using flashcards as it is less repetitive and more fun.
This is also a great resource for those learning English! Additionally, there are minimal vocabulary games for other languages, but the website is constantly improving, so in the future...
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I've found that most students have little to no difficulty understanding the difference between parallel and perpendicular lines when only one plane is involved. Either they never touch, or they intersect at a 90 degree angle, or they just plain intersect.
This concept is relatively easy to visualize because it is completely 2 dimensional.
Where the difficulty lies, is visualizing these same types of lines when different planes are involved, since it is 3d. To help, I utilize flash cards, or small pieces of paper. Have students draw a series of lines on each flash cards, making sure there
is at least a set of parallel lines, perpendicular lines, and intersecting lines on each, and give each line a name. Then move the flashcards in different ways, either stacking them or making parallel planes, and quiz them about the new relationships between
the lines.

I frequently work with students who wish to improve their conversational Spanish skills. I strongly believe learning to actually speak the language is the hardest part for most students, because it is almost impossible to practice unless you have someone
with whom to practice. I have certain students who I see on a weekly or bi-weekly basis, and only tutor them in conversational Spanish. For me, keeping these lessons interesting can be a challenge, especially with shy students. To combat this, I recently
purchased a conversation starter game called Rory's Story Cubes. These are ridiculously great and have been a huge success among my students. Not only do the cubes give students the opportunity to use their imagination, they are also a great way to practice
Spanish! I have challenged students to tell stories using only the past tense, or only the future tense, or by incorporating a command into each sentence. By putting stipulations on what they can and cannot say, you...
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This method requires one 6 sided die and a standard set of 52 cards (with or without jokers). It can be modified to help review a variety of concepts, this is just a basic version to practice present tense conjugation for beginning Spanish students.
For every value on the die, assign a person to conjugate for:
1- yo
2- tú
3- él, ella, ud.
4- nosotros
5- vosotros
6- ellos, ellas, uds.
Then assign a type of verb to each suit (ex. diamonds are ar verbs, spades are er verbs, clubs are ir verbs, and hearts are verbs with irregular present tense conjugations).
The student then rolls a die to pick who he is conjugating for and then picks a card from the deck to determine the verb he will conjugate.
By altering this activity there are hundreds of different options for reviewing both vocabulary and grammar.

Recently one of my students needed help on a "completing the square method" homework set. After a quick look at the problems I was 100% sure I had never seen this method before and was quite embarrassed that I didn't know how to help her.
I took a picture of her homework and went back home and researched the method on Google and came up with the following result:
#1:
1.) x² - 8x + 3 = 0
a. First move over the constant (in this case the 3):
i. x² - 8x = - 3
b. Then divide the whole problem by the coefficient in front of the x² term. In this case the coefficient is one so it stays how it is.
i. x² - 8x = - 3
c. Then divide the coefficient in front of the x term by 2.
i. Here the coefficient is -8 so we divide that by 2 to get -4.
ii. Next we square that number and add it to both sides (-4)²=16.
1. x² - 8x + 16 = -3 + 16
a. x² - 8x + 16 = 13 (after combining like terms)
d. Then you find the squares equation...
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