Precalculus/Trigonometry
at Guajome Park Academy
Grades: 10 to 12
Guajome Park Academy is a
charter school. It emcompasses
Kindergarten to 12th grade and has
an IB program.
23 students
All the students are English
speakers or EDL who have been
reclassified or redesignated.
Reflection on Teaching English Learners
1) I found out that graphic organizers helped all the
students, but particularly the English Learners, in their
notetaking and that they organized the concepts more
clearly. By filling them individually , then as a class,the
students improve their thinking and writing skills. It also
provided an excellent review opportunity and gave the
student a study sheet.
2) VIP were very effective. They structured the procedures
or the concepts. For some students, they were a huge help.
3) Analyzing the etymology of new words increased
understanding and gave the students tools to understand
future words. I also used that teaching moment as an
opportunity to introduce new connections with history,
language, culture… Reflecting on prior knowledge (words
from the same family they already knew) also was fruitful.
1) GRAPHIC
ORGANIZER
2)
VIP to find the
length of a side of
a triangle by using
trigonometry,
when you know
one side and one
angle
3) Etymology and words from same family
Word “secant”:
Comes form latin “secare”, to cut
Students found words such as C-section, segment, insect, a
sect, dissect,, intersection
We reviewed what the word segment means (line that is cut at
both ends), as well as the definition of ray and line.
We reviewed the meaning of intersection and bisect.
We talked about insect and the fact that the insect is “cut”
into three parts: head, thorax, and abdomen. We also talked
about the meaning of sect (cut away from main religious
group).
The students could not find words in Spanish or Tegalog from
Reflection on Best Practice
Combination and Permutation
The students could choose to play 1 game out of 4
games to win. They made a guess about what game would
give them the best chance to win.
After the lesson, they reconsidered their guess and
explained mathematically and in words why.
Then, they had a chance to gather clues in a double pair
activity. These clues lowered the list of posssible
outcomes and increased their probability to win.
After gathering their clues, they made the final decision
as to which game to play.
Name: ________________________________________________
I First Decision
Circle the game you want to play:
Game 1: Pick 5 balls with replacement. My numbers: ____
Game 2: Pick 5 balls without replacement, order of the
numbers picked does matter. My numbers: __________
Game 3: Pick 5 balls without replacement, order of the
numbers picked does not matter. My numbers: _______
Game 4: Find number of combination lock (4 numbers,
each from 0 to 9). My numbers: _________________
Explanation: Why did I choose that game? ____________
_____________________________________________________
After the Lesson
II Second Decision:
Do I want to change my choice?(check answer) Yes _____
No _______
My calculations:
Game 1: __________________________________________________________
Game 2: _______________________________________________________
Game 3: __________________________________________________________
Game 4: _____________________________________________________________
Explanation (why do you want to change your original choice or why do you
want to keep it):
_________________________________________________________________
___________________________________________________________________
III Final Decision (After getting the clues)
Clues: ________________________________________
How many possible combinations for the lock:
_________
Final Choice: Game ______________.
Guess: ____________________
Explanation:
_______________________________________________
_______________________________________________
Why Best Practice?
I like the fact that the students got engaged through
an activity(deciding what game to play) that made
sense to them and that they enjoyed. This activity
was a common thread that run through the entire unit
and was culminated by the final games.
Throughout the unit, they had motivation to reflect on
what they learned and to use this new knowledge to
make decisions.
It increased the students’ self-efficacy; it linked
abstract concepts with practical use for these
concepts. It encouraged the students to think at a
deeper level, to analyze, and to compare.
It created an opportunity for writing, since the
students needed to justify their choices.
Reflection on Personal
Growth
* Differentiation
* Time management
* Scaffolding
Differentiation
I applied more strategies for differentiation.
1) pairs or students are given the same problems, but in a
different order to help scaffolding. The pairs who have more
difficulties are given problems with increasing difficulty. The
more advanced groups may have difficult problems at first. If
you time this activity (you do not require that students do a set
number of problems), it guarantees that in the time given
students with difficulties build up their knowledge, while
advanced students get challenged. Teacher walks around room
and assist as needed.
2) homogeneous pairs or group of fours are given problems
with different level of difficulty (still covering the required
concepts).
3) heterogeneous pairs are given the same problems.
Jigsaw activity ( homogeneous groups of four)
1) All the students all have the same set of 7 problems.
Each group will only be responsible for 2 problems. The set
of problems have increased difficulties. Group 1 will prove
#1 and #2 (easier problems) , group 2 will solve #2 and #3…,
group 6 will have the last two, more challenging proofs.
2) 5 (or more) minutes for each student to work on the
problems on their own first.
3) then discuss strategies in 2 pairs or directly in group of
four
4) all students in group agree on one strategy for each
problem. Each student will write each proof individually.
5) when done, staple their papers. They need to make sure they
all understand proofs, because one student from their group
will be randomly asked (with a die) to come and present their
proof. (points will be given as a group for written work and for
presentation on board)
6) If they are done early with their two problems, they will work
on the other ones.
7) One student from the group present the proof with the same
number as his group (ex: group2 will present problem 2). For
groups who are not so confident, two students may come to
board as long as they both participate.
This way, they are only responsible for one proof, but they will
have done two. So, for the second one, they can see if they used
a different strategy from the one shown by other group.(in this
case, group 3)
“Around the World” (heterogeneous pairs)
The class can be divided into 2 groups, A and B. Group A and B are given
different problems, but the problems require the same strategies.
Ex: pair 1 group A proves that tan2 x (csc2 x-1) = 1 and pair 1 group B
proves cot2 x (sec2 x-1) ) = 1. Each pair for group A and B works that
way in parallel.
The pairs from group A and B post their proofs on separate sides of
the room. The pairs will only interact with pairs in their group. At the
end of the activity, one student from the pair will present his/her proof
while the other member walks around one side of the room and listens
to the other pairs present their proofs. The students in the pair then
switch. The other member now walks around.
What is great about this activity is that at the end you can assess
understanding by giving a quiz to group A with the proofs done by
group B and vice-versa. If there is real understanding of the concept,
the students should be able to apply the strategies to the problems,
since they are very similar.
Additionnally, each student, even the ones who have difficulties with
math should have become an “expert” at at least one of the proofs
Improvement in time
management
I used to have difficulty anticipating how long
different parts of a lesson would take and to stay
within a time frame for the activities.
I now am much better at judging how long
different activities will take and I learned to
judge when to shorten or stop an activity that is
too lengthy.
Scaffolding
I learned that you can never assume background
knowledge and to review prior knowledge before
introducing a new concept. Also, I learned to use parallels
or similarities between prior knowledge and new concepts
to make understanding easier.
Ex: when introducing trigonometric identities, divide the
board in two and compare to polynomials (ex: linear or
quadratic)
I also learned how to use VIP and graphic organizers, and
to alternate between mini-lectures, examples, and
practice problems.