A)Selección y adaptación de textos y andamiaje
Este Proyecto de aula
lo encontré hace unos años en primer lugar en www.eduteka.org
, pero estaba escrito en castellano. Como empecé a trabajar con alumnos bilingües
lo busqué en inglés y lo encontré en
A día de hoy, el
proyecto ya no está alojado en esa web. En cualquier caso el proyecto que
presento aquí es una adaptación del proyecto original.
Lleva andamiaje tanto
para el contenido como para el formato del informe final.
El resto de la unidad
didáctica que estoy desarrollando lleva textos escritos por mí y problemas de
enunciado que he encontrado por Internet (eso no supone ningún problema de
licencias pues los problemas de matemáticas no tienen derecho de autor).
Este es el texto
adaptado con el andamiaje:
THREE SQUIRRELS AND A PILE OF NUTS.
THE
PROBLEM.
Three squirrels, Steve, Keith and
Benjamin, have spent all day collecting nuts. At the end of the day they are
very tired and go to bed.
During the night, Steve wakes up and eats
a nut. He then decides to take one third of the remaining pile and hides it before
going back to sleep. Keith then wakes up. He too is hungry, so eats a nut. He
also takes one third of the remaining pile and hides it before
going back to sleep. Finally, Benjamin wakes up, eats a nut and hides a
third of the remaining
pile.
In the morning, all of the squirrels share
the remaining nuts equally between them and each goes off with two more nuts. Each squirrel then eats all the nuts he
now has.
How many nuts has Steve eaten in total?
HOW
TO SOLVE IT.
You
have three different strategies to solve the problem. You have to work in a
team and you must develop completely the three strategies and write a document
explaining the solution step by step.
STRATEGY 1.
WHAT TO DO: With this strategy, you'll be solving the
problem the way a squirrel would - one nut at a time!
1. Count out
the number of nuts your group would like to start with (not necessarily all you
have). Put these in your starter pile.
2. Make one
member of your team Squirrel 1, and have him or her tackle the pile of nuts the
way the first squirrel in the story did.
Warning: No fractions of nuts allowed! Let
Squirrel 1 take several tries until she or he ends up with whole amounts after
each step. Record these numbers.
3. Now the
teammate who's playing Squirrel 2 should work through the steps. Again, no
fractions - so both Squirrel 1 and 2 may need to go back and adjust their
piles. Record the numbers that work.
4. Finally,
Squirrel 3 should take his or her turn. Adjust as needed, and record the
results in your document.
5. When
Squirrel 3 is through, divide the nuts that are left. If the pile doesn't
divide by three, adjust all the way back through the problem. Record your tries
and your final answers.
6. From all
your notes, write several sentences (with pictures if you'd like) describing
the steps and numbers that finally gave you the right answer.
STRATEGY 2.
WHAT TO DO: In this step, you'll be setting up a spreadsheet
that will let you try out various combinations of numbers to solve the problem.
1. Label your rows for Squirrel 1, Squirrel 2, and
Squirrel 3. Label your columns "No. of nuts in pile," "No. of
nuts after s/he eats 1," and "No. of nuts s/he leaves behind."
A
|
B
|
C
|
D
|
E
|
|
No. of nuts in pile
|
No.of nuts after s/he
eats 1
|
Of nuts s/he leaves
behind
|
|||
Squirrel 1
|
|||||
Squirrel 2
|
|||||
Squirrel 3
|
|||||
2. Now, figure
out formulas for all the cells that will let you plug in and test out numbers.
Remember to make each cell relative to the others, so that a number you plug
into one cell's formula will affect the rest. Here are a few hints:
The formula in cell C2 should be =B2-1, because
the squirrel eats one nut from the pile in B2.
The formula for D2 is =(C2/3)*2, because
Squirrel 1 leaves two-thirds of the pile behind.
The formula for B3 is =D2, because Squirrel 2
finds the pile the way Squirrel 1 leaves it.
3. Once all
your formulas are in place, test out your spreadsheet by plugging a number into
B2. You may end up with a lot of weird-looking fractions - and you know these
squirrels aren't going to settle for anything less than whole nuts! Keep trying
numbers until you find one that gives you whole numbers throughout. What patterns
do you see?
4.- Include
your spreadsheet in the document twice, once showing the formulas and once with your whole-number solution in place.
STRATEGY 3(algebra power).
WHAT TO DO: With this problem-solving strategy, you'll be
setting up an algebra equation to solve.
1. Open the Excel worksheet used for Strategy 2,
leave the column and row headings. Now you have plenty of room to create a table
for defining your variables.
2. The variables you most need to solve for are:
x= nuts in original pile
y= number of nuts each squirrel gets in the end.
Record these at the bottom of your worksheet.
A
|
B
|
C
|
D
|
|
No. of nuts in pile
|
No.of nuts after s/he
eats 1
|
Of nuts s/he leaves
behind
|
||
Squirrel 1
|
||||
Squirrel 2
|
||||
Squirrel 3
|
||||
x= nuts in original pile
|
||||
y= number of
nuts each squirrel gets in the end
|
3. Here are some hints: Put in x as Squirrel 1's
"No. of nuts in pile."
When it comes to solving for y, remember that it
is one-third of however many nuts are left in the end, so y=1/3 (last entry in
table).
4. After you fill in your table, put together an
equation. You can type this in your worksheet below your table. Show steps for
simplifying the equation. Then test it out with several numbers.
5. Make sure your worksheet shows all the steps
you followed to write and solve the equation.
THE FINAL
REPORT
Your final
report must include
1.
A
cover (make a beautiful one, including photos or drawing a picture)
·
Title
·
Names
of the members of the group and their degree of involvement in the different
tasks.
·
Date
2.
Index
3.
Objectives
·
The
main objective of this project is to ___________________________
·
Other
objectives are___________________________________________ and
____________________________________________________________
4.
Description
and explanation of the three strategies
·
Strategy
1:
ü Description: In this strategy, each
member of the group behaves as a ______________,
then____________________________
ü Results: We think that the number of
nuts is______
·
Strategy2:
ü Description: In this strategy, we
have used a ______________, and then____________________________
ü Results: We think that the number of
nuts is______
·
Strategy2:
ü Description: In this strategy, we
have used ______________, and then____________________________
ü Results: We think that the number of
nuts is______
5.
Resources
6.
Conclusion
and personal opinion:
·
Combining
the ______________ strategies, we think that the number of nuts can be
___________________ because ______________________________
·
I
like or dislike this project because __________________________________
·
The
easiest strategy was ___________ because_________________________
·
The
most difficult strategy was______because_________________________
B) Ejercicios interactivos diseñados por mí.
A) He usado LearningApps y he diseñado 3 Cloze test, pues me ha parecido
interesante tenet alguna actividad de listening más activa que las que
desarrollo habitualmente en el aula
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