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Q&A #15996


Foundations of Math - block schedule

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From: Suzanne A. (for Teacher2Teacher Service)
Date: Oct 16, 2005 at 09:31:22
Subject: Re: Foundations of Math

Hi Michael,

I agree that the nice thing is that you have the freedom to do anything!
The other great thing is that you have 95 minutes together a day but
I agree that that can be a very long time if you don't think of it in
different stages. Let's see if I can explain a model that you might work
from to break that time up into reasonable, interesting, and productive
chunks.

Here's one timetable you might consider:

1. Math Message - 10 minutes
(an opening (written) activity at the beginning of class that is accessible
to all of the students - usually lasts about 5 minutes and then another
5 minutes can be taken to debrief the work)

2. Introduction of material - 10 to 15 minutes
(whatever the topic is for the day this is when you present it to the class)

3. Pairs or Group work - 20 minutes
(working on the material that you've introduced)

4. Discussion - 10 - 15 minutes
(bring the class back together to talk about what they've been working
on)

5. Mental Math - 5 minutes
(a short oral activity where the teacher gives a mental problem, the whole
class responds in unison)

6. Focus Group and Independent Activities, Session 1 - 20 minutes
(You work with 4 or 5 students on the math topic of the day. Meanwhile the
other 12 or 13 students are working in pairs or groups on activities that
they can do independently - I'll give an example of what that might be
below.)

7. Focus Group and Independent Activities, Session 2 - 20 minutes
(After Session 1, you work with a second group on the math topic of
the day and the pairs or groups working independently change to a new
activity to do independently. Using this model with 17 students, you can
have focused time with small groups of students every other day.)

This is about 95 minutes! Now let's see if I can give you an example of
how it might work.

So, you're probably wondering....what do I actually do for math topics,
etc. If I were teaching this class I would use the Problems of the Week
as the basis of what I do each week. I would probably use the Math
Fundamentals Problem one week and the Pre-Algebra Problem the other
week or I might use the problems that are in the Active Problem Library
and choose problems that are not too text intensive and then I could
vary the math topics as I would like.

So, let's think about this using the current Pre-Algebra PoW as an example:
 http://mathforum.org/prealgpow/

1. Math Message:
    The radius of a circle equals two times the diameter.
    Find the diameter if:

    1. r = 4 inches
    2. r = 17 feet
    3. r = 2 meters

    Find the radius if:

    4. d = 20 meters
    5. d = 8 inches
    6. d = 14 feet

Note: This questions should be written so that all of the students will
be successful. It's introducing a concept that will be needed to solve
"How Fast Is a Minute?" in a way that's quite basic. As the class discusses
the work, I would make sure that they fully verbalize the concepts of
radius, diameter, circle, multiply, and divide. Because the students are
ELL any time that you can encourage them to explain helps them both in the
language development and also their mathematical thinking.

2. Introduction of Material: I would pass out a copy of How Fast Is a Minute?
to each student having printed it using the Print This Problem link:

 http://mathforum.org/prealgpow/print_puzzler.ehtml?puzzle=270

I would give them a moment to read it independently and then either I
or another student could read it aloud leaving the "Extra" for later. After
reading I would use literacy techniques to check to see if the students
comprehended the question. I'm not trying to get them to solve the
problem at this point. I just want to make sure that they understand the
context and the question (reading comprehension).

3. Pairs or Group work
Now I have them work together to solve the problem.

4. Class Discussion
I would have a class discussion as soon as I think the students are ready.
Important at this point is not to acknowledge right or wrong answers.
Important is to encourage students to explain why they did this or that
and detail the steps that they took to solve the problem. In other words,
at this point students are verbally "writing" their explanation of their
solution.

Depending on how that went, there might be time to have each student
draft an explanation of their answer.

5. Mental Math
Sometimes I would have this "break" activity relate directly to the math
topic of the day and sometimes I might have it completely separate. At
first as with any of these "parts of the class routine" it takes a little
training time to get the students used to the activity. Some of my
favorite Mental Math starting activities are extremely simple but still
exercise the brain. Since you are dealing with an ELL population again
realize that not only are they challenged because of the mathematics
but also they are practicing listening, comprehension, and speaking
skills!

Idea #1: The teacher says, "When I say a number, you say the number
that is one more than."

     Example:
         teacher: 4        ALL students when I give the signal:  5

They will think it is trivial at first but then as you use other variations
and as you use larger numbers, it gets a bit more complicated.

variations include:  "one less than"   "two more than"   "two less than"
"half of"  "twice"  "a third of"   "the decimal equivalent"....etc.
So, in effect they're practicing addition, subtraction, multiplication,
division, fractions, percents, decimals, etc.

Idea #2: The teacher says, "When I say the radius, you say the corresponding
diameter including the units that I use."

      Example:
          teacher:  4 feet               ALL students in unison:  8 feet

6. Focus Group and Independent Activities
As the students are working on the problem you'll be able to assess
who is "getting it" and who might be struggling. I would form the first
focus group by selecting 4 or 5 students who seem to need the most
1:1 help on working the problem. While you are working with them,
the other students can be playing Everyday Mathematics games like

Top-It (a game played with cards and there are many variations of it)
See general directions here:
    http://everydaymath.uchicago.edu/educators/samplegames.shtml

Another idea for an "independent activity" could be that some of the groups
can continue writing their explanation, read it to each other, revise
and improve it, etc. without direct help from you. So, that's another
option.

7. Session II - Change to work with another group and also have
the students who were doing an "Independent Activity" change to another
activity.

If you have computers in your room, I have a lot of suggestions of
independent activities that use Java applets, etc. that are available on the
Web. Many of them are cataloged here:
   http://mathforum.org/mathtools/

I hope some of these ideas are helpful, Michael. If something resonates and
you'd like to discuss it more, just let us know.

Sincerely,

 -Suzanne A., for the T2T service

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