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This
activity was my first contact with the fourth grade math class. (I had lots to learn!) The classroom teacher said several of the students
were struggling with subtraction, particularly when regrouping was
involved. She asked if I could present
a lesson and work with them while she worked with another grade on another
topic. With travel time between the
elementary and high school buildings, I had about 35-40 minutes with the
students.
Description
Needed Materials: Chalkboard, overhead and TI overhead calculator (or a source of random subtraction problems).
Directions:
I introduced the lesson by telling the students we were going to look at subtraction “another way”. I emphasized that in math there are often many ways of getting something done and I wanted them to have the power to choose which one they liked best. I worked at the chalkboard to introduce the new way, and then used the overhead and a TI-83 calculator with view screen to randomly generate problems for them to practice.
The mathematical goal is to understand and do subtraction using place value and decomposition of the subtrahend.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
Oh,
my. Fourth graders are very different
from high school students! This “first
contact” for me was not what I would classify as tremendously successful. Just the novelty of using an overhead
projector was a major obstacle!
However, one student was a definite convert to “subtraction by parts.” After about 25 minutes of half-hearted
participation, one of the boys asked me, “Why are we doing it THIS way?”
(Unspoken
meaning: “Mrs. Alexander showed us a
different way.” This led me to wonder
why I bothered to carefully introduce the lesson—“why” often seems lost on
elementary students!)
Speaking to that group of boys I said, “Look at your
papers--have you noticed we’ve done all this subtraction and you’ve never had
to borrow, not even once?”
Marvin
looked up at me, eyes big--“I hate borrowing! You mean I don’t have to borrow if I do it this way?”
I
nodded my head. “That’s right.”
He returned
to his paper and worked with vigor for the remaining 10 minutes!
I really believe this approach
is valid! However, I jumped into the
middle of a group of students who had little or NO exposure to thinking about
numbers in this way. I expected way too
much, way too fast. Later in the
semester I discovered a game (Get to 1000!) that I
believe would assist the development of thinking about numbers “in parts.” At the beginning of the next school year, my
goal is to talk about methods of teaching mental addition and subtraction that
should be developed before the traditional rote carrying/borrowing method. All the teachers need to be involved, but
this type of instruction needs to in K-2.
An understanding of place value is imperative to good number sense!
_4_ Was the purpose of the activity clear to me?
_1_ Was the purpose of the activity clear to my students?
_3_ Did the activity support a range of learning styles?
_1_ Were the students engaged during this activity?
_9_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
…commiserating
with them at the beginning of the lesson about how borrowing seems rather
tedious. I told them I knew another way
that worked and I wanted them to know about it, too. I reviewed at the end of the lesson that what we had done was
“another” way to subtract that some people might like better while others might
prefer the pencil and paper method they were learning.
The part of the lesson that was student-centered was…
…virtually
nonexistent! Because the concept was
new and I discovered it was very different from any of their past experiences, the
entire lesson was teacher-centered as I tried to explain this new lesson. I did expect student participation as
modeled in the scripted lesson.
Let’s try this subtraction problem.
I
wrote it on the board horizontally--I knew if I wrote it vertically they would
simply do it the way they’d been doing subtraction up to this point.
86 - 32 = ___
A
couple of the students raised their hands--I knew they wanted to tell me the
answer, so I ignored their hands.
Now wait--I want us to think about this differently. Instead of starting at the back, let’s start
from the front. When you look at this
number, (pointing
at the 32) what are the first words you say?
I
called on a student who started to reply “thirty-two”, but I cut her off at “thirty”.
Right! When you see that number (pointing), you think “thirty” something. So, what’s 86 - 30?
Herein
lies my first difficulty. (Well, other
than they’d already made a big fuss over the not-familiar-to-them overhead
projector…) I expected the students to
“instinctively” know subtracting by tens without needing to use pencil and
paper. They did not--not any of
them. With a little prompting, I got
them to count backwards by 10s.
86 - 30 = 56. But we were supposed to subtract 32. That’s 2 more than what we already took away. We need to take away 2 more.
Thankfully,
most of them (but not all) seemed to understand that part!
56 - 2 = 54, so the answer to
86 - 32 = 54
Let’s try another one.
I had
intended to immediately do an example with regrouping, but because of their
difficulty with subtracting tens, I did a couple more examples without
regrouping. I told them a lot of the
work could be done quickly in their heads once they got the hang of it, but
showed them how to keep track of where they were for the time being.
How about
69 - 44 = ___?
How are you going to start?
I
called on a student who started to tell me that “9 - 4 = 5”--to which I
replied, “yes, but what about this new way?”
Another student volunteered 69 - 40.
On the board I kept track of subtracting the 10s by writing (vertically)
59, 49, 39,
Have I gone far enough? “No!”
When do I stop? “You need to go another one… You need to go down 4 times.”
Oh, OK…59, 49, 39, 29. So, 69 minus 40 is 29. Now what? “Take away 4 more.”
29 minus 4 is … “25” Great!
69 - 44 = 25
After
a couple like that, I began to think they were getting the hang of it, so I
decided to try one with “regrouping”.
Let’s try a tough one.
72 - 29 = ___?
72 minus 20 is … “52” and 52 minus 9 more is …
Dead
silence, but the wheels were turning with a few of the students. Some picked up their pencils, wrote the
problem on paper, and proceeded to do it by “borrowing”. (I discovered some of them DO write the
problem horizontally and STILL borrow by crossing out numbers and replacing
others--wow--that was new to me!) A few
others started counting backwards using their fingers. Two of the students gave me the answer--I
nodded, but didn’t acknowledge their answers verbally.
Wait! We need to take 9 from 52. How many does it take to get to 50?
Although
not immediately, one of the students replied, “2”.
Then how many more do we have to take away to make up that last 9 we were subtracting?
I lost
them with that one!
OK--don’t panic! We’re trying to take away 9. But we can’t do it all at once. If we take away 2, then take away 7 more, won’t that be the same as taking away 9?
Hesitant
nodding. (Note the poor questioning
technique. Obviously, I wanted them to
agree, so they agreed.)
If a number’s too hard to take away all at once, make it easier by breaking it up. 9 was too hard to take away from 52. So I broke it up into 2 and 7 because it’s easy to take 2 from 52. All I have to do to finish is take 7 from 50 and get …
Dead
silence. After the difficulty with
subtracting tens, I’m wondering if they instinctively know their “facts to
10”. Can they subtract any single digit
from a multiple of 10 without hesitation?
Time
was running out. I decided to put them
in small groups and then move from group to group to help. As the students moved their desks, I started
the TI 83 calculator (see program below) on the overhead and directed the
students to begin working on the problem they saw on the board. The remaining 10 minutes did not feel
particularly fruitful, as I found most of the students were unable to do the
problems independently at all. I ended
class with a promise that I’d be back the next week to continue helping them
with subtraction. I already had a plan
in mind using TI 73 calculators for assessment/drill to determine where the
students actually were with their basic subtraction facts. See Math Facts
Gameboy.
PROGRAM:ElemSubt
:ClrHome
:randInt(0,99) ®A 0 is the smallest possible number chosen, 99 is the largest.
:Repeat B<A These can be altered to suit your needs.
:randInt(0,99) ®B The Repeat guarantees problems with positive answers.
:End
:Output(2,2,A)
:Output(2,6,”-“) 2,6 is row 2, column 6 on the display. If you change
:Output(2,8,B) the size of your number, you may want to modify placement.