Grade Level: Second/Third
Math Engagement: Fractions
Materials needed: Grid sheets (8X8, 10X10, 12X12), color
pencils
Specific Emphasis: Splitting objects into equal parts to
demonstrate a fraction of a whole
(1)This generative activity is to find all the different
ways a square can be divided up into fourths. Students in a group are given
a sheet with square grids and instructed to divide the squares into four
shapes, four "funky" shapes, and to prove that they are four equal
shapes. This is proven by counting the individual squares in the shape.
(2)The class discussion begins with a drawing of a pizza on a chalk board.
The students are shown how it is divided into equal parts and what each
part is called as it is eaten. For example, a pizza divided into 4 equal
slices still makes one whole pizza but when one piece is eaten that piece
became a fourth of the pizza and three fourths of the pizza is left. The
pizza drawing is divided up into other fractional parts such as thirds,
fifths. sixths and so on to demonstrate the different fractional parts of
the whole. (6)The class will be structured by the introduction using the
pizza followed by the showing an example of one of the grids(the example
grid will be of a different size). The children will then split up into
groups and be given the grid sheets. (15) The students will be instructed
not to make easy equal "block" shapes but to be as creative as
possible with their shapes. Close to the end of the class period the class
will discuss how their groups divided up each grid and then be asked to
prove their methods. The "funkiest" shapes will be posted and
analyzed. (8)The main theme or big idea discussed will be the division of
a whole into smaller parts to make fractions of that whole. It will also
be to demonstrate the fractional parts of numbers. (10) The students will
use the grid sheets and pencils to "think" and count with. It
will be suggested to use a regular pencil to outline the shapes initially
and then to fill in the shapes with the colored pencils. (13) Different
sized and dimensioned shapes could be given for other activities to follow.
Actual food such as a pizza or a pie could be brought in and divided up
to show different fractional parts as well.
In my analysis of this activity, I tested two students to get an honest reaction to the credibility of the activity. The first was a first grade student at Buda Elementary. I picked this student because of her high level of achievement in the class. I have included her shape drawings. It was pretty obvious from the start that the whole concept of fractions was a little over her head. I basically had to walk her through drawing the first shape. I modeled what I was doing in creating the first shape and then instructed her to make the other three shapes. She was very interested and wanted to come up with different shapes. I kept stressing
that the shapes had to be equal and that she needed to
plan out her shapes to make sure they were equal. I think she was more interested
in the shapes than the fact that they were a fraction of the whole grid!
She did say she understood the fact that they were a part of the whole and
that they were smaller than the whole. This was encouraging even though
I'm not sure I believed her.
The second student that I tested was a second grader at
Kyle Elementary. He is one of the highest math students in the class. I
had a lot of fun with him. I started in with the pizza example and we talked
about how when you take one piece of the pizza away you will have three
fourths left (if it's divided up into fourths). He didn't have a problem
with that concept. He actually gave me some other examples like if it was
divided up into five pieces and you took one piece away you would have four
fifths left. I showed him the other students example and explained the directions.
He asked a few questions along the way. For example, he asked how would
you know how many squares to have in each shape. They haven't studied division
or multiplication yet so it was a little hard explaining that one. I told
him that I knew, because I had counted the squares, that there were 64 squares
in the grid that I had given him. I also told him, to save time, that I
knew each shape had to have sixteen squares because that way each shape
would have the same amount and be of equal size. I did explain that it would
be a different number if the grid had a different number of squares. He
seemed to understand this. As he counted his squares, we talked about how
you could even divide an individual square into smaller parts as long as
you divided up another square the same way. He understood how you would
divide up two squares into thirds and only use two from one square and one
from another to make a whole square. I included his drawings to demonstrate
his use of creative divisions to develop odd shapes. We had fun counting
the squares, and his division of the squares, to make sure we had equal
parts in each shape. He really seemed to enjoy the activity and I feel he
understood the very basic concept of fractions, even though he had never
been introduced to them before. He asked me to come test other projects
that I had because he liked learning and helping me at the same time!
The following grids are examples of different shapes that
could possibly evolve during the activity.
(3)(4)(5)
8X8 Grid
10X10 Grid
12X12 Grid
Examples of Student Work
(14)
These images were not scanned in color so much of the students' work is not clearly visible.
