Diana conducted an investigation to explore conservation of area by transforming a 1 square meter shape made of newspaper into different shapes while keeping the area the same. Her original shape was a square with an area of 1 square meter and perimeter of 4 meters. Her new shape was an octagon also with an area of 1 square meter, but with a greater perimeter of 15.95 meters. Through this investigation, Diana learned that changing the shape does not need to change the area and she questions if the perimeter could also remain the same during a transformation.

1. My Square Meter Investigation By Diana
The Task:
I was asked to make 1 square meter square using newspaper, scissors
and tape. Then, I needed to change the perimeter of the shape, but keep
the area the same. This is calledconservation of area.
It was a fun investigation because we had to cut the paper and Ialso like
to cut! I also think the taping part was fun because we cooperated and
did our best with our friends. I think doing something with our friends is
the most fun part. It was challenging
for me becausewe had to not lose
the area of the square.
Original Shape:
The dimensions of my shape were
1m x1m, or 100cm by100cm. This
shape was a square. It had an area of
1m2 or 10,000cm2. It had a
perimeter of 400cm or 4m.
New Shape:
My new shape was an octagon.The area of my new shape was still 1m2
or 10,000cm2. I know this because when we were in the process of
cutting, we didn’t lose any pieces of newspaper or square centimeters.
The perimeter of my new shape isgreater than the original. It is 1595cm
or 15.95m. I worked this out by measuring all the side lengths and
adding them together.I think the new perimeter is greater because the
orginal’s perimeter was 400cm, but after one is
19.95cm.
Reflection:During this investigation, I learned
that the shape could change without changing the
area. It made me think about whether we can
change the shape without changing the perimeter
and area. I enjoyed cutting the papers with my
group. I still have questions about how can a

2. shape change without the area changing. I would like to investigate
algebra math next.