Primary PoW Packet
Name That Shape!
http://mathforum.org/pows/
Welcome
Welcome!
This packet contains a copy of the problem, the “answer check,” sample solutions and some teaching
suggestions. This is Library Problem 4175. The text of the problem is included below. A print-friendly
version is available using the “Print” link from the blue-shaded box on the problem page.
Standards
In Name That Shape! students are asked about the number of lines of symmetry that a rectangle and
also a square have. If your state has adopted the Common Core State Standards, you’ll notice that this
problem does not align to any standards for Kindergarten through Grade 3. Although young students
are working with shapes including “Analyze, compare, create, and compose shapes,” the phrase
“lines of symmetry” is not introduced until Grade 4.
Grade 4: Geometry
4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure
such that the figure can be folded along the line into matching parts. Identify line-symmetric
figures and draw lines of symmetry.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
The Problem
Name that Shape!
Mia drew a shape with exactly 4 sides. It has 4 lines of symmetry.
Can the shape be a rectangle? Why or why not?
Can it be a square? Why, or why not?
Answer Check
After students submit their solution, they can choose to “check” their work by looking at the answer
that we provide. Along with the answer itself (which never explains how to actually get the answer) we
provide hints and tips for those whose answer doesn’t agree with ours, as well as for those whose
answer does. You might use these as prompts in the classroom to help students who are stuck and
also to encourage those who are correct to improve their explanation.
The shape cannot be a rectangle but it can be a square.
If your answer does not match ours, did you
• draw a picture?
• check this Ask Dr. Math page on Lines of Symmetry?
http://mathforum.org/library/drmath/view/55264.html
• talk in your group?
If your answer does match ours, did you
• explain?
• include a picture?
• help anyone in your group?
Our Solutions
Method 1: Draw a Picture
We noticed:
Mia drew a 4-sided shape.
The shape had 4 lines of symmetry.
A rectangle has 4 sides.
A square has 4 sides.
We talked about what symmetry means. If we have a shape and we draw a line through it and the
pieces that are made look the same then we think that’s a line of symmetry. We drew a freehand
picture of a rectangle and a square to think about the lines of symmetry.
We decided to look at them one at a time. We drew lines on our drawing. With the lines we thought if
the two pieces were the same.
The first two rectangles work but the third one has one piece with a short and a long side but the other
one has a long and a short side and so they don’t match. Mia’s shape wasn’t a rectangle.
Next we looked at the square and we found four lines that would work:
The two pieces made from the added line, are the same shape. We decided Mia’s shape was a
square.
Method 2: Use a Manipulative
After reading the problem I thought about if Mia had drawn a rectangle or a square. I had one of each
to think about on my paper:
I had some colored sticks to use for lines. As I put them on the two shapes I thought about the spaces
made and if the two spaces were equal. I found two lines that worked for the rectangle and four lines
that worked for the square.
Mia’s shape was a square!
© 2012 Drexel University
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Method 3: Folding Paper
We used pieces of paper to think about the problem. We had a square piece of paper and another
piece in the shape of a rectangle. We folded them in “half” as many ways as we could. We noticed that
we could fold the rectangle in half the long way and have two pieces the same size. We also noticed
that we could fold the rectangle in half the short way and have two pieces the same size. We tried
folding it on the diagonal but when we did that some of it stuck out and the two pieces didn’t match.
We decided that the rectangle only has two lines of symmetry.
Next we folded the square piece of paper. The “long way” and the “short way” were the same but
turned because a square has four equal sides. When we folded the square on the diagonal, nothing
stuck out but instead matched. We saw that we could fold it on another diagonal and that worked, too.
We decided that the square has four lines of symmetry.
Mia drew a square!
Teaching
Suggestions
This problem is one that was discussed during an online course offered to a group of primary level
teachers from Montgomery County, Maryland. Here are some thoughts that were shared in the course
about this particular problem:
Stacey’s Initial Thoughts
I would have individual copies of this problem for each student and I would have it copied as a poster
displayed on the front board. Students would work in assigned pairs to solve the problem. I would
read the problem aloud and then give students time to read and digest the problem individually. We
would start off by identifying the information we know from the problem, what information we do not
know, and what it is we are looking for. The answers to these questions would be recorded on the
poster paper. Knowing that we are looking for a 4-sided shape, we would brainstorm all of the 4-sided
shapes we are familiar with. I would have cutouts of these shapes ready for pairs to use in solving the
problem. Partners would solve the problem using the cut outs to find exactly 4 lines of symmetry.
Students would record their answer (shape and lines of symmetry) on their individual copies. After all
pairs were through, we would go through each 4-sided shape and discuss if that was the shape we
were looking for and why it is the solution or why it is not the solution.
We hope this information is useful in helping you make the most of the Primary Problems of the Week
in the Library. Please let me know if you have ideas for making them more useful.
~ Suzanne
© 2012 Drexel University
<[email protected]>
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