Primary PoW Packet
What Do I Have in My Bag?
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 #4487 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 What Do I Have in My Bag? students use the clues to determine what the mystery shape is. The
key concept is two-dimensional shapes.
If your state has adopted the Common Core State Standards, this alignment might be helpful:
Kindergarten: Geometry
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones,
cylinders, and spheres).
Grade 1: Geometry
Reason with shapes and their attributes.
Grade 2: Geometry
Reason with shapes and their attributes.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
The Problem
What Do I Have in My Bag?
In my bag I have a triangle, a rectangle, and a hexagon. I pull out a shape but
don’t show it to you.
I tell you it has more than 3 sides. Which shapes can it be?
Then I tell you that it also has fewer than 6 corners/vertices. Which shape is it?
Explain how both clues helped you discover which shape it was.
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 is a rectangle.
If your answer does not match ours, did you
• draw a picture?
• act it out?
• talk in your group?
If your answer does match ours, did you
• explain?
• help anyone in your group?
• make sure to explain how both clues helped?
Our Solutions
Method 1: Act It Out
Our teacher gave us a bag with shapes in it: a triangle, rectangle, and a hexagon. We took one shape
out and it was the triangle. We knew the story said “it has more than 3 sides.” Triangles have exactly
three sides and so the shape couldn’t be a triangle. We took the rectangle out of the bag and counted
the sides. It has 4 sides. We took the hexagon out of the bag and counted the sides. It has 6 sides. It
could be a rectangle or a hexagon. We looked at the story again.
We saw that the next clue in the story said “it has fewer than 6 corners/vertices.” We looked at our
rectangle again to count the corners. It has 4 corners. 4 is fewer than 6 and so we’re pretty sure the
shape is a rectangle but we want to check the hexagon. We looked at is and counted the corners. It
has 6. If the shape has “fewer” than 6 corners then it can’t be the hexagon. The shape is a rectangle!
Method 2: Use Manipulatives
We have a bucket of plastic shapes on our table. We took out a green triangle, a blue rectangle and a
yellow hexagon. We knew from the story we needed to think about the number of sides and the
number of vertices (corners) for each shape. We made this list:
triangle, 3 sides, 3 vertices
rectangle, 4 sides, 4 vertices
hexagon, 6 sides, 6 vertices
The first clue says that the shape has more than 3 sides. Both 4 and 6 are bigger than 3 and so we
decided that clue helps us know the shape could be either a rectangle or a hexagon.
The second clue says that the shape has fewer than 6 vertices. 4 is less than 6 and 6 equals 6 and so
we decided that clue tells us that the shape is a rectangle.
Method 3: Draw a Picture
After we read the story we drew each shape on our paper.
We counted the number of sides for each shape.
The first clue says that the shape has more than 3 sides. We crossed out the triangle. We had the
rectangle and hexagon left. The second clue says that the shape has fewer than 6 vertices. We
counted the vertices on the rectangle and the hexagon to decide.
4 is less than 6 but 6 is exactly 6 and not less. We decide the shape is a rectangle.
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 of the thoughts they shared in the
course about this particular problem:
Sarah’s Thoughts, Part 1 – Choosing an Appropriate PoW
This week I have chosen PoW #4487 "What Do I Have In My Bag?" I chose this problem because it will
build upon what we learned about last week. We focused on identifying 2-dimensional shapes and
describing the attributes of each shape. This week’s PoW will challenge the students to use what they
learned last week. They will need to think about the attributes of each shape to solve the mystery
shape by using the given clues. This problem will show me which students have a solid understanding
of shapes and their attributes and those who may need more reinforcement.
© 2011 Drexel University
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Sarah’s Thoughts, Part 2 – Preparing to Use the PoW including Planning Questions to Ask
This PoW connects to lessons we did last week in which the students became familiar with basic
2-dimensional shapes of square, rectangle, circle, triangle, and hexagon. In implementing the EIC, we
are integrating a question throughout each subject area. The unifying question is “How does exploring
how parts of something interact help me create new ideas?” In choosing my PoW for this week, I feel
like I have chosen one that will build upon what we did last week with identifying shapes and challenge
the students to think critically about using given clues to help identify an unknown shape. I will also
challenge my students to make connections between basic 2-dimensional shapes and how to put
these shapes together to form new shapes. Some questions I will ask my students while they are
working on the PoW include:
Give attributes of the shapes-triangle, rectangle, hexagon, which shapes have more than 3
sides?
Which shape has fewer than 6 corners/vertices?
Which clue was more helpful in solving the problem? Why?
What strategy did you use to solve the problem?
How did knowing attributes of each shape help you in solving the problem?
After reading and thinking about the section on Connections, I realize how important it is for young
children to make connections to real life situations to help better understand math concepts. In
teaching our unit on 2- and 3-dimensional shapes, we spend a lot of time discussing and identifying
shapes that they have seen at home and/or in the environment. This helps bring the students’ past
experiences into the classroom and helps the students make sense of what we are doing in the
classroom. I agree with the idea that these math skills and concepts need to be taught not in isolation,
but as connected and useful parts of the students’ experiences. This seems to be the goal of the EIC
(Elementary Instructional Curriculum).
Sarah’s Thoughts, Part 3 – What Happened in the Classroom
I put the problem on the ELMO as I have done before, but this time I also used my own props to act
out the problem. I had a bag with shapes in it: a triangle, rectangle, and a hexagon. This really got the
children excited. Then we read the problem together. I gave them time to look at the real shapes that
were in my bag and to think about the clues given in the problem. I had the children each solve the
problem in their math journals, which we haven’t done before. Then, they discussed their solutions
with a partner and had to give support for their answer. We had time to come back together as a whole
group and discuss possible answers for the problem. I noticed that many students had good support
for their answers and were able to use the clues given to get their answers. In one case, there was
disagreement and one student directed the other student back to the clues to prove the answer. This
problem was a good one because it built upon what we focused on last week as we described the
attributes of shapes. In this problem, the students needed to know attributes of each shape to solve
the problem. I wonder if they can now generate their own clues for a given shape. We will try this in an
upcoming lesson.
Beverly’s Thoughts
I really like how you got the children so excited using the bag of shapes to get their thinking started. I
am impressed that a student redirected a friend who was having difficulty and the friend responded
positively. Your classroom environment must be very open to risk taking and the children seem to feel
very comfortable and excited about math. I will try the mystery bag for one of my upcoming problems.
I wonder how excited my students will get. It would be great if we could compile a list of the different
introductions being used by everyone so that we can keep the excitement going.
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
© 2011 Drexel University
<[email protected]>
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