Primary PoW Packet
Building a Tower
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Welcome
Welcome!
This packet contains a copy of the problem, the “answer check,” sample solutions and some teaching
suggestions. This is Library Problem #4547. 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 Building a Tower students are asked to find out how many blocks Ming added to Ali’s tower. If your
state has adopted the Common Core State Standards, this alignment might be helpful:
Grade K: Operations & Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking
apart and taking from.
Grade 1: Operations & Algebraic Thinking
Use addition and subtraction within 20 to solve word problems involving situations of adding to,
taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g.,
by using objects, drawings, and equations with a symbol for the unknown number to represent
the problem.
Grade 2: Operations & Algebraic Thinking
Represent and solve problems involving addition and subtraction.
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
Building a Tower
Ali built a tower with 3 blocks. Ming came along and put more blocks on.
Now there are 7 blocks in Ali's tower. How many did Ming put on?
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.
Ming put 4 blocks on Ali’s tower.
If your answer does not match ours, did you
• act it out?
• draw a picture?
• talk in your group?
If your answer does match ours, did you
• explain?
• write a number sentence?
• help anyone in your group?
Our Solutions
Method 1: Act It Out
We have blocks in our room. I was Ali and my friend was Ming. I counted 3 blocks and stacked them
to make a tower. My friend got some blocks and started putting them on the stack I made. We
counted as she put the blocks on until we got to 7 total blocks. Ming put 4 blocks on Ali’s tower of
blocks.
Method 2: Draw a Picture
We used chart paper with a grid on it. We let each square be one block. We colored three squares to
show Ali’s tower. Our picture looked like this:
We counted from 3 to see how many it would be to 7 and after 3 it was 4, 5, 6, 7. We colored in four
more squares.
We double checked to make sure Ali’s tower is 7 blocks tall now. It is and so Ming put 4 blocks to
make Ali’s tower higher.
Method 3: Use Manipulatives
I used snap cubes to think about what Ali’s tower of blocks.
3 blocks
We know we have to add snap cubes so that Ali’s tower of blocks ends up 7 blocks tall.
We counted as we added each block and saw that we needed 4 blocks on the tower to make it a total
of 7 blocks tall.
© 2011 Drexel University
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Method 4: Write a Number Sentence
Ali’s tower is 3 blocks tall. Ming adds some blocks. The tower is now 7 blocks tall. I can write the
number sentence:
3+?=7
3+4=7
Ming added 4 blocks.
Method 5: Use a Numberline
I used a numberline. I knew Ali’s tower was 3 blocks tall. I knew Ming added some blocks. I knew that
after she added her blocks Ali’s tower was 7 blocks tall.
I jumped from the 3 to the 7 and counted how many jumps I made. I jumped 4.
Ming added 4 blocks to Ali’s tower.
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:
Beverly’s Initial Thoughts
I plan on using "Building a Tower". This problem addresses the skill of addition. Since we have been
working on problems with a missing middle I thought this would be appropriate. I will use the strategy
of "I notice, I wonder" to help the students with understanding the problem and help them to begin to
take ownership through discussion. Manipulatives will be used (connecting cubes) to gain a visual
picture. We will move onto writing/illustrating the problem to check for understanding. I am
"wondering" due to the amount of time we spend solving problems from the PoW, that the students
will be able to show me different ways of solving this problem without hesitation. We will again discuss
our solutions and "notice" how each one student worked to solve the problem. I always ask "Does
anyone have a different way of solving the problem?" It is amazing how clever the little ones can be.
Beverly’s Thoughts after using the PoW with her students
Today I introduced the "Building a Tower" to my class of 28 students using the Elmo and the
wonderful Scenario sheet Suzanne made for my problem. Just to let you know, the students are pretty
familiar with PoWs since we do about 2-3 a week. First we did "I wonder" and some of the responses
were
What color are the blocks?
What size are the blocks?
Do they connect?
Then we did "I notice" and responses included
They are girls.
I think Ming will have more blocks.
The problem has a missing middle.
After the initial discussion the students were each given a copy of the problem and math discourse
took place in pairs. Then more brainstorming took place in groups of 4. We shared out answers after
asking, “Does anyone have a different way of solving the problem?”
We do this a lot and the students enjoy hearing other solutions as well as feeling proud to share their
own. The students recorded their first solution in their math journals and again we shared in groups to
reflect and revise. When I first started using PoWs the process took about 30 minutes. As I have
continued to use PoWs with the students the process has become more efficient and quicker (15-20
© 2011 Drexel University
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minutes). I will continue to use PoWs during my math block. I have noticed how comfortable the
students are to try the problems and to use math vocabulary. They have become risk takers without
worrying about failure. Everyone gets to voice their thoughts/solutions while working in either pairs,
groups, or whole class. Everyone is involved and proud to share. I wonder if the children will continue
to stay involved and excited as the year goes on.
Jennifer’s Initial Thoughts
This week I chose the problem, Building a Tower #4547. I wanted to see how the students would do
with process of problem solving on combining/separating sets. This is was somewhat of a pre-test as
this has not been covered yet in the EIC. Computation, however, is something that I was wondering
about from the last session. This problem does connect to the geometry unit that we have working on
as the students are combining blocks to build a tower. I felt that the use of manipulative would also be
a resource for the students. Who knew so much decision making went in to choosing a problem?
I introduced the problem using the ELMO to make sure the problem was understood and vocabulary
was defined. Students immediately entered into a whole class brainstorming of how to solve the
problem. Students then worked with their math partner to develop their approach to the problem. Each
group chose the option to use manipulatives. The partners then joined to make groups of four. I
started to facilitate the discussions, but found that the students were questioning and giving each
other feedback. WOW! After working in small groups, each student was asked to show their response
using pictures and/or numbers. We then used the ELMO again to showcase student responses.
Almost all students were able to determine the answer of 4. Student drawings did represent the
solution for the most part. Only a handful of students were able to write a number sentence to match.
We had a fabulous discussion. I think that using the PoW process to see what students already know
worked great. It was a wonderful introduction into the concept of combining sets as well. I wonder how
using the process in kindergarten will promote math discussions in future years.
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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