Last week I had a 3rd grade teacher email me and ask if I could help her out because she was frustrated. She had been teaching lessons all week on:
OA.3 Students can solve multiplication/division word problems within 100 involving equal groups, arrays, and measurement quantities.
OA.8 Students can use any of the four operations to solve two-step word problems. Students can use mental math, estimation, and rounding to decide if their answer makes sense.
The results that she was seeing were disappointing and she asked if I could come down and take a look. She showed me their work and I saw the following:
- Some students were answering only part of the problem.
- Some were not checking to see if the solution they got actually answered the question. (making sense of the answer)
- Some were using the wrong operation, not understanding what they were trying to find, while others were just getting lost along the way.
- Many didn’t understand what they were being asked to do and just “played” with the numbers in the word problem.
- Some students seemed to just quit (SMP #1: perseverance!!!)
I went back to my office at the end of that day and sat down to think about it. I started by trying to create some fun word problems, or find some in the Exemplars Library, that went along with the standards. After I found/created one, I would try and look at it through the students’ eyes, and I would realize that the same issues would arise no matter which one I chose. I then remembered playing around with a group of 5th graders a few weeks back while they were learning about organizing fractional data on line plots. I had given them a paper bag with tiles in it. The tiles had fractions written on them such a 2/8 and 3/4. The students had to randomly pick a tile, record it, and place it back into the bag. I had them pick 20 times and then we had a discussion as to what they observed and how best to organize the data. I was amazed at the questions that they were asking each other about the line plots they created.
I sat back in my chair and thought, what if I could replicate this idea with these 3rd graders. How could I give them the data, let them mull it over, and then lead them to the questions that I want answered?
I began to realize that I was thinking along the same line as Dan Meyer, who created the concept of the 3 Act Task! (if you haven’t seen this or taught one, I STRONGLY suggest that you do!)
What if I could follow Dan’s lead and give them just the information and then make them design the questions that they want to answer?
The first thing I did was to go back into that Exemplars website and find some questions that the students could relate to. Once I did that, I would delete the questions and have the students read the word problem as though it was just a story. I was getting pretty excited and I couldn’t wait for Friday’s class with this teacher!
I gave them this one first:
I asked the class to read the story I “made up” and place their thumbs on their chest when they were finished. I began to smirk as I heard the students begin to grumble and whisper to each other. I asked, “What’s wrong? Don’t you like my story?”.
“It’s not that Mr. D, it’s just that there isn’t a question!” one young man said.
Gotcha! I thought to myself…I then asked the class to discuss with an elbow partner any questions that they think they could answer based on my story. As you can see, the two questions in blue are what they all decided they could answer based on the information in my story. As they discussed the questions, they began to formulate ideas on how to get the solutions. My favorite part of this was that last sentence on the board. I ended up typing that based on what one students said to me.
“Mr. D, it doesn’t say that they each caught three fish. That is just the limit. What if one quarter of them caught 1 fish, another quarter caught 2 fish and the rest caught the limit?”
WOW!!!!!! He extended the problem without being asked to. When he presented this idea to the class there was a chorus of “he’s right!” and a whole bunch of “what if’s”. I had to stop them to move on….right after we answered his question. Can you?
My next story was the following:
This time, the directions were: Find a partner and a place to sit. Then decide what questions you’d like to answer based on the story, being sure to write them down. Allow me or your teacher to review them and then you can work them out using any strategy you’d like.
Here are a few:
Many students did exactly what this student and her partner decided upon…
Other students had the same questions, but chose a different strategy…
Some wanted to use some manipulative to “check” to see if their solutions were correct…how do you think they used these?
The teacher couldn’t believe what she was seeing! She was watching her students look for and locate information within a word problem, create their own questions, apply their knowledge, and even extend their thinking! Many were making sure that their solutions actually made sense! Some wrote that the girl took $4.50 to the bank because 100 pennies is equal to $1! I was in heaven and having so much fun!
What they did here blew me away….some students came up with 7 questions! 4 more than what I actually anticipated….
Here are three of my favorites:
This young man figured out that 1/2 of the cookies were missing…
This young lady decided that since the story never said that we would share them equally…(decomposition of the answer!)
…and this last one caused a whole class discussion!
I told them that she shared with 2 friends because I was curious to see what they’d do with the left over cookies. As you can see, they didn’t disappoint!
My Take Aways:
- Students, when given the opportunities, never cease to amaze me
- Dan Meyer discovered something very powerful
- Allowing students make connections with word problems creates problem solvers
- How can we adapt this to help the students on their tests?
- Every group came up with the same basic questions before extending their thinking. Why did that happen?
- This class already has a very good conceptual understanding of fractions. This is excellent data for the teacher.
- Many students could see the division of 450 by 9 by using either multiples of 10, seeing 45 divided by 9, or by sectioning out the 400 into 2 parts of 50 per 100.
- When presented with information, these students wanted to see the mathematical implications of it.
- This lesson allowed the students to demonstrate SMP#1, #3, #4, #6 and #7, which I didn’t quite plan on…
What are your “take aways”?
Please feel free to comment and respond, for I would love to hear your thoughts!