Tomorrow I go into a 1st grade classroom to teach a lesson on addition and subtraction story problems. This Investigations lesson for the day centers on students solving these 6 problems, however I am looking to change it up a bit.

While reading my CGI book, Children’s Mathematics, to learn more about the trajectory in which students solve these types of problems, I found this diagram really helpful and interesting….

I went into this planning thinking I was going to be looking for how students combined numbers in the context of the diagram above. From there, I was planning to have students do a structured share of their strategies, comparing and contrasting along the way. However, as I got ideas from Jamie (@JamieDunc3) on Twitter, I started to think how much more I would learn about their thinking in talking about their noticings, wonderings, and number choices. My goal has now changed to looking at not only their strategies for combining but how they choose numbers in which they will have to combine.

So…I took the second question, removed the actual question and made it a notice/wonder:

Assuming the wonder of how many students were on the bus arose, I would see how students combined the numbers. Would they look for friendly combinations? Would they count all? Model it? Count on? or any combination of those?

Then, I thought I could keep the 13 and leave the other two numbers blank to see what numbers they chose.

Did they pick a combination that was easy to add to 13, like 5 and 5? or would they keep adding onto the 13? how would they add with the 13, would they choose 7 to make 20 and then another 1 digit number? would they choose all 2-digit numbers to challenge themselves?

But then, I thought what could happen if I took all three numbers out?

For some reason, without the numbers it seems more “wordy” to me. I don’t know why that is? So THEN, I went to this last option….

I really love this one, although, I must admit, I feel a bit out of control of the course of the lesson in choosing this one over the others. But, I think that is what makes it such a beautiful choice. After taking noticings and wonderings, I am thinking of having the students work in pairs to create their own story and solution for one of the wonderings.

In creating their stories, I am concerned that students will choose numbers such as 0 at two stops and 1 at the third and I won’t be able to get a picture of how they combine numbers, however I will have a possible picture of their number comfort level. If they do this and finish quickly, I will be ready with the second choice above to see how they deal with now having the 13 in the problem.

In their journals I will ask them to tell me why they chose the numbers they did for the problem.

I am still thinking about this, so please feel free to leave suggestions and comments! Thanks to Simon, Fran, Graham, and Bryan for their thoughts on Twitter, always appreciated!

~Kristin

howardat58Just as an experiment you could try some of the kids with your questions as written, and others with normal sentences, such as “There were some children on the bus, and at the next stop 13 more children got on. At the last stop some more children got on.”

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mathmindsblogPost authorI was thinking that too Howard! There are also 4 other 1st grade classrooms we could try each version out in next week!

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Simon GreggI like Howard’s idea. To have a real comparison would help us think about it lots, and we don’t often get a Groundhog Day to try things a different way and see if they’re better. Not in the same year anyway!

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Jamie DuncanI want to try this now! I would use the very last one first as a launch point and to start discussion. I think there is a lot of reasoning that could come out in this. Kids can estimate. What’s the fewest amount of students that could be on the bus? How do you know? What about the most? Why do you think that? How about a just right estimate?

Then, show the one with three blanks. I would put the word “some” where the blank lines are. Notice wonder

The rest I think depends on the goal. What are you trying to capture, you know?

Lately, I am always looking for kids to make tens. Would they add the 4+6, would they decompose the 13 to 10+3, then add 10+10 = 20 , then 20+3=23. Would they change 4+6 to 5+5? So many possibilities. In Student Centered Mathematics, Van de Walle says the making tens strategy is the most important addition strategy.

Maybe the sequel task for early finishers could be to create their own problem and then trade and solve with a partner???

Dang, I wish I wasn’t teaching time right now. I want to do this tomorrow instead!

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mathmindsblogPost authorI love this and so want to peer pressure you into doing it tomorrow too!! heehee! We could do connecting blog reflections….just sayin’ 😉

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Jamie DuncanWhat the heck, it’s the last day before break and I hate time. It’s on!

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mathmindsblogPost authorYes!!!!

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Ann Elise RecordI love following your thinking on this, but I just had a question for you. Are your first graders able to add 2-digit numbers like this right now? Does your district have full-day kindergarten? Our district just began all-day K this year and our first graders are nowhere near this. As Math Specialist K-5 I’m trying to figure out what number range would be appropriate for 1st graders at this time of year. I can’t wait to hear what your students do with this! As always, I appreciate you sharing!

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mathmindsblogPost authorHi Ann! Thank you so much for reading! Yes, we have all day K and yes they are adding two digit numbers with multiples of 10 right now. I just moved into the specialist position so I am kearning sooo much this year too!! I think you will see a huge difference after moving to full day K!

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Paula Beardell KriegI love how you kept paring down the question! It seems like your goal is to provide more room for the students to be directly involved with the numbers, and what you’ve done is given them ample room to be the creator of their numbers. In comparison, the original question seems so boxed in and dry. It’s like you’ve given them permission to be both powerful and playful with addition. I’m looking forward to hearing how it goes.

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Berounsky, BrendaI really like that it is scaled down so much. It leaves it completely open to all sorts of possibilities for the students and for the instructors. It is far better than the original problem.

You could have a discussion about how it couldn’t be zero because the statement says the bus picked up students at three stops along the way.

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JulieHi Kristin! I really enjoyed reading your post. It was like being part of your thinking and how you converted a more traditionnal problem to an open one to give the kids more liberty to think and to show you where they are in their number sense. I really enjoy doing open questions with kids…they amaze me and the creativity really pops out. Every kid has a fair chance to succeed. For your thoughts on the “0” kid getting on the bus this would make it an interesting conversation for the 0 property and to bring the kids to what they notice. Another idea, it would be interesting to have one stop where the bus drops off kids and to bring in the noticing if there are as much kids that come up at one stop and the same amount goes out the bus what happens to the other number? These 2 ideas could bring a little algebra into this problem 😉 Very excited to see what you experienced !

julie 😉

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Lauren GiordanoThank you Kristin, Jamie and Brian Bushart for inspiring me to take the plunge on a numberless word problem. Your blogs gave me such insight into the how and why that I felt comfortable giving it a try this morning when I had a last second opportunity to teach a Grade 2 subtraction word problem lesson. Students shared that they most enjoyed being able to choose “just right” numbers for themselves (I love the literacy connection). They said that the most challenging part was selecting numbers that “made sense” in the context of the problem. I loved that for some students, this was very important to them. This gives insight into their depth of understanding of the problem (background knowledge) as well as their number sense and estimation skills. My biggest regret is not having enough time for students to share and hear each other’s reasons for the numbers they selected, the models they used, and their computational strategies. However, I was able to connect with many students individually and their worksheets shed light on their strategies. I feel a huge sense of success in witnessing so many Standards for Mathematical Practice at play in this one short 30 minute lesson and in seeing so much engagement and interest on the part of the students. So much potential here. Thank you again. (FYI – the context for the problem was a late night crowded “T” after a game at Fenway. This resolved the issue of people getting on at the stops.) I’ll post some pictures via Twitter.

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