Category Archives: 1st Grade

Mathematizing Learning Lab

Each month, teachers choose their Learning Lab content focus for our work together. Most months, 1/2 of the grade level teachers choose to have a Math Learning Lab while the other 1/2 work with Erin, the reading specialist in an ELA Learning Lab. This month, however, we decided to mesh our ELA and Math Labs to do some mathematizing around children’s literature in Kindergarten and 1st grade! This idea was inspired by a session at NCTM last year, led by Allison Hintz, that left me thinking more about how we use read-alouds in our classrooms and the lenses by which students listen as we read.

In The Reading Teacher, Hintz and Smith describe mathematizing as, “…a process of inquiring about, organizing, and constructing meaning with a mathematical lens (Fosnot & Dolk, 2001). By mathematizing books commonly available in classroom collections and reading them aloud, teachers provide students with opportunities to explore ideas, discuss mathematical concepts, and make connections to their own lives.” Hintz, A. & Smith, T. (2013). Mathematizing Read Alouds in Three Easy Steps. The Reading Teacher, 67(2), 103-108.

Erin and I have literally been talking about this idea all year long based on Allison’s work. We discussed the ways we typically see read-alouds used, such as having a focus on a particular text structure or as a counting book in math.

As Erin was reading Kylene Beers & Robert Probst’s book, Reading Nonfiction she pointed me to a piece of the book on disciplinary literacy which automatically had me thinking about mathematizing.

Beers refers to McConachie’s book Content Matters (2010), in which she defines disciplinary literacy as, “the use of reading, reasoning, investigating, speaking, and writing required to learn and form complex content knowledge appropriate to a particular discipline.” (p.15) She continues to say, “…disciplinary literacy “emphasizes the unique tools that experts in a discipline use to engage in that discipline” (Shanahan and Shanahan 2012, p.8).

As I read this section of the book, my question became this…(almost rhetorical for me at this point)

Does a student’s lens by which they listen and/or read differ based on the content area class they are sitting in? 

For example, when reading or listening to a story in Language Arts class, do students hear or look for the mathematical ideas that may emerge based on the storyline of the book or illustrations on the page? or Do students think about a storyline of a problem in math class or are they simply reading through the lens of “how am I solving this?” because they are sitting in math class?

Mathematizing gets at just this. To think about this more together, Erin and I decided to jump right into the children’s book  The Doorbell Rang by Pat Hutchins. Erin talked about the ideas she had for using this in an ELA class, I talking through the mathematical ideas that could emerge in math class, and then we began planning for our K/1 Learning Lab where we wanted teachers to think more about this idea with us! We were so fortunate to have the opportunity to chat through some of our thoughts and questions with Allison the day before we were meeting with the teachers. (She is just so wonderful;)

The first part of our Learning Lab rolled out like this…

We opened with this talking point on the board:

“When you change the way you look at things, the things you look at change.” 

Everyone had a couple of minutes to think about whether they agreed, disagreed, or were unsure about the statement. As with all Talking Points activities, each teacher shared as the rest of us simply listened without commenting. The range of thoughts on this was so interesting. Some teachers based it on a particular content focus, some on personal connections, while I thought there is a slight difference between the words “look” and “see.”

After the Talking Point, Erin read The Doorbell Rang to the teachers and we asked them to discuss what the story was about with a partner. This was something Allison brought up that Erin and I had not thought about in our planning. I don’t remember her exact wording here, but the loose translation was, “Read for enjoyment. We want students to read for the simple joy of reading.” While Erin and I were so focused on the activity of exploring the text through a Math or ELA lens, we realized that the teachers first just needed to enjoy the story without a purpose.

For the second reading of the book, we gave each partner a specific lens. This time, one person was listening with an ELA lens while, the other, a Math lens. We asked them to jot down notes about what ideas could emerge through these lenses with their classes. You may want to go back and watch the video again to try this out for yourself before reading ahead!

Here are some of their responses:

Together we shared these ideas and discussed how the ELA and Math lenses impacted one another. A question we asked, inspired by Allison, was “Could a student attend to the math ideas without having a deep understanding of the story?”

Many questions came up:

  • Could we focus on text structures and the math in the same lesson?
  • Could we start with an activity before reading the book, like a probable passage?
  • Would an open notice/wonder after the first reading allow the lens to emerge from the students? Do they then choose their own focus or do we focus on one?
  • How could focusing on the problem and solution get at both the ELA and Math in the book?
  • How could we use the pictures to think about other problems that arise in the book?
  • How do we work the materials part of it? Do manipulatives and white boards work for K/1 while a story is being read or is it too much distraction?
  • What follow-up activities, maybe writing, could we think about after the book is read?

Unfortunately, our time together ended there. On Tuesday, we meet again and the teachers are going to bring some new books for us to plan a lesson around! So excited!

Formative Assessment

Assessment always seems to be such a broad, hot topic  There are rubrics to help create assessments, rubrics for reviewing assessments, and tons of reading about the benefit of assessments. While I agree assessment is an important topic of conversation and all of these things can be helpful, I just lose a bit of interest when it becomes so cumbersome. I feel the longer the rubric and steps to create an assessment, the more detached the assessment becomes from student thinking.  This could be completely be my short attention span speaking, however the way assessment is discussed feels either like data (a grade or number-type of data) or a huge process with tons of text in rubrics that I really, quite honestly, don’t feel like reading. Not to mention, I just love looking at student writing and listening to student thinking when planning my immediate next steps (formative) or checking in to see what students have learned over a longer period (summative). This is why I find the work we are doing each month in our Learning Labs such a wonderful way to think about formative assessment in an actual classroom context, in real time.

This passage from NCTM’s Principles to Action really captures how I feel about the work we are doing in our Learning Labs:

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In this most recent Learning Lab in 3rd grade, we planned the activity together using the 5 Practices model and reflected after the lesson. Since this blog is always my thoughts about student work, I thought it would be great to hear what the teachers took away from the activities we are doing in terms of the students’ understandings and impact on their future planning, formative assessment.  

The teacher mentioned in the blog said, I was surprised by how quick many of the students defended their responses that 1/2 will always be greater than 1/3, and then proving this response using visual representation of the same whole ( which is an idea that we have made explicit). I was impressed with “skeptics” in the crowd that were looking to deepen their understanding around the concept by asking those “What if” questions.  Going forward, I want to create opportunities that push and challenge my student’s thinking. I want them to continue to question and explore math – especially when it uses the word “always.”

Another teacher who taught the same activity after watching it in action in another classroom said, “I learned that almost half of my students assumed they were comparing the same size wholes.  They agreed with the statement, and each student gave at least two different ways to prove their thinking (area and number line model were most common).  The students that disagreed almost all provided their own context to the problem, such as an example with small vs large pizzas, or a 2 different-length races being run.  I found it so interesting that almost all students confidently chose one side or the other, and were able to defend their thinking with examples (and more than one-yeah!)  I was excited to see that they could be so flexible in their arguments as to why they felt as they did.  Three students responded that they were unsure, and gave reasons to support both sides of the argument. This impacted my instruction by giving me such valuable formative assessment information with a simple, non-threatening prompt.  It took about 5 minutes, and gave me tons of information.  It was accessible and appropriate for all.  Students were comfortable agreeing or disagreeing, and in some cases, saying “unsure-and here is why.”  I was most excited about that!”

She also said, From this activity, I learned that I really needed to revisit the third grade standard to see what is actually expected.  It says they should recognize that comparisons are valid only when the two fractions refer to the same whole.  My statement didn’t have a context, so how cool that some were at least questioning this!   This impacted my planning and instruction by reminding me how thinking/wondering about adding a context to the statement would influence their responses.  I am also reminded that I need to stress that students must consider the whole in order to make comparisons accurately.”

Earlier in their fraction unit, the third grade teachers used the talking point below to hear how her students were talking about fractions. (This work is actually from another teacher’s class, but you get the idea;)

A teacher who did this activity reflected, “From this activity, I learned my students had only ever been exposed to a fraction as a part of a whole (and wanted to strictly refer to fractions in terms of pizza). This impacted my instruction by being sure to have the discussion that fractions can represent parts of a whole, but we can also represent whole numbers with fractions.”

To me, these reflections are what assessment should be….the teachers learn about student thinking, the students think about their own thinking, and what we learn helps us plan future lessons with our students’ understandings in mind!

More examples from different grade levels where the teachers and I learned so much about student thinking that impacted future instruction:

Kindergarten: Adding

Kindergarten: Counting

1st Grade: Fractions and Adding

2nd Grade: Counting and Leftovers

4th Grade: Division

5th Grade: Fraction Number Line

1st Graders Talking and Using Half

Yesterday, I had the chance to teach a 1st grade math class. The teacher told me they are about to start their fraction lessons so I thought it would be fun to do a quick check in on what they currently think about half and then do a numberless story problem to see if they incorporated anything about half in that work.

I launched with “Tell me everything you know about half.”

One student started by telling me it is like half a piece of pizza, so I asked what that looked like to her and she said it was the whole thing (big circle with hand) and then cut in half (hand straight down vertically). That springboarded into half of lots of things, cookies, strawberries…and many other things. Each time I asked if each half was the same in the different things and they said no, they were different sizes. So, I asked what was the same and someone said they were all cut in the middle. I got some cool sports references, I asked when halftime happened and they said in the middle of the game. Then one girl said “5 is half of 10.” Awesome. I asked how she knew that and she said, “because 5+5=10.” Hands shot up everywhere after that with other numbers and their halves.

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Then I posed the following story on the board and read it to the class:

There was a pile of blocks on the table. Jimmy came into the room and took some of the blocks. He gave the rest of the blocks to his friend Kali. 

We did a notice/wonder and they wondered the things I had hoped: How many blocks were there? How many did Jimmy take? How many did Kali get? It was really cool that one student noticed there were none left on the table because Kali got “the rest.” I didn’t expect that one!

I let the partners choose their own numbers and as they got their answers, I asked if they could write an equation for their work. My plan for the group share was to have groups share, some who split the blocks in half, others who did not. My backup plan, because I never know what could happen, was to compare addition and subtraction equations for the same story to see if they noticed a relationship. I ended up with enough half/not-half that I went with that!

Here were some of the groups who split the blocks in half. The number choices were really interesting. I would love to put all of them up there for the class to talk about…why did they choose numbers that end in zero? What do we know about those numbers?

Some did not choose a number they could easily split in half. The group on the right noticed the commutative property right away and drew lines to show the same numbers in their equations.

Some really wanted to write as many equations as they could that didn’t necessarily match what was happening in the story but was great mathematical reasoning in their work!

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I cannot wait to see what this group does in their fraction unit, so many great thoughts and work about half!

Counting Collections Extension

Today in 1st grade, we did a counting collections activity. One thing I am thinking about as I see this activity happening in K-2 classrooms, is the extension. While choosing questions for students who are struggling is difficult, choosing questions for those who are finished quickly, and correctly, I find just as difficult. What questions can we ask those students who organize, count and can explain their count perfectly?

I have been toying around with this idea for a bit. I have thought about asking them to combine collections, ask how many more they would need to get to another number or mentally adding tens and hundreds to their count.

Today, I tried asking a student how many more to get to another number. It was pretty cool and led to some more ideas. He and his partner ended with 292. I asked how many more to get to 300? 8. 350? 58. He could explain using the 8 to get to 300 and how to move forward from there. Because of other groups I wanted to chat with, I left him with 500, 652, 1,000, and 1,250. He came back with the answers, but no explanation and said, “I don’t feel like writing all of that out.” I asked him to explain how he got to 500 and I would record the equation for it. He said he added 8 to get to 300 and then 200 more to get to 500, so 208. He was shocked to see it as an equation because he thought I meant to explain it all out in words. I asked him to try the next one and he started with adding 10. He said he wanted to keep the 2 ones to make it easier, awesome. When he said that, I had another idea to have students think about what place values are changing as they add to a certain number. I want to ask him why he ended with 8 ones on three of them but zero ones in another?

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I know I have seen tons of people on Twitter using counting collections and would love to hear of other ways we could extend this activity in the comments!

Obsessed With Counting Collections

If you have seen my recent Twitter feed and blog posts, you can probably tell I am currently obsessed with Counting Collections! Because of this obsession, during our recent K-2 Learning Lab I made it the focus of our conversation. This was our first chance to talk across grade levels during a Lab and to hear the variation in ways we could incorporate counting in each was so interesting! Based on this lab, yesterday, I had the chance to participate in both a 2nd grade and Kindergarten counting collection activity and while there were so many similarities, I left each thinking about two very different ideas!

2nd Grade: Naming A Leftover

Based on our Learning Lab discussions three 2nd grade teachers had the amazing idea to combine their classes for a counting activity. While it was a great way to give students the opportunity to work with students from other classrooms, it also offered the teachers a chance to observe and talk to one another about what they were seeing while the activity was in progress. I was so excited when they sent me their idea and invitation to join in on the fun! I have never seen so much math in an elementary gymnasium before!

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There was a lot of the anticipated counting by 2’s, 5’s, 10’s and a bit of sorting:

And while this is so interesting to see students begin to combine their groups to make it easier to count in the end, there were three groups counting base 10 rods that particularly caught my attention:

1st Group (who I missed taking a picture of): Counted each rod as 1 and put them in groups of 10.

2nd Group: Counted each rod as 10 because of the 10 cube markings, making the small cube equal to 1. They had a nice mix of 20’s in their containers!

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3rd Group: Counted each rod as 10 but had a mix of rods, small cubes and some larger blocks. It was so neat to see them adjust the way they counted based on size…the rod=10, small cube=1 and the large block=5 (because they said it looked like it would be half a rod if they broke it up). After this beginning picture, they arranged the 10 rods to make groups of 100.

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The second and third group ended up with a final count and recorded their thinking, however group 1 could not wrap it up so neatly. When they finished counting they had 141 rods but one small cube left over. Since they were counting each rod as 1, instead of 10, they were left trying to figure out how to name that leftover part. When I asked the group what they were thinking, one boy said, “It is kind of like half but smaller.” I asked him how many he would need for half of the rod and he examined the rod and said 5. I have to admit, I wasn’t sure where to go with this knowing their exposure to fractions is limited to half and fourths at this point. So, I asked him, “How much we do have of one rod” and he said 1.  I followed with, “Of how many?” and he answered, “Ten. So we have 141 and 1 out of 10?” Thankfully it was approaching time to clean up so I could think more about this one. I feel like I left that idea hanging out there and would love to bring it back to the whole class to think about, but I am still wondering, what question would have been good there? How would you structure this share out so this idea of how we name 1 is important and impacts our count? How do we name this leftover piece and why didn’t a group counting the same thing not have that problem? Also, I think it will important for these students to think about the question they could ask that their count would answer…For example, how many objects do you have – would that be accurate for the group who counted each rod as 10?

Kindergarten: Why Ten Frames?

Every time I am in Kindergarten I leave with so many things to think about! In this case I left the activity thinking about Ten Frames. I am a huge fan of ten frames, so this is not about do we use them or do we not, but more about….Why do we use them? How do we use them? What is their purpose? What understandings come from their use? What misunderstandings or misconceptions can be derived from their use? and Where do these misunderstanding rear their ugly head later?

To start the lesson, groups of students were given a set to count. With a table of tools available to help them organize their count, ten frames were by far the most popular choice. However, not having enough (purposefully) for everyone’s set pushed them to think of other means… which ended up looking like they were on a ten frame as well!

As the teachers and I went around and chatted with groups, we heard and saw students successfully counting by 10’s (on the frames or look-alike frames) and then ones. This is what we hope happens as students work with the ten frames, right? They see that group of 10 made up of 10 ones and then can unitize that to 1 group. It reminds me of Cathy Fosnot’s comment via Marilyn Burns on Joe’s post, which I had huge reflection on after this lesson too!

I was feeling great about the use of ten frames until a first grade teacher and I were listening to one group count their set. I wish I snagged a pic, but I was so stuck trying to figure out what to ask the girls, that I didn’t even think about it. They had arranged 4o counters on 4 ten frames and had one left over, sitting on the table, no ten frame. We asked how she counted and she said, 10, 20, 30, 40, 50…the 1 leftover was counted as a 10. I immediately thought of Joe’s post. Not knowing exactly what to do next, I tried out some things…

  • I picked up the one and asked her how many this was, “One” and then pointed and asked how much was on the ten frame, “Ten.” Ok, so can you count for me one more time? Same response.
  • I filled an extra ten frame pushed it next to her 4 other full ones and asked her to count: 10, 20, 30, 40, 50. I removed 9, saying “I am going to take some off now,” leaving the one on the ten frame and asked her to count again. Same response.
  • I asked her to count by 1’s and she arrived at 41. So I asked if it could be 41 and 50 at the same time. She was thinking about it for a minute but stuck with “that is what I got when I counted.”
  • Then I became curious if she had a reason for using the ten frame, I asked. She said it was to put her things on so I began wondering about the usefulness of the 10 frames for her. Was is something, as an object, that represents 10 to her but not able to think about the 10 things that make it up?

I left that class thinking about how complex unitizing is. We hope students are able to count 10 things, know those 10 things are still there even when we start calling a unit, 1 ten, and then combine those units but still know there are 10 in each one of them. WOW, that is a lot! However, they can easily appear successful in counting by 10’s, which is one of the many reasons Counting Collections are so powerful. They bring to light the misunderstandings or missing pieces in students’ thinking.

I then start to think of recent conversations I have had with 4th grade teachers about students who are struggling with multiplying a number by multiples of ten and wonder if this is where we can “catch” those misunderstandings and confusions before they compound?

What to do next with this class? Erin, the teacher, and I quickly discussed this as she was busy transitioning between classes. We were thinking about displaying an amount, lets say 23, with two full ten frames with 3 extra. Say to the class, “Here are two sets, do they look the same? How can  you tell? Two groups counted this amount two different ways.  One group counted it 10, 20, 21, 22, 23 and the other group counted it 10, 20, 30, 40, 50. Can it be both? If so, how? If not, which one is it?”

Would love any other thoughts. I am heading back to re-read all of the comments on Joe’s post to gain more insight, but I would love your thoughts too!

 

1st Grade: 1st Day of Subtraction

 

This week, I planned and taught with Kala in her her 1st Grade classroom! It was the students first day of subtraction in the official “take away context type of work”sense, so it was really exciting to see what they would do with it. During our planning, Kala discussed ways in which she anticipated students would solve the problems and we thought about the framework below that is also presented in the Investigation’s Teacher Notes for that unit.

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Since it was their first day with subtraction, we wanted to be sure to capture their strategies as clearly as possible to help in planning future lessons. To do this, we designed a quick table with the following headings that we planned on jotting notes about the students’ work on as the lesson progressed.Screen Shot 2015-12-05 at 12.46.32 PM.png

The lesson was supposed to open with giving students the following problem:

Max had 9 toy cars. His friend Rosa came over to play with him. Max gave 3 of the cars to Rosa to play with. How many cars did Max have then?

We decided to make this a Notice/Wonder to really allow students to think about what is happening in the context, over focusing on the numbers. So, instead, Kala posed this (we changed the names from above on accident):

David had some toy cars. One day his friend Max came over to play with him and David gave Max some of his cars.

Right away, they began to exclaim, “That was a short story!” As they shared, Kala recorded their noticings and wonderings. The very first notice was about not knowing how many David gave to Max because it said “some.” On the very last notice, the words subtract and minus came out. She couldn’t quite pronounce subtraction so she went with “minus” for her notice. She said David was a minus because he gave some, but Max was a plus because he got some. I loved that way of thinking and had not expected that at all! We then said we were going to answer some of their wonders….David had 9 and he gave Max 3. Then, like a Number Talk, they gave a thumbs up when they had an answer and we shared as a class. Kala and I just continually asked, how did you decide on the 9? Why did you do that with the 3? Where was that in the story? We decided not to write these strategies down because we didn’t want to influence their work during Roll and Record. We wanted to see where they were in their own thinking.

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I then put up the game board for Roll and Record and we talked about how this was the same and different than the Roll and Record they have been playing with addition. They did notice that this board started at 1 instead of 2 and ended at 11 instead of 12. This will be something I would love to have them thinking about more in later lessons…why is this board this way? We played a few practice rounds of rolling a number cube, taking away the number we rolled on the second die, sharing how we subtracted the two numbers and recording it on our sheet.

They then went back to their seats and played with a partner. They had cubes, number lines, and 100 boards available if they chose to use them. These are a few pics I could snap before the game boards were erased.

 

As they played, Kala and I both walked around with our sheets and recorded the strategies we saw happening around the room. I was really amazed at the thinking in so many ways! I could tell they were comfortable using a variety of tools and by the way they could explain their thinking, it was obvious they were very used to doing that as well. This was my completed sheet at the end of the period. There were a couple of students I missed and a couple were absent, but between Kala and I, we had a really great picture of where the students were in their thinking. I was really surprised I only saw a few directly modeling the subtraction. The arrows were from me just starting to write their thinking and forgetting to put it in the appropriate column!

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After they finished playing, we decided to give them the original problem context with two different numbers (8 and 5) to see if they could create a written response of how they solved the problem as well as they were able to verbally explain to us. We did this because Kala had mentioned during our planning that she often sees them resort to drawing and crossing out when asked to show their work even when she knows the student has a different strategy in mind. I completely felt that same thing in 5th grade as well!

They did not disappoint in their journals! I am wondering if, in us walking around and asking them to verbalize their thinking, it helped them have a clearer picture of what they did? Just a hunch. We also asked them to “show your thinking” instead of “show your work” because we think that has something to do with the direct modeling at times too.

Here was the direct model…

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We had some interesting counting backs. Some counted back dots, like the die. When doing this some put numbers next to the dots while others just used them as dots to count back on. I was so excited to see a student who had counted back on his fingers write out the process. He even wrote the number he started with and ended at the correct number. <- sometimes I see them count that 8 as part of the counting back process and end at 6.

We had a great variety of tools and models, whether used for direct modeling (like the ten frame and tallies) or used for counting back on the number line. The bottom papers were partners so it was interesting to see them do a jump of +3 versus -3. Just as class was wrapping up they were talking about where their answers were because the partner who subtracted 3, said it looked like her partner’s answer was 8 because he added three and landed at 8. Interesting convo to have later too! Their journals also made us realize that we didn’t use the word difference in a way that students knew the answer was called the difference and not sum (yeah, they know sum though:)! Something for us to think more about next time!

Then we saw some great related facts, like this one. I am assuming the number line above also was thinking this but put it on the number line instead of writing the fact. That is another interesting convo to have in future classes!

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This student used a known fact to get the answer and could not have explained it more clearly. I asked her to explain to me what she did and she said, “I knew 8-4=4, if I take one away from the 4 it makes it a 3 and the answer changed to 5.” Wow. Conjectures and claims here we come!

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What a great day! From here, the students do “Start With/Get To” cards as their Ten Minute math that will help emerge subtraction as distance as well as reinforce the relationship between addition and subtraction. They will also play Five in a Row which will allow ideas such as 7-5=6-4 emerge when looking at expressions with the same difference. Of course, many context problems follow from here too so it is going to be so fun to watch what they do with this work!

~Kristin

 

1st Grade Notice/Wonder

Yesterday, I had the chance to teach the 1st grade lesson I planned here. It was so much fun and SUCH a learning experience for me! After all of the conversation in the comments and on Twitter, I decided to start with the open, one sentence Notice/Wonder. Only having 45 minutes and this being the students first time doing a N/W, I decided not to begin with a number talk/routine (which I usually always do).

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The students started on the carpet, I put up the sentence, read it and asked, “What do you notice and wonder about this sentence?” Just then a student exclaims that he just noticed that “Notice” was not, “Not Ice.” At that moment, I began thinking maybe my question had them looking at the physical pieces of the sentence/words so I quickly rephrased, “I would love to hear what you notice and wonder about what is happening in the sentence.” They used their Number Talk signals, thumbs up when they had a notice or wonder and then used their fingers to indicate more than one. I was so impressed by all of their thoughts, but I did realize that is it hard to end their wonderings! The amazing thing was how all of their wonderings really could turn this sentence into a story in their ELA class because they were all really important details they could add to it. Here was how the board ended.

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I asked which wonder we could work on together today in class and there was a unanimous vote for “How many kids are on the bus?” however there were a few that suggested, “How many student can the bus hold?” because “math is counting things and we could count the seats.” I starred the  wonder “How many kids are on the bus?” and told them next time they get on their bus I would love to hear how many seats and students they found are there. We discussed whether they know how many students were on the bus by reading our sentence and they said no, they only know that there were 3 stops.  I asked, what they would want to know and they wanted to know how many kids were at the stops. I wrote that at the top.

When I told them they would get to choose how many students were at each stop, they were so excited! I gave them a paper with the sentence at the top, let them choose a partner and sent them on their way.

As I walked around and asked students why they chose the numbers they did, I quickly wondered how much I should have helped organize their work for them. I found so many with numbers everywhere and it was hard to see where their bus stop numbers were, let alone their total. Should I have put Bus Stop 1____, Bus Stop 2____, and Bus Stop 3_______ to have a clearer picture while also modeling for students how we can make our math work more clear? Quite a few looked like this…

 

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There were so many interesting papers, so I love WordPress’ new tiling feature for pictures to make it look less cumbersome!

 

Top Row, Pic 1: This student had 24 as two stops. When I asked him how many stops we noticed in the beginning, I got a “Oh gosh” and he wrote Bus stop 1, 2, and3. He then stuck with the 24 and when I came back he had 8, 8, and 8. I didn’t see this until after class so I am curious how he arrived at that answer. I also realized that these 1st graders move fast and it is SO easy to miss the cool things they do so quickly!!

Top Row, Pic 2:  They said 3 and 22 were easy to add and then they just chose another small number. The interesting thing here that I need to find out more about is the 5×6 with the one box shaded in. I loved the commutativity showing up here!

Top Row, Pic 3: This was so interesting because I had never thought that a student would first think of how many students were on the bus and divide it up from there. They thought 30 students would fit on a bus so they made the stops fit that information. (They saw the error on the last one during the share).

Bottom Row, Pic 1: This student said that because there were 3 stops, there were 3 students at each one and ended with 9.

Bottom Row, Pic 2 &3: This student wanted big numbers so his first response, after he insisted on re-writing the sentence, was 1,000 and 1,000,000 and 4. Then on the back of his paper he wanted 6 stops and chose 6 new numbers. This led to some great conversation during the share.

This student figured that if there were 1 or 2 at a seat then there would be 55 students on the bus. I love all of this work so much! Then when I asked her about the students at each stop, she said, 30, 20 and 5.

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We shared as a group back on the carpet and I tried to capture why they chose the numbers they did:

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I then gave them the original problem and asked them to solve it individually. After seeing them work on this problem, I think there are so many interesting conversations that could happen Monday morning!

This is where I had so many questions as to how we get the younger students to make their thinking more visible. I found so much of it happens on fingers, 100s chart, and number line on their desk that I was getting an equation on the paper.  It is great when I am sitting there asking, but that cannot obviously happen when they are done so quickly and there a bunch of them! Is this something that comes with practice? I did find that once I asked them if they could explain to me on the paper how they solved it, they did a great job. My next question is, would taking the 100s charts and number lines off the desks help push students to look for friendlier numbers? I found the majority of them went left to right, counting on instead of using the 6 and 4 first. This is something that I think a structured share out on Monday could bring to light for those who never thought of it.

Here are a sampling of the papers I look forward to chatting with the teacher, Lisa, about on Monday. We can chat about how we can structure this share out.

 

Lisa, through number talks and investigations, has been working a lot on having students noticing number patterns leading to generalizations. It was neat to see this work of adjusting addends and keeping the same sum showing up here too. It seemed to show  up most after they had their answer and were playing around with the numbers, which I love!!

I am happy to have started with the open notice/wonder because I learned so much about how they think about problems and I think the opportunity to choose their own numbers got them thinking about the context over solving for an answer to an addition problem. I am, however, extremely curious how it would have changed the work if I had given students the problem with the 13 given and the other two missing? Would I have seen more about how they choose numbers to make the 13 easier to add a third number? I am hoping to get into another 1st grade classroom to try this out with another teacher but I would love it if any other 1st grade teachers would there would love to try it out and report back!!

I am so looking forward to Jamie’s post on this because her student work looked amazing on Twitter yesterday!!

~Kristin

Yeah, Jamie’s post is up! Check it out here! Cannot wait for our Google Hang Out tomorrow to chat all about it!