Category Archives: Math & Literature

My One Hundred Hungry Ants Obsession

Lately, I have been obsessed with children’s literature across K-5. My most recent obsession is the book One Hundred Hungry Ants. I did this in Kindergarten and this in 4th grade and today I invaded a 3rd grade classroom with it!

I followed the same pattern I usually do, I read the story aloud and did a notice/wonder. These are all of the things they noticed:

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The last one led perfectly into asking about the ways the ants rearranged themselves. I wrote the combinations they recalled from the book and asked them to chat with a neighbor about patterns they see.

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The discussion started with the 50+50=100, 25+25=25 and 10+10=20. Another student said they had the same things but it sounded different because she saw 50 was half of 100. They moved away from that and went to divisibility by the numbers that did not show up like 3,6,7,8, and 9 and pointed out that all of the second factors were multiples of 5. At this point they were focusing primarily on the second factor until someone pointed out the increasing and decreasing pattern happening. Then we got into the doubling and halving, quadrupling and dividing by 4 and multiplying and dividing by 10 of the factors.

I asked them if that would work with any number I gave them. They were quiet so I threw a number out there for them to think about, 24. They had to move into another activity so I left them with that thought. Before I left, however, one student said yes for 24 because 2×12, 4×6,8×3. Another student said it could be sixteen 1 1/2s and then thirty-two 3/4s! Wow!

Tomorrow they are going to investigate this further to see if they can come up with a conjecture about this work! So excited!

Literature & Algebraic Reasoning

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I read the book One is a Snail, Ten is a Crab to two Kindergarten classes this week. If you have not read the book, Marilyn Burns does a great post about it here. After reading aloud, making predictions and doing a notice/wonder, I placed 10 tiles in the middle of our circle in an arrangement like this:

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I asked the students who could be standing on the beach and they quickly guessed a dog, two people and two snails. I asked if they could give me an equation for the feet they see and they said 4 + 2 + 2 + 1 + 1 = 10. I asked if anyone had a different equation and they switched the order of the numbers, but agreed there was still 10. I did a few more arrangements before sending them back to their groups to investigate with the tiles. The directions were for one student to put out the arrangement, the groupmates guess who was standing on the beach, and write an equation for what they see. Their equations were all so different but the ways they were composing and decomposing the tiles to make new arrangements was really interesting!

We brought them back to the carpet and asked what they noticed about all of their equations. They said they all ended in 10 and equaled 10, so I asked if that meant we could write the equations so they were equal to each other? I asked two groups to share one of their equations and I put them equal to one another on the board. I asked if that was true? How could be we prove it? Their first answer was like, duh, they both equaled 10 so yes. I asked if they could combine or break apart any of the numbers like they did with their tiles to prove it. One student talked about combing the 1’s circled in the picture below.

They had to leave for lunch so I left them with an equation to talk about when they got back!

This lesson was such an amazing way of allowing students the space to think about equality and the meaning of the equal sign. It took one student talking about the ways he combined the numbers to open up the conversation and possibilities for future equations. I would love to see what the students could do if I wrote one equation on the board and asked students to write all of the different ways they could fill in the other side of the equal sign.

One Hundred Hungry Ants – 4th Grade

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Next year, we are restructuring our RTI block to be a time when students are working in small groups in their classrooms. This is a really exciting change from our previous model in which students were pulled from their classroom for intervention. This change will shift our Learning Lab focus to planning small group activities, however the first, REALLY important, piece we need to focus on is how small groups work in the classroom. I think the K-1 teachers have a much better sense of how centers work within the classroom, although we still want to move from the current centers to more strategically planned small groups. So, with only a week and a half left of school, Erin and I are playing around with some ideas in the classrooms as a part of our planning! Fun!

Erin and I planned for a 4th grade class today where we were going to test out a small group scenario. We started in a way I imagine everyone could kick off the year next year, involving students in the process. We asked them what they needed in order to learn in small groups. Below are all of their great responses, most of which were accompanied by an example of something they had experienced during small group work.

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I launched the small group task by reading One Hundred Hungry Ants aloud, pausing occasionally to ask for predictions. After the reading, I didn’t preview the task, but instead sent them off to work in their small groups. This was for two reasons: to see if the wording of the task was clear enough for students to follow independently and to see how they worked as a small group. We choose to give everyone the same task today to see how it went but we are trying different small group tasks tomorrow.

Each group had a journal, storyboard, and this task card:

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They worked for about half an hour and had some great conversations. I especially liked the conversation sparked by the third question because number choice is something I find so interesting. They also had to do some serious negotiating to decide which number they would do as a group since everyone had different reasons. In one group a student wanted to pick 2 because they would “get there faster,” another wanted 75 because “it could make a lot of combinations, but be less than 100 so they could still make it in time.” In another group, a student was saying he didn’t want any prime numbers because you could only do two lines with them.

This one was great because they changed the storyline from finding a picnic to getting to Dairy Queen, but when they get there they had forgotten their money so they still got no food. Different story, same ending.

This one was so interesting because, unlike the book, they used the commutative property, seeing the arrangements as different situations, which the book did not do:

This group saw a lot of doubling going on in their arrangements when they chose 50 instead of the 100 in the book:

We came back together and talked about the patterns they saw.

While the math conversation was interesting and I can definitely see some great generalizations stemming from this work, tonight I am thinking more about the questions I am left with about small group work…

Could a teacher work with primarily with one group, realistically, without continuously checking in on the others?
How can we structure the work so everyone in the group is working on the recording at the same time and can see what is being written? We saw a lot of the journal or storyboard sitting in front of one student. Not that the others weren’t contributing, but they all couldn’t see what was being written. I think dry erase boards can work well here.
What type of formative checkin can we do with each group that doesn’t add to an already growing pile of papers to be graded or give feedback?
How do we control the noise? The students were not being purposely disruptive or off-task, they were just loud and began talking louder to hear one another.
What does this look like at other grade levels?
How can we keep this interesting for students to do every day while not making it a planning nightmare?
How can we embed more student choice in the task?

More to come tomorrow when we tackle these tasks:

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100 Hungry Ants: Math and Literature

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This week the Kindergarten and 1st grade teachers planned with Erin, the reading specialist, and I for an activity around a children’s book. This planning was a continuation of our previous meeting about mathematizing. We jumped right into our planning by sharing books everyone brought, discussing the mathematical and language arts ideas that could arise in each. I made a list of the books the teachers shared here.

We chose the book One Hundred Hungry Ants and planned the activity for a Kindergarten class. We decided the teacher would read the story and do a notice/wonder the day before the activity. We thought doing two consecutive readings may cause some students to lose focus and we would lose their attention. Based on Allison Hintz’s advice, we wanted the students to listen and enjoy the story for the first read-through. Here is an example from one classroom:

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So many great problem and solutions, cause and effects, illustration and mathematical ideas were noticed by the students.

The following day, the teacher revisited the things students noticed and focused the students’ attention on all of the noticings about the ants. She told the students she was going to read the story one more time but this time she wanted them to focus on what was happening with the ants throughout the story. We had decided to give each student a clipboard and blank sheet of paper to record their thoughts.

We noticed a few great things during this time..

Some students like to write a lot!

After trying to draw the first 100 ants, students came up with other clear ways to show their thinking. I love the relative size of each of the lines in these!

A lot of students had unique ways of recording with numbers. Here is one that especially jumped out at me because of the blanks:

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Students shared their recordings at the end of the reading and it was great to hear so many students say they started the story by trying to draw all of the ants, but changed to something faster because 10o was a lot!

After sharing, we asked students, “What could have happened if they had 12 or 24 ants?” We put out manipulatives and let them go! So much great stuff!

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Next time I do this activity, I would like to see them choose their own number of ants.

Just as I was telling Erin that I could see this book being used in upper elementary grades when looking at generalizations about multiplication, I found some great posts by Marilyn Burns on this book for upper elementary and middle school:

Excited to do this in a 1st grade classroom today!

Math Minds

In Math, the Journey IS the Destination.