How Many Buses?

Research tells us that authentic math situations that children care about are highly engaging and robust learning opportunities. My quest in FDK has been to embed mathematically meaningful experiences into our program each day. Today I presented the children with a problem and asked for their help.

 

On Monday we have an upcoming field trip. (After letting the office know my plan) I told the children that the office had requested that we calculate how many buses would be needed to bring all the kindergarten children, staff and volunteers to our destination. Too few buses and we wouldn't all make it there; too many buses and we would waste money that could be used for other trips.

 

The children were immediately engaged. They knew that the problem was important because the office had asked us to figure this out. I asked them what we needed to know in order to proceed.

 

They knew we needed to first calculate how many people altogether would need to ride the bus from our classroom. I used a ten frame to help represent this number because it made it easy to visualize just how many people there were and also because I wanted to provide entry points for all children. If I used just a numeral it might be too big for some to understand. I also wanted to create a situation where the children could manipulate the 'people' and fit them onto buses later on in the activity. Unifix cubes that the children could manually manipulate might have worked just as well, if not better (food for thought for next time).



 

Next we totaled how many people would be coming on the trip from the other two kindergarten classes including staff and volunteers. I used ten frames again to represent this number.

 

The children knew this was a big number and guessed we would need two or three buses. I reminded them that if we booked too many buses it would waste money. I asked them what they needed to know in order to find out. One child suggested that we needed to know how many seats were on a bus so we could figure out how many children could fit on the bus.

 

The children were motivated and excited by this work. I could tell by their concentration and enthusiasm that this problem really mattered to them. I asked them where we might find out the answer to our question. A few thought it would be a good idea to ask the bus driver on their way home tonight. In order to stress the urgency of the math problem I shared that we needed to order the buses today and that would be too late. I suggested we ask the office.

 

We took our data to Mrs. Tessier and showed her our calculations. She agreed that it appeared we had a correct total of people that needed to take the bus. She also answered our question and shared that 48 people can fit on one bus.

 

The children were thrilled! They knew that one bus wouldn't be enough because "there were already 60 kids in one class and they wouldn't all fit". They shouted that we needed two buses! I reminded them that we needed to be sure so that we didn't waste money ordering an unnecessary bus.

 

We returned to the classroom. I asked the children to pretend that one yellow piece of paper represented a bus and asked them what to do. The children suggested counting the dots on the ten frame to try and fit them onto the 'bus'. I suggested that to make it easy, we could cut the ten frames apart. We quickly filled one bus with 40 'people'.

 

The children then suggested adding a second bus to hold another 40 people.

We knew it would be close...the children then suggested cutting apart the remaining ten frames into single units and dividing these equally into the two buses.

We finally had a solution! Each bus would hold 47 people, and that meant that we needed two buses to bring everyone on our field trip!

We reported back to Mrs. Tessier to share our thinking and show her our work. She was so excited that the children had calculated this on their own and promised to order precisely two buses!

I was amazed at the end of this activity. The children were so confident problem solving with such a large number! I know that it was because they were highly motivated and invested in the math problem because it related directly to their lives and was something that was exciting and important. I look forward to finding more authentic math problems to bring to our whole group conversations.

If you have examples of real life math that has intrigued your children please tweet us and share @McLennan1977 or comment below!

Empowering Children to ask the Questions

An amazing thing happens when children are empowered to think mathematically in an emergent, inquiry-based classroom - they become the teachers! Our children have been incredibly motivated to explore growing geometric patterns, sparked by their interest in creating intricate structures from wooden blocks. Today some of the children decided to revisit the mini blocks and we challenged them to create their own growing patterns. We discussed what made the previous patterns successful and how others would recognize that their idea was also a pattern.

According to Jo Boaler mathematical mindset is a huge indicator of whether or not a child will be successful in math and that when children are provided opportunities to explore with rich learning materials in supportive situations, there is no limit to the math learning that will take place. Boaler suggests providing children with low floor high ceiling tasks that have multiple entry points and an endless number of ways to differentiate in order to challenge the most ambitious learners.

We were impressed with the growing pattern of one child in particular. He thought slowly and deeply as he manipulated the blocks, and then created a unique pattern that we have not yet explored together in our classroom. We were amazed at the complex nature of the pattern, how carefully planned and built it was, and how well this child could articulate his thinking.

He used the iPad to take a photo of his growing pattern and then set to work to transcribe it onto grid paper. "I want to remember what it looks like so I can show others!" he explained as he worked. He carefully referred back to the photo as he counted the squares and ensured that the pattern was as he wanted it.

When he was finished we took a photo of his work. "I made a mistake on the fifth tower," he shared. "I added an extra block but it wasn't a big deal because I crossed it out!" Accepting one's mistake as a learning opportunity and fixing the math to make it better is a major milestone in cultivating a mathematical mindset.

 

After sharing the pattern we asked if he would like to have it tweeted so that others could see what he had created. He was very excited about the possibilities of this and wanted us to ask other classes to see if they could explain what they noticed about his pattern. We showed him the previous experience of using padlet on the blog to gather math ideas virtually from many places and he excitedly asked us to do this. "It's like I'm the teacher now, " he grinned. "I'm helping other kids learn how to do math too!" For us, this was an incredibly proud moment. This child, so eager to engage in an open-ended math experience, had now shared his learning beyond the 'walls of the school' and was hoping to engage other children in rich, mathematical thinking. 

Please consider the growing pattern, either as a reader of this blog or as a teacher together with your students. If you have an idea about what you observe, please click directly on the padlet below and type your answers (or insert a photo or video) right on the screen! We will check it daily and then respond to your ideas! Thank you for helping us consolidate and share our math thinking beyond our classroom and help children see that math is a deep thinking, slow, collaborative process that can be fun and exciting!

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Virtual Math Question

In our school hallway we have a dry erase board that asks rich, low floor high ceiling questions. Students and staff that walk by are encouraged to consider the question for a few days and then contribute their ideas using dry erase markers.

It's an excellent way to create a culture of mathematical thinking and growth mindset as we learn together with one another! I've created something similar on this blog. The padlet image below is actually an interactive virtual 'whiteboard' where you can share ideas in an online space. Our class is hoping you might consider asking your students the question "If 24 is the answer, then what might the question have been?" and then posting your ideas, along with your location, to the padlet. We can't wait to see what you discover and also the reach that our blog has!

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