Tuesday, March 7, 2017

The Mitten Measurement Task

It's amazing the kinds of questions children can ask...
 
One of my favourite books to read in the winter in "The Mitten" by Jan Brett. The story is appealing to young children who love to retell the text and marvel at how big the mitten grows as each animal squeezes into it.  This week I read the book again upon request by one of the children.  At the end of the reading one child shared that she felt that the book wasn't really about "real things, because there was no way all those animals could fit into one small mitten". 
 
Sensing an opportunity for something rich, I questioned the children. I asked them to consider whether a mitten could really stretch that large to accommodate all the animals, and if it couldn't, how big did they think it would have to be in order to do so.
 

The children engaged in a lively discussion and agreed that the mitten would have to be very large - much larger than the one portrayed in the book - and it would be very time consuming to knit. We agreed that one would have to know exactly how big it had to be because if it was too small the animals wouldn't fit, and if it was too big it would waste the knitter's yarn and time.
 
I challenged the children to create a mitten the exact size it would need to be in real life to fit all the animals in the text: a mole, rabbit, hedgehog, owl, badger, fox, bear and mouse.  They readily accepted my challenge. The first thing we agreed upon was that we needed to know exactly how big each animal really was. The children weren't sure how to do this so I suggested researching their sizes on the internet. I helped them with this search.
 
Once we knew the size of the animals I helped the children measure out large butcher paper so that their drawings would be as realistic a size as possible. We discovered that the bear was the largest!
 
 
 







Here are the animals (excluding the bear) after the children researched, drew, and cut them out.


The next thing we needed to do was calculate how big the mitten needed to be. We referred to the book to see if the animals were side by side or on top of each other and then taped together large pieces of butcher paper to create the mitten.


The papers needed to be securely fastened...




...the outline of the mitten cut...
 

...and the seams stapled closed.


The children noticed that when complete the mitten was almost as big as our carpet!


The children enjoyed decorating it too!
 



We felt that it would be fun to retell the story while we placed each animal inside the mitten. We were eager to see if we were right and the animals all fit inside.




The children waited until it was their animal's turn and then gently placed their animal inside.










Once the retell was complete the children had one more question they asked to explore. Would a mitten that was large enough for all those animals hold 14 kindergarten children? They were quite eager to find out! One by one they hid inside the mitten, squeezing to the end and making room for their friends to join in!
 
This was also an incredibly rich math activity. The children had to consider the area of the mitten and if there would be enough room for all the children. They counted as each child entered the mitten and calculated how many more children were waiting on the carpet. They discussed how to preserve the integrity of their design as they entered the mitten so that it held together so all children could have a turn.
 






They were right! All 14 children did fit into the mitten!



 
But the best part of all? Getting out of the mitten!
 



Sunday, March 5, 2017

Read Alouds and Robust Math

I continue to be inspired by the idea of authentic, robust math as demonstrated in the 3 Act Math activities introduced by Dan Meyer. The challenge for me has been how to engage young children in kindergarten with this kind of layered math problem solving.  Because I often incorporate a read aloud in every circle time lesson and discussion, I felt a rich and engaging book would be the perfect spark for robust math engagement and thinking in our classroom.

I love spring and the weeks before March Break are a fun time to incorporate St. Patrick's Day activities. A new book arrived in our classroom and I was eager to read it to the children.  In "How to Catch a Leprechaun" children build a variety of interesting traps but are unsuccessful in catching a sneaky leprechaun and taking his gold.

 

My students are avid builders and love imaginary characters and scenarios. We delved into the book and looked at each trap; what was it made of, how did it work, why wasn't it successful in catching the leprechaun?

I then showed them a YouTube video about a little boy named Audri, who inspired by Rube Goldberg machines, built his own 'monster trap'. The children were amazed that Audri built this complex creation. His work inspired our children to do a bit of research on what Rube Goldberg machines are and see other examples of complex cause and effect creations.


During playtime the children gathered many materials from around our classroom. They were inspired by Audri and recalled the traps from the book. They worked diligently to invent their own leprechaun trap. When asked the children could explain how their trap worked and why they felt it was going to be successful catching the leprechaun. We decided to leave the traps out overnight and see what happened.


The children were so eager to arrive the next morning and rushed to their traps to see what had been caught. The leprechaun was not in any of them but had left them a note saying that he appreciated their efforts and had left them a pile of gold to share. The children, of course, were thrilled!

I displayed the gold on our carpet and asked them to consider how we would divide it up. I challenged them to think of a different strategy than ten frames, which had been used when we divided up a large amount of gummy bears the previous week.


At first the children wanted to divide the gold in half, because they thought it would help them figure out how much gold there was, which would then tell them how many pieces each child would receive. We tried this but it didn't seem to help.

"Let's put it in groups of ten because ten is a friendly number," one child suggested.

The children agreed and we grouped the coins by ten.

"Not enough groups for us...there are more than six kids here!" 


"Let's try five; five is a friendly number too and we just have to divide each pile in half," another child suggested. So we created groups of five.

"Still not enough! We have fifteen friends here today, not twelve. We need three more piles if we use five."


"Okay, let's try three! Three should work!"

So the children helped me reorganize the coins into piles of three.

"Now we have left overs! Twenty piles is way too many! That won't work either."  The children continued to brainstorm aloud and think about how to best divide up the gold. They wanted to maximize how many they each got!



"I know! I know! Let's try groups of four! Three is not right and five won't work. That leaves four!"

The children helped regroup the coins again, this time into groups of four.

After counting the piles the children realized that there were fifteen evenly divided groups of four. They were so excited and so was I! I shared that they had just divided a very large number in many different ways in order to ensure that everyone received an equal amount. They were highly motivated to engage in a very rich and complex problem and did not give up when they did not arrive at the answer right away. 

This is the essence of a mathematical mindset - persevering with an engaging task even when it's difficult and you are not exactly sure how to proceed. In kindergarten, math is everywhere and when the problem is exciting and fun, we work together and grow our mindsets each day!


Monday, February 27, 2017

Emergent Learning in the Early Years: Digital and Deliberate

On Thursday, February 9 I had the pleasure of being invited along with Jocelyne Brent to present "Emergent Learning in the Early Years: Digital and Deliberate" for TVO. In this webinar I shared the many ways we purposefully use technology to support, extend, document, and share the inquiries happening in our classroom. For those of you interested, you can view the webinar here:

https://youtu.be/SkwumPSkG3w



For easy location here are some links to the top technologies that I use in our classroom to support play, inquiry, communication and documentation. Click on the title to access links to various blog posts that further describe the technology and how we use it in our classroom.

1.  Children documenting their own learning using iPads.

2.  Using time lapse photography as a documentation tool.

3.  Creating digital documentation panels using iMovie.

4.  Encouraging digital community and voice using Padlet.

5.  The versatility of QR codes to inspire, research, document and share.

6.  Unplugged coding!

7.  Going old school with overhead projectors.

8.  Why Blog?

9.  Technology Buddies and Wordles

10. The Power of Twitter in the Classroom



Wednesday, February 22, 2017

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!
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