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!

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