How many beavers in the lodge?

That is the question our mathematicians tackled a week ago.  But how did we get to thinking about this question?

We have had an inquiry connected to animals that started early in the fall.  

Throughout the winter this inquiry has continued to provoke questions and ideas that a group of boys, who particularly love this centre, have had many discussions through small group oral language sessions, working on holding their own idea and listening and responding to others.  

Some of our wonderings:
Where are bears in winter?
Where are frogs in winter?
Where are snakes in winter?
Where are owls in winter?   

MJ - Where is the bear in winter?
KL - In a cave.
MJ - What did KL say?
JC - In a den or lair.
LF - A den is a bears' lair.
JC - This is a den.
KL - No it’s a cave.
LF - Sometimes bears go in a cave and sometimes bats do.
MJ - What did L tell us about bats?
JC - They sleep in a cave. When they sleep they hang upside down and they sleep upside down and they cover their head with their wings.
LF - They wake up in night.
MJ - Do they wake up in winter?
LF - No they wake up in summer when it is nice.
MJ - Where did you say snakes are in winter K?
KL - A snake hides under a big, big rock.

They created a wall story together, sharing information from research they had done as a small group.  The boys continually brought their questions and thinking back to the whole group, where new wonderings were voiced (i.e. RH - Where are bees in winter?)

When JC came up with a question “Where are beavers in winter?” it  led to some amazing research and ultimately some mathematical thinking.  

To understand a little more about beavers we watched some fantastic footage from Discovery Education: 

How Do Beavers Prepare for Winter

The Intricate Process of Building a Beaver Lodge 


Then we saw some amazing beaver footage from the following link from Calgary Alberta. 

“How many beavers could be in that lodge?”


It was when we watched a small portion of this next video clip Winter Beaver Lodge (stopping at 1:32) that we discovered some data to help us with our problem!

Students shared what information they had heard in the clip. Most agreed (thumbs up) that probably there was a mom, dad, 4 babies from this year and 4 babies from last year. (Note: The girl said there could be 3 or 4 each year so we decided to go with 4).


Using our usual prompts:
How many? 
How will you show it?

students were encouraged to share their thinking.  These are some of the results (I hope to show the variety of thinking as it was recorded). 

RH attempts to draw beavers. 

NB uses lines to represent his thinking.

DG explains his thinking: 4 and 4 and 1 adult and 2 are the mom and dad.  That's 11.

MJ - How do you know it's 11? 

D - I just know.

KB explains his thinking:
8 beaver babies and 2 more make 10.  That’s the adults is 10.

EA explains her thinking: 

Mom and dad, 4 last year, 4 this year.

I know 4 and 4 made 8 and 2 more makes 10 cause I just counted in my head and 1 more makes 9 and 1 more makes 10.

(EA demonstrates grouping by 4’s and then counting on).

LF explains his thinking:
 4 and 4 make 8 and 2 more makes 10.  (Here he is trying to show a string as he talks though his thinking.)

RK explains his thinking: 
4 and 4 makes 9.  I think it’s 9.

CL uses a string to show his thinking. He then uses words to explain his thinking (i.e. “Four plus four plus one plus one equals ten.”).

JC picture shows the mom and dad and babies (Remember our prompts:  How many? How will you show it?).  He demonstrated counting one by one to figure out how many but got confused when he got a different number each time.  (JC continues to work on the strategies of tagging and counting slowly)