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Wednesday, 13 January 2016

Working with BIG numbers

Sometimes we assume that students know what we know.  They might not!  We took the tin with all the little counting bears and put them on the floor.  I asked "How could we find out how many bears there are?"  The students had a few strategies:
One said we could make groups of two.  We did.  There were 95 bears.
Was there another way?
Another student said that we could make groups of five.  We did.  There were 95 bears.
Here was the ah-ha! moment.  One boy said "That's weird, it was the same number."
The third student suggested we could make groups of 10.  We did.  There were 95 bears.
The same boy said "That's freaky!  It is 95 again!"
The lesson had to stop there.  The conversation had to address this new idea for this one student.  He did not have a clear understanding of the conservation of numbers.

The concept that needs to be clear, is that an amount is the same UNLESS some more are added, or some are taken away.  No matter if the original group of items is organized in twos, fives, tens, twenties, or in one large pile.....the amount will be the same.  The amount is CONSERVED.
This wasn't a planned lesson, but it was SO important to remind the students of this concept.
We moved onto how a big number is written.  How would the students write these amounts?

What does the 6 in 63 represent?  Does the 6 mean the same in 16?  How do you know?
This is the concept of place value:  where the number is (the place) helps us know the value of that digit
The value of the digit changes depending on the place it sits at.

I asked one of the students how they would write the amount 112 on the red 2 digit card.  He made the perfect Grade Two mistake!
It allowed the students to have a conversation about what happens when a place is full.  The tens place cannot hold more than 9 groups of 10.  Using these manipulatives, I was able to demonstrate how 10 groups of 10 go together to make 100.  In our class, it is important that there are opportunities to use the concrete BEFORE the students are asked to think in the abstract.  Knowing what 112 is difficult without the experience of seeing what 112 is.  

I bring this up because sometimes parents forget that it is a big leap for some students to move from concrete  to abstract.  That is our goal though, to understand the system of numbers so well that we can think about this system abstractly.
We looked at the 100 chart.  We looked at the way it is organized.  The students noticed the patterns that can be seen in this chart.  With a yellow highlighter, the students found the even numbers in the chart.  They counted by twos.
Many of the students noticed that when one counts by fives, there is a column of fives.  They also noticed that the tens column already was outlined in yellow!  What does that mean?
Using the blue highlighter, the students also outlined the numbers that would be said if you counted by tens!  Goodness! Those numbers were also outlined in yellow and blue!  Why was that?  There is a great deal of learning in the exploration of big numbers to 100!
Look who came to our assembly today!  Jesus!
Today, our class told the story of how St. John the Baptist baptized many people in the River Jordan.  He was s surprised when Jesus also wanted to be baptised!  The water was some cloth held up by some reliable students!
After Jesus was baptized, a dove appeared.  The voice of God was heard from above!  It is the first time that Father, Son and Holy Spirit appear together in the Bible.  Did you know that this story appears in all four gospels?  That is a sure sign that it was an important event!
We related the baptism at the River Jordan to our own baptism.  We had the mom and dad and godparents bring the baby to be baptised by the priest,.  The students are very happy to be sharing their understanding and learning about Jesus with their friends in other classes at assembly!

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