Building Number Sense and Fraction Sense While #TMWYK

So this week, two situations arose involving my son’s food and math.  One built on some big ideas around Number Sense and the other built on his early Fraction Sense, but both gave me an opportunity to be Talking Math With Your Kids #TMWYK.

Scene #1: Building Number Bonds that Make 10 and Equality

We live in a very tiny town in Idaho and have to drive 45 miles to go to swimming lessons.  The town where swimming lessons is has a McDonalds.  One day this week, I ordered a ten pack of nuggets for my two older sons to share (my daughter doesn’t do chicken nuggets) after we got done with lessons.   My oldest son, 6 YO, starts a mathematical conversation about the nuggets:

J: “What is 7 plus 4?”

Me: “What is 7 plus 3?”

J: thinks and saids “10…oh, that is what I need!”

Curious Me: “What do you mean, that is what you need?”

J: “Well, if I give Cam 3 then I get 7.”

Impressed, but don’t stop there, Me: “So, what if you decided to give Cam 4 nuggets, how many would you get?”

J: instantly, “6.”

Me: “Now how did you know that so fast?”

J: “Cause if I give one to Cam, I minus one from mine.”

Me: “Nice thinking, dude.  What if you only wanted 5, how many would Cam get?”

J: “5, 5 and 5 make 10.”

And I stopped there.  My son was doing this without seeing the nuggets.  But I did take a picture once we pulled them out.  Not all kids can visualize the movement of one nugget leaving one person’s pile to go to the other person’s pile, so feel free to use the pic if you think it will help your kids or better yet use the actual nuggets so they can see it..  This short little glimpse into my child’s mind shows me he is progressing with the numbers that bond together to make 10.  He isn’t quite there as his opening comment shows me he thought it was going to be 7 and 4 to make the 10..but he is also very close, he didn’t think it was 9 and 4.  Our number system is a Base 10 system so being able to instantly tell how many to get to 10 (or the next 10) is essential.  This also brought up the idea of equality, now we didn’t write the equations down as we were driving in the car, but if we were at home I would have.  My son sees that if he has 7 and his brother has 3, there is still the same number of nuggets as when he has 6 and his brother has 4, i.e. 7+3 = 6+4 = 5+5.  These big ideas are REALLY BIG IDEAS because they aren’t just for the “basic facts,” they become very helpful as kids are solving problems like 49 + 26.  If a child is solid in their understanding of number bonds that make 10, they can quickly see they need just one more to put with the 49 to make the next ten of 50.  If the child is solid in their understanding of equality, they quickly see that they can just take one from the 26 to give it to the 49 and the problem stays the same, i.e. 49+26 = 50+25.

Note: As I went to Christopher Danielson’s blog to find the link for my Scene #2 below, I came across his post about understanding the equal sign, great read!

Scene #2: Understanding Parts can be put together to create a Whole via #TMWYK on Twitter

Christopher Danielson recently posted about the above photo that was posted to Twitter by Michael Fenton using the hashtag #TMWYK (aka Talking Math With Your Kids).  Michael’s picture and Christopher’s post entitled, Counting Grapes, encourages us to think about kids counting items versus counting WHOLE items.  I notice this a lot with my almost 3 year old.  He grabs some goldfish crackers and counts them equally, even though some of them are parts and some are whole.   So one day this week, while fixing my 6 YO son’s lunch I saw my own opportunity.  He had asked me for 3 hard boiled eggs and this is what I put on his plate (and posted to Twitter):

When I put his plate in front of him there was no reaction.  So…

Me: “Did I give you 3 eggs?”

J: “You gave me more.”

Me: “I did?  How did you know?”

J looks at it, but by that time had a cherry in his mouth and all he did was make gestures with his hands that basically said what is notated in the picture below and then help up 3 fingers and smiled:

His initial reaction is instinctual…we see what is right in front of us.  It looks like 6, but 6 what????  It is 6 parts.  Off on a bit of a tangent now…some might say 6 halves, but each is not a half of an egg.  We over use “half” when anything is cut into two parts, but those parts must be equal to call it half.  Kids in early elementary aren’t required to learn much about fractions, but we should still be introducing the ideas informally.  Basically, this type of task is asking kids to think about parts that come together to create a whole and that what we call the part (half, 3/4, etc) depends upon the part’s relationship to the whole.  Christopher gave me one more way to push him:

Happy Independence Day!  Hope you are getting to do something fun…I am off to make the trek to swim lessons again.