Subtraction Number Talks

This week we worked through Chapter 4 in our on-line book study of Making Number Talks Matter.  This chapter deals with various subtraction strategies.  I was a bit nervous to actually jump in to this for real, but it has been really fun and my sophomores (2 classes worth) seem to really enjoy it.

My classes did two subtraction number talks this week.  I invited my principal to come see me do the second one.  I thought I would be nervous, but my classes really get in to these (I had done several dot talks with them) that I was pretty sure THEY would be fine.  I am such a novice at this, I wanted her to come observe me to see if I was making sure not to call on too many boys, not trying to correct "weird thinking", etc.  I sent her a picture of my second planning guide.  Here are both the planning guides:

Here are some board shots for the first number talk.  I neglected to get shots of the second talk!

The one over on the right really through me for a loop.  I asked her to help me understand how she was doing this, and this was the best she could do.  I thanked her for sharing and then took a few more volunteers.  

When we were all done I pointed out to the young woman that it looked to me like the person who shared below her share, did pretty much the same thing, except they noted that the 5 and 2 really means 50 and 20.  Now I am asking readers: how would you deal with the 8-3 thing?  Do you just point out at the end that you can just subtract in the order you see?  That would 60 - 20 to get 40 and 3 - 8 to get -5....combine these and you get 35.

We were done, wrapping things up and one young man asked if he could PLEASE share his strategy?  How can you refuse?  And it was gorgeous.

"I took 20 from 60 to get 40, then took away the 8 to finish the 28 and got 32, but I still was 3 short from the 60, so I added it back in to get 35."






The principal was really impressed by the number of strategies and the "OHHHS!" when someone shared a new strategy.  She is hoping that after I have had some more practice, I will feel comfortable being video taped.  I am also open to have people come in a visit to see how this is happening.  It is pretty amazing!

I am SO grateful for this book study. It is forcing me to do the talks, which could easily have gone by the wayside since there is SO much else I need to get done.  These have been worth it, though!!

Spontaneous Number Talk: Multiplication

Today's warm up did not include a Number Talk.  At least, it wasn't SUPPOSED to.  Today's warm up was an error analysis of a fictional student's work on an order of operations problem.

If the problem was done incorrectly, it involved multiplying 12 by 4.  For a number of my freshmen this is NOT a number fact they own.  And it is something that they would most likely be wanting a calculator to do....or at least use pencil and paper.  

The problem asked them to not only find where the student went wrong, but to correct it as well. We had a multitude of answers (which freaked me out considering how many of these we have done, but it was an excellent learning opportunity).  After we talked about it for a while and decided which answer was the correct one, I asked if there were some people who wanted to share where they got derailed.  I talked about how mistakes are when our brains grow.  We get the chance to go "OH!!!  I see what I did, but this is what I was thinking..." and how we ALL learn from that.

There was one young woman who was secure enough to put it out there.  In the process of explaining what she did, she mentioned that she multiplied 12 by 4 and got 48.  She is not one with real strong number skills so I wondered how she had done that so quickly. After we were done talking about the errors and how we were thinking, I asked her to share how she multiplied those numbers.

It involved halving!!  I nearly fell over with excitement (but contained myself very well, I think).

Hers is strategy #1.  "When there are even numbers, I like to cut them in half until they get to where I can multiply in my head.  I cut 4 in half to get 2, and I know that 2 times 12 is 24.  I did that twice because I broke the 4 into 2 pieces.  Then I just added them together."

When I asked for other strategies, hands went up!  One young man gave us strategy #2:

"I just did 4 times 11 because that is so easy, and then added one more 4." 

"Why did you add one more 4?"

"To make 12 fours.  And so 4 times 11 is 44 and 4 more is 48."

Then another young lady shared strategy #3. 

 "I multiplied 4 by 1 and got 4, then 4 by 2 and got 8."  

When I wrote it the same way I wrote the first one, I said "and that gives us.....?"  She could "see" that the way I wrote it was going to make 12, so she asked if she could think a minute.  Then she and her partner came up with the strategy #4. "Oh, the 4 is in the tens place, so it must be 4 times 10 to make 40, then 4 times 2 to make 8 for 48"

Honest:  this REALLY happened today....and I didn't plan it.  I told them I loved them.

Number Talks: Chapter 2

I am participating in the online Number Talks Book Study.  It has been immensely helpful re-reading this book, and being able to read other teacher's experiences with trying number talks on a regular basis in their classrooms.

This week I did some of the dot cards in a class of sophomores.  I was a bit nervous about it, especially the whole "put your thumb on your chest" thing.  But it went great and it was fun to look around the room and see a lot of students with one, two, three fingers out as well, meaning they had more than one method of "counting" the dots that involved grouping them in some way.

We started with something very easy:  just some dice like set ups.  I asked them how they all knew how many dots there were so QUICKLY??  "I just KNOW," was the most common reply.  I explained that they were using a term called subitizing.  They have done this since they first played board games and knew how many places to jump when they rolled this:

We finished up with this "dot" card from the book.  

One girl who never says ANYthing in class practically leapt out of her seat when I asked for volunteers to share how they were able to figure out how many dots there were.

Yup, I'm a believer!