# Berndt-G3-9-15-04

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I dont want to know the answer yet. I want to know the thinking first.
Easy to tell the answer. I want to think about it.
Britney, excuse me, I want your eyes up here.
Mercedes, up here
You need to be participating to understand.
Ok. So lets go back to what number six says
Professor Peabody took a sample of 16 beans from a container
Thats how I got this 16. That's his total.
He recorded 2 for limas,
9 for pintos, but he forgot to record how many for navies
before he put them all back in the cup?
How do I figure this out?
We know this is the number set that can tell us
the answer. What is my strategy for thinking about it?
Arthur!
Well, you have 2 and 9 equals 11.
So now Arthur is thinking I know this much is 11.
Now you count up all the way to 16.
And tell your number how many did you get all the way to 16.
So you are using the counting up strategy?
So when you count up from 11 to 16
how many is that?
Umm,.. 5.
Did anybody have a different way to do this one?
Yes, Nicole.
5 + 12 + 2 equals 22
5 plus 12 plus 2?
Are you on problem 6?
No.
Okay. Let's get to 6.
Say that one when we get to that. Problem 9.
You guys solved 6?
Ok. Listen up.
Emma.
I know we had to pick a number.
So I knew that...
that 2 and 5 equals 7
and 7 and 9 equals 16.
So I picked the 5.
Okay. That should sustain. Wait a minute,
2.. Say it again.
You get 2 and 5 with 7.
and because you learned that factorally
you knew in your head that 7 an 9 equals 16?
No.. I said.. Yeah.
Okay. You already memorized that 7 plus 9 is 16.
So then you said, if I have got 2 from this 7, then I know I am missing 5.
Good thinking!
Would a picture help you with this one?
Remember when you had to draw our lab picture, Krystin?
The lab picture for this might look like
okay, which beans are these?
These are my limas.
Then I do one, two, three, four, five, six, seven, eight
nine. These are my pintos, right?
But I don't know what's in this last group called navies.
What I think of this is, okay, here's the whole
spoonful. Here's all the beans
that he took out of the sample first.
Two of them went to this pile.
So I know there are 16 beans here, right?
So 16 take away 2 so far
So 16 take away 2 is - There's 14 beans still here.
But now, I take the pintos out.
So now I have 14 left
and I take out the 9 for the pinto
What's left in this pile?
14 take away 9?
5 again, isn't it? So now I know
the answer is 5.
So I really could think of this as subtraction. couldn't I?
Bart!
But that doesn't make sense
because when you take the spoon out
you don't really know how many you have in there.
When you first do, you are exactly right Bart
but when I read the question
you don't really know.
Yes, Matt.
Well you can times it.
How do you times it, Matt?
2 times 8 equals 16, minus 11 equals 5.
Wait a minute, so you want to go 2 times 8 equals 16
16 minus 11 equals 5?
I don't see how that matches my data
You do have a correct calculation
2 times 8 is 16 and 16 take away 11 is 5.
5 is the answer.
But I don't understand this part.
Why do you think we should multiply?
Does that really fit what this problem is telling you?
No, but it would be faster.
Multiplication is faster when it is in a problem.
Do we have 2 groups of 8 anywhere in our problem?
No.
That's why it doesn't fit.
But in this part, how does the subtraction part fit?
Taylor and Luke, can you help us figure that out?
Subtraction fits this.
See, you tend to stop the wiggling back there or kicking or whatever else
you are doing. Chris, you haven't helped us do any thinking yet.
I need you to pay attention.
Go ahead, Jones. Let me know how the subtraction fits.
Subtraction fits, uh, by
if you,... if you have like 16 ... 16 in one spoonful
Dump it out and count till 16.
Then if you have, like,
How did we get this 11?
How does Matt's "take away 11 number set" fit?
Everyone should be able to look up here and figure it out
It does fit. I'm telling you.
Yes. It does. It works. You tell me how.
Amanda.
Where did Matt get 11?
It jumping up and jumping out after you guys look at the screen.
The arrow head says 11 right?
Where did that 11 come from?
Tell me 2 numbers. Aaron, settle down and give people a chance to think.
She sees the 11 here. Are you with her?
Yes!
She sees this. How did we get this?
Where did that come from?
Bart.
From pintos and navies.
Does it have the pintos and the navy together, the 2 plus 9?
No, its the lima.
So over here, in our drawing,
isn't that this part together?
Yes!
2 for lima and 9 for pinto.
So if I take away the ones I know
So I know theres 2 and 9
So taking away 11 beans from the 16
That tells me how many are left in this pile.
Joe, you see now why that works?
I don't think so. You were whispering with Krystin.
Ah. Well this works and then we don't listen.
Did we do question 4?
No. We did not.
4 students are playing a game of, oops, this is 4a
playing a game of turnover. The target number is 25.
Martha turned over an eight,
Stephanie turned, excuse me, Stephen
turned over a five.
Then Christine turned over a three.
What is the sum? Quickly
tell me what to do
Every hand should be up.
Some of us are just more busy wiggling
instead of thinking about Math. Its very disappointing.
Nathan, look at the book.
Matt, put the book over next to where Nathan can see it.
Emily, quick.
I forgot.
You forgot, aw.
What do I add? Tell me what to do.
You add 8 plus 5 plus 3
8 for Markus, 5 for Steven plus 3 for Christine, right?
Ok. What do they have so far?
Anne.
16.
16. 8 plus 5 is 13 and 3 more, we have 16 so far.
Excuse me, b now says
Now its Marciella's turn.
What card does she need to turn over to win the game?
Now, remember there are no tens. Its all 0 through 9.
What does she need?
Now we know they have 16 so far.
What are the going to end up at?
What's their target number?
Twenty five.
So is this the one where we have to say
what do we need to get to 25?
Arthur.
9. How did you get that?
Because 16 plus 4 equals 20.
and 20 plus 5 equals 25
So he's saying that 16 plus 4 equals 20
So I know I need at least 4
and then I want to go 20 up to 25, right?
So I know that is 5.
So then you add the 4 and the 5
equals 9
and you got 26.
25!
Ya. 25.
He counted it up to the even 20
added on the 5 more that he needed
so then he found out 4 plus 5 is a 9
So the card is a 9.
Could you do this by subtraction?
Yes.
How?
Chris.
We are trying to figure out question b by subtracting
Ok.
Nobody can figure out the subtraction way?
Emma again, tell it out Emma.
25 take away 16
You know the target number is 25
You know the first 3 cards added up to 16
Right? So if the take away the card that we already got to
Eleven?
Wait a minute.
If I have only 5 ones, 5 bits
can I take 6 of them away?
I have 5. How can I give you 6?
Don't I have to do some regrouping?
Its nineteen.
Ah. What's nineteen?
Wait a minute. Where am I getting
some more to make this? I need some more bits here.
Don't I have to do some regrouping?
What can I regroup?
The two.
The two. Oh. Its not 2, its two tens.
two skinnys
So if I exchange one of those skinnys
how many skinnys are we left?
One. Now that gives me 10 more bits
plus the 5 that we have here. How many bits?
fifteen.
Fifteen take away six is 9.
One skinny take away one skinny - No skinnys.
So did we get 9 again?
Okay!