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>>teacher: You will need to go shopping
for the best playground equipment.
The principal accidentally lost his budget
and can't remember the order of his numbers.
He remembers the numbers 2... 3... 6 and 9.
He needs your help to make a budget
and design the new playground. So today we're gonna do
Task 3. Now we're actually at the designing of the playground.
So the first thing we did was review what the actual scenario in the task
would be, and then we went over the rubric so that they had a clear picture of what the
expectations were for them in order to receive a proficient or
exemplary score on the task. And we talked about what it means to be a
mathematician and to think like a scholar. So I reviewed what those things
would be. Andrew, what is the mathematician do before he starts?
>>Andrew: Think about the problem. >>teacher: Think about the problem, Francisco
>>Francisco: Ask myself what sitting...
>>teacher: strategy >>Francisco: strategy will I use.
>>teacher: Ask myself which strategy will...
I knew when I started the task they were lacking
a lot of the skills that they needed to complete it, but went ahead and did it
because it's more of a formative assessment anyways gives me a clear
picture exactly where we're at and what I need to reteach
before we get to the post test for the unit.
Okay, look at this digit. What's-what digit is this?
First tell me the digit.
>>student: 2. >>teacher: 2. What place is that digit in?
>>student: Hundred. >>teacher: 200, so it's val-or it's in the hundreds
so it's value is? >>student: 200
Teacher: 200. Can I add this from the hundreds place and this from the thousands? If I
did that-wait, if I did that, would my answer be accurate or inaccurate?
>>student: Inaccurate >>teacher: Inaccurate. You need to fix it.
You gotta line up your numbers correctly.
My biggest role was just to be the facilitator. They're um very used to
someone telling them, first do this. Next do that. Each step
along the way which-there's a place for that. I've done a lot of that leading up to
the task, but now when we got to Part A,
I really wanted to step out as much as I could and tried to just
facilitate the conversation or ask them guiding questions that might
cause them to reflect or re-think maybe what they were doing.
>>Ethan: Yeah and then you gonna put the 2 - and then you're gonna put the 2
right here.
>>teacher: Oh, so you're showing him how to what?
>>Ethan: Do it correctly.
>>teacher: Okay, and use what? >>Dion: A good strategy.
>>teacher: Re-grouping? Okay, alright. Let Ethan finish-up.
>>Ethan: And then you're gonna...like-this...
>>Dion: The eight because 8 + 8 is 16, and you put the 1 right here.
to the 9, and that equals 19.
wait...13.
>>teacher: Did you and Ethan come up with the same solution? >>Ethan: Yes.
>>teacher: And Deja as well? Okay, so we're getting Dion caught up?
Ultimately I'm trying to lead them to the
correct answer in the end but I'm focusing way more on what the process is
to get there and how to develop their thinking skills. Rather than just
you know, do I have the right answer: yes or no?
So what do you think would be a good-where do you think you've gone wrong?
I see you have a whole list of items here.
Do you know you have enough money to buy all these things?
>>student 4: Yeah...because we bought a little bit more stuff
and we're checking um our work.
>>teacher: Okay, so you're checking your work but let me ask you-you
you've made a list, right and it said: create a list the items you selected and you
organized them from least to greatest. Did we do that step?
So for Part C they were to list each item they purchased,
The quantity that they selected of that item and then come up with a total cost,
and then subtract that from than 9,600 that they started with.
Just like you would in a check register and then do that item by item.
Until they got to what their remaining balance was.
>>student 5: Could you-could you subtract 4 - 3?
Could you subtract 4 - 3?
>>student 6: Huh? >>student 5: Could you subtract 4 -3?
>>student 6: No. >>student 5: You can't because there's just 3.
3 digits and the 3. And there's 4 in that. And 4 - 3.
>>student 7: With 3 you can't even do nothing.
>>student 8: 6- 9, you can't do that, so you borrow from the 2.
>>student 9: This? >>student 8: Yeah, you have to borrow from the 2.
You have to put a 1 from here because you borrowed from the 2.
Now the 6 has to become 16, so you...
>>student 9: Cross it out?
>>student 8: No, you don't cross it out, you put a little 1 next to it...a little 1.
>>teacher: I mean I've gained even more information from the task than I had before.
I knew they were-they were struggling and I could tell that from
activities and assessments that I've done along the way,
but I learned much more about exactly where the struggles are and even in
specific individuals - whose struggling with what?
>>student: Can you subtract 7... 0 - 7?
>>Dion: 7. >>student: 0 - 7?
>>Dion: 7 >>student: You can't subtract it. You're going to have to re-group.
You're going to have to cross out this, and...
>>teacher: They had a very difficult time with the subtraction with re-grouping.
And part of that is because it required them to subtract across the zeros,
so having to regroup with the zeros from the beginning
it-from the very first item, for a lot of them, threw them off track immediately.
So the zero becomes what? >>student: 8
>>teacher: An 8? Where am I getting an 8 from?
Sometimes I'll ask them to justify their answer even though I know it's incorrect
because I want to know what their thought processes is because that will help me
re-teach later when I know what they're thinking.
Because sometimes what they're thinking makes sense to them
led them to the wrong answer. But it's much easier to re-teach
when I know what their approach to the problem was.
When we started the task I knew the students were still having difficulty
with regrouping so I expected that most of them would score
in the progressing range. But what I found at the end is they were able to complete
all components of the task and many students scored in the proficient range.
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