Using Ratios to Solve Real-World Problems (CA Dept of Education)


My name is Travis Burke. I’m a teacher on
special assignment in Santa Maria-Bonita School District. I work in professional development,
specifically in math with other teachers. Today’s lesson was a formative re-engagement
lesson, which is essentially starting with the “act on evidence” piece to design the
lesson. So in our previous day’s work, this class worked on using ratios to figure out
the intensity of chocolate milk. And we made posters and we did a performance task, and
I took all of that work and I looked at it at home and decided here are some powerful
strategies that my students are using, and I’d like to examine those to promote those
with the class. So when we came in today, we started with clarifying our targets. Okay,
let’s read it together. all: I can solve real-life problems using ratio. This is a big group
of English language learners, so when we’re clarifying the learning targets, I make sure
I have a content target and also a language target. all: I can critique the work of others
and construct collaborative arguments. That’s a mouthful, right? Let’s look at this word
“critique.” Just hands up, you’ve heard this word and are familiar with it. Awesome, I
get to teach you something. So when you critique something, you decide on what’s good about
it, how it works, and what can be improved. Does that make sense? So sometimes people
would critique, like, a piece of art. So if you drew a tiger, and it was all orange, but
you forgot the stripes, someone could say you did a really great job on the orange,
the shape of the tiger’s great, but you need to add what? The stripes, okay? So that’s
critique. And then we break down the language. So in the session you would see me talking
about the words “collaborative” and “argument” and “intensity” and a few things so that they
get that real academic language and learn how to speak to each other in an academic
setting. This last part, “collaborative arguments.” I know you’ve worked on writing arguments,
right? In writing, you learned how to write arguments. It’s not the kind of arguments
you have with your brother and sister, though, right? Those are not collaborative arguments.
Those are “I’m gonna win, you’re gonna lose” arguments, right? And you’re not even gonna
play fair. So we’re not trying to have a fight in here today. That’s not what I mean by “argument.”
When we do an argument, we’re trying to come up with what’s best and prove it with evidence.
So today’s lesson, the students were going to look at two completed strategies of student
work and do some interpreting of the evidence they saw there. And then they were gonna teach
each other how these two strategies worked. And the goal in that is that the students
would get a lot of time to talk to each other and really start being part of the formative
process themselves. While this is going on, I went around the room with my clipboard and
I was listening for students who had really solid explanations and I preselected them
to share out with the group so that I could control the learning targets and really match
it back up to what was going on. Good explanation. When we share this, can I ask your group to
share first? When they’re talking to their partners, they were interpreting the evidence
of the work they saw on the page and preparing to teach their partners. The way I like to
do my instruction and design experiences for students is to really go around in circles
with that formative process, because then you’re really doing authentic work based on
students, and I always find they can teach each other in a way that I just can’t teach
them. And once you teach someone something, you really start to hold onto it a little
better. So after the students finished up teaching each other, I wanted them to critique
each other’s work, or critique the strategies they saw for which one was best and which
one was more efficient. And then as a group of four, they were interpreting really the
strategies they saw and eliciting evidence from each other and trying to convince each
other. So I-I had a couple of kids that were sceptics in the group and I-I would pick on
them to try to convince their peers that their way was right, or that their way was the way
the group was going to…vote on. See if you can convince your partners here to vote for
B. So that voting process was our collaborate arguments. I wanted the kids to talk about
which strategy they thought was the best, and why, and use mathematical evidence. I
like–I prefer A because I like seeing models like this. Okay. The model helps? As I went
around, I listened for some students who had arguments for both sides, and I chose them
to speak out to the class. Yeah. Would you mind sharing your argument when it’s time?
Building the instruction on top of student work was my goal, so right about that point
I started making sure I was instructing the efficiency of each strategy. The goal of this
lesson was to move our–my students more from the counting stage to scaling for ratios,
which is a much more sophisticated strategy. How many of you would choose strategy B if
you had to do a thousand? So after this session, they’ve basically looked at some completed
student work, unpacked it, learned a couple of new strategies, talked to each other. I’ve
done a little bit of instruction laid on top of that, and I felt they were ready to do
another individual performance task. I really wanted them to know I’m gonna take this work,
we’re gonna look at it, and I want to find out what you know. So I’m interpreting evidence.
Instead of grading it, Mrs. Burke and I are gonna look at these and we’re gonna figure
out what you know and what you still need to know, and we’re gonna see if there are
any surprises in there, and it’s gonna help her decide what you do next week in math.
Isn’t that cool? So this is like evidence. We’re like detectives. We’re looking for evidence.
And what we’re looking for is: Did you show you’re learning with the strategy for ratio?
And if you did, we’ll move on to some maybe more efficient strategies. And if there are
still some areas we need to work on, we’ll–we’ll help design some things that’ll get you there
and then we’ll try this again. I like to end by going back to our learning targets, so
I close the lesson and I notice some kids having a-ha moments and trying the new strategies.
I wanted to honor their effort and really build that growth mindset. Okay, I want to
celebrate some things I saw. I saw a lot of people trying the ratio table strategy and
a couple of you trying the bar model strategy. That’s huge to try something new. So good
job. Way to try that out. [chuckles] So you did good at–at trying all these goals. We
solved some real-life problems. You critiqued some work together. And you participated in
the academic conversations. Academic conversations, that’s going really well. I’ve seen even progress
in the last couple days on it, so keep up with that. That’s really gonna make you strong
and…help you do college or career or whatever goals you have in the future. For other teachers
out there that want to do formative lessons like this, I think some of the key ingredients
are…really looking at what your students are doing and moving from there, so acting
on that evidence. That helps me design the next lesson to be a real natural step for
my students. And it also gives me an anticipation of what they’re going to do, which, when I’m
monitoring around the classroom, I feel like I can make more effective moves and I can
choose on more effective students to share so that we really keep the learning level
up and we can ramp up. It also applies to areas like language arts. You can see this
in writing. So if you took a specific part of writing, say you were looking at…writing
with voice, and you really looked at two different student samples, the students could really
hone in on that and then improve in that area. And you can use this across all curricular
areas. It’s really just basing your work on what your students are doing, and then acting
on that in a way that’ll move them to the next level.

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