I volunteered to do the first lesson study for our professional learning team. Having had some experience with lesson study I figured I would take the risk and jump right in. This lesson was done in April of 2013. This particular idea comes from the Math Twitter BlogoSphere #MTBoS. The idea I brought to the group was based on three act math tasks via Dan Meyer. Cups are stacked inside each other and a model is created so that students can predict how many cups to get to a certain height. Read about it here.
Being our first lesson that we studied everyone was very interested in three act math tasks. Also our math coach from the board participated as well. Thank you Robin McAteer. (@robintg). She did an amazing job observing the lesson, creating a video and creating a summary of observations.
So what was discussed in our pre-planning:
1. Groups would be made by ability. (Since we have learned the negative consequences of this.)
2. The students would ask the questions based on the image of me standing beside a cup. Come up with a stacking plan, guess to low, too high and give a best guess. Letting the students decide how to stack the cups was a risk. Who knew what they would do?
3. Each group would be required to create a poster with the following: a table of values, a graph, an equation and a stacking diagram.
4. Once a group was done a particular stacking method they would redo the process.
5. Students would fill out an exit card at the end of class.
6. Observers would fill in this form while watching the lesson.
Lesson: Classroom Observations (Cups Lesson)
Learning Goals:
®
The
students will make connections between a real life context and a mathematical
model
®
The
students will use the mathematical model to solve a problem
®
The
students will use different representations, and make connections between
representations (algebraic, graphical, numerical / table of values)
Were the learning goals met?
Discouse / Accountable Talk
§ Were the students talking
about Math? Were they asking each other
questions?
Explaining to
each other?
§ Were the student thinking
critically?
– making
connections, conjectures,
choosing tools and strategies, reflecting on thinking, justifying
Differentiation / Engagement with task
· Was the task appropriate for students to engage in learning?
· Were students connecting to prior learning?
· Grouping for learning (Similar ability groupings)– did it work ?
Questioning
§ Student to Student questioning
§ Teacher questioning /
scaffolding – what did the teacher say?
how did students respond?
Other observations?
7. Here is a picture of the stems I used.
I blogged about the activity on my blog at slamdunkmath.blogspot.ca
Here are notes that I made to help me be organized.
CUP STACKS
·
Provide all observers with:
Photocopy of
names with pictures
Observation
sheet
Lesson plan
Group Guess
Sheet
Groupings
|
Timing
|
Teacher
Moves
|
Observations
/ Improvements
|
|
Before students arrive
|
·
Photo of Al with cup on floor
showing on the overhead
·
Desks grouped in 3’s
·
Groups of 3 by ability-pre
determined (variable depending on who shows up)-name tags on the desks
·
Scrap paper for students to
generate a question or questions
·
Cups, chart paper, markers,
rulers, meter sticks ready and waiting
·
Stems ready and waiting
|
|
|
As students arrive
|
·
Hand them a cup, and
encourage them to find their name at a set of desks
·
After announcements ask
students to write down any questions that come to mind when looking at the
picture
·
Write questions on the board
and settle on “How many cups to reach Mr. Overwijk’s height”-hopefully
|
|
|
9:10-9:20
|
·
Have each group decide how
they will stack their cups and fill in Guess Sheet for Cup Stacks
·
Ask them if they need any
information to help answer the question? Provide the information or the tools
to get the information.
·
Once they are committed they
can grab 10 cups, ruler, chart paper, markers, graphing calculator, anything
else they need
|
|
|
9:20-9:25
|
·
Outline product for chart
paper. Title, Group members names, diagram (picture) of stacking plan,
different representations ( table, graph, equation)
·
Calculation of number of cups
needed (multiple ways if possible)
|
|
|
9:25-9:55
|
·
Monitor group work and
discussions
·
Any groups that have
generated a poster can redo the entire process with a new stacking plan
|
|
|
9:55-10:05
|
·
Exit Card
·
Equipment away
|
|
A) France (the principal) commenting how nervous I was. This was nerve racking. Presenting a lesson in front of many people whom I respected deeply and did not want to disappoint. I think being slightly nervous can increase performance.
B) Other teachers in the room interacted with groups. This would be something that we would need to work on. The lessons needed to be something one teacher could pull off.
C) Student engagement was visible. Accountable talk was visible.
D) I mentioned that I was panicking once groups started because six of seven groups all stacked the same way (top bottom top etc.). I wanted to interrupt and steer some groups in another direction but this was not the plan. I let it go and groups quickly finished and went on to a second technique to stack. Whew!
Questions
The math coach (Robin) was kind enough to create a list of all the student questions.
Student Questions from the Teacher / Cup Picture
How many cups
would it take to be the same height of Mr. Overwijk?
How many cups does it take to make Mr. O’s height?
What is the difference in size?
How many times is the cup smaller than Mr. O?
How many cups does it take to make the same size?
How big is the cup?
How big is Mr. Overwijk?
What are the dimensions of the blackboard?
How many cups will equal Mr. Overwijk’s height?
In cups, what is the width of Mr. Ovewijk?
Why is the cup on the floor?ow tall is Mr. O?
What is the height of the cup?
If Mr. O is 6
feet tall, how tall is the cup?
How tall is the cup?
How tall is he?
How many cups would it take to reach Mr. O’s height?
What is the volume of the cup?
Why is Mr. Overwijk standing next to a cup?
What is the scale?
How do you find the height of the cup if you know Mr.
Overwijk’s height?
How many cups do you need to make a Mr. Overwijk?
Are you able to make an outer shell of Mr. Overwijk
with the cups?
Why does your shirt match your cup?
Why?
What is the difference in height between Mr. Overwijk
and the cup?
Height of the cup?
Height of Mr. Overwijk?
How many cups does it take to get to the same height of
Mr. Overwijk?
How far is the teacher from the cup?
How long is the cup?
How tall is the teacher?
How many cups do you need to reach up to the teacher?
How many more cups are needed stacked up on each other
to be the same height as Mr. “O”
How tall is this one?
How tall is Mr. “O”?
What’s the height difference between Mr. Overwijk and
the cup?
How far are they apart?
(cup/Overwijk)
Is it supposed to be a graph of some kind? If so, what kind?
What’s the difference in height?
What are you doing beside a cup?
Height difference?
Why the hell is that cup on the floor?
Stand up straight!
Your legs are cracking me up (oompa-loompa)
How many cups equal your height?
Again Robin summarized the exit card responses
Exit Card Summary
|
Describe what you learned today
Red – Math
Green-
Stuff about Mr. O
Brown –
Group work/ Social
Black - Other
|
After today’s activity, what are you unsure about or
wondering about?
Red – Math
Blue –
Context / situation
Brown –
Group work/ Social
Black – Other
|
Name
|
|
That the
result can change depending on how you stack them
|
If I’m in the right
class
If the
result will change if different cups were used (bigger width)
|
A
|
|
I learned
that Mr. O is same as 1 cups height which is 11.3
|
I’m not sure
about the equation
|
J
|
|
I learned how
to create proper graphs for this
|
I am still
kinda confused about equations
|
M
|
|
I learned how to find
out how tall you have to be if you want to stack 18 cups on top of each
other. I
also learned how tall Mr. O is.
|
I’m
wondering how many cups would need to be stacked up to reach my height
|
K
|
|
I learned
proper graphing skills and when to use linear regression
|
Not a lot, just some
formula crap
|
C
|
|
I learned that
you need at least 1 measurement to make a graph. It
would have been quite hard to figure anything out without the knowledge of
Mr. Overwijk’s height
|
I’m
wondering how you would begin to go about the same activity if you do not
know the height of the person
|
D
|
|
I learned that the
number of cups… the weight of Mr. Overwijk –
80. If cups is 20.4 cm.
|
There is nothing that I
am unsure about or wondering about
|
R
|
|
I learned
that you need to stack about 17 cups to make Mr. O’s height
|
Nothing
|
S
|
|
I learned how
to graph properly
|
I’m wondering
you could you start the graph with
|
I
|
|
I learned
how many cups Mr. O is in height
|
What is the point of this
|
A
|
|
I learned
how much cups are Mr. O’s height
|
How much
cups does Lebron James take
|
I
|
|
Stacking cups, teamwork , sharing
|
What was the point of
this, will this save my life one day stacking cups
|
J
|
|
I knew how to equal the
height and redo something.
|
Nothing
|
B
|
|
I learned that
with every sample of data, an equation and graph are required. I
also learned that John should never be a math teacher
|
Is it possible
to switch x and y?
|
H
|
|
Teaching
people is hard
|
Nothing
|
J
|
|
I’ve learned
that there are many ways to find the same answer
|
That why can
one point change the whole equation
|
Y
|
|
I learned
that Mr. Overwijk’s height in cups is 16.2 cups
|
I am
wondering how many cups would it take to reach my height
|
K
|
|
I learned
today that how much cups is there for Mr. Overwijk
|
Graphs
|
Y
|
|
I learned B is
cranky on Thursday’s, and that I do all the work
in the group and she just writes it out
|
Why
B’s cranky, and why people were watching us and taking pictures… kinda
weird
|
M
|
Robin also created a video which we cannot share (unfortunately). Too bad-it was pretty cool to watch.
At the end of the day we were all amazed at the learning that went on as this became a very student centered lesson as opposed to a teacher centered lesson. A great start to our journey.
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