Introductions
Name
How are you feeling about the fact that it’s a
Friday afternoon math workshop?
What’s a hope or goal that you have for today?
Getting onto Wireless
Connect to Asilomar Conference
Password 1: conference
Username: conf8690
Password 2: conf8690
About Me:
Work at The Math Forum @ Drexel.
Combined total of 60+ years of experience
working with kids on persevering and revising
their thinking, in writing, on non-routine tasks.
Author of the book of that collected wisdom:
Powerful Problem Solving
How I Lead a ProblemSolving Session
Notice and wonder
Check for and explore understanding of the
context
Independent/small-group work with targeted
share-outs as check-ins
Structured sharing-out with audience tasks
Trapezoid Teatime
What Did You See?
Trapezoid Teatime
What Did You See?
What Do You Wonder?
What Learning Goals
Could You Probe For?
Thoughts? Concerns?
What Happened with
Kids?
Keeping Kids Persevering
Where could kids get unproductive?
What kinds of work would be
productive/unproductive for YOUR goal?
What prompts or questions would encourage
kids to change focus or persevere?
WWAD?
Break! Find your new table!
Frog Farming
Farmer Mead would like to raise frogs. She wants to
build a rectangular pen for them and has found 36
meters of fencing in her barn that she’d like to use.
1.Design at least four different rectangular pens that
she could build. Each pen must use all 36 meters of
fence. Give the length and width for each of the pens.
2.If each frog needs one square meter of area (1 m2),
how many frogs will each of your four pens hold?
Context
Halfway through a 5th grade textbook unit on
area and perimeter
Assessing their ability to apply what they’d
learned
Wondering about their conceptual
understanding of area and perimeter
No manipulatives available to us
WWYD?
Talk in your groups about:
Launching the task
Preparing to support individual kids/groups who
are stuck/unproductive
Planning to have kids share their progress with the
whole group
WWYD?
Get Specific:
Kinds of stuck?
Questions to ask of those stuck kids?
How will you help kids connect to the concepts?
What strategies might you help kids to use?
Will kids need help with procedures/facts? How
will you help?
My Implementation
Kids notice and wonder about scenario on
projector: Think-Write-Share
Reveal the question & pass out copies
Teacher calls on a student to review what we are
being asked to find
Students work in their usual small groups to
solve the problem
Frog Farming
Farmer Mead would like to raise frogs.
She wants to build a rectangular pen for them and
has found 36 meters of fencing in her barn that
she’d like to use.
She knows each frog needs one square meter of
area (1 m2).
They noticed & wondered
We notice…
We wonder…
Farmer Mead would like to raise
frogs
Why does she want to raise
frogs?
She wants to build a pen
What is a frog farmer?
She has 36 meters of fencing
How big is the pen?
Each frog needs one square
meter of area
Why do frogs need one square
meter of area?
The frog is green
How many frogs does she have?
Farmer Mead is a girl
The fencing is in her barn
The pen is rectangular
What do we anticipate?
The ones who were stuck
Student Situation: Some students couldn’t get
started – they could identify one fact “She used
36 meters of fence.”
Teacher Action: Tell students, “Right, that means
the perimeter is 36 meters.”
The ones who were stuck
Student Response: When 36 meters of fence
was changed to “the perimeter is 36 meters” the
students stayed stuck and didn’t use any
strategies for finding side lengths give perimeter
The ones who took forever
Student Situation: Some students used guess
and check drawing different rectangles to find
ones that used 36 meters of fencing. It was
taking forever…
Teacher Action: Remind students of a hint: “The
first step is to divide it [the perimeter] in half.
What is half of 36? Can you find two numbers
that add to 18?”
The ones who took forever
Student Response: When given the hint to
“divide it in half” students start looking for four
numbers that add to 18 because they look at
their picture and remember rectangles have 4
sides.
Those who couldn’t do Part 2
Student Situation: Some students couldn’t start
Part 2. They could identify one fact “Each frog
needs 1 square meter of area.”
Teacher Action: Say, “Great, what do square
meters measure? Area? Yes! Now you need to
find the area of each pen you came up with in
Part 1.”
Those who couldn’t do Part 2
Student Response: When told to find area to
solve Part 2, the students stop working and raise
their hands to get more help: “I know how to find
area but I don’t get what that has to do with how
many frogs can fit in the pen.”
How would you coach the teacher?
What we tried next period
Student Situation: only knew “she uses
36 meters of fence”
Teacher Action: Confirm that matches
the story, ask them to find a way she
might have used the fence.
What we tried next period
Student Response: draw rectangles
and triangles and label them so they
add up to 36 (sometimes takes some
adjustment).
What we tried next period
Student Situation: guessed and checked inefficiently
Teacher Action: We got the group back together to
list possibilities in an organized way –
L
10
9
8
7
W
8
9
10
11
What we tried next period
Student Response: the whole class
almost instantly started yelling out all
the other possibilities as soon as they
saw our organization
What we tried next period
Student Situation: only knew “each
frog needs 1 square meter of space”
Teacher Action: Ask for guesses and
reasons about how many frogs could
fit in this pen.
What we tried next period
Student Response: Make guesses that all show
wrong thinking – 36 frogs fit in each pen, 9 frogs
fit in each pen since each frog “takes up” 4
meters of perimeter.
What we tried next period
Teacher Follow-Up: Invite students to use a
drawing to show how many frogs will fit.
Initial Response:
What we tried next period
But then…
“I did it this way but I wasn’t supposed to. It
should be 45 frogs but I drew the boxes too small.
All I had to do was multiply.”
“I can just multiply these! 6 rows and 12 columns
of frogs is 72 frogs!”
Reflections? Questions?
Current Reflections
Something you saw that you’d like to implement
or support a teacher to implement
An insight into good questions or techniques for
learning about students’ thinking while keeping
them moving forward
Other take-aways?
Questions?
Stretch Break!
At the end of 2 minutes
Please form a spectrum
Based on how much you are interested in
baseball
All you need to know…
A challenging problem
An even more challenging context
I’ll lead some of my favorite activities for
understanding a context well enough to
represent it algebraically
Find a WRONG ANSWER:
How many innings had he played
before the game started?
How many runs had he given up before the game
started?
How many runs had he given up after his ERA
changed?
How many innings had he pitched after his ERA
changed?
Final Reflections
Something you saw that you’d like to implement
or support a teacher to implement
An insight into good questions or techniques for
learning about students’ thinking while keeping
them moving forward
Other take-aways?
Questions?