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?
Notes:
Notes:
One Implementation
Kids notice and wonder about scenario on
projector: Think-Write-Share
Reveal the question & pass out copies
Teacher calls on one 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.
Student Response: draw rectangles and
triangles and label them so they add up to 36 (or
did with 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
W
10 8
9
9
8
10
7
11
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.
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?
Growing Worms [#5143]
In the land of Trianglia, the worms are made of
isosceles right triangles – and they grow fast! As you
can see above, a worm that is 1 day old is made of 4 of
these triangles. You can also see worms that are 2 days
old and 3 days old. If that growth rate remains constant,
how many triangles will be needed for a 4-day-old
worm? a 10-day-old worm? a 63-day-old worm?
How will you know they’re ready?
What do you hope they notice?
Hard words?
What questions do you want them focused on?
Thorny points they may disagree on?
Watching Tasks
What activities or general questions does Val use to
get students sense-making and telling her about their
thinking?
What are you learning about the students? What else
do you want to know about them to help them get
ready?
Reflections? Predictions?
Tweet #ncsm163 to share as you watch, if you want!
See Webpage for Video
http://mathforum.org/nctm/2014/session163.html
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?
Activities for sense-making
Can you draw a picture?
Pen vs. Pen
Can you act it out with materials? What materials
would you need?
http://mathfour.com/general/10-questions-toask-about-a-math-problem
Pick one to do with your group!
More activities for sensemaking
Students paraphrase the problem
Students use guessing to show what they
already know
Ask questions like, “What’s the story about?”
“What’s the action in the story?” “Does that
make sense in the story?” “Can you check if that
matches what it says in the story?”