Transcript Anticipate - The Math Forum @ Drexel

Practicing the 5 Practices
Using Archived Student Work
Max Ray-Riek, The Math Forum, NCTM
Twitter: @maxmathforum
[email protected]
The 5 Practices
1.
2.
3.
4.
5.
Anticipating
Monitoring
Selecting
Sequencing
Connecting
The Teddy Bears’ Banquet
Ursinus Hotel is one of the world’s few hotels just for
bears. The tables in its banquet room are regular
hexagons with room for one seat along each side. In
other words, one table standing alone seats six bears.
To make room for dancing at the Teddy Bears’
wedding banquet, the staff arranges the tables in a
long row along one side of the room.
Anticipate
What do you notice?
How do you count the bears?
Anticipate
What do you notice?
How do you count the bears?
Anticipate
What do you notice?
How do you count the bears?
Anticipate
How do you see the 10th step?
How do you count the bears?
Anticipate
Ursinus Hotel is one of the world’s few hotels just for bears. The tables in its
banquet room are regular hexagons with room for one seat along each side.
In other words, one table standing alone seats six bears.
To make room for dancing at the Teddy Bears’ wedding banquet, the staff arranges the
tables in a long row along one side of the room. When they connect two tables
together, here’s how the seating looks:
1. How many guests can sit at 10 tables?
2. How many guests can sit at 25 tables?
3. How many guests can sit at 100 tables?
Extra 1: Use either words or numbers and symbols to write a rule
for calculating the number of bears that can sit at any given number
of tables.
Extra 2: How many tables would it take, arranged in one straight
row, to seat 120 bears?
Anticipate
Challenge 1: Solve the problem (including at least
Extra 1) based on how you see the pattern and count
the bears. Then do Challenge 2.
Challenge 2: Solve the problem (including at least
Extra 1) based on a different way of seeing the
pattern. If time allows, do Challenge 3.
Challenge 3: Repeat Challenge 2.
Select
Establish Mathematical Goals to Focus Learning
Select
What are many different mathematical goals that we
could explore/learn about/assess using student ideas
about “Teddy Bears' Banquet”?
Select, Sequence, Connect
Read the student work that you received.
As a group of 3, decide:
• One of the many math topics to focus on.
• Which students would you SELECT to share their
work in light of that topic?
• What SEQUENCE would you ask the students to
share their thinking?
• What CONNECTIONS would you like students to
make as they look across student work?
Giving I notice… & I wonder… feedback
“I notice that you _________________________.
That was awesome because _______________.”
“When you said __________________________, I
wondered ______________________________.”
Select, Sequence, Connect
What did you consider in selecting? Why does
selecting matter?
What would it take to get better at selecting?
Select, Sequence, Connect
What did you consider in sequencing? Why does
sequencing matter?
What would it take to get better at sequencing?
Select, Sequence, Connect
How did connecting play a role in what you designed
for students to do?
What are other ways of connecting the ideas,
strategies, and representations?
What would it take to get better at connecting the
ideas, strategies, and representations?
Stop and Reflect
Question 1: Archived Student Work
Teachers could choose to look at student work this
way:
• Before doing a task, using student work
provided with the task or from other teachers or
previous years
• While doing the task, by breaking the task
across math sessions
• After doing the task, using the work they collect
from their students
STOP
Which of these options feel useful to you? What
would make them most useful?
Stop and Reflect
Question 2: Looking at Student Work Together
Teachers can look at student work:
• Alone
• With building colleagues
• With other local colleagues
• With colleagues online
STOP
Which of these options feel useful to you? What
would make them most useful?
Make a Plan
What happened in this session that you want
teachers you work with to do?
What is your plan for how they could make this
exercise maximally useful?
What would it take to make that plan happen?