Structure
Brainstorming
Categorizing
Why?
Brainstorming encourages
creativity and allows for
collecting many possible
answers.
Roles for team members while
brainstorming:
Speed Captain –The team
member assigned this role
would say such things as, “We
only have one minute left. Let’s
hurry! Let’s get quicker with
our responses.”
Suspend Judgement Captain –
The team member assigned
this role would say such things
as, “All ideas count. Let’s not
talk about the ideas now.”
Synergy Captain –The team
member assigned this role
would say such things as, ‘What
other ideas does that give you?
Review the list to help you
think of other ideas.”
Recorder Captain – To record
the ideas as quickly as possible,
each idea on a separate piece of
paper. Assigning this job to the
Speed Captain or the Suspend
Judgement Captain facilitates
the Brainstorming.
Categorizing provides a way for
students to classify, analyze,
and synthesize information.
Suggested Activities
Statistics – Brainstorm topics
for a survey.
Statistics – Brainstorm titles
for a graph.
Estimation – Brainstorm ways
to use estimation.
Measurement – Brainstorm
items to measure.
Measurement – Brainstorm
reasons to measure the area or
perimeter of objects.
Number Sense – Brainstorm
as many ways as possible to
express the number 6.
Example: 5 = 1, 18 divided 3, 3
sets of ears, 1 hand plus a
thumb.
Geometry – Brainstorm a list
of ojbects which are
rectangular solids (spheres,
cubes, or cylinders).
Algebra – Brainstorm
equations.
Logic – Brainstorm items to
categorize.
Patterns – Brainstorm
patterns (AB, ABBA, ABC, etc.)
to construct with concrete
objects.
Number Sense – Sort the
numbers one through twenty
into categories of Even
Numbers and Multiples of Four.
Statistics – Make a survey of
fifty students to see if they have
a cat, a dog, both or none.
Statistics – Conduct a survey of
students to see which sports
they are involved in at school.
Logic – Sort a set of shells and
label each category.
Logic – Sort a set of Attribute
blocks into sets of red blocks
and blocks with four sides.
Logic – Sort the students in the
classroom by those who are
wearing something blue, and
Co-op Co-op
Co-op Co-op is a cooperative
project design built around a
cooperative team project.
Students work individually
within their teams in order to
learn something to satisfy their
own curiosity about
themselves and the world.
Each team member then
contributes to the completion
of a team project that
synthesizes the information
from all the team members.
The final product is shared
with the whole class so that
other class members may also
benefit from the learning.
those who are wearing shoes
with Velcro.
Logic – Sort classroom objects
by size, shape, color, or use.
Problem Solving Strategies –
Sort a set of word problems by
the strategies which may be
used to solve them – draw a
picture, make a table, or look
for a pattern.
Number Sense – Sort twenty
large numbers by those
divisible by three and those
divisible by five.
Geometry – Sort geometric
shapes by types of angles:
acute, right, or obtuse.
Number Sense – Each team
selects a number sentence and
prepares a skit to act it out for
the class. Each team ember
must have a role in the skit.
Statistics – Each team surveys
100 people on a topic selected
from a class list of topics. Each
team member surveys 25 of the
people, contributes to a team
graph of the 100 responses,
and reports on certain
information determined in
analyzing the results.
Mathematics in Careers –
Each team selects a career field
from a class list to research.
Each team member interviews
people with jobs in that field to
see how they use mathematics
in their jobs. Each team
member is responsible for
certain aspects of the report to
the class.
Math Strands – Each team
selects a math strand to
research. Team members
report on the strand’s content,
uses, importance, etc. Each
team member is responsible
for parts of the research and
report.
Mathematics in Sports – Each
Corners
Corners is a class-building
structure which can be used in
a wide variety of ways. It
team selects a sport from a
class list. Teams research and
report on the history of the
game, explain the rules of the
game, tell how math is used in
the game, etc. Each team
member is responsible for
parts of the research and
presentation to the class.
Scale models – Each team
builds a scale model of an
object on the class list. Each
team member is responsible
for parts of the construction
and the class presentation.
Problem Solving – Each team
creates math problems for the
class to solve. Each team
member has a role in
presenting the problem to the
class and facilitating problem
solutions by the other teams.
Probability – Each team
conducts probability
experiments with a selected
material from the class list of
coins, dice, colored cubes,
cards, etc. Each team member
is responsible for conducting a
number of trials for the team
total and will have a role in the
report to the class.
Measurement – Each team
measures objects using units of
measure listed by the class.
Each team member must
perform ¼ of all the
measurements and have a role
in the class report.
Math Games – Each team
creates a board game which
provides practice in math skills
listed by the class. Each
member of the team is
responsible for constructing a
part of the game and teaching
the other teams how to play.
Statistics – Go to the corner of
the room which is labeled with
the topic you would like to
provides opportunities for
students to learn something
about the other students in
their class and to begin to
accept individual differences.
With academic content,
Corners can introduce a topic
to the class, provide students
an opportunity to discuss their
opinion with others who agree
with them, or provide an
opportunity to summarize key
points.
Formations
Formation has students form
shapes or figures with their
bodies by holding hands.
Sometimes they are not
allowed to talk. This can be
done in teams or with the
whole class. For primary
grades, begin by marking the
formation wanted on the
ground.
survey.
Statistics – Go the corner
which is labeled with the order
of your birth.
Statistics – Go to the corner
labeled with the kind of
siblings you have.
Geometry – Go to the corner
labeled with your favorite
figure.
Measurement – Go to the
corner labeled with your
favorite measuring instrument.
Math Strands – Go to the
corner which is labeled with
the strand in math that you like
best.
Number Sense – Pick a
number from one to four and
write it down. Go to the corner
labeled with your number.
Number Sense – Draw a
picture which illustrates ½,
1/8, or
1/16. Go to the
corner labeled with your
fraction.
Number Sense-Problem
Solving – Write a word
problem using +, -, x, or . Go
to the corner which is labeled
with the operation you used.
Statistics – Go to the corner of
the room labeled with the
season of the year in which you
were born.
Geometry – form a triangle.
Number Sense – Form a
numeral 4.
Number Sense – Form the
answer to 9 x 6.
Measurement – Form the
perimeter of the rectangle
drawn on the board.
Geometry – Form an obtuse
angle.
Measurement – Form the area
of the rectangle drawn on the
board.
Number Sense – Form a
division sign.
Group Discussion
Group Discussion is a two-step
structure for discussing an
issue or question presented by
the teacher. In step one, the
teacher asks a low consensus
question and in step two, the
students talk it over. Following
the group discussion, students
share their ideas with the class.
The key issue is to share with
as much student interaction as
possible.
Number Sense – Form a
picture of 3 x 6.
Number Sense – Form the
answer to 7.5 + 8.7.
Geometry – Form a figure with
exactly one line of symmetry.
Patterns – Form an AAB
pattern.
Number Sense – Discuss the
difference between estimation
and mental arithmetic. Give
some examples of each.
Problem Solving – Discuss the
strategies which might be used
to solve the assigned problem.
Mathematics in Careers –
Discuss careers which interest
you and the ways math might
be used in those careers.
Geometry – Compare and
contrast two-dimensional and
three-dimensional objects.
Number Sense – Discuss a
plan for acting out a problem of
your choice.
Statistics – Discuss the
information represented on a
graph.
Problem Solving – Discuss
your solution to a problem and
other ways the problem might
be solved.
Problem Solving – Discuss an
alternate version of the
assigned problem.
Number Sense – Discuss the
relationships of fractions,
decimals, and whole numbers.
Number Sense – Given a set of
problems with unreasonable
answers, have the students
discuss why the answers are
unreasonable.
Example: One bus holds 40
students. There are 90
students going on the field trip.
How many buses are needed.
John said the answer is 2 ¼
because 90 40 = 2 ¼ .
Discuss his answer.
Inside-Outside Circle
Inside-Outside Circle has a
variety of uses. It can be:
 A classbuilding activity
 An activity to introduce
a concept or have
students share prior
experience with a topic.
 To share specific
information about an
activity or assignment
about to be started or
just completed.
 To practice and learn.
For Inside-Outside Circle
students stand in two
concentric circles with the
inside circle facing out and the
outside circle facing in.
Line-Ups
Line-Ups can be used in a
variety of ways: for
classbuilding, to promote
communication, to learn
respect for individual
differences, to develop
concepts, and to create shortterm teams. The teacher
provides the prompt and sets
the end dimensions. Students
then line up in order of their
responses.
Teacher-Directed Review
Tell your partner:
The next three numbers in the
pattern 2, 4, 6, 8…
A figure which has exactly two
lines of symmetry.
The difference between a cube
and a square.
Three prime numbers.
Flash Cards
Ask your partner:
The definition of the math term
on your card.
The least common multiple of
the two numbers on your card.
The unit of measure which
would be used to measure the
object on your card.
Processing
Tell your partner:
Two things you learned in the
probability lesson.
How you solved the math
starter.
Characeristics
Line up by height.
Line up by age.
Line up by order of birthday
dates.
Line up by the number of
letters in your name.
Line up by the number of
blocks you walk to school.
Line up by the number of
people who live in your house.
Line up by the number of
buttons (pockets) on your
clothes.
Line up by the number of pets
you have.
Agree/Disagree
Line up by your agreement to
the statement, “Problem
solving is the most important
part of math.”
Line up by your agreement to
the statement, “It is necessary
for children to memorize the
basic math facts.”
Line up by your agreement to
Numbered Heads Together
Pairs Check
Its main strength is in building
mastery and reviewing
previously learned
information.
Students work in pairs in their
teams to practice a new skill. A
worksheet is set up with
problems placed in pairs, and
with reminders when to stop
and check with partners.
Person one in the pair does the
first problem, while person two
acts as a coach. If the coach
agrees that person one has
done the first problem
the statement, “Division is
more fun than multiplication.”
Geometry – Name three kinds
of angles.
Patterns – Tell what comes
next in the pattern 7, 14, 21, 28,
35, _____.
Problem Solving – Would you
add, subtract, multiply, or
divide to solve this problem?
Juna had a dozen cookies, Linda
had a dozen cookies, and Brad
had a dozen cookies. How
many cookies in all?
Estimation – What is the best
estimate for the number of ears
in this room: 76, 150, or 300?
Problem Solving Strategies –
Name three problem solving
strategies we have used in the
last two weeks.
Number Sense – Tell a number
story about this picture:
.
Geometry – What does the
word symmetry mean?
Number Sense – Tell four
ways we use multiplication in
everyday life.
Mathematics in Newspapers
– Name three ways math is
used in a newspaper.
Problem Solving – Make up a
story for 53 – 28.
Mathematics in Careers –
Who uses geometry more, a car
painter or an architect?
Explain.
Solve problems on
worksheets which ask for the
following:
Patterns – The picture which
comes next in a pattern.
Patterns – To continuation of a
number pattern.
Problem Solving – Answers to
word problems.
Geometry – Lines of symmetry
on figures.
Round Robin
Send-A-Problem
correctly, he/she gives him/her Number Sense – Answers to
some praise, then they switch
computational problems.
roles.
Measurement – The measure
of objects in the room.
Algebra-Functions – Ordered
pairs on a grid.
Statistics – Answer to
questions about a graph.
Problem Solving-Number
Sense – Stories to go with
number sentences.
Problem Solving – The “make
a table” strategy.
Round Robin is a simple, yet
Number Sense – Count in
effective, two-step cooperative sequence from 50 to 100.
learning structure. In step one, Number Sense – Say prime
the teacher asks a question
numbers.
with many possible answers
Number Sense – Tell the
and in step two, the students
answers to flash cards: add
orally respond in turn to share subtract, multiply or divide.
possible answers for the
Number Sense – Say fractions
question. Team members can
equivalent to ½.
help the student who is
Statistics – Tell topics for a
responding if he or she
survey.
requests help.
Number Sense – Count by 5’s.
Number Sense – Say numbers
divisible by 3.
Statistics – Say food items
which may be used in a survey
of favorite foods.
Patterns - Say an ABC pattern
using
.
Send-A-Problem is a practice
structure which is used for
review or additional practice of
concepts. There are three
steps to follow:
Step 1: Students author
review questions – Each
student on a team makes up a
review problem and writes it
down on a flash card.
Encourage high-consensus
problems which have right or
Each member may only say one
shape each turn.
Number Sense – Tell reasons
subtraction could be used.
Problem Solving – Write a
word problem. Ask for the
solution.
Patterns – Write a number
pattern. Ask for the next
number in the pattern.
Geometry – Draw a figure. Ask
for its name. For example:
Math Vocabulary – Write a
Similarity Groups
wrong answers, verifiable by
the text. For younger students,
the format might be
standardized by using truefalse, missing word, or multiple
choice. The author of each
question asks it of his or her
own teammates. If there is a
total consensus, the author
writes the answer on the back
of the card. If not, the question
is revised so that it produces
consensus. The side of the card
with the question is marked
with a Q; the side of the card
with the answer is marked with
an A.
Step 2: Teams Send-AProblem – They pass their
stack of review questions to
another team.
Step 3: Teams respond Student 1 reads the first
question. Each team member
individually writes down his or
her answer. The team
members then compare and
discuss their answers. If they
have consensus, they turn the
card over to see if they agreed
with the sending group. If not,
they write their answer as an
alternative answer. Student 2
reads the next question, and
the procedure is repeated. The
stacks of cards can be sent to a
third and fourth group, and so
on. Upon return of the cards to
the senders, there is
opportunity to discuss and
clarify any questions indicated
on the back of the cards.
Similarity Groups involves
students with each other and
gives them a chance to create
their own preference.
math term. Ask for the
definition.
Patterns – Draw a picture
pattern. Ask what comes next.
For example:
________.
Number Sense – Draw a
picture which represents a
fraction. Ask for the fraction.
Statistics – Draw a simple
graph. Ask a question about
the data.
Problem Solving – Write a
problem with missing
information. Ask what else is
needed to solve the problem.
Measurement – Write a
problem which asks students
to measure an object. Ask for
the measure. For example:
What is the width of our math
book?
Geometry – Draw an angle.
Ask for its measure and
whether it is obtuse, right, or
acute.
Form Groups by:
Characteristics
The number of people who live
in your house.
Your birth month.
The number of buttons on
clothes you are wearing.
Your place in the birth order in
Simultaneous Sharing
Teams consult
your family (oldest, middle,
youngest, or only)
The number of books you’ve
read this year.
Preferences
Your favorite math strand.
Your favorite sport (movie,
song, color)
Your favorite animal.
Your favorite number.
The most difficult problem on
the math homework.
Classroom White Board
Share – Each team sends a
representative to the board or
to a piece of chart paper to post
their best answers
simultaneously. The teams can
continue working while some
of their ideas are being
recorded and shared with the
class.
Small White Boards Sharing –
When recording, student use
small white boards equal to the
number of people with which
they will share. After the
recording is complete, the
students pass out the small
white boards to their
teammates or to other teams.
This can be used equally well
for team responses to be
shared with other teams or
individual responses to be
shared with teammates.
Carousel Share – One person
from each team stays seated in
each team’s place while the
other teams rotate from table
to table. The team’s
representative shares the
team’s information with all
other teams as they rotate
through.
Class Notebooks – Each team
records their ideas on a threeringed sheet of notebook
paper. The sheet is placed in a
three-ringed binder under a
divider labeled with the topics
being shared. The notebook is
available for other teams to
peruse.
Roam the Room – At a given
signal, all the students float
throughout the room observing
the products of the other
teams. At a given symbol, all
students return to their teams
and report on what they found
in their roaming.
Gallery Tour – Completed
team products are displayed
around the room. Near each
product should be a sheet of
paper for other groups to ask
questions write comments
about the products. Each team
stands in front of their own
product in the classroom. At
the teacher’s signal, they pass
from one product to the next
until they have viewed all the
products in the classroom.
Students are encouraged to ask
a question or make a comment
about each product they see.
Using small slips of paper,
students make a record of the
unique ideas they recorded
from the products. They can
also discuss any questions and
comments the other students
made about their product.
Stand Up and Share –
Following a group discussion,
each team makes sure that all
their team members have an
idea to share. All students in
the class stand up. Starting on
one side of the classroom,
students begin sharing. As
each person shares, he or she
sits down. Anyone in the room
who has the same idea or a
similar idea sits down also.
The sharing continues until all
of the student are sitting down.
Team Notebooks – Each team
Team Project
Team project is very useful for
the completion of a simple
project. Team projects should
be short and easy. Students
should be able to complete the
project anywhere from a few
records their ideas and places
them in a Team Notebook.
These notebooks can be
reviewed by other teams or by
the teacher.
Teams Consult – Each team
shares its best idea(s) with the
team next to them.
Teams Tour – Teams tour
provides an opportunity for the
students to share their
products with the other teams.
In each of the four rounds, one
of the team members travels to
another team to share his/her
team’s products with the team.
In Round 1, #1 travels with the
team’s product one team to the
right (or left). #2, #3, and #4
stay and listen to the
presentation by the visiting #1.
All members return to the
home teams.
In Round 2, #2 travels with the
team’s product two teams to
the right (or left). #1, #3, and
#4 stay and listen to the
presentation by the visiting #2.
All members return to the
home team.
In Round 3, #3 travels with the
team’s product three teams to
the right (or left). #1, #2, and
#4 stay and listen to the
presentation by the visiting #3.
All members return to the
home teams.
In Round 4, #4 travels with the
team’s product four teams to
the right (or left). #1, #2, and
#3 stay and listen to the
presentation by the visiting #4.
All members return to the
home teams.
Math Games – Make a math
game for the learning center.
Geometry – Create a picture
using shapes-circle, rectangle,
triangle, and square.
Geometry – Create a design
Think-Pair-Share
minutes to a class period.
Roles may be given to each
member of the team to ensure
equal participation and
individual accountability
during the project. For
example, each student may be
required to use a different
color marker on the project
and all of the colors must be
used equally. When a variety
of omaterials will be used on
the project, assign each team
member a responsibility for
one of the materials. Social
roles can also be assigned
separately or in tandem with
material roles. Some sample
roles are:
Material-Related Roles
Scissors
Paper
Glue or paste, staples, tape, etc.
Markers, crayons, pencils, etc.
Social Roles
Taskmaster
Praiser
Materials Monitor
Recorder
Think-Pair-Share offers all
students an opportunity to
express their response to a
question or discussion topic.
The teacher poses a problem or
asks a question.
Students think about the
answer.
Students pair up and discuss
their responses.
Students share their answers
with the class.
using 2 obtuse, 2 right, and 2
acute angles.
Number Sense – Create a skit
to act out a math sentence.
Geometry – Create a design
with at least one line of
symmetry.
Patterns – Create a pattern
with objects.
Measurement – Draw a map to
a hidden treasure.
Geometry – Create a puzzle
using tangrams.
Problem Solving – Write and
illustrate a word problem.
Geometry – Make a collage of
spheres using pictures from
magazines.
Number Sense – Think of ways
math is used in our every day
lives.
Number Sense – When do you
think you will use
multiplication most in your
life?
Problem Solving – What
would be a good strategy to try
in solving this problem?
Math in Careers – What are
some ways a librarian (store
owner, football player) would
use math?
Geometry – Name some
objects in our environment
which are shaped like a
rectangle.
Number Sense – How has the
calculator helped you?
Estimation – What is a good
Three-Step Interview
strategy for estimating the
number of candies in the jar?
Measurement – What are
some reasons for measuring
area or perimeter?
Problem Solving – Why do
you think that problem was
easy or difficult?
Problem Solving – Is there
another way to solve this
problem?
Three-Step Interview is a
Concept Development
simple information sharing
What would you most like to
structure. It works best in
learn about in…(math,
groups of four, but can be
statistics, problem solving)?
easily adapted to groups of
What are some ways you use
three or groups of five.
(measurement, estimation,
In pairs, one student interviews probability) in your everyday
the other.
life?
The students reverse roles.
How did you solve this
In their teams of four, the
problem?
students round robin to share
Can you find more than
what they learned from their
one…(answer, way to solve the
partner.
problem) for this problem?
How will you use what you
have learned?
Processing
What kind of math problem
is…(hardest, easiest, most fun)
for you?
Why do you think it is
important to know how
to…(add, subtract, use a
calculator)?
Which problem on your
homework did you find…(most
interesting, most difficult)?
What did you learn from this
lesson?
What would like to know more
about?