1. ì
Engaging
Students
in
Learning
CPSB
High
School
Mathema2cs
Inservice,
2012

2. Organized
Chaos

3. COMPASS
« Se#ng
Instruc-onal
Outcomes
(1c):
Establishing
clear,
rigorous
objec2ves
that
describe
what
students
will
learn.
« Managing
Classroom
Procedures
(2c):
Establishing
a
smoothly
func2oning
classroom
through
the
management
of
instruc2on
and
transi2ons
to
allow
for
maximum
learning
for
all
students.
« Using
Ques-oning
and
Discussion
(3b):
Strategically
using
a
varied
set
of
ques2ons
to
engage
all
students
in
discussion
around
rigorous
content.
« Engaging
Students
in
Learning
(3c):
Asking
all
students
to
do
work
that
is
rigorous
an
intellectually
challenging.
« Using
Assessment
in
Instruc-on
(3d):
Using
clear
assessment
criteria
to
drive
instruc2onal
choices
throughout
the
lesson
and
at
the
end.

4. Standards
of
Mathematical
Practice
« Make
sense
of
problems
and
persevere
in
solving
them.
« Reason
abstractly
and
quan2ta2vely.
« Construct
viable
arguments
and
cri2que
the
reasoning
of
others.
« Model
with
mathema2cs.
« Use
appropriate
tools
strategically.
« ALend
to
precision.
« Look
for
and
make
use
of
structure.
« Look
for
and
express
regularity
in
repeated
reasoning.

5. Attention
Getter

6. Marshmallow
Challenge
« 20
s2cks
of
spagheN
« 1
yard
of
tape
« 1
yard
of
string
« 1
marshmallow

7. Marshmallow
Challenge
« The
winning
team
is
the
one
that
has
the
tallest
structure
measured
from
the
table
top
surface
to
the
top
of
the
marshmallow.
« The
en2re
marshmallow
must
be
on
top.
« Use
as
much
or
as
liLle
of
the
kit.
« Break
up
the
spagheN,
string,
or
tape.
« The
challenge
lasts
for
18
minutes.

8. Marshmallow
Challenge

9. Marshmallow
Challenge
50
40
30
20
10
Height
(Inches)
0

10. Marshmallow
Challenge

11. Marshmallow
Challenge
« Why
do
kindergarteners
create
taller
and
more
interes2ng
structures
than
business
graduates?
« The
marshmallow
is
a
metaphor
for
the
hidden
assump2ons
of
a
project.
« What
are
your
assump2ons
this
school
year?

12. Mix-­‐N-­‐Match
« Each
student
is
given
a
card
with
some
type
of
problem
or
informa2on
on
it.
« Students
‘mix’
and
find
the
person
with
a
card
that
‘matches’
theirs.
« As
students
pair
up,
they
move
to
the
outside
perimeter
of
the
classroom
and
stand
together
as
a
pair.
« Once
everyone
has
found
their
match,
students
confer
with
another
nearby
pair
to
double
check
that
they
do
indeed
make
a
match.
« Redistribute
if
desired.

13. Mix-­‐N-­‐Match
Name
the
property
In
simplest
radical
form,
find
the
demonstrated:
distance
between:
7! 9!5 = 7!9 !5
( ) ( ) (1, !3), ( 7, 2)
Simplify
(posi2ve
exponents):
Sketch
the
graph
of:
!3 2
6x y
( ) y = 2sin x
7
x
Find
the
remainder
when
Evaluate
the
determinant:
3
2 " 1 !4 %
3x + 2x
! 5x ! 2 $ '
is
divided
by
(
x
+
2
)
# 3 !2 &

14. Line-­‐Ups
« Each
student
is
given
a
card
with
some
type
of
problem
on
it.
« Students
evaluate
the
answer
to
their
problem
and
then
line
up
in
order
from
least
to
greatest.
« Once
students
are
lined
up,
they
then
discuss
their
card
and
posi2on
with
a
nearby
partner.
« Partners
may
be
formed
by
pairing
up
or
by
‘folding’
the
line
in
half.

15. Line-­‐Ups
« Line
up
in
order
from
the
teacher
who
has
taught
the
most
years
to
the
teacher
who
has
taught
the
fewest.
« Fold
the
line.
« The
more
experienced
teacher
tells
the
less
experienced
about
their
most
embarrassing
teaching
moment.
« The
less
experienced
teacher
then
shares
with
the
more
experienced
how
that
situa2on
could
have
been
avoided.

16. Line-­‐Ups
« Frac2ons,
Decimals,
&
Percents
« Sta2s2cs
« Order
of
Opera2ons
« Algebraic
Expressions
« Angle
Measures
« Radian
and
Degree
Measures
« Arithme2c
and
Geometric
Sequences

17. Inside-­‐Outside
Circle
« Students
form
two
concentric
circles,
with
equal
numbers
of
students
in
each
circle.
Students
stand
face-­‐to-­‐face
with
a
partner,
one
person
from
the
inside
circle
and
one
from
the
outside.
« The
circles
rotate
according
to
the
teacher’s
instruc2ons.
« Partners
take
turn
asking
each
other
ques2ons,
quizzing
each
other
with
flashcards,
sharing
some
informa2on,
or
answering
ques2ons.

18. Inside-­‐Outside
Circle
« Structure
works
best
when
the
problems
being
solved
do
not
require
lengthy
paper-­‐pencil
solu2ons.
« Structure
is
more
conducive
to
short-­‐answer
or
higher
level
thinking
ques2ons
that
can
be
answered
verbally.
« Any
ideas?

19. Rally
Coach
« Students
pair
up
and
decide
who
is
Person
A
and
who
is
Person
B.
There
is
only
one
sheet
of
paper
and
one
pencil
for
each
student
pair.
« Teacher
poses
a
problem,
verbally
or
on
paper.
« Person
A
begins
contribu2ng
to
the
solu2on
of
the
problem
in
wri2ng
and
states
aloud
what
(s)he
is
doing.
« Meanwhile,
Person
B
watches,
listens,
and
coaches.
If
necessary,
Person
B
reteaches.
« Reverse
roles.

20. Rally
Coach
« Mul2-­‐Step
problems
« Comple2ng
worksheets
« Genera2ng
lists
« Constructed
response
items

21. Round
Table
« Similar
to
Rally
Coach
but
involves
four
students
instead
of
two.
« Students
take
turns
passing
the
paper
and
pencil,
each
wri2ng
one
answer
or
making
a
contribu2on.

22. Round
Table
« Given
three
points,
A
(4,
-­‐7),
B
(3,
1),
and
C
(-­‐2,
0)…
« Person
1
finds
the
slope
of
the
line
passing
through
A
and
B.
« Person
2
writes
the
equa2on
of
line
AB.
« Person
3
writes
the
equa2on
of
the
line
parallel
to
AB
and
passing
through
C.
« Person
4
writes
the
equa2on
of
the
line
perpendicular
to
AB
and
passing
through
C.

23. Mix
Pair
Rally
Coach
« Each
student
is
given
a
card
containing
some
informa2on.
« Students
‘mix’
around
the
room
and
find
a
partner,
Person
A
and
Person
B.
« Person
A
solves
the
problem
on
his/her
card
while
Person
B
watches,
checks,
and
praises.
« Person
B
then
solve
the
problem
on
his/her
card
while
Person
A
watches,
checks,
and
praises.
« Partners
reteach
as
necessary.

24. Showdown
« Teacher
selects
one
student
from
each
group
to
be
the
Showdown
Captain.
« The
Showdown
Captain
draws
the
first
card,
reads
the
ques2on,
and
provides
think
2me.
« Working
alone,
all
students,
including
the
Showdown
Captain,
write
their
answers.
« ‘Showdown’
is
called
and
teammates
share
and
discuss
their
answers.

25. Showdown
« The
Showdown
Captain
leads
the
checking.
« If
correct,
the
team
celebrates;
if
not,
teammates
tutor,
then
celebrate.
« Repeat
with
a
new
captain.
« Modifica2ons—oral
ques2ons,
ques2ons
from
a
handout,
or
ques2ons
displayed
by
a
projector

26. Classroom
Setup

27. Stations
« Sta2on
1:
Students
will
be
given
eight
index
cards
with
func2ons
and
func2on
answers
on
them.
They
will
match
the
func2ons
with
the
appropriate
func2on
answers.
Then,
they
will
evaluate
func2ons.
« Sta2on
2:
Students
will
use
a
ruler
to
perform
the
ver2cal
line
test
on
graphs
of
rela2ons.
They
will
determine
if
the
rela2on
is
a
func2on.
They
will
construct
a
graph
that
is
a
func2on.
Then,
they
will
determine
if
a
rela2on
is
a
func2on
by
analyzing
coordinate
points.

28. Stations
« Sta2on
3:
Students
will
be
given
a
calculator
to
help
them
solve
a
real-­‐world
linear
func2on.
They
will
write
and
solve
a
linear
func2on
based
on
two
data
points.
« Sta2on
4:
Students
will
be
given
a
number
cube.
They
roll
the
number
cube
to
populate
a
rela2on.
They
find
the
domain
and
range
of
the
rela2on
and
determine
if
it
is
a
func2on.
Then
for
given
rela2ons,
they
determine
the
domain,
range,
and
whether
or
not
it
is
a
func2on.

29. Questions

30. References
« Kushnir,
Dina.
(2001).
Coopera*ve
learning
and
mathema*cs:
High
school
ac*vi*es.
San
Clemente,
CA:
Kagan
Publishing.
« The
Marshmallow
Challenge:
hLp://marshmallowchallenge.com