Team members:
(Revised 4-16-13)
Date of lesson:
Time and location:
Instructor:
Grade level/ Course: 3rd / 4th Grade
Title of the Unit: Unit 9: Divide Greater Numbers
Title of the Lesson: Divide 1-Digit Numbers into 3-Digit Numbers, PART I
1.
Mathematical Practice to Focus on during this Lesson Study.
Other Overarching Goals (not specific content goals)
Look for and express regularity in repeated reasoning.
2.
Important Mathematical Concepts of this Lesson (Include Standard)
CA Standard
NS2.2 memorize to automaticity the multiplication table for numbers between 1
and 10.
Leads to:
NS 2.5: Solve division problems in which a multi-digit number is evenly divided by
a one-digit number.
CCSS Standard:
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10-90
(e.g., 9x80, 5 x 60) using strategies based on place value and properties of
operations.
Multiplication of multiples of ten
Subtraction
Place value
Division is equal groups of a whole (Fair sharing)
3.
Research Question
What do you hope to learn about student understanding/misunderstanding from this lesson
study? What evidence will be collected during the lesson?
Will students have difficulties with multiples of ten?
Vargas/CaMSP/PVUSD 2013
Page 1
Will students understand that the number increases because of the increase in place value?
Will students be able to select the multiple of ten that most efficiently addresses the target
number or do they need to make several tries with multiples of ten?
Vargas/CaMSP/PVUSD 2013
Page 2
Progression of Lesson
Materials Needed:




Document camera
Number Talk problems
Worksheet for guessing
closest friendly number
Worksheets with grid for
working out division
problems
Activity/Questions
I.
Things for teacher to
remember/Anticipate
students’ responses
What observers should
look for
Have students show with
their hands if they
understand and agree
with the norms.
Do students
demonstrate by waving
their hands that they
have heard and agree
with the norms?
Anticipatory Set
Introduce myself.
Present the norms for the lesson
(based on CGI):




We all make mistakes.
Listen respectfully.
Be ready to re-voice what
other students have said.
Be ready to share out what
was discussed in your group.
I DO
Number Talk: We are going to work
with some numbers that are called
“friendly” numbers. After we work
with these numbers I will ask why
Make clear that the digit
you think they are called “friendly”
1 stands for a different
numbers.
number each time. First
it is in the ones place,
Ask students: What is…
then tens place, then
hundreds place.
2x 1 =?
2x 5 =?
2 x 10 = ?
2 x 100 = ?
Ask students: Why do the products
increase?
Ask students to multiply:
Vargas/CaMSP/PVUSD 2013
Keep in mind that the
students are not “adding
a zero” but multiplying
twenty tens, thirty tens,
Do students answer that
adding zeros is the
reason why the
products increase?
Do students understand
that the digit 1 stands
for a different number
each time?
Do students want to
explain by saying they
got the answer by
Page 3
etc. Model if necessary.
2 x 20 = ?
2 x 50 = ?
2 x 80 = ?
2 x 300 = ?
2 x 700 = ?
multiplying 2 x 2 and
adding a zero?
Example: 20 + 20 =
What reason do
students give for calling
the numbers friendly?
Ask students,

“What pattern do you see?”

Circle the Friendly Numbers
and ask: Why do you think
these are called “friendly”
numbers?

What examples do
students give for
unfriendly numbers?
What answers and
examples do students
give for making an
unfriendly number into
a friendly number?
What do you think would be
an example of an
“unfriendly” number?
Extension:
Ask: What is the answer to:
2 x 1000 = ?
2 x 3000 = ?
Remind students that
the digit 1 is one
thousand and we are
summing 2 groups of
1000.
1000 + 1000
Do students say they
multiplied 2 x 1, got 2
and put three zeros
after the number?
Explain how you got your answer.
II. MainActivities/Tasks/Questions
WE DO
Pass out student worksheet: Guess
the Friendly Number
To scaffold this activity, ask the
student for some Friendly Numbers
and write them above the box for the
student’s name. (ex. 5, 10, 20, …,100,
200, 300, …, 1000, 2000, …).
If students suggest other
friendly numbers that
are not as efficient, ask
students if this number
will get you the closest to
the target number.
Have students practice selecting
friendly numbers that will come
close to a given number, when
multiplied by the one-digit number
(2).
Use Math Talk/Number
Talk strategies
throughout the
presentation of the
Vargas/CaMSP/PVUSD 2013
Do students have
difficulties selecting the
multiple of ten that is
most efficient?
Page 4
lesson.
Students’ guesses may not result in
numbers larger than the given
number.
YOU DO
Have students work on their own (or
in groups/partners) to come up with
friendly numbers that come close to
a given number, when multiplied by
a one-digit number (3).
Have students share their guess and
explain how they got their guess.
Students may need more practice
before going to Part II which uses
Friendly Numbers for division. The
WE DO and YOU DO may be
spread out as a Math Talk over the
course of a week, taking only 10-15
minutes a day.
Strategies:






Ticket Out the Door:

Have students on their own make
guesses using friendly numbers to
find products that come closest to a
given number.
Go over student work and select
papers to show class (Do not show
students’ names.).
Select papers that have interesting
strategies to find the friendly
number. Show papers with
misunderstandings and those that
did not follow the directions to use
friendly numbers.

Thinking time.
Show you have
an answer with a
thumb against
chest
Use other fingers
to show how
many ways can
come up with an
answer.
Students share
how got the
answer. Why?
With class
determine if one
of the answers is
the right answer.
Use Think, Pair
Share and have
students share
out what was
said in their
group.
Use re-voicing to
promote
participation and
reinforce
strategies.
Ask students if
they have
anything to add
on.
To complete the lesson on this strategy go to Friendly
Numbers and Rectangular Division, Part II
[See below for worksheets to Part I.]
Vargas/CaMSP/PVUSD 2013
Page 5
Number Talk
2x 1=
2 x 20 =
2x 5=
2 x 50 =
2 x 10 =
2 x 80 =
2 x 100 =
2 x 300 =
2 x 1000 =
2 x 700 =
2 x 3000 =
Vargas/CaMSP/PVUSD 2013
Page 6
What are some Friendly Numbers?
What
NAME: _______________________________________
Guess the Friendly Number!!!!!!!
Multiplying
2 by the Friendly Number
M
u
l
t
i
p
l
y
Multiplying i2 by the Friendly Number
nM
gu
l
bt
yi
p
tl
hy
Multiplying 2ei by the Friendly Number
Mn
ug
F
rl
it b
ei y
np
dl t
lyh
yi e
Multiplying 2n by the Friendly Number
M
guF
N
ulr
bti
m
byie
epn
rtld
hyl
Vargas/CaMSP/PVUSD
2013
eciy
on
FgN
m
comes closest to the number ___23____.
M X
= ____________
u
l
t
comesi closest to the number ____41___.
p
l
y
i
n
= ____________
M X
g
u
l
b
t
comesyclosest to the number ___124_.
i
p
t
l
h
y
e
i
n
= ____________
F X
M
g
ur
lbi
tye closest to the number __72___.
comes
in
pt d
lhl
yey
= ____________
iM X
u
nFN
gr ul
Page 7
m
it
bebi
ynep
rl
(YOU DO)
NAME: _______________________________________
Guess the Friendly Number!!!!!!!
Multiplying 3
by the Friendly Number
M
u
l
t
i
p
l
y
Multiplying i3 by the Friendly Number
nM
gu
l
bt
yi
p
tl
hy
Multiplying 3ei by the Friendly Number
Mn
uFg
lr
ti b
iey
pn
ldt
yl h
iye
Multiplying 3n by the Friendly Number
M
gNF
u
ulr
bmi
t
ybe
i
epn
tr d
l
Vargas/CaMSP/PVUSD
2013
hl
y
ecy
i
on
F
mN
comes closest to the number
32
.
M X
= ____________
u
l
t
comesi closest to the number
17
.
p
l
y
i
n
= ___________.
M X
g
u
l
b
t
comesy closest to the number
157 .
i
p
t
l
h
y
e
i
n
= ____________
F X
M
g
r
u
lbi
tyeclosest to the number
comes
138 .
in
pt d
lhl
yey
= ____________
iM X
nFN
u
gr ul
Page 8
m
t
i
bebi
ynep
(TEMPLATE)
NAME: _______________________________________
Guess the Friendly Number!!!!!!!
Multiplying
by the Friendly Number
M
u
l
t
i
p
l
y
Multiplying i by the Friendly Number
nM
gu
l
bt
yi
p
tl
hy
Multiplying ei by the Friendly Number
Mn
uFg
lr
ti b
iey
pn
ldt
yl h
iye
Multiplying n by the Friendly Number
M
gNF
u
ulr
bmi
t
ybe
i
epn
tr d
l
Vargas/CaMSP/PVUSD
2013
hl
y
ecy
i
on
F
mN
comes closest to the number ___________.
M X
= ____________
u
l
t
comesi closest to the number ___________.
p
l
y
i
n
g X
= ____________
M
u
lb
comes
t y closest to the number ___________.
i
pt
lh
ye
i
= ____________
M
nF X
r
ug
li
tbe closest to the number ___________.
comes
iyn
pd
lt l
yhy
= ____________
ieM X
nN
u
gFul
Page 9
m
t
r
bi bi
yeep
Ticket Out the Door
Name: ________________________________
Multiplying 4M by the Friendly Number
u
l
t
i
p
l
y
i
n
Multiplying 4g by the Friendly Number
M
ub
yl
t
it
hp
le
y
Multiplying 4iF by the Friendly Number
M
rn
giu
l
e
bnt
ydi
p
l
tyl
hy
i
eN
n
u
g
F
m
br
Vargas/CaMSP/PVUSD
2013
ieb
y
re
n
dct
comes closest to the number
21
.
= ____________
M X
u
l
t
i
comes closest to the number
86 .
p
l
y
i
n
X
= ____________
M
g
u
lb
ty closest to the number
comes
172
.
i
pt
lh
ye
i
nF
X
= ____________
gr M
u
i
bel
ynt
i
d
tl p
Page 10
hyl
y
e
i
N
n
F
u