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October 2009 DynaMath T1
Teachers ediTiOn
October 2009Vol. 28, No. 2
ISSN 0732-7773
A SupplemeNt to Dynamath
scholastic DynaMath557 Broadway, room 4052
new York, nY 10012(212) 343-6458
dynaMath@scholastic.com
sUBscriPTiOn/deLiVerY inQUiries:
1-800-schOLasTic(1-800-724-6527)
www.scholastic.com/custsupport
This past June, the Association of Educational Publishers honored DynaMath as its Periodical of the Year for grades K5. Receiving this award
means a lot to everyone on our staff.But were not resting on our
laurels. Were always eager to hear
how DynaMath is working in your class, what were doing well, and what could still use improvement.
So feel free to send us comments or concerns at the addresses to the right. Wed love to hear from you.
Mathematically yours,
Matt Friedman, Editor
Periodical of the year!
Content and SkillS Guidedifficulty Level: H = Easy HH = On-Level HHH = Challenging
PaGe arTicLe TiTLe,diFFicULTY LeVeL
PriMarY MaTh sKiLL sUPPLeMenTarYsKiLLs/aPPLicaTiOns
ncTM sTandards(see below for details)
cover Pile on the Patterns HH Finding a pattern Reasoning 6, 7, 8
23 Numbers in the News HH Mixed skills Place value, money math 1, 4, 6, 9
45 Wild Dividing HH division with remainders Problem solving 1, 6, 7, 8
67 Change It Up HH Making change Decimal +, 1, 6, 7, 8, 9
89 Exactly the Party I Want! HH estimate vs. exact Word probs to equations 1, 6, 7, 8, 9
1011 2 Many Txts? H reading a pictograph Computation +, , 5 1, 2, 5, 8, 9, 10
1213 CAN You Multiply? HH Multiplying 2-digit numbers Two-step problems 1, 2, 6, 8, 9
1415 Mouse in the House! HH issue skills review Problem solving 1, 2, 5, 6, 8
16 Maxs Wild Equations HH solving equations Algebra 1, 2
T4 Problem Solved Prep Page H When to estimate pp. 89 warm-up 6, 7
T5 Batty About Estimation! HH Visual estimation pp. 89 extension activity 1, 3, 4, 68, 10
T6 Vampire Variables HHH Value of a variable p. 16 extension activity 1, 2, 8
issue dates: 9/09 10/09 1112/09 1/10 2/10 3/10 4/10 5-6/10
need Funding for DynaMath?Go to www.scholastic.com/classmags and click on Looking for Funding to learn how DynaMath qualifies for funding, such as NCLB grants.
ncTM standards 1. Number and Operations 2. Algebra 3. Geometry 4. Measurement 5. Data Analysis & Probability
6. Problem Solving 7. Reasoning and Proof 8. Communication 9. Connections 10. Representation
Standards listed above in a bold box (such as 1) indicate that the article also connects with a new NCTM Curriculum Focal Point.
Your students can win a dYnaMath t-shirt!ask your students to be on the lookout for interesting events or places that theyd like DynaMath to feature in numbers in the news. have them send a copy of, or a Web link to, their news idea. if we use it in the magazine, theyll win a T-shirt. see page 3 of this issues student edition for details.
2009 WINNER
DISTINGUISHED ACHI
EV
EMEN
Taep
-
COVER: PILE ON THE . . .
RESOURCE: WEB SITE
Find a fun pattern guessing game
that also helps build critical thinking
skills at http://pbskids.org/cyber
chase/games/data/
23: NUMBERS IN THE NEWS
RESOURCE: OUR WACKY WORLD
Read the entire incredible story of
Bobbie the Wonder Dog at www
.oregonencyclopedia.org/entry
/view/bobbie_the_wonder_dog/
45: WILD DIVIDING
STRATEGY: EQUAL SHARING
Emphasize the underlying concept
of division as equal sharing. Model
the given example using base 10
blocks. Explain to students that the
steps to a long division problem are
simply a way to organize the shar-
ing of the hundreds, tens, and ones
places in any given problem.
EXTENSION: CHECKING WORK
Have students check each answer
using the following process: Multiply
the quotient by the divisor, then add
the remainder. The answer should
be the dividend.
67: CHANGE IT UP
STRATEGY: SUMS TO 100
As a warm-up to the content in this
article, have students exercise their
mental-math skills by making sums
to 100. Give the students a number,
such as 53. Ask the students what
number should be added to make a
sum of 100. In this case, the answer
is 47. Discuss strategies that stu-
dents can use to get to 100, such as
counting up or subtracting. To dif-
ferentiate instruction, give simpler
numbers such as 30, 50, or other
multiples of five or 10 to students
who need to build confidence. Give
more challenging numbers such as
37.5 or 92.3 for more mathemati-
cally advanced students.
89: EXACTLY THE PARTY I . . .
NOTE: See the Problem Solved Prep
Page reproducible on page 4 of this
Teachers Edition for more informa-
tion to assist with this article. Go
over the strategies on the page in
class before having students attempt
the activity.
STRATEGY: BRAINSTORM LIST
Have students brainstorm two lists:
one for real-life situations in which
exact math is needed, and another
list for situations in which estima-
tion is appropriate. For example, you
do not need an exact measurement
between steps to walk down a flight
of stairs successfully. We estimate the
distance between the steps. Howev-
er, when baking bread, we need an
exact amount of flour. A baseball
batter estimates the speed of a ball
when it is pitched. He doesnt use
exact math. However, exact math is
used when calculating baseball sta-
tistics such as batting averages.
1011: 2 MANY TXTS?
STRATEGY: DEFINING TERMS
Build background by having students
work in small groups to formulate a
definition for pictograph. Students
may not use the word graph within
their definitions. Then have the small
groups share their definitions with
the entire class. Formulate a class
definition based on the ideas.
STRATEGY: LABEL FIRST
Encourage students to label each
age group with the number of texts
represented by the symbols before
working on the questions.
16: MAXS WILD FACTORS
STRATEGY: THINK ALGEBRAIC
Instead of just working backward
to find an answer, have students
view each side of the equation as
an independent part (expression).
Explain that for an equation to be
true, the expressions on either side
of the equal sign must be of equal
value.
EXTENSION: BUILD EQUATIONS
Have students build equations in
which both sides are expressions of
equal value, such as 5 + 1 = 9 3 or
5 5 6 = 15 + 15. Vary the complexity of
the equations based on the abilities
of your students.
Dale Beltzner
Mr. Beltzner is the Math Subject
Area Leader for the Southern Lehigh
School District in Bethlehem, PA.
Lesson plans
T2 DynaMath October 2009
-
TEACHERS: Make one copy per student, or assign one problem each day to start your math lesson!
October 2009 DynaMath T3
Prob
lem
of
the
Day
Try
one
of t
hese
qui
ck e
xerc
ises
eac
h da
y as
a f
ast,
fun
way
to
star
t yo
ur m
ath
less
on!
Nam
e __
____
____
____
____
____
____
____
____
____
Problem of the Day by Dale Beltzner. Scholastic Inc. grants teachers permission to reproduce this page. 2009 by Scholastic. All rights reserved.
DA
Y 1
F
> P
, P
> S
, an
d
F +
P +
S =
6. W
hat
is
the
val
ue o
f
each
let
ter?
DA
Y 6
The
val
ue o
f tw
o
coin
s eq
uals
35
.
One
of
the
coin
s is
no
t a
qua
rter
. W
hat
are
the
two
coin
s?
DA
Y 1
1 H
ow m
any
diffe
rent
nu
mber
s ca
n be
crea
ted u
sing
the
dig
its
6, 9,
and
2 o
ne
tim
e ea
ch?
DA
Y 1
6
The
ave
rage
Am
eric
an
uses
10
0 g
allo
ns o
f w
ater
eve
ry d
ay. H
ow
man
y qua
rts
is t
hat?
(H
int:
1 g
allo
n =
4 q
uart
s.)
DA
Y 2
A
kite
is f
low
n us
ing
300
fee
t of
str
ing.
H
ow m
any
inch
es is
that
? (H
int:
1 f
oot
=
12 inc
hes.
)
DA
Y 7
R
ed is
3. B
lue
is 4
. G
reen
is
5. N
ame
a co
lor
that
is
6.
DA
Y 1
2
Find
the
low
est
pos
sible
val
ue t
hat
ca
n be
crea
ted b
y sw
itch
ing
only
tw
o dig
its
in t
his
num
ber
:
374
,526
DA
Y 1
7
Wha
t nu
mber
am
I?
I h
ave
2 d
igit
s.
B
oth
dig
its
are
even
.
My
seco
nd d
igit
is
3
tim
es m
y firs
t.
DA
Y 3
S
choo
l st
arts
1 1 __ 2
hour
s af
ter
Bob
by w
akes
up.
B
obby
wak
es u
p a
t 7:
30 a
.m. W
hat
tim
e doe
s sc
hool
beg
in?
DA
Y 8
Fi
ll in
the
nex
t tw
o nu
mber
s in
the
pat
tern
: 6
, 2
, 8
, 4
, 16
, 12
, 4
8,
___,
___
Da
y 1
8
Ord
er f
rom
lea
st t
o m
ost:
Han
k ha
s m
ore
cats
tha
n dog
s or
fis
h.
He
has
mor
e bir
ds
than
ca
ts. H
e ha
s fe
wer
dog
s th
an f
ish.
DA
Y 4
FI
VE
= 3
0
FIN
E =
22
H
ow m
uch
mor
e is
V
w
orth
tha
n N
?
DA
Y 9
Ta
ra s
pen
t $
2.7
5 e
ach
day
in
the
cafe
teri
a fo
r 5
day
s. H
ow m
uch
did
sh
e sp
end a
ll to
geth
er
on t
hose
day
s?
DA
Y 1
4
If y
ou w
rote
all
of t
he
num
ber
s fr
om 1
to
100,
how
man
y ti
mes
wou
ld
you
wri
te t
he d
igit
2?
DA
Y 1
9
Sol
ve t
his
pro
ble
m
to f
ind t
he n
umber
of
bon
es in
one
hand
.
64
4
+ 1
1 =
___
DA
Y 5
A
is
10 les
s th
an B
.
C =
11.
A +
B +
C
= 4
5. W
hat
are
the
valu
es o
f A
and
B?
DA
Y 1
0
A p
lane
flie
s at
a
spee
d o
f 53
5 m
iles
per
hou
r fo
r 3
hour
s.
How
far
doe
s th
e pla
ne t
rave
l?
DA
Y 1
5
How
man
y diffe
rent
w
ays
can
you
mak
e
15 c
ents
usi
ng
dim
es, ni
ckel
s, a
nd
pen
nies
?
DA
Y 2
0
Whi
ch n
umber
, in
w
ord f
orm
, ha
s al
l of
its
let
ters
in
alpha
bet
ical
ord
er?
(Hin
t: T
he n
umber
is
a m
ulti
ple
of
10.)
SK
ILL
S P
AG
E
DA
Y 1
3
Joe
orde
red
a sa
lad
for
$3.
25. H
e ad
ded
chee
se
for
$.5
0 a
nd o
lives
for
$
.75.
He
paid
with
a $
5 bi
ll. H
ow m
uch
chan
ge
shou
ld h
e ge
t ba
ck?
-
Name______________________________________
Problem Solved Prep Page
Estimate or ExactYoure about to learn exactly how to do the activity on pages 8 and 9. First, read clue words to help you tell if a problem needs an exact answer or an estimate. Then pick up some estimation tips too!
Look for these clue words to let you know when you need an . . .
Exact answEr EstimatEexactly estimateprecisely aboutsum approximatelydifference aroundproduct averagequotient typical
3 Look at the lowest number in the problem. If the number has more than one digit, what is its greatest place value? 3 Round all the numbers in the problem to that place value.3 Add, subtract, multiply, or divide the rounded amounts.
Example: Juanita jogged 584 yards. Gary jogged 92 yards. About how much farther did Juanita jog than Gary did?3 The question asks About how much farther did Anita jog? So we can estimate the answer.
3 The lowest number in the problem above is 92. So round both numbers to the tens place.3 584 rounds to 580 and 92 rounds to 90.3 Now find the difference: 580 90 = 490.Juanita jogged about 490 yards farther.
3 If the question had asked Precisely how much farther did Juanita jog? youd simply subtract: 584 92 = 492 yards. So 490 was a good estimate!
Act
ivity
by M
att
Frie
dm
an. S
chol
asti
c In
c. g
rant
s te
ache
rs p
erm
issi
on t
o re
pro
duc
e th
is p
age.
2
00
9 b
y S
chol
asti
c In
c. A
ll ri
ghts
res
erve
d.
Now youre ready for Exactly the Party I Want on pages 8 and 9. We hope that solving those problems will be no problem at all!
Warm-Up Activity
T4 DynaMath October 2009
Exact or Estimate Clue words
estimation advice
-
Name______________________________________
Problem Solved Prep Page
Estimate or ExactYoure about to learn exactly how to do the activity on pages 8 and 9. First, read clue words to help you tell if a problem needs an exact answer or an estimate. Then pick up some estimation tips too!
Look for these clue words to let you know when you need an . . .
Exact answEr EstimatEexactly estimateprecisely aboutsum approximatelydifference aroundproduct averagequotient typical
3 Look at the lowest number in the problem. If the number has more than one digit, what is its greatest place value? 3 Round all the numbers in the problem to that place value.3 Add, subtract, multiply, or divide the rounded amounts.
Example: Juanita jogged 584 yards. Gary jogged 92 yards. About how much farther did Juanita jog than Gary did?3 The question asks About how much farther did Anita jog? So we can estimate the answer.
3 The lowest number in the problem above is 92. So round both numbers to the tens place.3 584 rounds to 580 and 92 rounds to 90.3 Now find the difference: 580 90 = 490.Juanita jogged about 490 yards farther.
3 If the question had asked Precisely how much farther did Juanita jog? youd simply subtract: 584 92 = 492 yards. So 490 was a good estimate!
Act
ivity
by M
att
Frie
dm
an. S
chol
asti
c In
c. g
rant
s te
ache
rs p
erm
issi
on t
o re
pro
duc
e th
is p
age.
2
00
9 b
y S
chol
asti
c In
c. A
ll ri
ghts
res
erve
d.
Now youre ready for Exactly the Party I Want on pages 8 and 9. We hope that solving those problems will be no problem at all!
Warm-Up Activity
T4 DynaMath October 2009
Exact or Estimate Clue words
estimation advice
-
Name______________________________________
T6 DynaMath October 2009
Vampire VariablesSink your teeth into this activity to find the answer to our joke!
A 6 + k = 15
Subtract 6 from both sides:
6 6 + k = 15 6
0 + k = 15 6
k = 9
So, we wrote a k in the blank above the 9.
B 21 = 2 + t
t = _____
Write a t in the blank above this number.
C c 5 11 = 55
c = _____
D 3 + i = 27
i = _____
E 81 e = 27
e = _____
F r 5 4 = 32
r = _____
G 8 5 n = 16
n = _____
H 40 a = 34
a = _____
What is a vampires favorite fruit?
__ __ __ k __ __ __ __ __ __2 3 5 9 19 6 8 24 2 3
What to DoFind the value of the variable in each
equation below. Match the value of the variable to a number listed under the blanks below. Fill in each blank with the matching variable letter to complete the answer to the vampire riddle. Well show you how in the first equation.
Act
ivity
by D
ale
Bel
tzne
r an
d C
arli
Ent
in. S
chol
asti
c In
c. g
rant
s te
ache
rs p
erm
issi
on t
o re
pro
duc
e th
is p
age.
2
00
9 b
y S
chol
asti
c In
c. A
ll ri
ghts
res
erve
d.
Extension Activity
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