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MATH

enVision Mathomatics Wost
Virginia 2028 Grade kK

MATH

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Virginia 2028 Grade 1

envision Mathematics West
Virginia 2025 Gracie 4

enVision Mathomatics West

Virginia 2028 Grade 2

MATH

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Virginia 2028 Grade 3

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TOPIC 8 FOCUSES ON
CLUSTER Use place value understanding and

properties of operations to perform multi-digit

arithmetic

Read and Write Numbers to 10,000 ....................... WV1-1A

M.3.10, MHM4, MHM7, MHM8&

Vocabulory Review

Reteaching

Top Assossment

Topic Performance Tosk.
Cumulative /Benchmark Assessment
Werks hn ee ee

Addition Properties ............................205.
M.3.13, M.3.8, MHM1, MHM7

57 + 35 = 35+ 57

TOPIC 8
Use Strategies and Properties
to Add and Subtract

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Vocabulary Cards and Activity
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143.11, MM? MHS MEMS

Order 4-Digit Numbers . WV3-1A
343.11, MAH? THHAS Bie MS

LET'S INVESTIGATE! Summ Farm ....--....--...---..----.------ On Realize
Sug ports Lessons e-|, 2-2. and e-3
M313, 143.5, MHI], PHM MH MRS

Additian Properties ..... c - - . see 2BIA
M313, M28 HME VHM7

Algebra: Addition Patterns tre 2938
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Mental Math: Addition .....-.........---..---..--.-+----+-- 297A
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Mental Math: Subtraction ........... Siew gate eprssae OTE:
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Round Whole Numbers ‘ 305A
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343.13, W312, 4.3.97, MH 2, MHS

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PASS, BAST 20, MAT, Siete

PROBLEM SOLVING Model with Math ‘“ xpensns 1 SA
1A-PA4, AHI, HME, BAS, 3, M32

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envision Mathematics West Virginia 2025 Grade 3

Table of Contents

Virtual Learning Resources ep
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Only

Teacher Resources

West Virginia Resources for
Review

Teacher's Edition: Grade 3

eText del Spanish Companion:
Grado 3

Teacher's Edition Program
Overview: Grade 3

Grade 3 Family Engagement

Classroom Videos

Grade 3 Reaciiness Tests

Math Practices Animations

Academic Vocabulary

Topic t Understand

Kultinfination and Mivieinn nf Ss

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Student Lesson: Grade 3 Lesson WY-1

enVision Mathematics 2024 Grade 3 > Topic 8: Use Strategies and Properties to Add and Subtract > WY-1;
in ri if 10,000

Student Lesson: Grade 3 Lesson WV-1

Teacher Lesson: Grace 3 West Virginia Lesson WV-1 W

enVision Mathematics 2024 Grade 3 > Topic 8: Use Strategies and Properties to Add and Subtract > WV-1;
Read and Write Numbers to 10,000

Teacher Lesson: Grade 3 West Virginia Lesson WV-1

WV-1: Enrichment
Soe TTS ETT > Topic 8: Use Strategies and Properties to Add and Subtract > WV-1;

WV-1: Lesson Plan

enVision Mathematics 2024 Grade 3 > Topic 8: Use Strategies and Properties to Add and Subtract > WV-1;
Read and Write Numbers to 10,000 > WV25 3 WY-1 TS CONT

(iC) NUMBER SENSE ROUTINES

OVER OR UNDER

Students mentally compute and use estimation skills to determine
whether the sum or difference of two given numbers is over or under a
specified amount. After having some time to think, they signal whether
they believe the sum or difference is over the target number (thumbs
up) or under it (thumbs down).

Purpose Practice estimation of sums and differences of multi-digit
whole numbers.

Suggested Use Lesson 7-2 and on, especially Lessons 8-2, 9-4

(CY NUMBER SENSE ROUTINES

Number and Operations Routines
OVER AND UNDER

366 + 177

NUMBER SENSE ROUTINES

Number and Operations Routines NUMBER AND OPERATIONS ROUTINES
The chart suggests lessons where the routines may be introduced (cells in darker green).

OV E R A N D U N D E R It also suggests specific lessons where the routines may be practiced. Teachers may incorporate
these routines in a different sequence and with more frequency after introducing them.

Place Value
Multiplication and Division
Decimals

Fractions
__ Algebraic Reasoning TONG | FNC | ORT | Wor | Top | WOR | ToC | ste | Tog | ToC | vor |

j f 9
J 4 CATEGORIES | ROUTINES VOLUME 1 VOLUME 2

. Agree or Disagree (A)

TOPIC | TOPIC | TOPIC
13 14

® Connect Four (8)
° Connect Four (C)
° Head or Hand

. Line Up the Data
| Ot a
. Number Detective (A)

Te " Number Strings (A)
1 = 1a Number Strings (8).
. ii Over or Under
| . ] Quick Look (A)
° ° | Quick Look (8)

° Quick Look (C)
© Tilt or Balance

e ele @ What's the Pattern?

f JC STRUCTURE OF A LESSON DESIGN

STEP | STEP 2 STEP 3
Problem- Visual Assess and
Based Learning Differentiate

Learning

‘envision Viathematics

West Virginia

STEP 1 - PROBLEM BASED LEARNING RICH TASKS

- .
soley Sfiare
Ms. Witt bought 4 boxes of paint with

5 jars of paint in each box. Ms. Karp bought 3 boxes
of paint with 6 jars in each box. Who bought more
jars of paint? How many more?

You can use
counters, bar diagrams,
drawings, or equations to
make sense and persevere

in solving the problem.

PROBLEM BASED LEARNING

x rea lize reader. @ Synced to Device Q A a Jennifer ~

t= Table of Contents *s* > Lesson 1-1 Relate Multiplication and Addition > Solve & Share

Solve & Share © Math Tip

. Annotations & Highlights <q) Ms. Witt bought 4 boxes of

paint with 5 jars of paint in
each box. Ms. Karp bought : PF OF peat hoes
l@ Notebook 3 boxes of paint with 6 jars . =
in each box, Who bought
more jars of paint? How
az Glossary many more?

BR Bookmarks

fa Custom Basket
4 Manage Offline Access

< Settings

I Bookshelf Look Back

quat) How
"uations to help * CAN YOU Use Couns
te

sof Sand »
"ive the Problems? Sand addition

Algebra Tiles

Fraction Tiles

Pattern Blocks

miZSFOMm ea. ae «A

a @

Base Ten
Blocks

Geoboard

Place Value
Disks

Clock

77 Ed 7
87 FT) so

Hundred Board

- oe
eo -

Rekenreks

Color Tiles

Linking Cubes

Two-Color
Counters

“Ay

Cuisenaire®
Rods

Fraction Circles

0123

Number Lines

XY Coordinate
Board

addition in preparation for exp!

between addition and multiplication. Their work shows
prior and emerging understandings Y y can build on
during the Visual Learning Bridge.

4.introduce the Solve & Share Problem

Give 20 two-color counters (oF Teaching Tool 9) to each
student pair if needed.
What tools can you use to solve this problem?
What does "how many more” mean?

. Observe Students at work Ls]
To support productive struggle. observe: and if needed,
ask guiding questions that elicit thinking.
+ What tools do use to

of jars Ms. witt pought? Students might
arrange counters in different groups. if needed, ask
How can you show 4 groups of 5 counters?

+ Do students make the connection between
the groups of counters and repeated addition?
Students should write the addition problem to show
the number of counters. if needed, ask What equation
can you write to show the total number of counters?

aoe LASS

ical Available Online

How did Phyllis show

- of iare each

Phyllis’s Work
8800
5060 Aa
Bebo is)
goa
5451545220 A00
Gx b+ 6-18

Ms, Witt bou
30 jars of an Ms. Kosp bought 18 jars.

20 -1g=2
Ms. Witt bought 2 more jars of paint.

4. Introduce the Solve & Share

Problem
Give 20 two-color counters (oF Teaching Tool 9) toe

student pair if needed.

2. Check for of the Prob
What tools can you use to solve this problem?
What does “how many more” mean?

DURING * SMALL GROUP

i tudents at Work 7]
To support productive struggle, observe, and if ne
ask guiding questions that elicit thinking.
tools use to
number of jars Ms. Witt bought? Students mic
arrange counters in different groups: \f needed, @
How can you show 4 groups of 5 counters?

. po students make the

ups counters @ repeated additic
Students should write the addition problem to st
the number of counters. eeded, ask What ea!

can you write to show the total number of coun

~~ 1 WHOLE CLASS

Ross’s Work

| skip Count by 4, + f;
c my 8 how AAS ; °
Ms, Witt bought. mez of paint
bay 4 216

| skip court by 35 to find how wmy Ms. Keep bought:

Ba Bx3 234303 78
sing subtraction - 19- 1G22.

at, Rarp bought 2 mere. jars ot pot

ANALYZE STUDENT WORK. —
How did Phyllis show
4 - number of jars each

(iC) STRUCTURE OF A LESSON DESIGN

STEP 2

Visual
Learning

‘envision Mathematics

West Virginia

fish did
Ww many gold

mber of goldfish in each bag. Ho

e nu

She put the sam

Jessie used 3 bags to bring home the
9ldfish she WON at the Fun Fair. She
the same number of IOldfish in each
bag. How m, many goldfish did she win?

she win? Let's find out.

‘

00:26 / 03:24
bE
Es —
Ll

Ww The Counters show
3 on Of 8 goldfish,

# i #

oad CaN use addition to
Join Bal gretip

san
Mat gives the Sat

when youjoin pee &rOups
a

Sockdish in

ch bag
3 iia 8 equals 24
3 x 8 = 24

facton Product
are the numbers
that are as Multiplied
The S the answer
toa multiplication Problem,

2 -
beoe ETS
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An 5 a sSymbo/
tha @ number
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Addition Scantlons
8+848

8+848~ 4
Multiplication equation:
3x8=?

3x8=24
Jeesie won 24

SUPPORTING JEFFERSON COUNTY STUDENTS AT HOME

Family E t
Name oy Fagen

Date

Solve Equations Your child will use visual models and equations to solve a variety
of real-world problems involving multiplication and division facts. Your child will
practice finding the unknown number in any position in an equation.

Dear Family,

Your child’s login on SavvasRealize.com contains family resources you can use to help
your child succeed in mathematics and to help you better understand the organization of
enVision® Florida B.E.S.T. Mathematics and Florida's B.€.S.T. Standards: Mathematics. Look
for an introduction, benchmark explanations and examples, topic overviews, math help

CONNECT THE MATH A

You can connect the math in this topic to everyday experiences. For example, you
might say, “We have 8 eggs and each batch of pancakes uses 2 eggs. How many
batches can we make?" To provide practice with evens and odds, look for

de sample problems and home activities, visual learning, games,

opportunities to put items into pairs, such as snacks or small toys, Ask your child to
determine whether each item has a partner or there is one left over, For example,
if a box of raisins is opened as a snack, you could ask, “Is the number of raisins
even or odd? Does each have a partner? Is there one left over?”

SCHHSSHHESSESHSEESHSSHESHESHEOHOEHSHSEHOHHSSEESESEEEEEEEE

TOPIC 4 LESSONS

Lesson 4-1
Lesson 4-2
Lesson 4-3
Lesson 4-4
Lesson 4-5
Lesson 4-6
Pr:
Lesson 4-8 Solve Multiplication and Division Equations
Lesson 4-9 PROBLEM SOLVING

Make Sense and Persevere

Lesson 4-7

STEP 2 - TEACHER SUPPORT

ENGLISH LANGUAGE LEARNERS EET)

Use with the Visual Learning Bridge.

Reading

Ask 6 volunteers to stand. Divide students into 3 groups of 2. Give each
student note cards labeled Factor and Product. Factors are the numbers you
multiply, How many groups are there? How Many are in each group? On
the board Write, “3 groups x 2 students = 6 in all.” Repeat after me. 3 and 2
are the factors, 6 is the product.

> Convince Me! 6 Sormative

Model with Math Students connect repeated addition
with multiplication and use Strategies to solve a real-
world problem.

Coherence The first lesson in Grade 3 transitions

from the primary grades, where the foundations for Entering Ask students to use the note cards to complete and read aloud

the following: “3 and 2 are the . 6 is the ne

Developing Ask students to complete and read aloud the following:
“In3x2= 6, 3 and 2 are the , and 6G is the .” Ask students to

multiplication acts as a foundation for learning division
define factor and product in their own words.

Expanding Ask students to read the following sentences, identify the
€rrors, correct them, and explain why they made the corrections: “3 and 2
are the products, 6 is the factor.”

involves joining equal groups and can be solved using
multiplication (5x8 = 40) or by adding equal groups
(8+8+8+848~ 49)

Receptive
Language

Oral
Written Language
Language

oo.

Language Support
Handbook

GRADE 3
Professional Reading: Language Support in
Mathematics

Academic Vocabulary Resources
Language Support Activities

enVision \Viathnemarics

Productive
Language

eo Math Symbols This lesson may be the first time
Students have seen Parentheses in a math book.

Write on the board: () parentheses

Pronounce the word Parentheses. Have students repeat
the word. Explain that in math Parentheses are used

at times when more than one operation needs to be
completed in a specific order. Write the following on the
board from the Visual Learning Bridge:

7x4=(5x4)+(2x 4)

Place your hands around the 5 x 4 and then around the
2 x 4. Tell students the Parentheses indicate they should
multiply the factors inside the Parentheses before they
complete the addition.

—— ——-~
| Compete 4 and & ne the paar
to help. |

3. Jessie buys 4 pactages of stones. There
28 6 stores Ineo package How
many stones does Jessie buy?

Une coumters to represent the problem.

6464646 =~ HY therm:
Sx 6 = 24 tones

| Levated Practice Coretete 6 art 7. Uve the pictures ts hei.

“Sh MV seeeesesss

| tn.9-15, complete each equation. Use counters.or deawa picture to help. |
@ 7 7 47 «3x7

yer eye
11, 646+6s606> Sx 6

10.9049 6 9 a3e %

Topic 3 Lesson #1 ?

Guided Practice or:

ERROR INTERVENTION item 3

If students use the number of packages for the addition equation
rather than the number of stones,

then ask How many packages or groups of stones did Jessie buy?

[4 packages or groups} Add to find the total number of stones.
(6+ 6 +6 +6 = 24] How many times did you add 6? Why? [Sample

answer: | added 6 four times because there are 4 groups.) Can you
use multiplication to solve this problem? [Yes] If you multiply, how
do you know which numbers are factors? [Sample answer: The
numbers that are multiplied are the factors; 4 and 6 are the factors.]
How do you know which number is the product? (Sample answer;
The product is the total in a multiplication equation; 24 is the
product because 4 x 6 is 24.)

G& interactive Practice Burl ic at SavvasRealize.com.
P |—( fo . ©)
rntiinstwg - GQUided Practice x

Do You Understand?

12. Cetra Geaws this tape on thee
het rotetcrs

What is the name of the shage
draws) Mow do you know)

}4. Migher Order Thinking Lil

an ahecaps wh and you can

4. Toman 12 ears ot ead
Labte evan atone He sty
equal goups Which sent
Torn use to Gevertine Mag
that oer Correct,

OC Wmaemget?
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Bom ewrodt
@ om aaged?
OC bm aceged

Item 13 Model with
multi-step problem, using rep
break the problem into simpler steps. What

RACTICE WITH A PURPOSE

1. Can you write 5
you +54+54+5=20
multiplication €quation? Explain -
Yes; The 9roups are equal .
4x 5=20

2. Can you write 3 + 4 + 7=14asa
multiplication €quation? Explain

3. Jessie buys 4 Packages of stones. There

are 6 stones in each
Package. H.
Many stones does Jessie si =

Use counters to 5
present the probi
write an addition equation eis ,
multiplication €quation to solve
6+6+646~ stones
Yx6=2 mies :

equation can you write to

find how many cards Salvatore has after giving some cards to Madison?

[SO - 22 = 28)

Item 15 Students explain how addends need to be the same for an
addition equation to be written as a multiplication equation,

Item 16 Students understand the relationship between addition and
multiplication by recognizing that both the third and fourth options
are possible ways to represent the problem.

EVALUATE

QUICK CHECK Oi==S

af A hark mart indicates tame dns neacerihina dilarantiatinn an the

fu)

Complet
S shia €4and 5. Use the Pictures

Cee ee

2 groups of 4
44+4= 8

2x4 - 8

_3 groups of 6
6+ 64 6 ~18
3x 6 = 18

’ Conyrumates+5+5+5= 2050 [ Complete & tnd Uae th paces
‘Yor; The groups are equal, j
ux S=2

Can you witte 447 = i4ase
multiplication equation? Exptain
No; The groups are not equal

Jewsie buys 4 packages of stones. Thone
are 6 shone in each package How
ninacaenneamnic
Use comrners to represent the problem sssssssss
Then write an addition equaton aed a 3 gags ote
ar este eae 6+ 6+6 = 18
64646466 storm:

ino wo 8

Independent Practice”

as
—— Perens er eee)
t+ 52 0 ..=
2x $ «10 a

9 Fe 747 «3x7

V. 6e6+6e6e6e Sx 6

Topic Lesson 1-1 ,

ELABORATE

Guided Practice ot

ERROR INTERVENTION item 3
if students use the number of packages for the addition equation
rather than the number of stones,

then ask How many packages or groups of stones did Jessie buy?

[4 packages or groups} Add to find the total number of stones.

(6 +6 + 6 +6 = 24] How many times did you add 6? Why? [Sample
answer: | added 6 four times because there are 4 groups.} Can you
use multiplication to solve this problem? [Yes] If you multiply, how
do you know which numbers are factors? [Sample answer: The
numbers that are multiplied are the factors; 4 and 6 are the factors.)
How do you know which number is the product? [Sample answer:
The product is the total in a multiplication equation; 24 is the
product because 4 x 6 is 24.)

Problem Solving
12. Detra Gray this Pape on the back of
New noted

What is the name of the shape Debra
draws! Meow bo yous bene?

Debra draws a hexagon. A hesagen
heat six sides ond six vertices.

4. Higher Order Thinking Lube says you
an) sheep, ahd ated yous Cary abeeanys
mmastepy to joes grou. It bee coment?

16. Torn has 12 ary of Medd Con to mahe
tabhe dec ce one. He art amejes Goren in
equ gown Whach sentences coud
Tom use to Gescribe bis groupe! Setect
af thal are convect

CD Perm aranged 2 groups of 4 ears
OC Pm aranged 4 gous of 2 ears
tor reget 6 gougn of 2 an
Bom aeae ges 3 pours of 4 ears
CD Wm aranged | goupef ean

bd Topic t Leen Ft

Prater

eo 2

12 Model with Math Satwatore gets
SO wardens Card fot hen bietiny Hee grees
T2cands to Madhon. and Madion gives
ME Cards to Sadvatore Then Sabvatorwy
water pees Nee Hdd Home ray
acing cards does Salvatore Rave now?
Use muah bo represent the prottem.
cowds; Sample anewer:

SO ~ 22 = 28; 28 + 18 = 86;
6+ ae 60

15. Lots says any addition equation where
the addons ane all the une can be
writen 21 a muttiphication epastion Is
Lom connect! Exptain whay on winy mot

17. Jorma han 4 flowers She ananges them
Ar aes Wty an ecjusl mune off Somes
in each wane. Whech sentences coud
Jeera uve Vo devcitioe Noes Mowers! Setect
a8 Bast are convect,

BD eerie meget 4 fowernin cach
At vane

(CD rena aeanged 3 fowersin eacty
of 9 vmes

deena seeanged 5 fhowers in acts
of S waves

(CD denna aranged 6 flowersin each
of Svaies

BB etna eegeds ower in each
of vanes

10.949 . 9

Independent Practice and Problem Solving

Item 13 Model with Math Remind students that when doing a
multi-step problem, using representations, such as equations, helps to
break the problem into simpler steps. What equation can you write to
find how many cards Salvatore has after giving some cards to Madison?

{S50 ~ 22 = 28]

Item 15 Students explain how addends need to be the same for an
addition equation to be written as a multiplication equation.

tem 16 Students understand the relationship between addition and
multiplication by recognizing that both the third and fourth options
are possible ways to represent the problem.

EVALUATE

QUICK CHECK @i==tr

PB cheek meek Le lentns le eees Moe mensccthinn MMdesnatlatlon on tha

2 groups of 5
5+_5 10
2x_5 - 10

8.8+8+8+8=4% 8

=3x 9

her notebook,

12. Debra draws this shape on the back of

What is the name of th
draws? How do you a re Debra

wat

or unequal,
to join

the groups are equal”

S groups of 4

4944444 4 + 4 Pe 20

Sx 4 ~ 20
7474 7 23x7

1. 6+6+6+646- § ee

13. Model with Math
50 trading cards for his bi hday. He gives
rt! Hi

22 cards to Madison, and Madison >

18 cards to Salvatore. Then Sthetows
sister gives him 14 cards, How many
Wading cards does Salvatore have now?
Use math to Fepresent the problem

Salvatore gets

60 cards;

50-22 9g" answer:
60

can always add and 15. Lols says a
you can alwa
multi ys
. . tiptication equation, |
No; Sample answer: I can add to Lois correct? Explain why or why not ,
whether the groups ia answer: All

but I can
only when

Do You Understand?

1. Conyou mite $4 5454+5= ase
mmuuttgiic ation eqquatom? Expat
Yee; The groups are equal.
uxSe2

Complvte 4 1d 8. Une the pactuses
to help.

‘ee ee
ee ¢e

Con you mtite 3446 T= lease

groups ot ©
teaet
ee a |

Jevie buys 4 packages of stones There
200 6 sores In each package How
rary owes does dessie bay?

(Use comers to reprevent the problem
Then write an addition equation and a
imutigcation equation to setve
6464646 = Bh storm:

4 S > 4 ‘
3 qoute

6+ 6-6 =
ax 6 =

| Leweled Practice Complete 6 and 7. Use the pictures to help.

A +

a8 Sqroupset &
2 group
4edede th 4 © 2
s+ 5.610 pod iar
2x 5 «10 =

tn 8-11, complete each equation. Use counters or draw a picture to help. |
@ fe20.2.08a?

B Rete teteax 8

10.949 4 9 a3 9 11. 646+606s6— 5 & 6

Fopic ) Lesson 1

ELABORATE

Guided Practice ot=

ERROR INTERVENTION item 3

if students use the number of packages for the addition equation
rather than the number of stones,

then ask How many packages or groups of stones did Jessie buy?
[4 packages or groups} Add to find the total number of stones

(6 + 6 + 6 + 6 = 24) How many times did you add 6? Why? [Sample
answer, | added 6 four times because there are 4 groups.) Can you
use multiplication to solve this problem? [Yes} If you multiply, how
do you know which numbers are factors? [Sample answer: The

numbers that are multiplied are the factors; 4 and 6 are the factors.)

How do you know which number is the product? (Sample answer:
The product is the total in a multiplication equation; 24 is the
product because 4 x 6 is 24.)

12. Debra draws this Pape on the:
hee notebook

What is the name of the supe D
drarwes Mew do yon now!

Torn hae 12 ear of Nekl corn to mabe
table decor atone He arramapes Bvee iy
equal groups Which sentences coud
Tom use to Gesrtie hes groups! Select
i thal are Correct,

CO) Worm areeget 2 ron of 4 ears
CO) tom aranged 4 gous of 2 ears
or eget 6 gours of 2 earn
Bom ae xeged 3 gous ot 4 earn
OC Womaranged | goupet 10 ears

. Topic ¥ | Lon It

6. Tom has 12 €ars of field corn to make

table decorations. He
» He arranges them j
qual groups. Which sentences could

Tom use to describe
hi Selec
all that are correct. eee .

O Tom arranged 2 groups of 4 ears
O Tom arranged 4 groups of 2 ears
a Tom arranged 6 groups of 2 ears
a Tom arranged 3 groups of 4 ears,
O Tom arranged 1 group of 10 ears

17. Jeena han 24 flowers Sve aanges then
Wr ways WAS an equal numitees of feowers
in each vase. Which sentences coud
Jeena uve to dexcsitte her Rowers? Sadect
Dut ave conrect,
BD ere neg et ¢ hewersin exch
of bvenen,
(senna anaeged 3 towers in each
= |
CD serra seanged 5 flowensin wach:
tives
(CD denna aranged ¢ flowersin eacts
ot} vanes
| ey

Sven.

Independent Practice and Problem Solving

item 13 Model with Math Remind students that when doing a
multi-step problem, using representations, such as equations, helps to
break the problem into simpler steps. What equation can you write to
find how many cards Salvatore has after giving some cards to Madison?

{SO . 22 = 28)

item 15 Students explain how addends need to be the same for an
addition equation to be written as a multiplication equation,

Item 16 Students understand the relationship between addition and
multiplication by recognizing that both the third and fourth options
are possible ways to represent the problem.

PEVALUATE UATE

QUICK CHECK Ot

an — mes_——at-o8-— -— on -

a Jenna arranged 4
of 6 vases. flowers in each

©) Jenna arranged 3 flo
oF 9 veces. wers in each

©) Jenna arranged 5 flo
Of vases, wers in each

©) Jenna arranged 6 flower
Of 3 vases, sm each

Do You Understand?
1, Can you write S4.54545=20m2
reultg tic ation equates) (phan

You; The groups are equal

&xSe2 “@ ee
Can you wite 34462 = ldase
reedipsie ation eqpusbon? Erztaen
No; The groups cre not equal

Do You Know How?

[ Congilete 4 and & One the pictures |
totaly, j

2 groups of
trae t

Jessie buys 4 pacitages of stones there
sre 6 Stones i each paduage How
many somes does deve tary!

Use cowrners to reprevent the problem.
Then mite an addition equation and a
rulapaic soon equabon to valve
6464646 — Wh storms;

3 goupsots
6+ 6+6 a8

Sqroupset_&
4etete hy WD
~«S -D

each equation Use counters or draw a picture to help |

x8 % 2.0.7.0 2 03?
x 9 11, 6064606s6= Sx 6
fopic Lassen ft ,

Guided Practice ot

ERROR INTERVENTION item 3

If students use the number of packages for the addition equation
rather than the number of stones,

then ask How many packages or groups of stones did Jessie buy?

{4 packages or groups] Add to find the total number of stones.

(6+ 6+ 6 +6 = 24] How many times did you add 6? Why? [Sample
answer: | added 6 four times because there are 4 groups.) Can you
use multiplication to solve this problem? [Yes) If you multiply, how
do you know which numbers are factors? [Sample answer: The
numbers that are multiplied are the factors; 4 and 6 are the factors.)
How do you know which number is the product? (Sample answer:
The product is the total in a multiplication equation; 24 is the
product because 4 x 6 is 24.)

@ Interactive Practice Buddy is at SavvasRealize.com.

Problem Solving

12. Oetee draws this Pape on the back of 1. Model with Math Suhetore gets

hee rotates $0 waddieny Cards for hes biePeday He grees,

22 cards 10 Madmen and Madinon ghves
A cands to Sabvatore: Men Savatcne’s
water pees Mas 14 cats. Mow ramp
Bading Cards oes Sabvatore have tow?
Wha |i the name of the Bape Detea Use math to represent the protitem
yams) Mena do you hmemw? pee ag yr ian
Debra drowsy a Ahesogen ~ 22 = 28; 28 + =

5 46+ 1h = 60

on equasten where
the wene can be

abon equation 1.
Lota cormect? Expisin why oF aby fot

Jeena uve to derctibe her fhawers? Select
ot Daas ave convect,

Berns srenged 4 fewersin cach

of hemes.

Torn am arayed 2 rouge of 4 mary
Tom aranged 4 goups of 2 ear

Tom arsnged 6 gouge of 2 ear CD senna ananged 3 fhewersin each
atvmes

ereva secameyed $ fhoweers in eas
et Sven

oO
8
Bom aranged 3 gous of tears
C0 tomannged 1 goupef 10e0n

se)

(Denna seaeged 6 thowersin each
of D vases

mere ered 8 flowers in each
ofS wanes
. Topic | Lesson 3 castes

Independent Practice and Problem Solving

item 15 Students explain how addends need to be the same for an
addition equation to be written as a multiplication equation.

Item 16 Students understand the relationship between addition and
multiplication by recognizing that both the third and fourth options
are possible ways to represent the problem.

VALUATE

QUICK CHECK Qi=m%r

ob chek meek Mele ntes lees fas eenscstlnn MiMeswatlaslon on sho

‘S Practice Buddy *

@» Jill has 16 buttons and 2 boxes.
She puts |0 buttons in one box.
How many buttons does Jill put in the
other box?
Enter the numbers to solve.
You can use the ten-frames to help.

» lé6is ten and ones.
Jill put buttons in the other

box.

Digital Practice K-5 Adaptive Practice 3-5

w/ Pre-requisite and
enrichment support

(iC) STRUCTURE OF A LESSON DESIGN

STEP 3

Assess and
Differentiate

‘envision Mathematics

West Virginia

Name

Do You Understand?

Leveled Practice Complete 6 and 7. Use the pictures to help.

5 groups of

10.

Can you write 5 4 5454+5= 20888
multiplication equation? Explain.
Yes; The groups are equal.

4 x 5 = 20

. Can you write 3 + 4+7=14asa

multiplication equation? Explain.

No; The groups are not equal.

. Jessie buys 4 packages of stones. There

are 6 stones In each package. How
many stones does Jessie buy?

Use counters to represent the problem
Then write an addition equation anda
multiplication equation to solve.

6 + 6+ 6 + 6 = 2h stones;

4 x 6 = 24 stones

2 groups of 5
5+_5 =10
9x_5_=10

—

8-11, compl

———————

948+8+8=4x 8
94+ 9_+9 =3% 9

—————

Do You Know How?

to help.

ese Aand 5. Use the pictures

2 groups of y

4+4=
2x 4

‘ esaisesiess

3 groups of 6
6+ 6 + 6 = 18

3x _6

- 18

—

4444444 + 4 = 20

sx_4

ete each equation. Use counters of draw a picture to help. |
———— ot oS ——————

= 20

9. ¥ 7 + 7 =3x7

11. 64+64+6+4+6+6= 5 x 6

Topic 1 | Lesson ra

ete

more inches than feet

4
mY

more yards than feet

4) Listen

Ch
oe measures the len
W will his measurem
e

th
gth of the bookcase usi
nts compare? in

oS RMN

Choose Yes or No

more centi
entimeters than inches | Yes |
a
more m
eters than centimeters | No
| *|

Yes

9 different units.

PERFORMANCE ANALYSIS TIED TO WVCCR

Standard Analysis Question Analysis Student Analysis Performance Analysis

View student performance analysis and assign resources for remediation or enrichment. You can drag and drop students between the
performance bands.

Ungrouped Students
Students who scored less than 70% Students who scored more than 70%

Assign Resources Alverez, Lucia

Novak, Melanie % (4.2/10) Buxton, Robertt 72% (7.2/10)
Bird, Gillian

Callaghan, Dan % (4.5/10) Zimmerman, Eric 75% (7.5/10)
Sturky, Nick

Kinney, Lucien % (4.5/10) Salgado, Joe 78% (7.8/10)

Oneal, Victor % (5.8/10) King, Jenna 80% (8/10)

Kouma, Ayva %) (6.5/10) Palacios, Arianna 85% (8.5/10)

| Drew, Ivy 85% (8.5/10)

Standard Analysis Question Analysis Steen Performance Analysis

View student performance analysis and assign resources for remediation or enrichment. You can drag and drop students betv

performance bands.

Performance by | Overall Score 7

Students who scored less than 70% who scored more than 70%

A nr

gn Resources

Novak, Melanie 42% (4.2/10)

Callaghan, Dan 45% (4.5/10)

| Kinney, Lucien 45% (4.5/10)

Oneal, Victor 58% (5.8/10)

65% (6.5/10)

| Kouma, Ayva

Drag and drop

| Ashton, Kelly 90% (9/10)

Show Performance

Ungrouped Student:

Alverez, Lucia

pecan |
cog

Sturky, Nick

INTERVENTION ACTIVITY (7 )
and Addition

Relate Multiplication
Materials

* Repeat the acti
counters; for e
9 counters ors

vity with Other 9roups of
xample, 2 9roups of

Two-color co
unters (or Teachi
ching Too} 9) Groups of 6 counters,

* Have students ys

board.

Number of Counters. oo i
* Have anoth i
muha er student Write a ra o= io
a '0N equation to find the total
pea a Counters ang then €xplain : —
€ actors and Prod 7
uct mean 7 :

Student Analysis Performance Analysis

Standard Analysis Question Analysis

View student performance analysis and assign resources for remediation or enrichment. You can drag and drop students between the

% Show Performance

performance bands.

Performance by | Overall Score v

Students who scored less than 70% who scored more than 70%

f Dp gn Resources

if Ashton. Kelly 90% (9/10)

Novak, Melanie 42% (4.2/10)

| Callaghan, Dan 45% (4.5/10)
| Kinney, Lucien 45% (4.5/10)

| Oneal, Victor 58% (5.8/10)

65% (6.5/10)

| Kouma, Ayva

Ungrouped Students
Alverez, Lucia ~
Bird, Gillian -
Sturky, Nick -

Name
Reseach to Buily

Understanding

1-1

LS] Vocabulary

1. Equal grou,
PS are grow
the same number fame Of objects that contain (o) @ fe) )
©

There are 2
qual groups of
Counters each

2. Multiplicati
On Is an Operation th
Number ; at give:
umber when you join equal groupe, oe total

2x ae

3. There are boxes
Each box bige/\./ |
has toys Bee | + [aide
4. : =
Merge an addition equation to represent
ne total number of toys in the boxes
+ + =
5. ;
Write a Multiplication equation to represent the

total number of toys in the boxes

8. Write an addition

@quation @nd a multipy S22 eam
to represent the total number in the pe a
Addition equation a

Multiplication equation

On the Back!

7. Use the pict
ure to describe the a
additio; ual
dition equation and a multiplication pa si

FER
Sy 0
> 2.
Q XH
eo Oy
1 (e)
Ty scy

DIFFERENTIATED INSTRUCTION

J S *

*enVisionCENTERS ,

Problem-
Problem-Solving

Solving
Reading Mats Reading

| Activities

: Digital
Pick a Project enVision® STEM Math Tools
Activities Activities

Fluently Mu
within 109

F Eesontics Question:
Mulfipli

Itiply and Divide

)
Lm)

What are Strotegies tg solve
colon and division facts®
fea

Together

- The weather

The money we —

| fram day to doy and from )
ns as jill . ae fo ie - ~
to COl from arent. Se “ =
From cows to co irom mon ==
» Cowrie shells

LF money. Then. small
models of tools we =e

“= used. These were
1000 and 500 8.C

Knife-shaped coin

State granaries

Gauls vs. geese

), Groin wos used like Do Research Use the Journal: Write 4 Report Include what you found,
ina Lang naan ore ploces Internet or other sources
a the saved money ‘ money t. These
° e Romans once kept 390 B.C., the Gouls where grain is kep!
Banking begins her sutisannee mham aan ook
| things safe this money. But man
, P special things . tried to toke
People like fo kee; Babylonia put
ple in
In 3000 B.C... peo

: B.C
these items in tempies. In 1800

ted
lows. He won
robi mode

King Hommu

people fo trode

foirly

id the Romons found out! They though

> on

noise SS nomed Juno Moneto 1ONK,
anthem The word money =

cons from her nome 4 HONK’

s
ploces were used os bonk

Also in Your report:
to find the Weather in

different Places gn Earth,
Find the weather at diffe rent
times of day. Write down

the temperature for each
Place. Also write down any

Conditions SUCH as rain
Or snowy,

* Tell how Many places You checked,

* Tell how ma

fy times you checked the Weather in
one day.

ww |
a
a

SECT Motivates students
— because THEY choose!

Name

. Code Talkers: --

Code Talkers were Navajos who made a
code for the United States armed forces B
during World War Il. The code was used to

send secret messages.

Cc H How do you follow a recipe?
Twenty-nine Navajos created the first code. :
Ithad 211 words and an alphabet that used © ; Project: Exploring Recipes

pes

Navajo names for animals or birds. The code
grew over time, and eventually the Navajos
wrote a Code Talker dictionary.

After the Navajos made their code, they
practiced with atest message. They
translated the message Into their code, sent
it, and translated It back Into English in just
two and a half minutes, Other code breakers
using non-Navajo codes took hours to do
the same thing.

From then on, the Code Talkers sent many
messages for the United States
armed forces, and the code was never broken.

Your Project, Create a Fraction Code

Develop a code that you can use to find an

equivatent fraction for any fractions with 9 H
denominators of 2, 3, 4, 5, 6, 8, 10, 12, or 100. :

=8 }
Start by letting different colors, shapes, OF H
objects stand for the numbers 2, 3, and 5. =3 H
Then, use combinations of these symbols to :

stand for the numbers 4, 6, 8, 10, 12, and 100.

Create a Code dictionary showing the symbol that stands for each number; then practice. i
Write a fraction, and then write an equivalent fraction using your Code dictionary. H

PICK A PROJECT

OVERVIEW

A variety of rich projects is provided for each topic. Students may :
select the project that « most interesting to them. Fecpes that use greater amounts of

ingredients, such as 3} cups. Have
students continue to double the greater
amounts.

@anrssa

Ask tw

PROJECT 9B

Materials Paper, penci!
Extensions Ask students to look for
patterns in their codes that they think
code breakers might identify if they

SELECTING A PROJECT

introduce each project option with the students. Sharing the

resource masters with students might them choose.
— an use their dictionaries to solve them.

DURING THE TOPIC @ nessa anre.x
Pacing Projects will be completed over a number of lessons and
are referenced in the Lesson Activity Center. The amount of time PROJECT 9C
students spend on each project will vary. You may wish to let
early finishers choose an additional project. Materials Peper, pencil
. Sons Ask wo the PROJECT %

Grouping You might have students work alone or with a partner
oF small group.
Content Projects are related to the content of this topic and will

fractional amounts in their skits to use
different fractions with the same sum.
Ask students who worked on different
skits to demonstrate how to use a model

work on projects throughout the topic, new math ideas should to find the sum of the fractions from
be incorporated. another pair's skit.
Project Sharing Students shouid share their completed projects @nresa

with a partner, a small group, or the whole class. Encourage
students to identify math practices. Provide students an
opportunity for reflection by asking what interesting information
they learned and what math they used in the project.
Extensions Extension suggestions are included for each project.
Look For Did students achieve the goal of the project? Did they
apply math correctly in the project?

331 Topic 9 31a

LET’S INVESTIGATE

Let's Investigate!

Name | Big Celebrations

Supports Lessons 3-5 and 3-6.

Marta's family is having a 3-day celebration.

There are 7 people in her family. The guests are:

Day | Alex’s family, 8 people ——

Day 2 Jackson's family, 6 people — —\F

Day 3 Alaina’s family, 9 people __ Hew many procs

Marta plans to always fill the table of 10 first. ‘worwica e oor
; many on Day 2?

How many on Day 3?

Solve the problems. You may use counters and
ten-frames to help. Use drawings, words, or numbers

to show your thinking. To learn together, value
ideas from others.

Topic 3
aie Look Back! Explain How is the table with ten chairs different from a ten-frame?

BEFORE (GQ wrote crass

1. Introduce the Let's Investigate! Problem
Give 16 two-<olor counters (or Teaching Tool 6) and ten-frames
(Teaching Too! 14) to each student or group.

2. Check for Understanding of the Problem
Three Reads

Read the problem to the class.
What is the problem about?

Have students read the problem by themselves.
What information is given in the problem?

Have a student read the problem to the class.
What is the problem asking you to find?

DURING 4ah SMALL GROUP
3. Observe Students at Work

MONITOR

Monitor students’ solutions. Ask q

ASSESSING QUESTIONS

Questions for You as You Observe

« How are students representing the people in both families?

« What prior knowledge are they using to help solve the
problem?

Questions for Students to Understand Their Thinking
© Can you tell/show me what you did?
*@ What do those counters/pictures/numbers mean?

ADVANCING QUESTIONS

Questions to Ask Students Who Need Help

© if students cannot get started, ask How can you show the
two families using objects or pictures? What are some ways
you can combine them?

© If a student's work is incorrect, ask How did you get that
answer? Then listen for misunderstandings and careless
errors.

Questions to Help Students Think More Deeply

* Can you write an equation to show your answer?

MONITOR Practices

Monitor students’ solutions. Ask questions to assess and
advance students’ thinking.
SELECT AND SEQUENCE

ASSESSING QUESTIONS
Questions for You as You Observe

« How are students representing the people in both families?

@ What prior knowledge are they using to help solve the
problem?

Questions for Students to Understand Their Thinking
* Can you tell/show me what you did?
e What do those counters/pictures/numbers mean?

ADVANCING QUESTIONS

Questions to Ask Students Who Need Help

e If students cannot get started, ask How can you show the
two families using objects or pictures? What are some ways
you can combine them?

CONNECT answer? Then listen for misunderstandings and careless
errors.

* There's no need to introduce making a 10
number line. The next two lessons include tl

Questions to Help Students Think More Deeply
« Is there another way to solve the problem?

* Can you write an equation to show your answer?

EXTENSION
Ask Which pair of families had the most people? Why? [Sample
answer: Marta’s family and Alaina’s family because Alaina’s family
has the most people_] What size family would Marta need to invite
if she only wanted to have 12 people in all? How do you know?

[Sample answer: S because 7 +5 = 12.)

Ye 3-ACT MATH
nN Wo
Ty 5 Ck

Builds students’ confidence
about solving a real problem.

ACT 1: The Hook
ACT 2: The Model
ACT 3: The Solution

oROTS)
3-ACT MATH

Use this 3-Act Math task any time after
Lesson 5-5.

3-ACT MATH PREVIEW

Page 188 This page gives students a preview of
the 2-Act Math task for Topix 5. Read the robot's
speech bubble to students

Generate Interest Ask students if they have

ever helped with laundry at home. Say: Have you
helped fold dean laundry? Have them share about
finding pairs of socks.

TASK OVERVIEW

Essential Understanding Many rea! world
problems can be represented with a mathematical
model, but that model may not represent a real
world situation exactly.

Students use the 3.Act Math task to practice
mathematical modeling. They.

* identify an enportant problem,

* identify the important information,

* develop a model that represents that situation,
* use the model to propose a solution, and

* test the appropriateness of that math model.

In the 3-Act Math for Topic 5, students draw on
thew conceptual understanding of addition and
subtraction. They make use of representations and
tools such as

* counting objects,
* diagrams, and
* addition and subtraction strategies.

TASK PLANNING

The following pages contain specific support for
using this task with your class.

Before introducing the 3-Act Math task, consider
when you'd prefer students to draw or write thelr
angwers on their Recording Sheets and when they
should share their answers verbally.

For emerging readers and writers, you may wish
to record student responses on the board ina
numbered or color coded list. Students could write

3.ACT MATH PREVIEW

Gefore worching fe vee fre
How do you help ei laundry #
yar house’ A geal way © fetp
the ervrorened! #0) aah rome
of your undry aah cond wearer

The Gotan sf get cheon, ond

yOu bave vp & FO pecent of Te
«ony

TASK CONTENT
In every task, students apply a variety of concepts and skills.

Lesson Concept/Skill
$4 Break apart numbers to subtract
$5 | Subtract using compensation
S2land53 | Subtract using an open number line

They also combine conceptual understanding with math practices and processes in
every step of the task.

ACT 1: THE HooK

SewvasRenize com

a ONC KET

ver ee g
®e® Sect RE
2-ACT MATH Recording Sheer = CORDING SHEET

may say: How many socks are P

Jerome's Work
Js =40
40+ =50
Rs) ths Sg

Comprehensive | Flexible | Customizable

topic T

Perlormonce Tatk

Name ~~
Getting to Work tof $20 for lunch. He buys
Liam has a weekly budge uck every day for one

yd ee a pends is shown
week. The a!

in the table

Use the Lunch ere
answer Questions ?

f money Liam 5 Monday

: <) Exit Multiplication as Repeated Addition: Quick Check W

Tuesday —

cay 1. Bri drew a Picture,

expression represe
of small squares?

is Week table to —
Spent Th’ Wednesday — Which multiplication
Thursday nts the total number

jam spent on junch at

tas ition equation

4? Write an addi

4) Listen
Choose the addition equation and the multiplication equation that represent the picture.

4. How much money
the end of the wee

to solve. 5 een
— eS a
Sm —_—_—_—— ‘
? Explain.
han his budget ——e
2. Did Liam spend nore’ eae
—
|
2. Aar
| EOE A BOOKS on each of 3 shelves
——— , + Write an e :
\ ‘quati
BO a week, he will only buy unch 4 many books Anat represents
3. Liam decides that or ae uch will Liam spend on lune —_ nas nl
sday, and Friday. | ee
Thursday, 5 | 3+34+34+3=12
} j
\ _——— |
——<— hat he we Points that Dani
Lam decides © ——___ iniel Scored?
lunch spending, hee ——..__J =
4, After reviewing Hi aren Faiday He plans to sore B. How many Books does Aaron ha ® sx3- 15 4+44+4=12
junch every day © jer for $32. HOW many weeks wl in all? ve ® sx 1- ‘
to buy a new bien’ Cc © 3.
money? \_J books = 3m -. 444444+4=16

‘ttmehiinn a ——
6 books in en-pont f books with . 3x4=12

h box. Writ
'e
expression that re; an

Number of books
Number of books

( J thm ——

— can
water for ROTI holds enough

in
Plants can Noa 9 2 plants. How many

n water if he fil
watering can 4 times? shes

4x4=12

f )
__jplants

Review progress Ques of 5 € Back Next >

Sonts in a class

| 10, There are 24 stu
them into & equal

7. Zander has 15 basketballs. He
separates them exqually ORO The teacher puts
% ona rack’ groups. Hove many st yctents are 7: Apohacag
ere each group? chante tennis balls, She sepa
A. Wie a dinision equation tat paiek equally into 3 different techen 10, Thes
shaws the number of basketballs ( ehclarls A. Wile a division 5% here are 48 students in a
oneoch mack the number of esac that shows oe puts them into @ Class. The
a
TT Fa aennc te shane with her basket. nis balls in each IW Many students are in BER
ree—_. * group?
| students
Name ———___
“J =< na .
each 1. Bri drew a picture. Which multipécation 4. Fred organized his cofn © basker? 1. face r |
expression represents the total number array, What is the multiplication e Sew a pictur S | S
of small squares? for the array? Draw a different tennis balk of Pression repens Whicty eres
d oo Soo and Int
Sel “a Neen L .
=i guaseegs = ° SO" | non ervention
friends \ il | fi gave 3 pe
riends. Wi) Wha
nurs = ain ch e e mu :
®2 oe number of pene ? tplicats,
@6 @ 4x ® 3x1=3 Orewa ditferers
+ th x7 = DOK | MDIS
on B 4x4 © 7x3e21
= @ 3x309
—_——s 2. Aaron has 3 books on each of 3 shelves.

9. Al needs to py
has 45 hats. Ww
that shows ho

-
—

A. Write an equapon that represents
how many books Aaron hasin all,

5. Daniel kicked five 3-point
his football game. Which
equation represents the
points that Daniel xor

—_ |

a ® sx3=15
B. How many books does Aaron have ® sxins
? 3
= inal © 3x3=9 ‘
(— ) * How man
Jbooks @ sx5~25 in aye” “ttles dove
Aidan have

. Frances has 3 boxes of
6 books in each box.
expression that reper
number of books. F

3. Noah's watering can holds enough
water for watering 2 plants. How many
plants can Noah water if he fills his
watering can 4 times?

\ plants
Ld

Item Analysis for Diagnosis
and Intervention

envision

Envision

has 15 basketballs, "4

sly onto

Ts bails. Sho sepa Name no B44

Y int

A: Whit aciiaies: ache pu themn ns aie Arrays and Multiplication rE

as them eq

Materials 16 counters per student

1. Show an array of 4 rows with 2 coun

2 : ee . ARRAYS AND MULTIPLICATION

b ve
Arrays and Mud plication ne
3. ters are in the array?
4. Show an array of 2 rows with 4 coun
in each row
5. Write a multiplication sentence for th
Number Number of
of Rows Counters in t
6. How mony co are in this array?
7. Both orrays have 8 counters ne
So,4x2=2 —
evwys ord Pihilietion no

8. Since both arrays have 8 counters the Error Intervention if sodees bave »

4xX2=8,and2 x4 them eecd the mul ¥ so *

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DATA DRIVEN INSTRUCTION

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Discuss Class Performance @ @100% * @90% @ 80% @ 70% @ 70%
Settings Student Name YY Standards Progress + > > > > >
> Bilson, Billy 4 Zn Lv) tv) o ix) o
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> Brandle, Brad 4/5 iz fv) tv) Lv) 9 x]
> Catson, Cathy 3s as Lv) Lv) x) x) @
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(JC) MTSS (INTERVENTION SUPPORT

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¢ 100% Alignment to Standards

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Drag each dec¢pal to its name.

¢ Personalized learning for
every student

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¢ Calibrates with every
question

« Up-to-the-minute mastery
and growth data

¢ Direct connections to
envision Mathematics

and division,

MULTIPLICATION SITUATIONS

* Equal-Group Situations Lessons 1-1 and 1-2 focus
the important connection between addition and mu
Students learn that both repeated addition and mult
used to represent situations involving equal groups.

An equal-group situation builds on students’ kno
because an expression describing equal groups can b
repeated addition or as multiplication.

5 groups of 4
444444444 of Sx4

sslesiesiss

Notice how this bar diagram and number line also
of 4.

20 in all —> 20
groupe —>] 4] 414] 4] 4)
t

4 in each group

‘ ‘ 2 Fi]

© Arrays Arrays are special cases of equal-group situ
finding the total number based on the number of ro
number in each row, Both repeated addition and mu
can be used to find the total number in an array.
provides a variety of array situations and uses arrays
Commutative Property of Multiplication,

4x5=#20

Math Background: Focus

Understand Multiplication and
Division of Whole Numbers

Topic 1 focuses on developing understanding of multiplication

LOOK BACK

How does Topic 1 connect to what students
learned earlier?

Grade 2

* Doubles In Topic 1, students learned about
doubles and recorded them as addition
sentences: 44+ 4 = 8.

* Work with Equal Groups In Topic 2,
students explored even and odd numbers
and used arrays to find totals, They also
learned to write equations for arrays using
rows or columns.

4+4+4=12
3434343=12

* Number Line Representations |n Topics
9, 10, and 11, students learned to show skip
counting on a number line and to represent
addition and subtraction on a number line.

Skip count by Ss from 110.

WW ™
——

110 aS) 120 125

Video

Math Background: Coherence

Understand Multiplication and Division
of Whole Numbers

TOPIC 1

How is content connected within Topic 17

* Equal Groups Multiplication and division
are interpreted as equal-group situations
throughout the topic, In a multiplication
equation, any part can be unknown. If the
product is unknown, the problem can be
solved using multiplication; if a factor is
unknoven, the problem can be solved using

* Skip Counting In Lesson 1-2, skip
counting is used to connect addition to
multiplication as represented on a number
line, In Lesson 1-3, skip counting is used,
again, to connect addition to multiplication
as represented by an array,

* Visual Representations Throughout the
topic, arrays, bar diagrams, number lines,
and pictures of equal groups are used
to represent multiplication and division
situations.

12 toys

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4 toys for
each friend
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Total Number Number
of equal in each
groups group

LOOK AHEAD

How does Topic 1 co
will learn later?

Later in Grade 3
.

will learn the mos)
facts: 2s, 5s, 9s,
multiply by 0 and
learn the rest of t

* Relate Multip!
Topic 4, students
of multiplication
as they focus on dj
multiplication fi
to develop stud:
multiplication and

* Connect Area to

Topic 6, students

know about arr.

develop und
between multiplid

Grade 4
* Mul
students will exter

Arigorous curriculum emphasizes conceptual understanding,
procedural skill and fluency, and applications.

CONCEPTUAL UNDERSTANDING

* Equal-Groups Throughout Topic 1, students build their conceptual
understanding of how multiplication and division relate to equal-
group situations. They come to understand that equal-group
situations can be represented using multiplication or division,
depending on what information is known and what is unknoven.
Bar diagrams help students understand and explain how the numbers
are related.

Equal-Group Situations
Total Unknown Delbert puts 7

5 nickels in each of his 3 piggy ee

banks. How many nickels did doioortanie »[ 6 | 6 | & |

Delbert put in the banks? ry
Salokels im coch bank —

Eighteen eggs are divided into
3 rows. How many eggs are in

exchvow? Leta] |
| Number of Groups Se z
Unknown June has 10 + gant
strawberries to serve to her cS ned
guests. If each guest eats it

2 strawberries, how many guests tot aoe gusset

can June serve?

* Commutative Property Lesson 1-3 introduces students to the
Commutative Property of Multiplication. Deep understanding of this
property is important as students will use it throughout their work in
mathematics.

Math Background: Rigor

Understand Multiplication and
Division of Whole Numbers

PROCEDURAL SKILL AND FLUENCY
There are no fluency expectations in Topic 1.

* Use Understandings of Multiplication and Division to
Solve Problems Topic 1 introduces students to the meanings of
multiplication and division, They use this understanding and a variety
of procedures to solve multiplication and division problems. These
procedures include repeated addition, repeated subtraction, skip
counting, and interpreting visual representations,

4x2<?

01234567 8 9101112131415

4x2=8

APPLICATIONS

* Multiplication and Division Students solve a variety of real-world
problems involving equal groups and arrays, These situations allow
students to apply their understandings of multiplication and division
in context.

Dana keeps her swimming medal collection in a display on the
wall, The display has 4 rows. Each row has 5 medals. How many
medals are in Dana's collection?

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Apply Properties:
Multiplication Facts for
3,4, 6, 7,8

Jane F. Schielack, PhD

Essential Understanding

The Distributive Property can be used to
break a large array into smaller arrays.

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