Lesson 2  Place Value —Part 1

Objective
• Identify the value and the place of each Lesson 2 2
Place Value — Part 1
digit in a four-digit number.

Lesson Materials Think

• Place-value Cards (BLM) How many beads do I have altogether?

• Place-value discs
• Place-value Organizer (BLM)

1,000

Think
10

8 100
10

Provide students with place-value discs and a Place- 10

value Organizer (BLM). Have them try to solve the

100

10

Think problem independently.

10

Learn 1,000 10
100

Discuss the Learn examples. Ask students:

• What is meant by the “value” of each digit?

• What does a digit stand for, and what is its value? 8 1-2 Place Value — Part 1

Students will continue working with digits and their

values throughout the Do portion of this lesson. Learn

In addition to asking how many tens there are, ask,

“What is the value of the digit in the tens place?” 1,000 1,000 100 100 100 10 10 10 10 10 1 1 1 1 1

10 1 1 1

Thousands Hundreds Tens Ones

2 3 6 8

2,000 + 300 + 60 + 8 = 2,368

Dion has 2,368 beads.

The digit 2 in 2,368 is in the thousands place.

2,0 0 0 It stands for 2 thousands.
Its value is 2,000.
9
The digit 3 in 2,368 is in the hundreds place.
3 0 0 It stands for 3 hundreds.
Its value is 300 .

The digit 6 in 2,368 is in the tens place.

6 0 It stands for 6 tens.
Its value is 60.

The digit 8 in 2,368 is in the ones place.

8 ones
It stands for 8 _____.
Its value is 8 .

2,3 6 8

1-2 Place Value — Part 1 9

10 Teacher’s Guide 3A  Chapter 1 © 2017 Singapore Math Inc.

 Do
If needed, provide additional practice with different Do
1 Show 4,573 with place-value cards.
four-digit numbers and questions similar to 2 and
5 , where the values given are not necessarily in 4,0 0 0
5 0 0
7 0
order from greatest to least. 3

5 It is important that students are able to compose the (a) The digit 4 in 4,573 is in the ________
thousands place.

number when the numbers being added are not in ( b) The digit 5 in 4,573 stands for 5 ________.
hundreds

order from greatest to least. (c) The digit 7 in 4,573 stands for 7 ________.
tens

(d ) The digit 3 in 4,573 is in the ________

ones place.
If students are confused, give them Place-value
Cards (BLM) to make the number and think about 10 2
1,000 1,000 1,000 1,000 1,000 10 10 10 10 10 1 1 1 1 1

1,000 1,000 1,000 1,000 10 10 10

what is missing. Thousands Hundreds Tens Ones

9 0 8 5

Activity (a) The digit 5 in 9,085 is in the ones place.

( b) The digit 0 in 9,085 is in the ________

hundreds place. Its value is 0.

Place-value Hangman (c) The value of the digit 9 in 9,085 is 9,000 .

Students play hangman using four-digit numbers. (d ) The digit 8 in 9,085 stands for 8 tens.

Player One makes a four-digit number and draws

4 lines:
10 1-2 Place Value — Part 1

_____ , _____ _____ _____

Player Two tries to guess the number by asking yes/no

3 Write the number.
questions like: 1,000 1,000 1,000 1,000 1,000 100 100 100 100 10 10 10 1 1 1 1 1
(a)
1,000 1,000 1 1 1 1

• Is there a 3 in the tens place? 7,439

1,000 1,000 1,000 1,000 1,000 100 100 100 100 100 1 1 1 1
( b)
• Is the digit in the hundreds place greater than 5? 1,000 1,000 1,000 100

8,604
• Is the value of the thousands digit less than 4? (c)
1,000 1,000 1,000 1,000 1,000 100 100 100 100 100 10

100 100 100 100

5,910

4 (a) Write the number in words.

Exercise 2 • page 4 four thousand, nine hundred eighty two

4,982
two thousand, three hundred eight
2,308 9,250 5,029

nine thousand, two hundred fifty five thousand, twenty-nine

( b) In what place is the digit 2 in each number, and what is its value?
11
ones, 2 thousands, 2,000 hundreds, 200 tens, 20

5 (a) 6,069 = 6,000 + 60 +9

( b) 7,402 = 7,000 + 400 + 2

(c) 5,300 = 5,000 + 300

(d ) 5,008 = 5,000 + 8

(e) 1,953 = 900 + 1,000 + 3 + 50

( f ) 8,808 = 8 + 800 + 8,000

Exercise 2 • page 4

1-2 Place Value — Part 1 11

© 2017 Singapore Math Inc. Teacher’s Guide 3A  Chapter 1 11

 Lesson 9  2-Step Word Problems

Objective
• Solve two-step word problems involving all Lesson 9 9
2-Step Word Problems
four operations.

Lesson Materials Think

• Strips of paper Mei had 30 m of ribbon.

She cut off 2 pieces of ribbon.
The second piece is 3 times as long as the first piece.
There is still 18 m of ribbon left on the spool.
How long is each piece?

Think Learn
I need to find the total length
of the two cut pieces first.

Pose the problem in Think and have students draw first piece

models. Discuss the students’ models. 128 second piece 30

left on spool

18
Ask students:
4 units 30 − 18 = 12
• How is the problem similar to the ones we did 1 unit 12 ÷ 4 = 3

yesterday? (It is about multiplying and dividing. The first piece is 3 m long.

I think I can draw a comparison model.)

• How is it different? (There are more steps in this 3 units 3×3= 9 Check your answers.
Does 3 + 9 + 18 = 30?

one. It’s longer.) The second piece is 9 m long.

Learn 128 4-9 2-Step Word Problems

Have students discuss the bar model in Learn and

compare their own models with the one in the textbook.

What information do we know? 30 m of Ribbon at First

• Mei has some ribbon and she cut off 2 pieces. Ribbon left on spool Ribbon cut off
• The 2nd piece of ribbon is longer than the 1st piece. 18 m ?
• There is still ribbon on the spool.

What do we need to find? 30 m − 18 m = 12 m

• How long each piece of ribbon is. Then finding the length of the 2 pieces:

Have students begin by drawing models to represent

the 1st and 2nd pieces of ribbon, adding the third bar 1st piece
to represent the amount of ribbon left on the spool. 12 m
2nd piece
Students begin by subtracting the amount of ribbon
left on the spool:
4 units 12 m
1 unit 12 ÷ 4 = 3 m
3 units 3×3=9m

152 Teacher’s Guide 3A  Chapter 4 © 2017 Singapore Math Inc.

 Do
2 This model shows a part-whole representation of Do
1 Mei made 3 times as many ants as spiders.
addition and multiplication. Ask students: She made 12 ants.

• Why are some of the parts equal and one is not? (a) How many animals did she make?

• Could this be drawn with two models? (Or with a ( b) How many more ants than spiders did she make?
12
comparison model?) ants
?
Find the value
of 1 unit first
spiders
? and use that for
3 This problem is a sum and difference bar model. This 3 units 12 both problems.
1 unit 12 ÷ 3 = 4
pattern will be used throughout the Dimensions
(a) 4 units 4× 4 = 16 She made 16 animals.
Math® program.
( b) 2 units 2× 4 = 8 She made 8 more ants than spiders.
129
Sofia’s thought provides a hint. If there are equal
2 Ms. Davis bought 6 skeins of wool yarn for Find the cost of
units, this becomes an easier problem. Dion can $5 each and a set of knitting needles for $12. the yarn first.
How much did she spend?
make 2 equal units by taking 5 from the total amount
5 12
of dinosaurs.
?
1 unit 5
6 units 6 × 5 = 30 (cost of yarn)

Alex 30 + 12 = 42 (total spent)

23 − 5 = 18 She spent $ 42 .

Emma
? 4-9 2-Step Word Problems 129

To demonstrate Sofia’s thoughts, use two strips of

3 Alex and Emma together made 23 dinosaurs.
paper that are proportional in length to the bars in the Alex made 5 more dinosaurs than Emma.
How many dinosaurs did Emma make?
textbook. Fold behind or tear off the piece of Alex’s If I take 5 away,
Alex they will both have
bar that represent 5 dinosaurs to show that what 23 the same number.
Emma
remain of Alex’s bar and Emma’s bar are equal units. ? 5

We need to find how many Emma made.

Once we find two equal units, we can divide to find the Make her bar the unit.

value of one unit.

2 units 23 − 5 = 18

4 — 5 When discussing these problems, ask students: 1 unit 18 ÷ 2 = 9

130 Emma made 9 dinosaurs.

• Why are there two models? 4 2

• Are these comparison problems? 4 Dexter bought 3 packs of foam brushes.

There were 4 thin brushes and 2 thick
brushes in each pack.
How many brushes did he buy?
1 unit 4+2=6 ?
3 units 3 × 6 = 18 18 brushes 23 17
5 Sita polished 23 rocks on Monday
and 17 rocks on Tuesday.
She put the rocks equally into 5 boxes.
How many rocks are in each box?
23 + 17 = 40 ?
40 ÷ 5 = 8
8 rocks

130 4-9 2-Step Word Problems

© 2017 Singapore Math Inc. Teacher’s Guide 3A  Chapter 4 153

 6 Discuss Alex’s thought. Ask students:

• Why is Dion being used to represent 1 unit? 6 Mei and Dion together made 11 turtles. Make Mei’s bar the unit.
Mei made 3 more turtles than Dion. If Dion had made 3 more
How many turtles did Mei make? then...
Additionally, this problem can be solved similarly to
?
3 by subtracting the difference between Mei and Mei
11
Dion, leaving 2 equal units. Dion
3
2 units 11 + 3 = 14
1 unit 14 ÷ 2 = 7 7 turtles
7 Asimah has 9 tulips.
She has 3 times as many daisies as tulips.
Mei She arranges 6 flowers in each vase.
How many vases does she use?
11 − 3 = 8
tulips daisies
Dion 9

4 × 9 = 36
131
? 36 ÷ 6 = 6
6 vases

6 6

2 units 8 turtles 8 A pack of 5 paint pens cost $3.

Mr. Ikeda bought 20 paint pens.
1 unit 8 ÷ 2 = 4 turtles 20 How much did he pay? 20 ÷ 5 = 4 (packs)
4 × 3 = 12 (cost of 4 packs)

“Mei made 4 + 3, or 7, turtles.” 5

9
$12
Hudson has 4 times as many crayons as Elena.
24
He has 24 more crayons than Elena does.
Hudson
7 Students may need to draw the two steps separately How many crayons do they have altogether?
1 unit 24 ÷ 3 = 8
?
Elena
to see “3 times as many,” and then find how many 5 units
Exercise 9 • page 119
5 × 8 = 40 40 crayons

flowers in all.
4-9 2-Step Word Problems 131

?
Daisies Exercise 9 • page 119
? flowers in all
Tulips
9

1 unit 9 flowers
4 units 4 × 9 = 36 flowers

36
? vases needed
6 6

36 ÷ 6 = 6. Asimah uses 6 vases.

8 — 9Discuss the models students draw and any

alternative methods they use to solve the problems.

154 Teacher’s Guide 3A  Chapter 4 © 2017 Singapore Math Inc.

 Lesson 10  Practice

Objective
• Practice topics from the chapter. Lesson 10 P 10
Practice

1 Find the value.

Have students practice with activities from the (a) 8 ÷ 4 2 ( b) 4 × 7 28 (c) 14 ÷ 2 7

chapter to ensure they know their multiplication and (d ) 4 × 4 16 (e) 32 ÷ 4 8 ( f ) 0 × 10 0

division facts for 2 through 5. ( g) 35 ÷ 5 7 ( h) 27 ÷ 3 9 ( i ) 18 ÷ 3 6

Provide additional support and practice opportunities ( j ) 16 ÷ 2 8 ( k) 5 ÷ 5 1 ( l ) 0 ÷ 10 0

as needed.
2 (a) 5 × 4 = 20 ( b) 0 ×5=0 (c) 24 =8×3

5 A sample model is given. Students may draw the 132 (d ) 3 ÷ 1 =3 (e) 0 ÷5=0 (f ) 2 =4÷2

models differently to answer individual problems.

3 Find the quotient and remainder.

(a) 7 ÷ 2 3R1 ( b) 10 ÷ 3 3R1 (c) 22 ÷ 4 5R2

$10 (d ) 16 ÷ 5 3 R 1 (e) 42 ÷ 10 4 R 2 ( f ) 88 ÷ 10 8 R 8

Balloons ( g) 26 ÷ 3 8 R 2 ( h) 26 ÷ 4 6R2 ( i ) 26 ÷ 5 5R1

4 Are the following numbers odd or even?

Yarn
(a) 12 even ( b) 11 odd (c) 13 odd (d ) 16 even
12 ÷ 2 = 6 11 ÷ 2 is 5 R 1 13 ÷ 2 is 6 R 1 16 ÷ 2 = 8

Glue
132 4-10 Practice

(a) 5 units $10

1 unit $10 ÷ 5 = $2
5 Katie is making decorative balls out of yarn to sell at the farmer’s
market on Kids Vending Day.
( b) 1 unit $2 She bought 1 pack of balloons, 10 skeins of yarn, and 2 bottles of glue.
She spent $10 on the pack of balloons.
10 units 10 × $2 = $20 The balloons cost 5 times as much as 1 skein of yarn.
The 2 bottles of glue cost the same as 3 skeins of yarn.

(c) 1 unit $2 $10

Balloons
3 units 3 × $2 = $6 Yarn

(3 units of yarn = 2 units of glue) Glue

1 unit of glue $6 ÷ 2 = $3 (a) How much does 1 skein of yarn cost?

10 ÷ 5 = 2; $2
( b) How much did she spend on the yarn? Different models may be
(e) 10 × 2 = 20; $20 drawn for each step.
(c) How much does 1 bottle of glue cost? Methods of solution may
133
9 4 3 × 2 = 6; 6 ÷ 2 = 3; $3 vary.
(d ) How much did she spend in all?
9 × 4 + 4 = 40 10 + 20 + 6 = 36; $36
(e) Katie made 9 each of red, yellow, orange, and green balls.
She made 4 brown balls.
5 ? 5 She displayed the balls by putting 5 in each bowl. 9 × 4 = 36
How many bowls did she use? 36 + 4 = 40
40 ÷ 5 = 8
( f ) She sold all 9 red balls. 8 bowls
One buyer gave her $1 extra as a tip.
She received $28 from selling the red balls.
(f) How much did she sell each red ball for?
28 − 1 = 27
28 − 1 = 27
? 1 27 ÷ 9 = 3; $3

4-10 Practice 133

© 2017 Singapore Math Inc. Teacher’s Guide 3A  Chapter 4 155

 6 (a )
?
6 Josef made a total of 5 birdhouses and sold them all for $9 each at the
$9 market on Kids Vending Day.

(a) How much money did he receive? 5 × 9 = 45

$45
( b) The materials for each birdhouse cost $3.

1 unit $9 The fee for the booth at the market was $5.
How much did he spend? 5 × 3 = 15

5 units 5 × $9 = $45 15 + 5 = 20
(c) How much profit did he make? 45 − 20 = 25
$25
Josef received $45.
7 Evan collected 2 more Arman
pinecones than Arman.
Mila collected twice as Evan 2 30
( b) many pinecones as Evan.
? 134 Altogether, they collected Mila 2 2
30 pinecones.

$3 $5 (a) How many pinecones did Arman collect?

3×2=6
4 units 30 − 6 = 24
6 pinecones 1 unit 24 ÷ 4 = 6
( b) How many pinecones did Mila collect?
6+2=8
8 × 2 = 16 16 pinecones
1 unit $3 8 Alisha collected 3 more pinecones than Fuyu.
Lucas collected 3 times as many pinecones as Alisha.
5 units 5 × $3 = $15 Altogether, they collected 47 pinecones. 4 × 3 = 12
5 units 47 − 12 = 35

$15 + $5 = $20 (a) How many pinecones did Fuyu collect? 1 unit 35 ÷ 5 = 7
7 pinecones
( b) How many pinecones did Lucas collect?
Fuyu
Josef spent $20. 7 + 3 = 10
10 × 3 = 30 Alisha 3 47
Exercise 10 • page 123
30 pinecones
Lucas 3 3 3

(c) 134 4-10 Practice

$45 earned
spent profit
$20 ? Shuffle fact cards and 3 Kaboom Cards (BLM)
together and place them facedown in a pile. Players
take turns drawing a card and stating the product or
7 Arman represents the unit. Evan has 1 unit + 2 more
quotient.
pinecones. Mila has twice as many as Evan, or
2 units + 4 more pinecones. Altogether they have Students keep the cards they answer correctly, and
4 units + 6 more pinecones = 30. return the ones that they answer incorrectly. When a
student draws a Kaboom Card (BLM), he must return
4 units 30 − 6 = 24
all of his collected cards to the pile.
1 unit 24 ÷ 4 = 6 pinecones
The player with the most cards at the end of the time
8 Encourage students to consider 7 to help draw a model.
limit is the winner.

Activity Exercise 10 • page 123

Multiplication and Division Kaboom
Materials: Kaboom Cards (BLM), multiplication and
division fact cards for 0 to 5

156 Teacher’s Guide 3A  Chapter 4 © 2017 Singapore Math Inc.

Lesson 4  Multiplication with Regrouping Ones

Objective
• Multiply a two-digit number by a one-digit Lesson 4 4
Multiplication with Regrouping Ones
number with regrouping ones.

Lesson Materials Think

• Place-value discs

Mei ran 24 miles each week for 3 weeks to prepare for the race.
How many miles did she run to prepare for the race?
Think
Learn
Provide students with place-value discs and have 24 × 3

them work the Think problem independently. 152 10 10 1 1 1 1

H T O
2 4
× 3

Have students write an equation and discuss how Multiply the ones.
Regroup the ones. H T O
they found their answers. 10 1
10 10 1 1 1 1 2 4
1 1 1 1 × 3
Ask students: 1 1 1 1 2
4 ones × 3 = 12 ones

• How is this problem different from the ones = 1 ten 2 ones 4 ones × 3

you solved in the previous lesson? (We have to Write the regrouped
ten above the tens.
regroup ones.)
• How is it the same? (We can still multiply the
digits in each place.) 152 5-4 Multiplication with Regrouping Ones

Discuss student strategies for solving the problem.

Ask them what they can do when they have more
than 9 in the ones column.

Learn
Work through the Think problem with students as
demonstrated in Learn. Have students work along
with place-value discs as the steps are modeled.

Emphasize how to record the regrouped tens in the

written algorithm, and the fact that this regrouped
ten is not multiplied again when multiplying tens, but
added in after multiplying tens.

© 2017 Singapore Math Inc. Teacher’s Guide 3A  Chapter 5 185

 Discuss the regrouping from 12 ones to 1 ten and
2 ones. Ensure that students trade ten 1-discs for one
Multiply the tens. This ten is from
10-disc and place it above the rest of the 10-discs. 10
multiplying the ones.
10 10 1 1
Do not multiply it again.
Help students to understand that the regrouped tens 10 10

10 10

do not get multiplied. Students who struggle with 2 tens × 3 = 6 tens

this will have a difficult time with problems where

regrouping occurs in both the ones and the tens place. Then, add in the regrouped ten. H T O
1
10 10 10 10 10 1 1 2 4

Ask students: 10 10 × 3
7 2
6 tens + 1 ten = 7 tens

• What is similar about the ways the problem has (2 tens × 3) + 1 ten

been solved by Dion, Emma, and Sofia? 24

153
× 3
• Whose way is quickest and why? (“Emma’s 72

method, because you don’t have to add again,” or,

24 I can use mental math.
“Sofia’s method, because we can do it mentally.”) × 3 24 × 3 = 60 + 12
12 4×3
20 4
60 20 × 3
After the students have worked the problem with 72

place-value discs, have them compare their methods

from Think with the method shown in the textbook. Mei ran 72 miles.

5-4 Multiplication with Regrouping Ones 153

186 Teacher’s Guide 3A  Chapter 5 © 2017 Singapore Math Inc.

 Do
1 Struggling students may need to work these problems Do 10 10

10 1 1 1 1
1 Multiply 14 by 5.
with place-value discs to see the regrouping step. 10 1 1 1 1

10 1 1 1 1
2
10 1 1 1 1

Mei reminds students not to multiply the regrouped tens. ×

1 4
5
10 1 1 1 1

7 0
5 Students can use any of the methods they have 4 ones × 5
14
learned. Have them share why they chose their (1 ten × 5) + 2 tens
× 5
20 4×5
methods after solving the problem. 50 10 × 5
Remember not to multiply
70
the regrouped tens.

Exercise 4 • page 139 154

10 10

10 10 1 1 1 1 1
2 Multiply 3 by 28.
1 1 1

10 10 1 1 1 1 1
2
1 1 1
2 8
10 10 1 1 1 1 1
× 3
1 1 1
8 4

154 5-4 Multiplication with Regrouping Ones

10

10 10 10 10 1 1 1 1 1
3 Multiply 49 by 2.
1 1 1 1

10 10 10 10 1 1 1 1 1
1
1 1 1 1
4 9
× 2
9 8

4 What are the missing digits?

(a) 3 ( b) 1
1 8 3 5
× 4 × 2
7 2 7 0

5 Find the value.

155
(a) 17 × 5 85 ( b) 38 × 2 76 (c) 25 × 3 75

(d ) 24 × 4 96 (e) 7 × 15 105 ( f ) 5 × 19 95

6 BAGEL
BUDDIES
BARGAIN
SHOP
CRAFTY
TOWN
SPORT
CO.
PRETZEL
PEOPLE

SNOW PET SAMMY'S NORTH SLEEP

PALACE
CONE PROFESSOR
CLEAN'S SANDWICHES CONSTRUCTION MATTRESS
ZONE

FLOYD'S BAXTOR'S COFFEE Flowers&

Botanicals
HEALTHY SHIP IT
CUPCAKES BURGERS BEAN MOUNTAIN
FAST

There are 18 sponsors for the race.

Each sponsor donated 3 raffle prizes. 18 × 3 = 54
How many raffle prizes are there? 54 raffle prizes

Exercise 4 • page 139

5-4 Multiplication with Regrouping Ones 155

© 2017 Singapore Math Inc. Teacher’s Guide 3A  Chapter 5 187