Basic Arithmetic Operations and When to Use Them - I
Singapore Math Bar Model
The Singapore model method teaches students to represent quantities with bars of varying lengths
and determine which operation to choose in one-step problems. Although the bar model method
clarifies the choice of operation for one-step problems, its real beauty lies in the simplicity it lends
to more complex, multistep problems.
1
Part-Whole Model for Addition and Subtraction
Example 1 Miss Lucy has 27 students in her morning ballet class. She has 39 students in her
afternoon ballet class. How many students does she have in both classes? (66)
Practice 1 Connie has 33 marbles. Juan has 28 more marbles than Connie. How many marbles does
Juan have?
33 + 28 = 61
Example 2 There are 278 people at a camp. 26 of them are teachers and the rest are children.
How many children are there? (252)
Practice 2 There are 92 pumpkins and 38 cornstalks in a field. How many more pumpkins are there
than cornstalks?
92 – 38 = 54
Example 3 Daniel has 228 craft sticks for his project. He needs 350 more craft sticks. How many
craft sticks does he need for his project? (578)
Practice 3 Town Sports has 99 scooters. The store sells some of them and has 45 scooters left. How
many scooters does Town Sports sell? (54)
99 – 45 = 54
2
Practice 4 During summer vacation, Emma worked 82 hours, and Julie worked 33 hours. Don
worked 18 more hours than Julie. How many more hours did Emma work than Don?
Don = 33 + 18 = 51
82 – 51 = 31
Practice 5 James has 37 baseball cards. Paul has 23 more cards than James and 15 more cards than
Ronald. How many cards do the three boys have altogether? (142)
37 × 3 + 23 × 2 – 15 = 111 + 46 – 15 = 142
J: 37; P: 37 + 23 = 60; R = 60 – 15 = 45; J + P + R = 37 + 60 + 45 = 142
Example 4 There are 183 tennis balls in Basket A and 97 tennis balls in Basket B. How many
tennis balls must be transferred from Basket A to Basket B so that both baskets contain the same
number of tennis balls? ((183 – 97) ÷ 2 = 43)
Practice 6 I am a number between 1 and 100. I am an even number and when you subtract me from
100 and then subtract 10, I am equal to 76. What number am I? (14)
76
6
10
6
100 – 76 – 10 = 14
Practice 7 I am an even number between 2 and 50. When you take ½ of me and then subtract 14,
you get 6. What number am I?
10
6
14
6
½
(6 + 14) × 2 = 40
Practice 8 Jillian got her math test back. She had 10 points less than Joey. Joey’s score was lower
than Terri’s score but 1 point more than Tommy’s score. Terri’s score was the highest in the class
and it was 2 more than Tommy’s. Terri got a 95. What was Jillian’s score? (84)
Tommy = 95 – 2 = 93;
Joey = 93 + 1 = 94;
Jillian = 94 – 10 = 84
3
Practice 9 A table and a chair cost $40. The table cost $24 more than the chair. How much will 1
table and 6 chairs cost? (80)
(40 – 24) ÷ 2 = 8;
Price for one chair
8 + 24 = 32;
Price for one table
32 + 8 × 6 = 32 + 48 = 80
10. Wendy attended a recent Pawtucket Red Sox game. She had $10 to spend at the stadium gift
shop. She bought two of the items below and received $3.50 in change. Which two items did
Wendy buy?
10 – 3.5 = 6.5 = sticker & program
11. John was born 25 years before his son Mark. John's father is 52 years older than Mark. Can you
determine John’s age this year? Can you tell how old was John’s father when John was born?
Draw how the situation might look.
12. John, who born in 1981, was 25 years old when his son Mark was born. John's father is 52 years
older than Mark. Can you tell how old was John’s father in 2014?
1981 + 25 = 2006
2006 – 52 = 1954
2014 – 1954 = 60
13. Mark is the youngest in his family. He has 2 brothers. The difference in age between his brother,
Jim, and his oldest brother, John, is 2 years. The difference in age between Mark and Jim is also
2 years. If Mark is 12, how old are the other two boys?
Jim – 14; John - 16
4