Appendix A: Collection of Problems
Addition and Subtraction
Starter Problems for Singapore Bar Models
1) The sum of 6 and 8 is _____.
2) The sum of 9 and 7 is _____.
3) Find the sum of 65 and 89.
4) The difference between 9 and 7 is _____.
5) Find the difference between 96 and 68.
6) Find the difference between 387 and 512.
7) When 376 is subtracted from a number the answer is 825. Find the number.
Join R - Result Unknown C - Change Unknown S - Start Unknown
8R) Nancy has 5 M&M's. Jermaine adds 3 M&M's to her pile. How many do they have altogether?
8C) Nancy has 5 M&M's. Jermaine adds his to her collection. Now there are 8 M & M's. How many did Jermaine have?
8S) Nancy has some M&M's. If Jermaine adds 3 to her collection they will have 8. How many does Nancy have at the start?
Separate R - Result Unknown C - Change Unknown S - Start Unknown
9C) Mrs. Rogers made 150 pineapple tarts for a party. After the party, there were 16 tarts left. How many tarts were eaten at the party?
9R) Mrs. Rogers made 150 pineapple tarts for a party. The guests ate 134 tarts. How many tarts were left?
9S) Mrs. Rogers made some tarts for the party. The guests ate 134 tarts. She had 16 left. How many tarts did Mrs. Rogers make?
Part Part Whole P- Part Unknown W - Whole Unknown
10P) Sharon is blowing up 52 balloons for a party. She has 24 left to blow up. How many has she already blown up?
10P) Sharon is blowing up 52 balloons for a party. She has blown up 28. How many balloons does she have left to blow up?
10W) Sharon is blowing up balloons for a party. She has blown up 28. She has 24 left to blow up. How many balloons will she have blown up when she is finished?
Compare D - Difference Unknown C - Compare Unknown R - Referent Unknown
11R) Bob's sister 23 years old. She is 9 years older than Bob. How old is Bob?
11C) Bob is 14 years old. His sister is 9 years older. How old is his sister?
11D) Bob is 14 years old. His sister is 23 years old. How many years is the age difference between them?
12C) Mr. Jones traveled 386 km on Monday. He traveled 147 km more on Sunday than Monday. How many kilometers did he travel on Sunday?
13D) Randy collected 124 matchboxes. Josiah collected 283 matchboxes. Who collected more matchboxes? How many more?
14R) There are 3,402 boys at the parade. There are 987 more boys than girls. How many girls are there? How many pupils are there altogether?
Multiplication and Division
Starter Problems for Singapore Bar Models
15) Find the product of 41 x 5.
16) Find the product of 3 x 52.
Grouping/Partitioning Problems
M - Multiplication DM - Division-Measurement DP - Division-Partitive
17DP) Tim printed 900 pamphlets. He packed them equally into 8 boxes. How many pamphlets were there in each box? How many pamphlets were left over?
18M) Jessica put some cookies equally into 3 jars. If each jar had 24 cookies, how many cookies were there altogether?
19DM) Molly sold 70 flowers. They were in bunches of 5. How many bunches of flowers did she sell?
Rate Problems
M - Multiplication D - Division-Measurement DP - Division-Partitive
20DP) Molly saved $32 in 4 weeks. She saved the same amount of money each week. How much did she save in a week?
21M) Kayla used 4 kg of flour to make cakes. She used 18 eggs for each kilogram of flour. How many eggs did she use?
22DM) A bucket holds 7 liters of water. A tank holds 637 liters of water. How many buckets of water can the tank hold?
Price M - Multiplication DM - Division-Measurement D - Division-Partitive
23DM) Mrs. Gray paid $98 for the basket of fish. 1kg sells for $7. How many kg did she buy?
24DP) A fruit seller sold 12 kg of grapes. He collected $96. How much does 1kg cost?
25M) Mr. Smith sells fruit for $8 per kg. He sells 37 kg in one day. How much money did his customers spend on fruit at his fruit stand?
Multiplicative Comparison
26) Roy has 3 times as many comic books as Samy. If Samy had 7 comic books, how many comic books did Roy have?
27) There are 20 monkeys in a zoo. There are 4 times as many monkeys as tigers. How many tigers are there?
28) A florist has 145 yellow roses. She has 8 times as many red roses as yellow roses. How many more red roses than yellow roses does she have?
Multistep (annotated to show components)
1st step -Partitive Division
29) 8 students sold 272 concert tickets at $3 each. Each student sold the same number of tickets. How much money did each student collect? (partitive division/ price -muliplication)
1st step - Measurement Division
30) Mr. Stone bought some books for $301. Each book cost $7. His wife helped him carry 18 books and he carried the rest. How many books did he carry? (price- measurement division/ part-part-whole subtraction missing part)
31) Mr. Lee sold 462 flowers in bunches of 6 each. Each bunch sold for $5. How much money did he receive? (grouping/partition-division-measurement/ price-multiplication)
32) Miss Brown baked 600 pineapple tarts for sale. She packed them into packets of 6. She sold 45 packets. How many packets were not sold? (grouping/partition -measurement division/ separate- result unknown)
1st step Multiplication (grouping partition)
33) Rebecca bought four boxes of doughnuts. There were 6 doughnuts in each box. She divided the doughnuts equally among eight people. How many doughnuts did each person receive? (grouping/partition-multiplication/grouping/partition partitive division)
34) Jordan had 9 bags of paper plates. There were 10 plates in each bag. 25 plates were used for a party. How many plates were left? (grouping/partition- multiplication/ separate- result unknown)
35) Steven bought 7 planks, each 3 m long. He bought another plank 2 m long. Find the total length of the 8 planks. (rate - multiplication/ join - addition - result unknown)
36) Marty reads 8 pages of a book a day. After reading the book for 4 days, she still has 5 pages to read. How many pages are in the book? (rate -multiplication/part-part-whole-addition)
1st step Multiplicative Comparison
37) A toy car costs $5. A toy airplane costs 4 times as much as the toy car. How much more does the toy airplane cost than the toy car? (multiplicative comparison/ compare-subtract- result unknown)
38) A pole is 3m long. A rope is 8 times as long as the pole. If the rope is divided into 4 pieces, what is the length of each piece of rope? (multiplicative comparison/ grouping/partition - partitive division)
39) There are 650 men and twice as many women working in a factory. How many workers are there in the factory? (multiplicative comparison/ part-part-whole - addition- missing whole)
1st step Subtract
40) Rani had $47. After paying for 3kg of shrimp, she had $20 left. Find the cost of 1kg of shrimp. (price- subtract -unknown change/ price - partitive division)
41) A computer cost $1,900. A television set was $650 cheaper than the computer. Mr. Ray bought both the computer and the television set. How much did he pay? (compare - subtract - difference unknown/ join- addition- result unknown)
42) Pablo earns $3,000 a month. He spends $2,200 a month and saves the rest. How much money can he save in 6 months? (price - separate -difference unknown/ price - multiplication)
1st step Part-Part-Whole
43) A farmer had 2,000 chickens and ducks. After selling some of them, he had 650 chickens and 520 ducks left. How many chickens and ducks did he sell altogether? (part-part-whole - addition - missing whole/ separate- difference unknown)
44) 4 men and 5 women shared the cost of a present equally. The cost of the present was $117. How much did each of them pay? (part-part-whole - addition - whole unknown/ price - partitive division)
Comments: