Continental Math League (CML) Practice Questions
Grades 2 & 3
100 Free CML Practice Problems – Prepare for Continental Math League competitions with engaging problems designed to match actual CML contest difficulty. Perfect for students in grades 2 and 3!
📚 What’s Included:
- ✅ 100 CML-style practice questions covering all topics
- ✅ Step-by-step problem solving to build critical thinking
- ✅ Downloadable PDF for offline practice
- ✅ Complete answer key for easy checking
- ✅ Elementary-level math – Perfect for grades 2-3
📝 CML Practice Questions (1–100)
These questions are designed to match actual CML contest difficulty for grades 2-3. Work through them carefully and show your work!
1) How much larger is (7 + 6 + 3) than (21 + 3 – 14)?
2) a Δ b means (a + b) – (a – b). For example, 8 Δ 4 = (8 + 4) – (8 – 4) = 12 – 4 = 8. Express 5 Δ 3 in simplest form.
3) Ellen has 75¢ in nickels, dimes and quarters. She has at least one of each coin. What is the difference between the most number of coins she could have and the least number of coins she could have?
4) Point B is halfway between Point A and Point C. Point D is halfway between Point C and Point E. The distance from Point A to Point B is 12 inches. The distance from Point D to Point E is 14 inches. The distance from Point B to Point D is ___ inches.
5) Steve and Juwan were playing handball. Steve won 5 games and Juwan won 6 more games than Steve. If there were 4 tie games, how many games of handball did they play?
6) In the addition problem at the right, find the sum of the digits represented by A and B. Different letters represent different digits. Each time the same letter appears it represents the same digit. 274 + 5A = BBB
7) If 7 + 6 = 20 – □, find the number that belongs in the box.
8) In the two problems at the right, the larger answer is ___ more than the smaller answer. 133 + 148 and 321 – 73
9) If Mr. O’Brien was able to cut a board of wood into exactly eight 3-foot pieces, then he could have cut the same board into ___ 4-foot pieces.
10) There are 17 people meeting in Room 101. There are 7 people meeting in Room 201. If ___ people were moved from Room 101 to Room 201, there would be twice as many people in Room 201 as in Room 101.
11) A, B and C represent different digits. AB represents a 2-digit number. AB + C = 50; BC + A = 41. In the answer column, place the values for A, B and C.
12) In a bank, Mrs. Wallace, Mrs. Thomas and Mrs. Ramiriz held the positions of bank teller, loan officer and branch manager, but not necessarily in that order. The teller, who just began working that year, earned the least. Mrs. Thomas and Mrs. Ramiriz worked for the bank for many years. Mrs. Thomas earned more than the loan officer. Who was the loan officer?
13) How much larger is (9 + 8 + 2) than (15 + 7 – 11)?
14) x ★ y means (x + y) + (x – y). For example, 10 ★ 6 = (10 + 6) + (10 – 6) = 16 + 4 = 20. Express 12 ★ 5 in simplest form.
15) Maria has 90¢ in nickels, dimes and quarters. She has at least one of each coin. What is the difference between the most number of coins she could have and the least number of coins she could have?
16) Point M is halfway between Point K and Point N. Point P is halfway between Point N and Point Q. The distance from Point K to Point M is 8 feet. The distance from Point P to Point Q is 10 feet. The distance from Point M to Point P is ___ feet.
17) Amy and Ben were playing checkers. Amy won 7 games and Ben won 5 more games than Amy. If there were 2 tie games, how many games of checkers did they play?
18) In the addition problem 426 + 8C = DDD, find the sum of the digits represented by C and D. Different letters represent different digits. Each time the same letter appears it represents the same digit.
19) If 8 + 9 = 25 – □, find the number that belongs in the box.
20) In the two problems at the right, the larger answer is ___ more than the smaller answer. 257 + 136 and 418 – 95
21) If Mrs. Smith was able to cut a ribbon into exactly six 5-inch pieces, then she could have cut the same ribbon into ___ 3-inch pieces.
22) There are 24 students in Class A. There are 12 students in Class B. If ___ students were moved from Class A to Class B, there would be twice as many students in Class B as in Class A.
23) R, S and T represent different digits. RS represents a 2-digit number. RS + T = 65; ST + R = 53. In the answer column, place the values for R, S and T.
24) Three friends – Luis, Maria and Carlos – have three different pets: a dog, a cat and a fish, but not necessarily in that order. Luis is allergic to fur. Maria’s pet can swim. Carlos walks his pet every day. Who owns the cat?
25) How much larger is (12 + 5 + 3) than (18 + 6 – 12)?
26) a ◊ b means (a × 2) + b. For example, 5 ◊ 3 = (5 × 2) + 3 = 10 + 3 = 13. Express 7 ◊ 4 in simplest form.
27) Tom has 65¢ in nickels, dimes and quarters. He has at least one of each coin. What is the difference between the most number of coins he could have and the least number of coins he could have?
28) Point R is halfway between Point P and Point S. Point T is halfway between Point S and Point U. The distance from Point P to Point R is 15 cm. The distance from Point T to Point U is 9 cm. The distance from Point R to Point T is ___ cm.
29) Lisa and Jake were playing basketball. Lisa scored 9 baskets and Jake scored 4 more baskets than Lisa. If there were 3 games total, how many baskets were scored in all?
30) In the addition problem 195 + 6E = FFF, find the sum of the digits represented by E and F. Different letters represent different digits. Each time the same letter appears it represents the same digit.
31) If 13 + 8 = 35 – □, find the number that belongs in the box.
32) In the two problems at the right, the larger answer is ___ more than the smaller answer. 348 + 127 and 529 – 186
33) If Mr. Davis was able to cut a rope into exactly twelve 2-foot pieces, then he could have cut the same rope into ___ 3-foot pieces.
34) There are 30 apples in Basket A. There are 18 apples in Basket B. If ___ apples were moved from Basket A to Basket B, there would be twice as many apples in Basket B as in Basket A.
35) P, Q and R represent different digits. PQ represents a 2-digit number. PQ + R = 72; QR + P = 64. In the answer column, place the values for P, Q and R.
36) Three children – Emma, Noah and Sophia – live on three different streets: Oak Street, Pine Street and Maple Street, but not necessarily in that order. Emma does not live on Oak Street. Noah lives on the street that comes first alphabetically. Who lives on Maple Street?
37) How much larger is (15 + 7 + 4) than (23 + 5 – 16)?
38) m ♥ n means (m + n) – 5. For example, 12 ♥ 8 = (12 + 8) – 5 = 20 – 5 = 15. Express 14 ♥ 9 in simplest form.
39) Sarah has 80¢ in nickels, dimes and quarters. She has at least one of each coin. What is the difference between the most number of coins she could have and the least number of coins she could have?
40) Point V is halfway between Point T and Point W. Point X is halfway between Point W and Point Z. The distance from Point T to Point V is 11 inches. The distance from Point X to Point Z is 13 inches. The distance from Point V to Point X is ___ inches.
41) Mike and Kate were playing tennis. Mike won 8 games and Kate won 3 more games than Mike. If there were 5 tie games, how many games of tennis did they play?
42) In the addition problem 537 + 4G = HHH, find the sum of the digits represented by G and H. Different letters represent different digits. Each time the same letter appears it represents the same digit.
43) If 11 + 7 = 28 – □, find the number that belongs in the box.
44) In the two problems at the right, the larger answer is ___ more than the smaller answer. 462 + 159 and 637 – 174
45) If Mrs. Lee was able to cut a string into exactly ten 4-inch pieces, then she could have cut the same string into ___ 5-inch pieces.
46) There are 26 books on Shelf A. There are 14 books on Shelf B. If ___ books were moved from Shelf A to Shelf B, there would be twice as many books on Shelf B as on Shelf A.
47) X, Y and Z represent different digits. XY represents a 2-digit number. XY + Z = 84; YZ + X = 78. In the answer column, place the values for X, Y and Z.
48) Four students – Alex, Bella, Carlos and Dana – finished a race in different positions: 1st, 2nd, 3rd and 4th. Alex finished before Bella but after Carlos. Dana finished last. Who finished 2nd?
49) How much larger is (14 + 9 + 5) than (25 + 8 – 19)?
50) p ◆ q means (p × 3) – q. For example, 6 ◆ 4 = (6 × 3) – 4 = 18 – 4 = 14. Express 5 ◆ 7 in simplest form.
51) David has 70¢ in nickels, dimes and quarters. He has at least one of each coin. What is the difference between the most number of coins he could have and the least number of coins he could have?
52) Point J is halfway between Point H and Point K. Point L is halfway between Point K and Point M. The distance from Point H to Point J is 13 cm. The distance from Point L to Point M is 7 cm. The distance from Point J to Point L is ___ cm.
53) Rachel and Tom were playing cards. Rachel won 11 games and Tom won 6 more games than Rachel. If there were 4 tie games, how many games of cards did they play?
54) In the addition problem 628 + 7J = KKK, find the sum of the digits represented by J and K. Different letters represent different digits. Each time the same letter appears it represents the same digit.
55) If 16 + 9 = 40 – □, find the number that belongs in the box.
56) In the two problems at the right, the larger answer is ___ more than the smaller answer. 573 + 148 and 745 – 192
57) If Mr. Wilson was able to cut a wire into exactly fifteen 2-cm pieces, then he could have cut the same wire into ___ 5-cm pieces.
58) There are 32 marbles in Jar A. There are 16 marbles in Jar B. If ___ marbles were moved from Jar A to Jar B, there would be twice as many marbles in Jar B as in Jar A.
59) L, M and N represent different digits. LM represents a 2-digit number. LM + N = 93; MN + L = 89. In the answer column, place the values for L, M and N.
60) Three teachers – Mr. Brown, Ms. Green and Mrs. White – teach three different subjects: Math, Science and Reading, but not necessarily in that order. Mr. Brown teaches the subject that comes last alphabetically. Ms. Green does not teach Math. Who teaches Science?
61) How much larger is (17 + 8 + 6) than (28 + 9 – 21)?
62) c ● d means (c + d) × 2. For example, 7 ● 3 = (7 + 3) × 2 = 10 × 2 = 20. Express 8 ● 5 in simplest form.
63) Jenny has 95¢ in nickels, dimes and quarters. She has at least one of each coin. What is the difference between the most number of coins she could have and the least number of coins she could have?
64) Point D is halfway between Point B and Point E. Point F is halfway between Point E and Point G. The distance from Point B to Point D is 16 feet. The distance from Point F to Point G is 12 feet. The distance from Point D to Point F is ___ feet.
65) Anna and Ben were playing soccer. Anna scored 13 goals and Ben scored 7 more goals than Anna. If there were 6 games total, how many goals were scored in all?
66) In the addition problem 749 + 8L = MMM, find the sum of the digits represented by L and M. Different letters represent different digits. Each time the same letter appears it represents the same digit.
67) If 19 + 12 = 45 – □, find the number that belongs in the box.
68) In the two problems at the right, the larger answer is ___ more than the smaller answer. 684 + 137 and 856 – 205
69) If Mrs. Anderson was able to cut a fabric into exactly twenty 3-inch pieces, then she could have cut the same fabric into ___ 6-inch pieces.
70) There are 35 crayons in Box A. There are 19 crayons in Box B. If ___ crayons were moved from Box A to Box B, there would be twice as many crayons in Box B as in Box A.
71) G, H and J represent different digits. GH represents a 2-digit number. GH + J = 76; HJ + G = 71. In the answer column, place the values for G, H and J.
72) Four friends – Leo, Mia, Nora and Oliver – have four different favorite colors: Red, Blue, Green and Yellow. Leo’s favorite is not Red or Blue. Mia likes Green. Oliver likes the color that rhymes with “bed.” Who likes Blue?
73) How much larger is (18 + 11 + 7) than (32 + 6 – 24)?
74) w ▲ v means (w – v) + 10. For example, 15 ▲ 7 = (15 – 7) + 10 = 8 + 10 = 18. Express 20 ▲ 12 in simplest form.
75) Kevin has 85¢ in nickels, dimes and quarters. He has at least one of each coin. What is the difference between the most number of coins he could have and the least number of coins he could have?
76) Point N is halfway between Point L and Point P. Point Q is halfway between Point P and Point R. The distance from Point L to Point N is 14 inches. The distance from Point Q to Point R is 18 inches. The distance from Point N to Point Q is ___ inches.
77) Sophie and Max were playing video games. Sophie won 15 games and Max won 8 more games than Sophie. If there were 7 tie games, how many games did they play?
78) In the addition problem 863 + 9N = PPP, find the sum of the digits represented by N and P. Different letters represent different digits. Each time the same letter appears it represents the same digit.
79) If 22 + 14 = 50 – □, find the number that belongs in the box.
80) In the two problems at the right, the larger answer is ___ more than the smaller answer. 795 + 126 and 967 – 218
81) If Mr. Taylor was able to cut a chain into exactly eighteen 2-link pieces, then he could have cut the same chain into ___ 4-link pieces.
82) There are 40 pencils in Container A. There are 22 pencils in Container B. If ___ pencils were moved from Container A to Container B, there would be twice as many pencils in Container B as in Container A.
83) D, E and F represent different digits. DE represents a 2-digit number. DE + F = 88; EF + D = 85. In the answer column, place the values for D, E and F.
84) Five students – Alice, Brian, Carla, David and Emma – are standing in a line. Alice is not first or last. Brian is directly behind Carla. David is first. Emma is not next to Alice. Who is second in line?
85) How much larger is (20 + 13 + 9) than (36 + 12 – 28)?
86) s ■ t means (s + 8) – t. For example, 11 ■ 5 = (11 + 8) – 5 = 19 – 5 = 14. Express 16 ■ 9 in simplest form.
87) Nicole has 100¢ in nickels, dimes and quarters. She has at least one of each coin. What is the difference between the most number of coins she could have and the least number of coins she could have?
88) Point S is halfway between Point Q and Point T. Point U is halfway between Point T and Point W. The distance from Point Q to Point S is 19 cm. The distance from Point U to Point W is 15 cm. The distance from Point S to Point U is ___ cm.
89) Eric and Fiona were playing chess. Eric won 17 games and Fiona won 9 more games than Eric. If there were 8 tie games, how many games of chess did they play?
90) In the addition problem 974 + 5Q = RRR, find the sum of the digits represented by Q and R. Different letters represent different digits. Each time the same letter appears it represents the same digit.
91) If 24 + 17 = 55 – □, find the number that belongs in the box.
92) In the two problems at the right, the larger answer is ___ more than the smaller answer. 846 + 175 and 987 – 234
93) If Ms. Parker was able to cut a paper strip into exactly twenty-four 1-inch pieces, then she could have cut the same strip into ___ 3-inch pieces.
94) There are 45 stickers in Album A. There are 25 stickers in Album B. If ___ stickers were moved from Album A to Album B, there would be twice as many stickers in Album B as in Album A.
95) U, V and W represent different digits. UV represents a 2-digit number. UV + W = 97; VW + U = 94. In the answer column, place the values for U, V and W.
96) Six children – Amy, Ben, Cara, Dan, Eva and Frank – have six different pets: dog, cat, bird, fish, hamster and rabbit. Amy has a pet that flies. Ben’s pet has fur and hops. Cara has a fish. Dan has a pet with four legs that barks. Eva’s pet is smaller than Dan’s. Who has the hamster?
97) How much larger is (23 + 16 + 11) than (42 + 15 – 32)?
98) f ♣ g means (f × 2) + (g × 2). For example, 6 ♣ 4 = (6 × 2) + (4 × 2) = 12 + 8 = 20. Express 9 ♣ 7 in simplest form.
99) Ryan has 60¢ in nickels, dimes and quarters. He has at least one of each coin. What is the difference between the most number of coins he could have and the least number of coins he could have?
100) Point Y is halfway between Point W and Point Z. Point A is halfway between Point Z and Point C. The distance from Point W to Point Y is 22 feet. The distance from Point A to Point C is 26 feet. The distance from Point Y to Point A is ___ feet.
📖 Answer Key
Check your answers below. Remember: showing your work is important!
1) 6
2) 6
3) 10
4) 18
5) 25
6) 13
7) 7
8) 33
9) 6
10) 6
11) A=4, B=6, C=4
12) Mrs. Wallace
13) 8
14) 24
15) 12
16) 18
17) 21
18) 15
19) 8
20) 70
21) 10
22) 8
23) R=6, S=2, T=3
24) Maria
25) 8
26) 18
27) 8
28) 24
29) 22
30) 13
31) 14
32) 132
33) 8
34) 12
35) P=7, Q=1, R=5
36) Emma
37) 14
38) 18
39) 10
40) 24
41) 27
42) 13
43) 10
44) 158
45) 8
46) 10
47) X=8, Y=2, Z=4
48) Alex
49) 14
50) 8
51) 8
52) 20
53) 36
54) 14
55) 15
56) 168
57) 6
58) 12
59) L=8, M=9, N=4
60) Mrs. White
61) 15
62) 26
63) 12
64) 28
65) 33
66) 15
67) 14
68) 170
69) 10
70) 14
71) G=7, H=3, J=6
72) Nora
73) 22
74) 18
75) 10
76) 32
77) 53
78) 16
79) 14
80) 172
81) 9
82) 16
83) D=8, E=5, F=3
84) Carla
85) 22
86) 15
87) 14
88) 34
89) 60
90) 15
91) 14
92) 268
93) 8
94) 18
95) U=9, V=4, W=3
96) Eva
97) 25
98) 32
99) 6
100) 48
Excellent work completing all 100 problems!
Remember: Practice makes perfect. Keep challenging yourself!
🏆 CML Competition Success Tips
- Practice Regularly: Work through 5-10 problems daily to build consistency
- Time Yourself: CML contests are timed – practice under time pressure
- Show Your Work: Develop clear problem-solving strategies
- Review Mistakes: Learn from errors to avoid repeating them
- Master Fundamentals: Strong basic skills are essential for advanced problems
- Think Multi-Step: Break complex problems into manageable parts
📚 More CML Practice Resources
📢 Share This Resource!
Help other students prepare for CML competitions
ℹ️ About Continental Math League (CML)
The Continental Math League is one of the most popular elementary and middle school mathematics competitions in North America. Each year, thousands of students participate in monthly contests designed to challenge their mathematical reasoning and problem-solving abilities.
CML contests consist of 6 questions that students complete in 30 minutes. Problems require multi-step thinking and cover topics including arithmetic, algebra, geometry, word problems, and logical reasoning. Success in CML competitions helps students develop critical thinking skills that benefit them throughout their academic careers.
Why Practice with K8MathSpark? Our CML practice materials are carefully designed to match the difficulty, style, and format of actual CML contests. We provide hundreds of free practice problems to help students build confidence and excel in competitions.
🎓 Ready to Excel in CML?
Join 50,000+ students using K8MathSpark to prepare for math competitions!