Quick sums by pairing, missing numbers, pictures that stand for numbers, age problems, counting chicken and dog legs, fence posts, sharing until equal and letter sums. This is the biggest strand in most math olympiad papers.
Quick calculating
Solving tip: Pair the first number with the last, the second with the second to last… All the pairs are equal.
Work it out quickly, then fill in the answer in the empty box.
Show solution
Answer: 21
How to think: Pair the first number with the last, the second with the second to last… All the pairs are equal.
Solution: There are 3 pairs, each equal to 7: 3 times 7 equals 21.
What number goes in the box
Solving tip: Is the empty box a part, or the whole?
What number goes in the empty box?
Show solution
Answer: 17
How to think: Is the empty box a part, or the whole?
Solution: 87 minus 70 equals 17. Check: 70 plus 17 equals 87.
Pictures for numbers
Solving tip: Start with the line that has only one kind of picture.
Each kind of picture stands for a number. What number is the fish?
Show solution
Answer: 6
How to think: Start with the line that has only one kind of picture.
Solution: We see that the corn cob is 3, so the fish is 9 minus 3 equals 6.
Sharing to make it equal
Solving tip: First: how many more apples does the puppy have than the frog?
At first, the puppy has 19 apples and the frog has 1 apple. How many apples must the puppy give the frog so they both have the same number of apples?
Show solution
Answer: 9
How to think: First: how many more apples does the puppy have than the frog?
Solution: The extra is 18 apples. Give your friend half: half of 18 is 9. Then each friend has 10 apples.
Age puzzles
Solving tip: Each year, how many years older do Mom and the puppy each get?
This year, Mom is 20 years older than the puppy. In 4 years, how many years older than the puppy will Mom be?
Show solution
Answer: 20
How to think: Each year, how many years older do Mom and the puppy each get?
Solution: Each year, both get 1 year older, so Mom is still 20 years older than the puppy.
Counting animal legs
Solving tip: Each hen has 2 legs, and each dog has 4 legs.
In the yard there are 5 hens and 4 dogs. How many legs are there in all?
Show solution
Answer: 26
How to think: Each hen has 2 legs, and each dog has 4 legs.
Solution: 5 hens have 10 legs, 4 dogs have 16 legs. In all: 10 plus 16 equals 26 legs.
Planting trees and sawing logs
Solving tip: Each time, 3 bowls cook together.
A pot can cook 3 bowls of noodles at once, and each cooking takes 7 minutes. What is the shortest time to cook 7 bowls?
Show solution
Answer: 21
How to think: Each time, 3 bowls cook together.
Solution: We need to cook 3 times, 7 minutes each time: 7 plus 7 plus 7 equals 21 minutes.
Fill in plus and minus
Solving tip: Try each set of signs and work from left to right to see if you get the answer.
Put a plus or a minus sign in each empty box to make the sum correct. Choose the right signs.
Show solution
Answer: + − +
How to think: Try each set of signs and work from left to right to see if you get the answer.
Solution: We fill in: 1 plus 2 minus 3 plus 4 equals 4. Work from left to right: 1, 3, 0, 4.
Letter sums
Solving tip: Take A away from 14 and you get A again. So what is A plus A?
Each letter stands for a number. The same letters are the same number. Fill in the empty box.
Show solution
Answer: 7
How to think: Take A away from 14 and you get A again. So what is A plus A?
Solution: 14 minus A equals A, so A plus A equals 14. Two equal numbers that add up to 14 are 7 each. So A is 7.
More than and times as many
Solving tip: Draw a bar model: the bear cub has 1 part, the frog has 3 parts of the same size.
The frog has 3 times as many carrots as the bear cub. The frog has 6 more carrots than the bear cub. How many carrots does the bear cub have?
Show solution
Answer: 3
How to think: Draw a bar model: the bear cub has 1 part, the frog has 3 parts of the same size.
Solution: The frog has 3 parts, the bear cub has 1 part, so the difference is 2 parts. 2 parts are 6, so 1 part is 3. So the bear cub has 3 carrots.
A new operation
Solving tip: The first line is the rule: a is the number before the star, and b is the number after it.
There is a new operation called the star. The first line shows how it works. Work out the second line.
Show solution
Answer: 62
How to think: The first line is the rule: a is the number before the star, and b is the number after it.
Solution: Brackets first, with 2 for a and 12 for b: (2 plus 12) times 2 equals 28. Then 28 for a and 3 for b: (28 plus 3) times 2 equals 62.
Quick multiplication
Solving tip: 102 is very close to 100. Multiply by 100 first, it's easier.
Work it out quickly, then fill in the answer in the empty box.
Show solution
Answer: 306
How to think: 102 is very close to 100. Multiply by 100 first, it's easier.
Solution: 102 is 100 and 2 more. 3 times 100 equals 300, and 3 times 2 equals 6. 300 plus 6 equals 306.
Keep practising these types in the Karotto app
In the app every problem type above is a lesson with the question read aloud, three levels of hints when your child is stuck and a step-by-step solution. Problems are generated fresh, so every attempt is a new set.