Counting numbers in a range, odd and even, tens and ones, the nth term of a sequence, counting digits, making numbers from digits, digit sums, divisibility and remainders. Children learn to list in order so nothing is missed or counted twice.
Counting numbers
Solving tip: Don't count 60 or 68.
How many numbers are bigger than 60 and smaller than 68?
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Answer: 7
How to think: Don't count 60 or 68.
Solution: 68 minus 60 equals 8. We don't count 68, so 8 minus 1 equals 7 numbers.
Even or odd
Solving tip: You don't need to work out the whole sum. Just count how many odd numbers there are.
Is the answer to this sum even or odd?
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Answer: Even
How to think: You don't need to work out the whole sum. Just count how many odd numbers there are.
Solution: There are 4 odd numbers. They pair up with none left over, so the answer is even.
Tens and ones
Solving tip: Which digit is fixed? Which digit can you choose freely?
How many two-digit numbers have 9 as the tens digit?
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Answer: 10
How to think: Which digit is fixed? Which digit can you choose freely?
Solution: The ones digit has 10 choices, from 0 to 9. The numbers are 90, 91, … up to 99: 10 numbers.
Which term of the sequence
Solving tip: How many steps is it from the first number to position 8?
The numbers go 22, 32, 42, 52, … Which number is in position 8?
Show solution
Answer: 92
How to think: How many steps is it from the first number to position 8?
Solution: Keep going step by step: 22, 32, 42, 52, 62, 72, 82, 92. The number in position 8 is 92.
Counting digits
Solving tip: A one-digit number takes 1 digit, and a two-digit number takes 2 digits.
If you write all the numbers from 1 to 21 in a row, how many digits do you write in all?
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Answer: 33
How to think: A one-digit number takes 1 digit, and a two-digit number takes 2 digits.
Solution: From 1 to 9 you write 9 digits. From 10 to 21 there are 12 numbers, so you write 24 digits. In all: 9 plus 24 equals 33.
Making numbers from digits
Solving tip: Put the biggest digit first.
Use the digits 8, 5, 6, each one at most once. What is the biggest number with 2 digits you can make?
Show solution
Answer: 86
How to think: Put the biggest digit first.
Solution: Pick the biggest digits and put them from biggest to smallest: you get 86.
Adding up the digits
Solving tip: For the biggest number, the first digit must be as big as possible.
Find the biggest number with 2 digits whose digits add up to 6.
Show solution
Answer: 60
How to think: For the biggest number, the first digit must be as big as possible.
Solution: The biggest first digit possible is 6, so the number is 60.
Two numbers from four digits
Solving tip: A digit in the tens place is worth 10 times as much as in the ones place. Which digits go in the tens place?
Use all four digits 1, 2, 4, 5, each one once, to write two 2-digit numbers. What is the smallest possible sum of the two numbers?
Show solution
Answer: 39
How to think: A digit in the tens place is worth 10 times as much as in the ones place. Which digits go in the tens place?
Solution: The two smallest digits 1, 2 go in the tens place, and 4, 5 go in the ones place: 14 plus 25 equals 39.
Divisible by both numbers
Solving tip: List the numbers you can divide exactly by 5, then find one you can also divide by 3.
From 1 to 35, how many numbers can be divided exactly by both 3 and 5?
Show solution
Answer: 2
How to think: List the numbers you can divide exactly by 5, then find one you can also divide by 3.
Solution: The smallest number you can divide by both 3 and 5 is 15. The numbers are 15, 30. That makes 2.
Exact division and remainders
Solving tip: A number that leaves 5 when divided by 13 is a number that 13 goes into exactly, plus 5.
What is the smallest three-digit number that leaves 5 when divided by 13?
Show solution
Answer: 109
How to think: A number that leaves 5 when divided by 13 is a number that 13 goes into exactly, plus 5.
Solution: 104 is the smallest three-digit number that 13 goes into exactly. 104 plus 5 equals 109.
Sum and difference
Solving tip: Take away the extra that the kitten has over the chick, and the two are equal.
Together, the kitten and the chick have 204 strawberries. The kitten has 32 more strawberries than the chick. How many strawberries does the chick have?
Show solution
Answer: 86
How to think: Take away the extra that the kitten has over the chick, and the two are equal.
Solution: 204 minus 32 equals 172. 172 divided by 2 equals 86. So the chick has 86 strawberries.
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.