CBSE Class 6 Mathematics Number Play Assignment Set 01

Very Short Answer Questions

Question 1. Some children are standing in a line and each child says how many of the children next to them are taller. One child says 2. What does this tell us about that child’s neighbours?
Answer:
The child has two neighbours and both of them are taller than the child.

Teacher's Note:
1. Saying 2 means two taller neighbours.
2. Such a child cannot be at an end of the line.

Question 2. What is a supercell in a table of numbers?
Answer:
A supercell is a cell whose number is greater than the numbers in all the cells next to it.

Teacher's Note:
1. Compare only with neighbouring cells.
2. Learn the definition word for word.

Question 3. Between which two thousands does the number 2,754 lie on the number line?
Answer:
2,754 lies between 2,000 and 3,000, closer to 3,000.

Teacher's Note:
1. The thousands digit gives the lower thousand.
2. 754 is more than 500, so it is nearer 3,000.

Question 4. How many 4-digit numbers are there in all?
Answer:
The 4-digit numbers run from 1,000 to 9,999, so there are 9,999 − 1,000 + 1 = 9,000.

Teacher's Note:
1. Remember to add 1 when both ends are counted.
2. 9, 90, 900, 9,000 is the pattern.

Question 5. What is a palindromic number? Write any one 3-digit example.
Answer:
A palindromic number reads the same from left to right and from right to left. Example: 575.

Teacher's Note:
1. The first and last digits must match.
2. Any number like 121, 575 or 909 is fine.

Question 6. Which number is called the Kaprekar constant, and for numbers of how many digits does it work?
Answer:
6174 is the Kaprekar constant. It is reached by the Kaprekar steps for 4-digit numbers.

Teacher's Note:
1. The digits must not all be the same.
2. For 3-digit numbers the number is 495.

Question 7. Write any one palindromic time that can be seen on a 12-hour clock.
Answer:
11:11 (10:01, 12:21, 1:01 and 2:02 are also correct).

Teacher's Note:
1. Ignore the colon and read the digits both ways.
2. Make sure the time exists on a 12-hour clock.

Question 8. Fill in the blank: 39,800 = 40,000 − ____
Answer:
40,000 − 39,800 = 200, so 39,800 = 40,000 − 200.

Teacher's Note:
1. Count up from 39,800 to 40,000.
2. Check by subtracting.

Question 9. A picture is made of 12 cells and the number 25 is written in each cell. Find the total in a quick way.
Answer:
Instead of adding 25 twelve times, multiply: 12 × 25 = 300.

Teacher's Note:
1. Equal numbers: multiply instead of adding.
2. Four 25s make 100, so twelve make 300.

Question 10. While making a Collatz chain, what do you do when the number you have is even?
Answer:
Take half of it and write that as the next number of the chain.

Teacher's Note:
1. Even: halve.
2. Odd: 3 times the number plus 1.

Question 11. Round off 4,286 to the nearest thousand.
Answer:
The hundreds part 286 is less than 500, so 4,286 rounds down to 4,000.

Teacher's Note:
1. Look at the hundreds digit for the nearest thousand.
2. Below 500 round down; 500 or more round up.

Question 12. In Game #2 of this chapter, which number must a player reach in order to win?
Answer:
A player must reach 99 to win Game #2.

Teacher's Note:
1. Game #1 ends at 21, Game #2 at 99.
2. In Game #2 players add 1 to 10.

Question 13. Five children of different heights say the number of taller children standing next to them. Can two children standing next to each other say the same number? Give one example.
Answer:
Yes. If the five stand in increasing order of height, each of the first four says 1 and the tallest says 0.
So neighbours (for example, the 1st and 2nd children) say the same number, 1.

Teacher's Note:
1. One example is enough to answer 'yes'.
2. Increasing order is the easiest arrangement.

Question 14. A row has 7 cells and 7 different numbers are written in them. What is the greatest number of supercells that this row can have?
Answer:
Neighbouring cells cannot both be supercells, so they can sit only in alternate cells: 1st, 3rd, 5th and 7th.
So the greatest number is 4.

Teacher's Note:
1. Put big and small numbers one after the other.
2. Example: 9, 1, 8, 2, 7, 3, 6.

Question 15. The marks on a number line go up in steps of 1 and one of the marks is 9,999. Which numbers are written on the next two marks to its right?
Answer:
The next two marks are 10,000 and 10,001.

Teacher's Note:
1. After 9,999 comes the smallest 5-digit number.
2. Moving right means increasing.

Question 16. Which is the largest 5-digit number whose digits add up to 14?
Answer:
Keep the biggest digits at the front: 9 + 5 = 14, and the rest are 0.
The number is 95,000.

Teacher's Note:
1. For the largest number, fill from the left.
2. Check: 9 + 5 + 0 + 0 + 0 = 14.

Question 17. Start with 48 and keep reversing the digits and adding. In how many steps do you reach a palindrome, and which palindrome is it?
Answer:
48 + 84 = 132 and 132 + 231 = 363.
It takes 2 steps and the palindrome is 363.

Teacher's Note:
1. Check each answer for a palindrome before continuing.
2. 132 is not a palindrome, so one more step is needed.

Question 18. Carry out one round of the Kaprekar steps with the number 9531 and write the number you get.
Answer:
Largest = 9531, smallest = 1359.
9531 − 1359 = 8172.

Teacher's Note:
1. Here the number itself is already the largest arrangement.
2. Subtract with care.

Question 19. A clock shows 2:02 just now. After how many minutes will it show the next palindromic time?
Answer:
The next palindromic time is 2:12, so it comes after 10 minutes.

Teacher's Note:
1. Times like 2:x2 are palindromic.
2. Count minutes from 2:02 to 2:12.

Question 20. Is the statement “a 5-digit number plus a 5-digit number gives a 5-digit number” always true, only sometimes true, or never true? Give one example.
Answer:
It is only sometimes true.
12,000 + 25,000 = 37,000 has 5 digits, but 60,000 + 40,000 = 1,00,000 has 6 digits.

Teacher's Note:
1. Give one example of each kind.
2. Large numbers can carry into a new place.

Question 21. In a number pattern, 20 is written in each cell of a shape made of 3 rows with 6 cells in each row. Find the sum in a quick way.
Answer:
Number of cells = 3 × 6 = 18.
Sum = 18 × 20 = 360.

Teacher's Note:
1. Rows × cells in a row gives the cell count.
2. Then multiply by the number in each cell.

Question 22. Write the Collatz chain that starts with 6.
Answer:
6, 3, 10, 5, 16, 8, 4, 2, 1.

Teacher's Note:
1. 6 is even → 3; 3 is odd → 10.
2. Stop when you reach 1.

Question 23. Estimate 6,120 + 2,890 by rounding each number to the nearest thousand.
Answer:
6,120 → 6,000 and 2,890 → 3,000.
Estimate = 6,000 + 3,000 = 9,000.

Teacher's Note:
1. Look at the hundreds digit to round to the nearest thousand.
2. The exact sum, 9,010, is very close.

Question 24. In the game in which players add any number from 1 to 10 and the one who says 99 wins, which player can always win? Which numbers should that player say?
Answer:
The second player can always win.
That player should say the multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88 and 99.

Teacher's Note:
1. The first player cannot reach 11 in one turn.
2. Work backwards from 99 in steps of 11.

Question 25. How many times is the digit 7 written while writing all the numbers from 1 to 100?
Answer:
Ones place: 7, 17, 27, …, 97, that is 10 times. Tens place: 70 to 79, that is 10 times.
Total = 20 times (77 has two 7s and both are counted).

Teacher's Note:
1. Count each place separately.
2. Do not forget the double digit in 77.

Question 26. When the Kaprekar steps are carried out with 3-digit numbers, which number starts repeating?
Answer:
495 starts repeating, because 954 − 459 = 495 again and again.

Teacher's Note:
1. 495 is to 3 digits what 6174 is to 4 digits.
2. Check: 954 − 459 = 495.

Question 27. Which is the smallest 5-digit palindrome that is an even number?
Answer:
An even palindrome must end in an even digit, so it must also start with that digit. The smallest such first digit is 2.
The number is 20,002.

Teacher's Note:
1. The first digit cannot be 0.
2. First digit = last digit in a palindrome.

Question 28. Write four different numbers in a row of four cells so that exactly two of the cells are supercells. Name the supercells.
Answer:
Example: 8, 3, 9, 5.
8 is greater than 3, and 9 is greater than both 3 and 5. So 8 and 9 are the only supercells.

Teacher's Note:
1. Many answers are possible.
2. Put big and small numbers alternately.

Question 29. Starting from 0, two players take turns adding 1, 2 or 3 and the player who reaches 22 wins. Which number should the first player say in the very first turn, and why?
Answer:
Going back from 22 in steps of 4, the safe numbers are 22, 18, 14, 10, 6, 2.
The first player should say 2, then keep saying 6, 10, 14, 18 and 22. Whatever the other player adds, the first player can jump back to the list.

Teacher's Note:
1. The step is one more than the largest number allowed.
2. Find the smallest safe number.

Question 30. Why is the Collatz conjecture very easy to check for the starting number 64?
Answer:
64 is a power of 2, so every number of the chain is even and is simply halved:
64, 32, 16, 8, 4, 2, 1.

Teacher's Note:
1. Powers of 2 halve straight down to 1.
2. No odd number appears before 1.