Numbers as reports
A number can describe a row.
Each child counts the neighbours taller than themselves and calls out that count. The number is not a height. It is a report on who is standing nearby.
📚 Chapter Learning Kit
Number Play · Class 6 Mathematics · Ganita Prakash
English 4 topics 116 leveled MCQs 60 flashcards 7 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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Why an end child cannot say 2
Ends have one neighbour.
Saying 2 means two taller neighbours. A child at the end of the row has only one neighbour. There is nobody on the other side to be counted.
The tallest child
Somebody must say zero.
The tallest child has no taller neighbour anywhere, so the answer is 0. A zero always appears somewhere in the list. That rules out a row of all ones.
How many numbers of each size
Nine, ninety, nine hundred.
What a digit sum is
Throw away place value.
Add the digits and forget what each one is worth. The digits of 89 come to 17, and so do the digits of 764 and of 98,000. Size has nothing to do with it.
Finding the smallest for a digit sum
Few digits, fat ones.
Use as few digits as possible and put the biggest figures at the back. For a digit sum of 17 that gives 89. For the largest five-digit one, load the front and pad with zeros.
📖 Smart notes
What you'll study, topic by topic
1
What Numbers Can Tell Us
Numbers can describe an arrangement, not only a quantity. Children in a row report their taller neighbours, boxes in a table compete with the boxes beside them, and a number line turns size into position.
- A number can report an arrangement. Each child calls out how many of their neighbours are taller than they are.
- A child at the end of a row has one neighbour only, so 2 is never an answer there.
- The tallest child in a row always calls out 0, so a row of all ones cannot happen.
~32 min · full explanation, examples & memory tricks in the app
2
Playing with Digits
Digits can be added, reversed and rearranged. Digit sums group very different numbers together, palindromes read the same both ways, and one stubborn routine drags every four-digit number to 6174.
- There are 9 one-digit numbers, 90 two-digit numbers, 900 three-digit numbers and 9000 four-digit ones.
- A digit sum adds the digits and ignores place value, so 89, 764 and 98,000 all come to 17.
- A three-digit number whose digits run on has a digit sum of three times its middle digit.
~35 min · full explanation, examples & memory tricks in the app
3
Numbers in Time, and Sums in Your Head
Clocks and calendars are full of number patterns, and large sums often come apart into friendly pieces. Both reward looking before calculating.
- A clock reading is tested for a palindrome exactly like a number, once the colon is ignored.
- A 12-hour clock shows 57 palindromic times, six in each single-digit hour and one each at 10, 11 and 12.
- A date written as day, month and year can read the same both ways, as 21/02/2012 does.
~34 min · full explanation, examples & memory tricks in the app
4
Estimating, and Winning Games
One simple rule leads to a problem nobody has solved, estimates answer questions that counting cannot, and a game of adding numbers turns out to have a rule hidden inside it.
- The Collatz rule halves an even number and trebles an odd one before adding 1.
- A power of two falls straight to 1, because halving it never produces an odd number.
- The run from 27 climbs as high as 9,232 and takes 111 steps to finish.
~36 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
116 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Five children of different heights stand in a row and each calls out the number of taller neighbours. What is the very first thing you should check for a child?
Beginner
A How tall that child is in centimetres
B Whether the child is standing on the left of the row
C How many children are in the row altogether
D How many neighbours that child has
Show answer & explanation
How many neighbours that child has
An end child compares with one person and a middle child with two, so the count of neighbours comes first.
A child standing at the end of a row calls out a number. Which numbers are open to that child?
Beginner
A Only 0
B Only 1
C 0 or 1
D 0, 1 or 2
Show answer & explanation
0 or 1
One neighbour means at most one taller neighbour can be counted.
Heights in centimetres along a row are 118, 126, 148, 140 and 132. What does the child of 148 cm call out?
Beginner
A 0
B 1
C 2
D It depends on the row length
Show answer & explanation
0
Both neighbours, 126 and 140, are shorter, so no taller neighbour is counted.
Heights in centimetres along a row are 118, 126, 148, 140 and 132. What does the child of 126 cm call out?
Intermediate
A 2, because the row is uneven on both sides
B 0, because 118 cm is shorter than she is
C 1, because she stands next to the end of the row
D 1, because only the 148 cm neighbour is taller
Show answer & explanation
1, because only the 148 cm neighbour is taller
Her neighbours are 118 and 148, and only one of those beats her.
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