☰ Year plan · Mathematics

Comparing, ordering and rounding big numbers

Week 2 · Comparing, ordering and rounding big numbers · 3 lessons
2

Smallest to largest and back again

Discover Mathematics P4: Term 1, Unit 1, Lessons 7–11
GoalOrder big numbers from least to greatest (ascending) and from greatest to least (descending).
New words
ascending · in order from the smallest number to the greatestdescending · in order from the greatest number to the smallestorder · to put numbers in a line by their size
Explanation

To order a group of numbers, first sort them by the number of digits. The numbers with the fewest digits are the smallest. Then compare the numbers that have the same number of digits, place by place from the left. Ascending order starts with the smallest number and ends with the greatest. Descending order starts with the greatest and ends with the smallest. A good way to check is to read your list again and ask, for each neighbouring pair, whether the sign < (ascending) or > (descending) is true. Do not forget to copy all the numbers: count them before and after ordering.

OrderNumbers
Ascending987,654 < 1,205,999 < 1,250,030 < 1,250,300
Descending1,250,300 > 1,250,030 > 1,205,999 > 987,654
Worked examples
YearVisitors
11,250,300
2987,654
31,205,999
41,250,030
A museum had 1,250,300, 987,654, 1,205,999 and 1,250,030 visitors in four years. Only 987,654 has 6 digits, so it is the smallest. The others have 7 digits and start with 1,2. Compare the next digits: 1,205,999 has 0, the others have 5, so 1,205,999 is next. Last, 1,250,030 < 1,250,300. Ascending: 987,654, 1,205,999, 1,250,030, 1,250,300.
0500010 00015 000480012 500910012 0507600ABCDEbooksBooks
The graph shows the number of books in five school libraries. Reading the bars gives 4,800, 12,500, 9,100, 12,050 and 7,600. In descending order: 12,500 > 12,050 > 9,100 > 7,600 > 4,800. The longest bar is library B and the shortest is library A.
Check an order: is 345,000 < 354,000 < 3,054,000 ascending? The first pair is fine (the tens of thousands digits are 4 and 5). The second pair is fine too, because 354,000 has 6 digits and 3,054,000 has 7 digits. Yes, the list is ascending.
Class activity

Human number line. Write six different numbers between 100,000 and 9,999,999 on six papers. Each player holds one paper. Without talking, the players line up from the smallest to the greatest. Then check each neighbouring pair with the sign <. Play again in descending order.

Practice
1
Write in ascending order: 5,210, 52,100, 521, 5,021.
2
Write in descending order: 3,400,000, 340,000, 3,040,000, 3,004,000.
3
Which is the greatest: 98,765, 89,765, 98,675 or 89,675?
4
Put the digits 2, 5 and 9 once each to make three-digit numbers. List all of them in ascending order.
5
Nour ordered 8,120 < 8,012 < 8,210. What is wrong, and what is the right ascending order?