Ordering 3-digit numbers
Task
1. Arrange the following numbers from least to greatest:
$$ 476 \qquad \qquad 647 \qquad \qquad 74 \qquad \qquad 674 \qquad \qquad 467 $$
______ ______ ______ ______ ______
2. Arrange the following numbers from greatest to least:
$$ 326 \qquad \qquad 362 \qquad \qquad 63 \qquad \qquad 623 \qquad \qquad 632 $$
______ ______ ______ ______ ______
IM Commentary
Each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number. Each group also contains a two-digit number so that students have to do more than just compare the first digit, the second digit, etc.
Solution
1. Least to greatest:
Arranging the numbers from least to greatest means writing the numbers in an ordered list according to their values. The smallest number should be written on the left, with the next smallest number written to its immediate right. The process continues for all the given numbers, the largest of which should be on the right.
First we look for the smallest number given. $74$ is the smallest number given because it is the only number with no 100s. (There is an implied zero in the hundredâs place.)
We now look for the second smallest number. There are two numbers, $476$ and $467$, with four $100$s (fours in the hundredâs place). We must now consider the tenâs place. $467$ is the next smallest number because it only has six $10s$ (a six in the tenâs place), while $476$ has seven $10$s (a seven in the tenâs place).
The next smallest number is $476$ because it only has four $100$s (a four in the hundredâs place), while all the other remaining numbers have six $100$s (sixes in the hundredâs place).
We now have two numbers remaining, $647$ and $674$. Both numbers have six $100$s (sixes in the hundredâs place), so we must compare their $10$s. $647$ is smaller than $674$ because in has just four $10$s (a four in the tenâs place), rather than seven $100$s (a seven in the hundredâs place).
This leaves $674$ as the largest number.
$$ 74 \qquad \qquad 467 \qquad \qquad 479 \qquad \qquad 647 \qquad \qquad 674 $$
2. Greatest to least
Arranging the numbers from greatest to least means writing the numbers in an ordered list according to their values. The largest number should be written on the left, with the next largest number written to its immediate right. The process continues for all the given numbers, the smallest of which should be on the right.
First we look for the largest number given. There are three numbers that begin with six: $63$, $623$ and $632$. However, the $6$ in $63$ is in the tens place, not in the hundreds place. There are zero hundreds, making $63$ the smallest number, the only number that is less than $100$.
$623$ and $632$ both have six $100$s (sixes in the hundredâs place), so it is necessary to compare the digits in the $10$âs place. $623$ has two $10$s (a two in the tenâs place), while $632$ has three 10s (a tens in the tenâs place. Since the value of the three in the $10$'s place is larger than two in the $10$'s place, $632$ is the largest number and $623$ is the second largest number.
The two remaining numbers both start with three. Comparing $326$ and $362$, which both have $3$ hundreds (a three in the hundredâs place), means comparing the numbers in the tenâs place. Six tens (a six in the tenâs place) is larger than three tens (a three in the tenâs place), so $326$ is smaller than $362$.
$$ 632 \qquad \qquad 623 \qquad \qquad 362 \qquad \qquad 326 \qquad \qquad 63 $$
Ordering 3-digit numbers
1. Arrange the following numbers from least to greatest:
$$ 476 \qquad \qquad 647 \qquad \qquad 74 \qquad \qquad 674 \qquad \qquad 467 $$
______ ______ ______ ______ ______
2. Arrange the following numbers from greatest to least:
$$ 326 \qquad \qquad 362 \qquad \qquad 63 \qquad \qquad 623 \qquad \qquad 632 $$
______ ______ ______ ______ ______