Comparisons 1

Task

Are these comparisons true or false?

1. $2$ hundreds + $3$ ones $\gt 5$ tens + $9$ ones
2. $9$ tens + $2$ hundreds + $4$ ones $\lt 924$
3. $456$ $\lt 5$ hundreds
4. $4$ hundreds + $9$ ones + $3$ ones $\lt 491$
5. $3$ hundreds + $4$ tens $\lt 7$ tens + $9$ ones + $2$ hundred
6. $7$ ones + $3$ hundreds $\gt 370$
7. $2$ hundreds + $7$ tens = $3$ hundreds - $2$ tens

IM Commentary

This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.

Solution

1. True. It reads, “Two hundreds and three ones is greater than five tens and nine ones.”

   $203\gt 59$

   $203$ is, in fact, greater than $59$ because $203$ has two $100$s (a two in the hundred’s place), while $59$ has no $100$s (a zero in the hundred’s place).

2. True. It reads, “Nine tens, two hundreds, and four ones is less than 924.”

   $294\lt 924$

   $294$ is, in fact less than $924$ because $294$ has two $100$s (a two in the hundred’s place), while $924$ has nine $100$s (a nine in the hundred’s place).

3. True. It reads, “$456$ is less than five hundreds.”

   $456\lt 500$

   $456$ is, in fact, less than $500$ because $456$ has four $100$s (a four in the hundred’s place) and some tens and ones that total less than one hundred, while $500$ has five $100$s (a five in the hundred’s place).

4. True. It reads, “Four hundreds and $9+3=12$ ones is less than $491$.” $12$ ones is the same as one ten and three ones, so let’s rewrite the previous sentence. “Four hundreds, one ten, and two ones is less than $491$.”

   $412\lt 491$

   $412$ is, in fact, less than $491$. Although both numbers have four $100$s (fours in the hundred’s place), $412$ only has one ten (a one in the ten’s place), while $491$ has nine tens (a nine in the ten’s place).

5. False. It reads, “Three hundreds and four tens is less then seven tens, nine ones, and two hundreds.”

   $340\lt 279$

   $340$ is, in fact, greater than $279$ because $340$ has three $100$s (a three in the hundred’s place), while $279$ has two $100$s (a two in the hundred’s place).

6. False. It reads, “Seven ones and three hundreds is greater than 370.”

   $307\gt 370$

   $307$ is, in fact, less than $370$. Although both numbers have three $100$s (threes in the hundreds place), $307$ has no $10$s (a zero in the ten’s place), while $370$ has seven $10$s (a seven in the ten’s place).

7. False. It reads $2$ hundreds + $7$ tens = $3$ hundreds - $2$ tens

   $270 = 280$

   While both numbers have $2$ hundreds (a two in the hundreds place), $270$ has 7 tens (a seven in the tens place) while $280$ has an $8$ in the tens place. Therefore $270 \lt 280$