Comparisons 1
Task
Are these comparisons true or false?
- $2$ hundreds + $3$ ones $\gt 5$ tens + $9$ ones
- $9$ tens + $2$ hundreds + $4$ ones $\lt 924$
- $456$ $\lt 5$ hundreds
- $4$ hundreds + $9$ ones + $3$ ones $\lt 491$
- $3$ hundreds + $4$ tens $\lt 7$ tens + $9$ ones + $2$ hundred
- $7$ ones + $3$ hundreds $\gt 370$
- $2$ 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
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True. It reads, âTwo hundreds and three ones is greater than five tens and nine ones.â
$203\gt 59$
$203$ is, in fact, greater than $59$ because $203$ has two $100$s (a two in the hundredâs place), while $59$ has no $100$s (a zero in the hundredâs place).
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True. It reads, âNine tens, two hundreds, and four ones is less than 924.â
$294\lt 924$
$294$ is, in fact less than $924$ because $294$ has two $100$s (a two in the hundredâs place), while $924$ has nine $100$s (a nine in the hundredâs place).
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True. It reads, â$456$ is less than five hundreds.â
$456\lt 500$
$456$ is, in fact, less than $500$ because $456$ has four $100$s (a four in the hundredâs place) and some tens and ones that total less than one hundred, while $500$ has five $100$s (a five in the hundredâs place).
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True. It reads, âFour hundreds and $9+3=12$ ones is less than $491$.â $12$ ones is the same as one ten and three ones, so letâs rewrite the previous sentence. âFour hundreds, one ten, and two ones is less than $491$.â
$412\lt 491$
$412$ is, in fact, less than $491$. Although both numbers have four $100$s (fours in the hundredâs place), $412$ only has one ten (a one in the tenâs place), while $491$ has nine tens (a nine in the tenâs place).
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False. It reads, âThree hundreds and four tens is less then seven tens, nine ones, and two hundreds.â
$340\lt 279$
$340$ is, in fact, greater than $279$ because $340$ has three $100$s (a three in the hundredâs place), while $279$ has two $100$s (a two in the hundredâs place).
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False. It reads, âSeven ones and three hundreds is greater than 370.â
$307\gt 370$
$307$ 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 tenâs place), while $370$ has seven $10$s (a seven in the tenâs place).
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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 $270 \lt 280$
Comparisons 1
Are these comparisons true or false?
- $2$ hundreds + $3$ ones $\gt 5$ tens + $9$ ones
- $9$ tens + $2$ hundreds + $4$ ones $\lt 924$
- $456$ $\lt 5$ hundreds
- $4$ hundreds + $9$ ones + $3$ ones $\lt 491$
- $3$ hundreds + $4$ tens $\lt 7$ tens + $9$ ones + $2$ hundred
- $7$ ones + $3$ hundreds $\gt 370$
- $2$ hundreds + $7$ tens = $3$ hundreds - $2$ tens