Number and Operations>Ordering Rational Numbers in Mathematical and Real-World Contexts(TEKS.Math.6.2.D)

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Texas 6th Grade Math › Number and Operations>Ordering Rational Numbers in Mathematical and Real-World Contexts(TEKS.Math.6.2.D)

Questions 1 - 5
1

Temperature readings: Monday 2.5°F, Tuesday -1.3°F, Wednesday -0.5°F, Thursday 3°F. Order the days from coldest to warmest.

Thursday, Monday, Wednesday, Tuesday

Tuesday, Wednesday, Monday, Thursday

Wednesday, Tuesday, Monday, Thursday

Monday, Thursday, Tuesday, Wednesday

Explanation

Coldest means the lowest number. On a number line: -1.3 < -0.5 < 2.5 < 3, so Tuesday (coldest), then Wednesday, Monday, Thursday (warmest). A common mistake is to look at absolute values and think -0.5 is colder than -1.3 because 0.5 < 1.3, but real temperatures get colder as the value becomes more negative.

2

Golf scores relative to par: Alex -2, Bella +1, Carlos -3, Dana 0. Order the players from best to worst performance.

Bella, Dana, Alex, Carlos

Dana, Alex, Carlos, Bella

Alex, Carlos, Dana, Bella

Carlos, Alex, Dana, Bella

Explanation

In golf, lower scores are better. Order the numbers from least to greatest: -3 < -2 < 0 < +1 gives Carlos (best), Alex, Dana, Bella (worst). A trap is to think 0 is automatically best or to compare absolute values; but performance aligns with the actual order on the number line, not closeness to zero.

3

Bank account balances: Emma -$15.50, Jayden $4.75, Mia -$3.25, Noah $0. Order the balances from lowest to highest.

Emma, Mia, Noah, Jayden

Jayden, Noah, Mia, Emma

Emma, Jayden, Mia, Noah

Noah, Emma, Mia, Jayden

Explanation

Lowest balance means most negative. On a number line: -15.50 < -3.25 < 0 < 4.75, so Emma, then Mia, then Noah, then Jayden. A common error is to ignore the signs and order by the size of the digits, or to think 0 is lower than negatives. In real life, owing money (negative) is less than having no money or a positive balance.

4

Depths relative to sea level: Buoy A -3 m, Buoy B -2 m, Buoy C -0.5 m, Buoy D +1/3 m. Order the buoys from deepest below sea level to highest above sea level.

Buoy D, Buoy C, Buoy B, Buoy A

Buoy A, Buoy C, Buoy B, Buoy D

Buoy A, Buoy B, Buoy C, Buoy D

Buoy B, Buoy A, Buoy C, Buoy D

Explanation

Deeper means more negative. Order the values from least to greatest: -3 < -2 < -0.5 < +1/3, so Buoy A, Buoy B, Buoy C, Buoy D. A trap is confusing opposites and reciprocals: -2 and -1/2 are reciprocals, not opposites, and -1/2 is actually greater than -2 (so it is shallower).

5

Stock price changes in one day: Company W -$1.25, Company X +$1.10, Company Y -$0.75, Company Z +$0.40. Order the companies from worst (largest loss) to best (largest gain).

Company X, Company Z, Company Y, Company W

Company W, Company Y, Company Z, Company X

Company Y, Company W, Company Z, Company X

Company W, Company Z, Company Y, Company X

Explanation

Largest loss is the smallest (most negative) number; largest gain is the greatest (most positive). Order: -1.25 < -0.75 < +0.40 < +1.10, so W, Y, Z, X. Reversing the order or mixing a positive gain in between losses ignores how the number line models losses (negative) and gains (positive).