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Back to Understand that positive and negative numbers describe quantities having opposite directions or values

Positive and Negative Numbers: Opposite Directions and Values

For each problem, identify the reference point (0) and the direction (positive or negative) before writing your answer.

Grade 6·21 problems·~30 min·Common Core Math - Grade 6·standard·6-ns-c-5
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which number is to the left of 0 on a number line?

2.

On a number line, which number is closest to 0?

3.

Which statement about the number 0 on a number line is true?

B

Fluency Practice

1.

A bank account shows a withdrawal of $75. Which signed number represents this transaction?

2.

Which signed number best represents 'a gain of 12 yards in football'?

3.

The temperature in Anchorage, Alaska is 18 degrees below zero Fahrenheit. Write this as a signed number.

4.

In the context of a bank account, what does a balance of $0 mean?

Vertical thermometer showing the positions of five cities: Nome, Denver, Barrow, Miami, and Chicago, with 0°F marked as the reference line
5.

A weather report shows temperatures for five cities:

  • Nome, AK: 12°F below zero
  • Denver, CO: 28°F above zero
  • Barrow, AK: 31°F below zero
  • Miami, FL: 84°F above zero
  • Chicago, IL: 5°F below zero

Write the signed number for Nome, AK's temperature.

C

Varied Practice

1.

Which context matches the signed number +250+250?

2.

Match each description to the correct sign:
"20 feet above sea level" uses the   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   sign.
"20 feet below sea level" uses the   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   sign.

sign for above:
sign for below:
3.

In the context of elevation, what does an elevation of 0 meters represent?

4.

The signed number −85-85 in an elevation context means:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   meters   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   sea level.

magnitude:
direction word:
5.

A student wrote: 'The temperature is −12-12 degrees below zero.' What is wrong with this statement?

D

Word Problems

1.

A scuba diver descends from the surface to a depth of 30 meters below sea level, then rises 8 meters.

Write the signed numbers.
Starting depth (surface):   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
Depth after descending 30 meters:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

starting depth:
depth after descending:
Cross-section diagram showing sea level at 0 m, summit at +4,500 m above, lake at −15 m below, and base camp at −200 m below sea level
2.

A mountain climber records the following elevations during her hike: Base camp: −200 m (below sea level). Summit: +4,500 m. A lake along the route: −15 m.

1.

Which locations are above sea level?

2.

What does 0 meters elevation represent in this context? Use one complete sentence.

3.

A student says: 'A temperature of 0°C means there is no temperature.'

Complete the response.
Is the student correct?   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
0°C represents the   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   of water.

correct or incorrect:
meaning of 0 degrees Celsius:
E

Error Analysis

1.

Davia compared two temperatures: −3°F-3\degree F and −10°F-10\degree F. She said: '−10°F-10\degree F is greater than −3°F-3\degree F because 10 is greater than 3.'

What error did Davia make?

2.

Marcus was asked: "What does 0°C mean in the context of temperature?" He answered: "0°C means there is no temperature — it is the absence of heat."

What error did Marcus make?

F

Challenge / Extension

1.

The temperature dropped from +5°F+5\degree F to −8°F-8\degree F overnight. Without computing the exact change, explain: (a) in which direction did the temperature move on the number line, and (b) which temperature has the greater absolute value and what that means.

2.

Create your own real-world context (not temperature, elevation, money, or electric charge) where positive and negative numbers make sense. Describe: (a) what the positive direction represents, (b) what the negative direction represents, and (c) what 0 means.

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