6th Grade Math Worksheet (Age 12) — 6.NS.C.7.A: Integer Inequalities & Number Line Distance

Instructions

This worksheet focuses on comparing negative numbers, understanding their position on a number line, and calculating the distance between them. Read the instructions for each section carefully and complete all tasks.

1. Use a pencil and write your answers clearly in the spaces provided.
2. When comparing numbers, remember that numbers further to the right on the number line are always greater.
3. For distance calculations, always use absolute value, as distance is never negative.

Section 1: The Direction Detective

Task: Insert the correct inequality symbol ( > or < ) to make each statement true. Think about where the numbers would sit on a standard horizontal number line.

1. -10 ____ -4
2. 5 ____ -12
3. -1 ____ 0
4. -15 ____ 15
5. -25 ____ -20
6. 8 ____ -8
7. -100 ____ -99
8. |3| ____ |-3|

Section 2: Mapping the Distance

Task: For the given pair of numbers, first state the correct inequality, and then calculate the absolute distance between them. Distance is calculated using the formula: Distance = |A - B|.

Section 3: Communicating Position

Task: Explain the meaning of the given inequality in terms of position on the number line. Use the word 'right' or 'left' in your explanation.

1. Inequality: -5 > -12

   Explanation:

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2. Inequality: -10 < 3

   Explanation:

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Section 4: Real-World Application: Temperature Check

In meteorology, negative numbers are essential for measuring cold temperatures.

Scenario: A weather station tracks three temperatures (in Celsius) recorded over three hours.

• Hour 1: -6°C
• Hour 2: -1°C
• Hour 3: -10°C

1. Write an inequality comparing the temperature from Hour 2 and Hour 3.

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2. Which hour recorded the warmest temperature? Explain why using number line position.

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3. What is the absolute difference (distance) between the coldest temperature (Hour 3) and the warmest temperature (Hour 2)? Show your work. Work: ____ Difference: ___ °C

Section 5: The Critical Thinker Challenge

Task: Answer the following complex questions using your knowledge of integers and distance.

1. Always, Sometimes, or Never? If two negative integers, A and B, are compared, the one with the larger absolute value is the lesser number. (Circle one)

   Always / Sometimes / Never

2. The Missing Integer: Find an integer (X) that satisfies both inequalities simultaneously:

   X > -4 AND X < -1

   X = _____

3. Distance Puzzle: A number, P, is 7 units away from 2 on the number line. What are the two possible values for P?

   P = __ and P = __

Answer Key

Section 1: The Direction Detective

1. -10 < -4
2. 5 > -12
3. -1 < 0
4. -15 < 15
5. -25 < -20
6. 8 > -8
7. -100 < -99
8. |3| = |-3| (Note: The prompt requires > or <, but this tests understanding of absolute value. If forced to choose an inequality symbol, state the equality: 3 = 3)

Section 2: Mapping the Distance

Section 3: Communicating Position

1. Explanation: -5 is greater than -12 because -5 is located to the right of -12 on the number line.
2. Explanation: -10 is less than 3 because -10 is located far to the left of 3 on the number line.

Section 4: Real-World Application: Temperature Check

1. -1°C > -10°C (or -10°C < -1°C)
2. Hour 2 recorded the warmest temperature (-1°C). This is the warmest because -1 is the number furthest to the right on the number line, indicating a higher temperature.
3. Work: |-1 - (-10)| = |-1 + 10| = |9| Difference: 9 °C

Section 5: The Critical Thinker Challenge

1. Always (Example: -10 has a larger absolute value than -5, and -10 is less than -5).
2. X = -3
3. P = 9 and P = -5 (P could be 2 + 7 = 9, or P could be 2 - 7 = -5)