Math Problem Statement

Give the interval of each number line and create a number line with an interval of 7. Describe how a number line works.

Solution

Let's go through the worksheet step by step:

  1. Top Number Line: You have a number line from 8-8 to 66, and two blanks at 44 and 22 are already filled in.

  2. Second Section (Intervals):

    • The task here asks to determine the interval (the difference between consecutive numbers) for each line.
      • The first line ranges from 26-26 to 10-10. The numbers are evenly spaced: 26,22,18,14,10-26, -22, -18, -14, -10. The difference between consecutive numbers is 44. So, the interval is 4.
      • The second line ranges from 1010 to 8585. The numbers are: 10,25,40,55,70,8510, 25, 40, 55, 70, 85, with a difference of 1515 between consecutive numbers. So, the interval is 15.
      • The third line ranges from 21-21 to 9-9: 21,18,15,12,9-21, -18, -15, -12, -9. The interval between the numbers is 33, so the interval is 3.
      • The fourth line ranges from 8-8 to 88: 8,4,0,4,8-8, -4, 0, 4, 8. The difference between numbers is 44, so the interval is 4.
  3. Creating a Number Line with an Interval of 7:

    • The line starts at 00, and you should move by 7 in both directions.
    • Moving right from 00: 7,14,21,28,7, 14, 21, 28, \dots.
    • Moving left from 00: 7,14,21,-7, -14, -21, \dots.
  4. Key Concept (Describing a Number Line):

    • A number line is a visual representation of numbers on a straight line. As you move from left to right, the numbers increase (become more positive). As you move from right to left, the numbers decrease (become more negative). The center of the line is typically 00, with positive numbers on the right and negative numbers on the left.

Would you like me to explain any of these concepts in more detail?

Here are 5 questions to explore further:

  1. What does an interval represent on a number line?
  2. How do you find the interval between consecutive numbers?
  3. Why are negative numbers placed to the left of 00 on a number line?
  4. What happens if you continue moving left indefinitely on the number line?
  5. How do intervals change if the scale of the number line changes?

Tip: Always check the pattern between numbers on a line to identify the interval—it helps in understanding the scale!

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Math Problem Analysis

Mathematical Concepts

Number Line
Intervals
Positive and Negative Numbers

Formulas

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Theorems

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Suitable Grade Level

Grades 3-5