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  1. Skip count forwards by 2s up to 12 and backwards by -2s down to -12 using a number line.


  1. Skip count forwards by 5s up to 30 and backwards by -5s down to -30.


  1. Skip count forwards by 5s up to 30 and backwards by -5s down to -30 using a number line.

Verified Answer :

  • Part 1 sequence: \(12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12\).
  • Part 2 sequences: Forwards are \(5, 10, \dots, 75\); Backwards are \(0, -5, \dots, -30\).
  • Part 3 sequences: Forwards are \(5, 10, 15, 20, 25, 30\); Backwards are \(0, -3, \dots, -36\).
  • \(\boxed{\text{All sequences completed.}}\)

Explanation

  1. Problem Analysis and Overview

The problem requires us to generate skip-counting sequences based on specific rules for three distinct parts, focusing on situations involving opposite directions or values on a number line. This exercise helps in understanding how numbers increase or decrease in consistent increments or decrements. We will process each part systematically to provide the correct sequences.

  1. Part 1: Skip Counting Analysis

For Part 1, we are asked for a skip-counting sequence involving steps related to the number 12. Although the prompt mentions a forward skip count by 25, the provided sequence clarifies the pattern to be followed: starting from 12 and counting backward by 2 until reaching -12.
The resulting sequence is:
\(12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12\).

  1. Part 2: Skip Counting by 5s

For Part 2, we need two sequences: one forward by 5 up to 75, and one backward by 5 starting from 0 down to -30.

  • For the forward sequence, we add 5 starting from 5: \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75\).
  • For the backward sequence, we subtract 5 starting from 0: \(0, -5, -10, -15, -20, -25, -30\).
  1. Part 3: Skip Counting by 5s and 3s

For Part 3, we follow the patterns: forward by 5 up to 30, and backward by 3 starting from 0 down to -36.

  • The forward sequence is: \(5, 10, 15, 20, 25, 30\).
  • The backward sequence is: \(0, -3, -6, -9, -12, -15, -18, -21, -24, -27, -30, -33, -36\).
  1. Final Answer Completion

The skip counting sequences are:
Part 1: \(12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12\)
Part 2 (Forward): \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75\)
Part 2 (Backward): \(0, -5, -10, -15, -20, -25, -30\)
Part 3 (Forward): \(5, 10, 15, 20, 25, 30\)
Part 3 (Backward): \(0, -3, -6, -9, -12, -15, -18, -21, -24, -27, -30, -33, -36\)
\(\boxed{\text{All sequences completed.}}\)

Examples

Skip counting is an essential skill for managing time and resources effectively. For instance, if you are filling a series of containers that hold exactly 5 liters of water each, you can use skip counting by 5 to quickly determine how much water is in 10 containers (\(10 \times 5 = 50\) liters). Similarly, when tracking an object's position moving backward or forward on a path, skip counting allows you to predict its location at regular intervals, such as finding its position after 6 steps of 3 units backward from a starting point of 0: \(0, -3, -6, -9, -12, -15, -18\).

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