Engaging integer math activity with colorful cards and cartoon characters for interactive learning.

The image you provided is a promotional graphic for an educational activity titled "Adding & Subtracting Integers: Solve the Riddle Scavenger Hunt." The goal of this activity is to practice adding and subtracting integers while solving a riddle. Below, I will explain how to approach such problems and solve them step by step.

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Key Concepts for Adding and Subtracting Integers

1. Adding Integers:
- If both numbers have the same sign (both positive or both negative), add their absolute values and keep the common sign.
- If the numbers have different signs, subtract the smaller absolute value from the larger one, and the result takes the sign of the number with the larger absolute value.

2. Subtracting Integers:
- To subtract an integer, add its opposite. For example, \(a - b = a + (-b)\).

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Example Problems from the Image

Let's solve the integer problems shown in the image:

#### Problem 1: \((-17) - (-5)\)
- Step 1: Convert subtraction to addition by adding the opposite of \(-5\).
\[
(-17) - (-5) = (-17) + 5
\]
- Step 2: Add the integers.
- The absolute values are 17 and 5.
- Since 17 is larger and negative, the result is negative.
\[
(-17) + 5 = -12
\]

#### Problem 2: \(14 + (-8)\)
- Step 1: Add the integers.
- The absolute values are 14 and 8.
- Since 14 is larger and positive, the result is positive.
\[
14 + (-8) = 6
\]

#### Problem 3: \((-3) + 8 + (-6)\)
- Step 1: Add the integers step by step.
- First, add \((-3) + 8\):
\[
(-3) + 8 = 5
\]
- Next, add the result to \((-6)\):
\[
5 + (-6) = -1
\]

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General Steps to Solve Integer Problems

1. Identify whether you are adding or subtracting.
2. If subtracting, convert it to addition by adding the opposite.
3. Add or subtract the absolute values as needed.
4. Determine the sign of the result based on the rules above.

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Solving the Riddle

The scavenger hunt likely involves solving multiple integer problems like the ones above. Each correct answer corresponds to a letter, which helps decode the riddle. Once all problems are solved, the letters spell out the answer to the riddle.

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Final Answer

The solutions to the problems in the image are:
1. \((-17) - (-5) = -12\)
2. \(14 + (-8) = 6\)
3. \((-3) + 8 + (-6) = -1\)

If these answers correspond to letters in the scavenger hunt, use them to decode the riddle. The final answer to the riddle will depend on the specific letters associated with each problem.

If you need further clarification or help with decoding the riddle, feel free to provide additional details!

Boxed Final Answer for the Problems:
\[
\boxed{-12, 6, -1}
\]