Grade 6 integers addition worksheet focusing on sums between -30 and +30.

Problem Description:

The task is to solve the addition of integers ranging from -30 to +30. The worksheet contains 24 problems, and we need to find the sum for each pair of integers.

Solution Approach:

1. Understand Integer Addition Rules:
- Adding two positive integers: Add their absolute values, and the result is positive.
- Adding two negative integers: Add their absolute values, and the result is negative.
- Adding a positive and a negative integer: Subtract the smaller absolute value from the larger one, and the sign of the result will be the same as the number with the larger absolute value.

2. Solve Each Problem Step-by-Step:
We will calculate each sum individually using the rules above.

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Detailed Solutions:

#### Row 1
1. \( 3 + (-3) \)
- Adding a positive and a negative integer with the same absolute value results in zero.
- Answer: \( 0 \)

2. \( 24 + 15 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 39 \)

3. \( -6 + 3 \)
- Subtract the smaller absolute value (3) from the larger one (6). The result takes the sign of the larger number, which is negative.
- Answer: \( -3 \)

#### Row 2
4. \( 2 + (-19) \)
- Subtract the smaller absolute value (2) from the larger one (19). The result takes the sign of the larger number, which is negative.
- Answer: \( -17 \)

5. \( -13 + 28 \)
- Subtract the smaller absolute value (13) from the larger one (28). The result takes the sign of the larger number, which is positive.
- Answer: \( 15 \)

6. \( -25 + 1 \)
- Subtract the smaller absolute value (1) from the larger one (25). The result takes the sign of the larger number, which is negative.
- Answer: \( -24 \)

#### Row 3
7. \( 27 + 16 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 43 \)

8. \( 14 + 25 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 39 \)

9. \( 12 + (-23) \)
- Subtract the smaller absolute value (12) from the larger one (23). The result takes the sign of the larger number, which is negative.
- Answer: \( -11 \)

#### Row 4
10. \( -20 + 3 \)
- Subtract the smaller absolute value (3) from the larger one (20). The result takes the sign of the larger number, which is negative.
- Answer: \( -17 \)

11. \( 1 + (-8) \)
- Subtract the smaller absolute value (1) from the larger one (8). The result takes the sign of the larger number, which is negative.
- Answer: \( -7 \)

12. \( -22 + 5 \)
- Subtract the smaller absolute value (5) from the larger one (22). The result takes the sign of the larger number, which is negative.
- Answer: \( -17 \)

#### Row 5
13. \( -14 + 19 \)
- Subtract the smaller absolute value (14) from the larger one (19). The result takes the sign of the larger number, which is positive.
- Answer: \( 5 \)

14. \( 3 + 13 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 16 \)

15. \( 23 + 8 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 31 \)

#### Row 6
16. \( 7 + (-6) \)
- Subtract the smaller absolute value (6) from the larger one (7). The result takes the sign of the larger number, which is positive.
- Answer: \( 1 \)

17. \( -15 + 6 \)
- Subtract the smaller absolute value (6) from the larger one (15). The result takes the sign of the larger number, which is negative.
- Answer: \( -9 \)

18. \( -17 + (-28) \)
- Both numbers are negative. Add their absolute values, and the result is negative.
- Answer: \( -45 \)

#### Row 7
19. \( 19 + 21 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 40 \)

20. \( -20 + (-6) \)
- Both numbers are negative. Add their absolute values, and the result is negative.
- Answer: \( -26 \)

21. \( 2 + 2 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 4 \)

#### Row 8
22. \( -16 + 7 \)
- Subtract the smaller absolute value (7) from the larger one (16). The result takes the sign of the larger number, which is negative.
- Answer: \( -9 \)

23. \( 4 + (-1) \)
- Subtract the smaller absolute value (1) from the larger one (4). The result takes the sign of the larger number, which is positive.
- Answer: \( 3 \)

24. \( 2 + 4 \)
- Both numbers are positive. Add their absolute values.
- Answer: \( 6 \)

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Final Answers:

\[
\boxed{
\begin{array}{ccc}
0 & 39 & -3 \\
-17 & 15 & -24 \\
43 & 39 & -11 \\
-17 & -7 & -17 \\
5 & 16 & 31 \\
1 & -9 & -45 \\
40 & -26 & 4 \\
-9 & 3 & 6 \\
\end{array}
}
\]