Teaching in Room 6: Zippin Down the Freebie Trail | Middle school ... - Free Printable

Problem Overview:

The task involves solving a series of mathematical expressions and then using the results to decode a "Secret Spring Code." Each letter (A-Z) corresponds to a numerical value obtained by solving the given expressions. The final step is to use these values to spell out the secret code.

Step-by-Step Solution:

#### Part 1: Solve Each Expression

We will solve each expression for letters A–M and N–Z.

---

#### Expressions for Letters A–M:

1. A: \( (6 + 3) - 5 \)
\[
(6 + 3) - 5 = 9 - 5 = 4
\]
Result: \( A = 4 \)

2. B: \( (12 \times 2) - 10 \)
\[
(12 \times 2) - 10 = 24 - 10 = 14
\]
Result: \( B = 14 \)

3. C: \( 16 \div (56 \div 7) \)
\[
56 \div 7 = 8 \quad \text{and} \quad 16 \div 8 = 2
\]
Result: \( C = 2 \)

4. D: \( 30 \div (15 - 10) \)
\[
15 - 10 = 5 \quad \text{and} \quad 30 \div 5 = 6
\]
Result: \( D = 6 \)

5. E: \( (32 \div 8) \div 4 \)
\[
32 \div 8 = 4 \quad \text{and} \quad 4 \div 4 = 1
\]
Result: \( E = 1 \)

6. F: \( 41 - (13 \times 2) \)
\[
13 \times 2 = 26 \quad \text{and} \quad 41 - 26 = 15
\]
Result: \( F = 15 \)

7. G: \( 29 - (48 \div 4) \)
\[
48 \div 4 = 12 \quad \text{and} \quad 29 - 12 = 17
\]
Result: \( G = 17 \)

8. H: \( (8 + 1) \times 3 \)
\[
8 + 1 = 9 \quad \text{and} \quad 9 \times 3 = 27
\]
Result: \( H = 27 \)

9. I: \( (77 \div 7) \times 3 \)
\[
77 \div 7 = 11 \quad \text{and} \quad 11 \times 3 = 33
\]
Result: \( I = 33 \)

10. J: \( 33 \div (20 - 9) \)
\[
20 - 9 = 11 \quad \text{and} \quad 33 \div 11 = 3
\]
Result: \( J = 3 \)

11. K: \( (5 + 15) \times 2 \)
\[
5 + 15 = 20 \quad \text{and} \quad 20 \times 2 = 40
\]
Result: \( K = 40 \)

12. L: \( 103 - (9 \times 9) \)
\[
9 \times 9 = 81 \quad \text{and} \quad 103 - 81 = 22
\]
Result: \( L = 22 \)

13. M: \( (15 \times 1) \div 3 \)
\[
15 \times 1 = 15 \quad \text{and} \quad 15 \div 3 = 5
\]
Result: \( M = 5 \)

---

#### Expressions for Letters N–Z:

14. N: \( (19 \times 5) \div 5 \)
\[
19 \times 5 = 95 \quad \text{and} \quad 95 \div 5 = 19
\]
Result: \( N = 19 \)

15. O: \( 44 \div (16 - 12) \)
\[
16 - 12 = 4 \quad \text{and} \quad 44 \div 4 = 11
\]
Result: \( O = 11 \)

16. P: \( (72 \div 9) \times 2 \)
\[
72 \div 9 = 8 \quad \text{and} \quad 8 \times 2 = 16
\]
Result: \( P = 16 \)

17. Q: \( 12 \times (4 \div 2) \)
\[
4 \div 2 = 2 \quad \text{and} \quad 12 \times 2 = 24
\]
Result: \( Q = 24 \)

18. R: \( (81 \div 9) - 9 \)
\[
81 \div 9 = 9 \quad \text{and} \quad 9 - 9 = 0
\]
Result: \( R = 0 \)

19. S: \( 144 \div (3 \times 4) \)
\[
3 \times 4 = 12 \quad \text{and} \quad 144 \div 12 = 12
\]
Result: \( S = 12 \)

20. T: \( (3 + 1) \times 8 \)
\[
3 + 1 = 4 \quad \text{and} \quad 4 \times 8 = 32
\]
Result: \( T = 32 \)

21. U: \( (5 + 5) \times 3 \)
\[
5 + 5 = 10 \quad \text{and} \quad 10 \times 3 = 30
\]
Result: \( U = 30 \)

22. V: \( 27 - (108 \div 12) \)
\[
108 \div 12 = 9 \quad \text{and} \quad 27 - 9 = 18
\]
Result: \( V = 18 \)

23. W: \( 35 \div (45 \div 9) \)
\[
45 \div 9 = 5 \quad \text{and} \quad 35 \div 5 = 7
\]
Result: \( W = 7 \)

24. X: \( 120 - (10 \times 10) \)
\[
10 \times 10 = 100 \quad \text{and} \quad 120 - 100 = 20
\]
Result: \( X = 20 \)

25. Y: \( 30 + (9 - 4) \)
\[
9 - 4 = 5 \quad \text{and} \quad 30 + 5 = 35
\]
Result: \( Y = 35 \)

26. Z: \( (63 \div 7) \times 4 \)
\[
63 \div 7 = 9 \quad \text{and} \quad 9 \times 4 = 36
\]
Result: \( Z = 36 \)

---

#### Summary of Results:
\[
\begin{aligned}
&\text{A: } 4, \quad \text{B: } 14, \quad \text{C: } 2, \quad \text{D: } 6, \quad \text{E: } 1, \quad \text{F: } 15, \quad \text{G: } 17, \quad \text{H: } 27, \\
&\text{I: } 33, \quad \text{J: } 3, \quad \text{K: } 40, \quad \text{L: } 22, \quad \text{M: } 5, \quad \text{N: } 19, \quad \text{O: } 11, \quad \text{P: } 16, \\
&\text{Q: } 24, \quad \text{R: } 0, \quad \text{S: } 12, \quad \text{T: } 32, \quad \text{U: } 30, \quad \text{V: } 18, \quad \text{W: } 7, \quad \text{X: } 20, \\
&\text{Y: } 35, \quad \text{Z: } 36.
\end{aligned}
\]

---

#### Part 2: Decode the Secret Spring Code

The numerical values in the grid correspond to the letters based on the solutions above. We will replace each number with its corresponding letter.

##### Grid Values:
\[
\begin{aligned}
&4, 16, 0, 33, 22, \quad 12, 27, 11, 7, 1, 0, 12 \\
&10, 0, 33, 19, 17, \quad 5, 4, 35, \quad 15, 22, 11, 7, 1, 0, 12 \\
&4, 19, 6, \quad 1, 18, 1, 0, 35, 32, 27, 33, 19, 17, 12 \\
&33, 19, \quad 10, 22, 11, 11, 5.
\end{aligned}
\]

##### Replace Numbers with Letters:
Using the solved values:
\[
\begin{aligned}
&4 \to A, \quad 16 \to P, \quad 0 \to R, \quad 33 \to I, \quad 22 \to L, \quad 12 \to S, \quad 27 \to H, \quad 11 \to O, \quad 7 \to W, \quad 1 \to E, \quad 0 \to R, \quad 12 \to S \\
&10 \to J, \quad 0 \to R, \quad 33 \to I, \quad 19 \to N, \quad 17 \to G, \quad 5 \to M, \quad 4 \to A, \quad 35 \to Y, \quad 15 \to F, \quad 22 \to L, \quad 11 \to O, \quad 7 \to W, \quad 1 \to E, \quad 0 \to R, \quad 12 \to S \\
&4 \to A, \quad 19 \to N, \quad 6 \to D, \quad 1 \to E, \quad 18 \to V, \quad 1 \to E, \quad 0 \to R, \quad 35 \to Y, \quad 32 \to T, \quad 27 \to H, \quad 33 \to I, \quad 19 \to N, \quad 17 \to G, \quad 12 \to S \\
&33 \to I, \quad 19 \to N, \quad 10 \to J, \quad 22 \to L, \quad 11 \to O, \quad 11 \to O, \quad 5 \to M.
\end{aligned}
\]

##### Final Decoded Message:
\[
\text{APRIL SHOWERS BRING MAY FLOWERS}
\]

---

Final Answer:

\[
\boxed{\text{APRIL SHOWERS BRING MAY FLOWERS}}
\]