Tasa =
Problema 11
Letra: E
En la clase de arte, la razón de pintura azul a amarilla es \(1 : 5\). Si usas 5 oz de azul, ¿cuántas oz de amarillo necesitas?
Amarillo =
Problema 12
Letra: I
Halla la tasa unitaria / constante de proporcionalidad (\(k = \frac{\text{Costo}}{\text{Lápices}}\)):
Lápices (\(x\)): 1
2
3
Costo (\(y\)): $3
$6
$9
\(k =\)
¡Coloca la letra de cada problema sobre su número correspondiente abajo!
12 Pistas
“¿Por qué la profesora de matemáticas trajo una escalera el primer día de clases?”
20
8
10
8
8
4
21
8
7
15
8
10
4
8
9
20
18
24
25
7
21
3
8
9
! .
Autocorregible: Cada letra corresponde a números enteros positivos de tus soluciones. Página 2 de 2
Step 2: Multiply both sides by 3:
\(k = 7 \times 3 \implies k = 21\)
Watch: dividing 7 by 3 instead of multiplying Answer: k = 21
Problem 6: Combining Like Terms C (EN) / N (ES)
Original: \(2w + 3w = 35\)
Step 1: Combine like terms: \(2w + 3w = 5w\)
Step 2: Set up: \(5w = 35\)
Step 3: Divide both sides by 5: \(w = 7\)
Confirm: only combine terms with identical variables Answer: w = 7
Turn to Page 2 for Part 2 Solutions & Dual Riddle Decoders Page 1 of 2
Part 2 Solutions & Riddle Punchlines
Locker Codebreaker
Problem 7: Unit Rate (Highlighters) H (EN) / Z (ES)
Step 1: Unit rate \(= \$9 / 3 = \$3\) per highlighter.
Step 2: Cost of 5 \(= 5 \times \$3 = \$15\).
Method: Unit price multiplication Answer: $15
Problem 8: Solving a Proportion I (EN) / S (ES)
Method A (Scale Factor): Denominator \(5 \times 3 = 15\), so numerator \(3 \times 3 = 9\).
Method B (Cross-Multiply): \(5x = 45 \implies x = 9\).
Scale factor is fastest mental math Answer: x = 9
Problem 9: Percent of a Quantity G (EN) / O (ES)
Step 1: Convert 50% to fraction (\(\frac{1}{2}\)) or decimal (0.50).
Step 2: Discount \(= 0.50 \times 36 = \$18\).
Notice: Question asks for discount, not total Answer: $18
Problem 10: Typing Unit Rate P (EN) / T (ES)
Step 1: Set up rate ratio: \(\frac{48\text{ words}}{2\text{ minutes}}\).
Step 2: Divide numerator by denominator: \(48 \div 2 = 24\) wpm.
Unit rate always has denominator of 1 Answer: 24 wpm
Problem 11: Ratio Reasoning (Paint) W (EN) / E (ES)
Step 1: Ratio \(\text{Blue} : \text{Yellow} = 1 : 5\).
Step 2: For 5 oz of Blue, multiply Yellow by 5:
\(5 \times 5 = 25\text{ oz of Yellow}\)
Proportional scale: \(\frac{1}{5} = \frac{5}{25}\) Answer: 25 oz
Problem 12: Constant of Proportionality S (EN) / I (ES)
Definition: Constant \(k = \frac{y}{x}\) for any row.
Row 1: \(k = \frac{3}{1} = 3\); Row 2: \(k = \frac{6}{2} = 3\).
Key 8th Grade Concept: \(y = kx\) where \(k = 3\) Answer: k = 3
Riddle Decoder Solutions Complete letter mapping
English Edition Answer
“Why did the math teacher bring a ladder to the first day of school?”
TO REACH HIGHER POWERS!
T=20, O=8 | R=10, E=4, A=21, C=7, H=15 | H=15, I=9, G=18, H=15, E=4, R=10 | P=24, O=8, W=25, E=4, R=10, S=3
Spanish Edition Answer
“¿Por qué la profesora trajo una escalera el primer día?”
¡PARA ALCANZAR LAS POTENCIAS!
P=20, A=8, R=10, A=8 | A=8, L=4, C=21, A=8, N=7, Z=15, A=8, R=10 | L=4, A=8, S=9 | P=20, O=18, T=24, E=25, N=7, C=21, I=3, A=8, S=9
Diagnostic Debrief Tips for Day 1–3
Self-Checking Benefit: If a student's answer doesn't appear under any blank, guide them to identify whether the error was an inverse operation slip (e.g., adding instead of subtracting) or arithmetic. Problem 12 establishes the foundational 8th-grade linear form \(y = kx\) (slope/proportionality).
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