Notation Power Guided Notes
Grade 8 Math • MA 8.EE.A.4
Scientific Notation • Notas Guiadas
Name / Nombre: ___________________
Date / Fecha: ____________
Class / Periodo: ___________________
🎯 Goal • Meta:
I can MULTIPLY (×) and DIVIDE (÷) numbers.
Puedo multiplicar (×) y dividir (÷) números.
\(a \times 10^b\) 1 ≤ a < 10
1 The Golden Rule • La Regla de Oro
First number (a) • Primer número:
Between 1 and 10
Entre 1 y 10 (ejemplo: 3.5 ✓ , 25 ✗)
Exponent (b) • Exponente:
Positive or negative integer (+ / −)
Entero positivo o negativo (ej: 10⁴, 10⁻³)
2 Division (÷) • División: SUBTRACT exponents (Resta)
\(10^m \div 10^n = 10^{m-n}\)
Example 1 • Ejemplo 1: Teacher Model
\(\frac{8 \times 10^{16}}{4 \times 10^{12}}\)
• Divide numbers: \(8 \div 4 =\) ______
• Subtract exponents: \(16 - 12 =\) ______
Answer: ______ × 10______
Your Turn • Tu Turno: Practice
\(\frac{9 \times 10^{8}}{4.5 \times 10^{3}}\)
Work area • Espacio de trabajo:
Answer:
3 Multiplication (×) • Multiplicación: ADD exponents (Suma)
\(10^m \times 10^n = 10^{m+n}\)
Example 2 • Ejemplo 2: Teacher Model
\((2 \times 10^3) \times (3 \times 10^8)\)
• Multiply numbers: \(2 \times 3 =\) ______
• Add exponents: \(3 + 8 =\) ______
Answer: ______ × 10______
Your Turn • Tu Turno: Practice
\((3 \times 10^7) \times (3 \times 10^2)\)
Work area • Espacio de trabajo:
Answer:
Lesson 10 • Operations with Scientific Notation Page 1 of 3 • Página 1 de 3
Adjusting Numbers & Word Problems • Ajustar Números
Part 2 • Parte 2
HOW TO FIX • CÓMO AJUSTAR
Check the first number (1 ≤ a < 10)
🔴 TOO BIG (≥ 10) • Demasiado grande:
Move LEFT (←) ➔ Exponent + 1
32.2 × 10¹⁶ ➔ 3.22 × 10¹⁷
🟡 TOO SMALL (< 1) • Demasiado pequeño:
Move RIGHT (→) ➔ Exponent − 1
0.5 × 10³ ➔ 5 × 10²
4 Problem 1: Humans and Ants • Humanos y Hormigas
Action: MULTIPLY (×)
🧍 HUMANS (Humanos): 7 billion = 7 × 10⁹
🐜 ANTS PER HUMAN (Hormigas): 4.6 × 10⁷
❓ TOTAL ANTS (Total): Multiply: (7 × 10⁹) × (4.6 × 10⁷)
1. Multiply numbers: \(7 \times 4.6 =\) 32.2 ⚠️ 32.2 is TOO BIG!
2. Add exponents: \(10^9 \times 10^7 = 10\)______
3. Adjust (Move comma left ←): \(32.2 \times 10^{16} \rightarrow 3.22 \times 10\)______
Total Ants in Scientific Notation:
5 Problem 2: Social Media Likes • "Likes" en Redes Sociales
Action: DIVIDE (÷)
❤️ LIKES (Total Me Gusta): 990 billion = 9.9 × 10¹¹
👥 USERS (Usuarios): 8.9 × 10⁸
❓ LIKES PER USER: Divide: \(\frac{9.9 \times 10^{11}}{8.9 \times 10^8}\)
Work area • Espacio de cálculo:
Scientific Form:
Standard Form:
Lesson 10 • Operations with Scientific Notation Page 2 of 3 • Página 2 de 3
Exercises & Language Routine • Ejercicios y Práctica
Part 3 • Parte 3
6 Exercise 1: Speed of Light • Velocidad de la Luz
Action: DIVIDE (÷)
☀️ DISTANCE (Distancia): 1.5 × 10¹¹ meters
⚡ SPEED (Velocidad): 3 × 10⁸ m/s
❓ TIME IN SECONDS: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
Divide: \(\frac{1.5 \times 10^{11}}{3 \times 10^8}\) • Show steps:
⚠️ \(1.5 \div 3 = 0.5\) (Too small!). Adjust (Move right →): 0.5 × 10³ ➔ ______ × 10______
Standard Form (Seconds):
7 Exercise 2: Mass of Moon and Sun • Masa de la Luna y el Sol
Action: MULTIPLY (×)
🌑 1 MOON (1 Luna): 7.3 × 10²² kg
☀️ SUN = (Sol =): 2.6 × 10⁷ moons
❓ SUN MASS: (2.6 × 10⁷) × (7.3 × 10²²)
Work area • Espacio de cálculo:
Final Mass of Sun (kg):
🗣️ Quick Math Words • Palabras Clave Circle the right word • Encierra en un círculo
MULTIPLY (×): [ ADD / SUBTRACT ]
DIVIDE (÷): [ ADD / SUBTRACT ]
[✓] I can divide (÷) [✓] I can multiply (×) [✓] 1 ≤ a < 10
Lesson 10 • Operations with Scientific Notation Page 3 of 3 • Página 3 de 3
Notation Bilingual Guide
Grade 8 Math • MA 8.EE.A.4
Scientific Notation Guide • Guía Bilingüe
Name / Nombre: ___________________
Date / Fecha: ____________
Class / Clase: ___________________
📐 Parts of Scientific Notation • Partes Rule: 1 ≤ a < 10
a × 10b
a = Number (Número)
Between 1 and 10.
Entre 1 y 10 (1 ≤ a < 10).
b = Exponent (Exponente)
Integer power (+ / −).
Entero (+ o −).
🔤 Math Words & Cognates • Palabras Clave
Similar words in English and Spanish
| English Word | En Español | Simple Meaning / Significado | Action |
|---|
| Scientific notation | Notación científica | Number written with powers of 10 | \(a \times 10^b\) |
| Standard form | Forma estándar | Regular number with zeros and commas | 7,000,000 |
| Multiply (×) | Multiplicar (×) | Multiply numbers, ADD exponents | ADD (+) |
| Divide (÷) | Dividir (÷) | Divide numbers, SUBTRACT exponents | SUB (−) |
| Adjust | Ajustar | Fix first number so it is between 1 and 10 | 1 ≤ a < 10 |
⚡ 2 Rules for Operations • Las 2 Reglas
MULTIPLICATION (×) Suma exponentes
1. Multiply numbers (Multiplica números)
2. ADD exponents (Suma exponentes)
\((a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m + n}\)
Example • Ejemplo:
\((2 \times 10^3) \times (4 \times 10^5) = \mathbf{8 \times 10^8}\)
DIVISION (÷) Resta exponentes
1. Divide numbers (Divide números)
2. SUBTRACT exponents (Resta exponentes)
\(\frac{a \times 10^m}{b \times 10^n} = (a \div b) \times 10^{m - n}\)
Example • Ejemplo:
\(\frac{8 \times 10^{12}}{2 \times 10^4} = \mathbf{4 \times 10^8}\)
Unit 1: Operations with Scientific Notation • Notación Científica Page 1 of 2 • Página 1 de 2
How to Adjust & Practice • Cómo Ajustar y Práctica
Student Reference
QUICK FIX • CÓMO ARREGLAR
Make the number between 1 and 10
🔴 TOO BIG (≥ 10)
