Understand Absolute Value of Rational Numbers
Name Period
Objectives / Objetivos
Content Objective: I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
Language Objective: I can explain absolute value using the words distance, zero, opposite, and rational number.
Key Idea / Idea clave
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign
I Notice / Observo
- What does the negative sign tell you about the treasure chest's location?
- Which location is farther from sea level — the chest at -4 or the tower at +6?
I Wonder / Me pregunto
- Can two different integers have the same absolute value?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Integers and Absolute Value Enteros y valor absoluto | Integers are whole numbers and their opposites; absolute value is their distance from zero. Los enteros son números enteros y sus opuestos; el valor absoluto es su distancia desde cero. |
| Integer Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. Un número entero que puede ser positivo, negativo o cero. |
| Positive Positivo | A number bigger than zero, to the right of zero on a number line. Un número mayor que cero, a la derecha del cero en la recta numérica. |
| Negative Negativo | A number smaller than zero, to the left of zero on a number line. Un número menor que cero, a la izquierda del cero en la recta numérica. |
| Absolute value Valor absoluto | How far a number is from zero. It is never negative. Qué tan lejos está un número de cero. Nunca es negativo. |
| Opposite Opuesto | Two numbers the same distance from zero, on opposite sides, like 3 and -3. Dos números a la misma distancia de cero, en lados opuestos, como 3 y -3. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the absolute value of -9?
- A -9
- B 0
- C 1
- D 9
Answer:
2. Plot these integers and circle pairs that have the same absolute value: -6, 6, -2, 2, -4, 4
Mark and label: A; B; C; D; E; F
3. Complete the table with each integer's absolute value and its opposite.
Complete each empty cell. Show your reasoning below.
| Integer | Absolute Value | Opposite |
|---|---|---|
| -7 | ||
| 4 | ||
| -12 | ||
| 0 | ||
| 9 |
4. Find the Absolute Value Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: