Understand Absolute Value of Rational Numbers

6.NOS.8 · Unit 7 · Lesson 3

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 / TérminoDefinition / 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

  1. What is the absolute value of -9?
    1. 9
    2. -9
    3. 0
    4. 1
  2. Plot these integers and circle pairs that have the same absolute value: -6, 6, -2, 2, -4, 4
  3. Complete the table with each integer's absolute value and its opposite.
  4. Find the Absolute Value Error
    1. Step 1: Problem — Find |-6|
    2. Step 2: Student thinking — The number is -6, and absolute value makes it the opposite
    3. Step 3: Student answer — |-6| = 6, and since we take the opposite, the answer is -6

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: