Understand Equations and Their Solutions

6.AT.8 · Unit 8 · Lesson 1

Name   Period

Objectives / Objetivos

Content Objective: I can write an equation for a real situation and check whether a given value is a solution by substituting it.

Language Objective: I can explain a solution using the words substitute, solution, true, and equal sign.

Key Idea / Idea clave

Equations & Solutions. Formula: Left Expression = Right Expression. 1. An equation is a mathematical sentence stating two expressions are equal. 2. A solution is a value for the variable that makes the equation true. 3. Check: Substitute the value into the equation and verify that both sides balance

I Notice / Observo

  • What quantity is unknown in this situation?
  • What does 'plus 8 more' tell you about the operation?

I Wonder / Me pregunto

  • What if the clue said 'twice a number equals 20' instead?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Write Equations
Escribir ecuaciones		Represent a relationship with expressions joined by an equal sign.
Representar una relación con expresiones unidas por un signo igual.
Equation
Ecuación		A math sentence with an equal sign showing both sides are the same.
Una oración matemática con un signo igual que muestra que ambos lados son iguales.
Variable
Variable		A letter that stands for a number that is unknown or can change.
Una letra que representa un número desconocido o que puede cambiar.
Equal sign
Signo igual		The = sign, showing both sides are the same.
El signo =, que muestra que ambos lados son iguales.
Expression
Expresión		A math phrase with numbers and letters, but no equal sign.
Una frase matemática con números y letras, pero sin signo igual.
Constant
Constante		A fixed number in an expression or equation that does not change.
Un número fijo en una expresión o ecuación que no cambia.

Practice Preview / Vista previa de práctica

  1. Which equation represents: 'A number plus 12 equals 30'?
    1. n + 12 = 30
    2. n − 12 = 30
    3. 12n = 30
    4. n / 12 = 30
  2. Match each situation to its equation
    • → ___
    • → ___
    • → ___
  3. For each situation, identify what the variable represents and write the equation.
  4. Find the Equation Error
    1. Step 1: Situation — Twice a number is 16
    2. Step 2: Identify operation — Twice means addition
    3. Step 3: Write equation — n + 2 = 16

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

Reflection / Reflexión

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