Understand Equations and Their Solutions
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 / Término | Definition / 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
Read each task. Show your work in the spaces provided and explain how you know.
1. Which equation represents: 'A number plus 12 equals 30'?
- A n + 12 = 30
- B n − 12 = 30
- C 12n = 30
- D n / 12 = 30
Answer:
2. Match each situation to its equation
Write the letter of the matching item in the blank.
| 1. | A detective has some cases. After getting 9 new cases, she has 22. | A. | 4n = 28 | |
| 2. | A suspect's age divided by 3 equals 12. | B. | n + 9 = 22 | |
| 3. | Four times the number of fingerprints equals 28. | C. | n / 3 = 12 | |
| 4. | A detective had some clues. After removing 6, she had 15 left. | D. | n − 6 = 15 |
3. For each situation, identify what the variable represents and write the equation.
Complete each empty cell. Show your reasoning below.
| Situation | Variable Represents | Equation |
|---|---|---|
| A box holds some files. After removing 5, there are 13 left. | ||
| A detective split 48 photos equally into folders. Each folder has 6 photos. |
4. Find the Equation Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: