Identify Equivalent Algebraic Expressions
Name Period
Objectives / Objetivos
Content Objective: I can show that two expressions are equivalent by simplifying and combining like terms.
Language Objective: I can explain my work using the words equivalent, simplify, like terms, and combine.
Key Idea / Idea clave
Equivalent Algebraic Expressions. 1. Equivalent expressions produce the same value for any substitution of the variable. 2. Simplify expressions using algebraic properties (Distributive, Commutative, Associative). 3. Test equivalence by substituting two different test numbers
I Notice / Observo
- Why did both formulas give the same answer?
- What did Producer B do differently from Producer A?
I Wonder / Me pregunto
- Can two expressions look completely different but always give the same answer?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Equivalent Expressions Expresiones equivalentes | Expressions that look different but have the same value for every allowed variable value. Expresiones que se ven diferentes pero tienen el mismo valor para cada valor permitido de la variable. |
| Equivalent Equivalente | Expressions that always have the same value. Expresiones que siempre tienen el mismo valor. |
| Simplify Simplificar | To rewrite an expression in a shorter form that is still equal to the original. Reescribir una expresión en una forma más corta que sigue siendo igual a la original. |
| Like Terms Términos semejantes | Terms with the same letter raised to the same power, like 2x and 5x. Términos con la misma letra elevada a la misma potencia, como 2x y 5x. |
| Combine Combinar | To add or subtract terms with the same letter into one. Sumar o restar términos con la misma letra en uno solo. |
| Coefficient Coeficiente | The number in front of a letter, like the 3 in 3x. El número frente a una letra, como el 3 en 3x. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. Which expression is equivalent to 4x + 3x?
- A 7x
- B 7x²
- C 12x
- D 43x
Answer:
2. Match each expression with its simplified form. Write a letter for each expression, then show the steps for one match.
Write the letter of the matching item in the blank.
| 1. | 8y + 2y | A. | 7t | |
| 2. | 3(a + 6) | B. | 3a + 18 | |
| 3. | 5n + 4 + 2n | C. | 8x − 4 | |
| 4. | 9p − 3p | D. | 7n + 4 | |
| 5. | 4(2x − 1) | E. | 6p | |
| 6. | 6t + t | F. | 10y |
3. Match each expression to its simplified equivalent.
Write the letter of the matching item in the blank.
| 1. | 6x + 2x | A. | 5a + 7 | |
| 2. | 3(n + 5) | B. | 6y − 8 | |
| 3. | 4a + 7 + a | C. | 5x + 10 | |
| 4. | 2(3y − 4) | D. | 6m + 1 | |
| 5. | 10m − 4m + 1 | E. | 3n + 15 | |
| 6. | 5(x + 2) | F. | 8x |
4. Find the Simplification Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: