Equivalent Expressions — Notes Packet

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

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.

📖 See Learn It for the explanation and worked examples, and the Vocab tab for the words. These are your notes to fill in and keep.

✏️ Fill in each blank as we go. Use the Word Bank to help you.

📚 Word Bank — fill each blank with the best word

👆 Tap any word to see what it means and a picture.

Level 3: try the blanks from memory first, then check the bank.

1 — Expressions that always have the same value.
2To write an expression in its shortest equal form is to it.
3Terms with the same variable raised to the same power, like 4x and 9x, are .
4To add or subtract like terms into one term is to them.
5A number multiplied by a variable is a .

Write About the Math Guided ESOL writing

Use the support level you need. Every level answers the same math question.

1. Understand the Question

justify

How can you prove 2(n + 4) and 2n + 8 are equivalent? What two strategies could you use?

Your job: Answer the question. Use math evidence. Explain how the evidence proves your answer.Responde la pregunta. Usa evidencia matemática. Explica cómo la evidencia demuestra tu respuesta.

2. Plan Your Math Words

Check at least two words you will use.

Equivalent — Expressions that always have the same value.Equivalente — Expresiones que siempre tienen el mismo valor. Simplify — To write an expression in a shorter, simpler way.Simplificar — Escribir una expresión de forma más corta y simple. Like Terms — Terms with the same letter raised to the same power, like 2x and 5x.Términos semejantes — Términos con la misma letra elevada a la misma potencia, como 2x y 5x. Combine — To add or subtract terms with the same letter.Combinar — Sumar o restar términos con la misma letra. Coefficient — The number in front of a letter, like the 3 in 3x.Coeficiente — El número frente a una letra, como el 3 en 3x.

Say it first: Say your idea to a partner or quietly to yourself before you write.Di tu idea a un compañero o en voz baja antes de escribir.

They are equivalent because distributing 2(n + 4) gives ___.Son equivalentes porque distribuir 2(n + 4) da ___.

3. Build Your Explanation

Model the parts: This model shows the parts of an explanation. It does not answer your writing question.

Claim: 3x + 2x combines to 5x, so the two forms are equivalent.

Evidence: Students explain 3x + 2x = 5x (combining like terms), so both equal 5x + 10, and verify by substituting a value like x = 4 to get 30 both ways.

Reasoning: This evidence connects the definition of equivalent to the mathematical claim.

Start

Most language support

Complete the frames. Use the word bank.Completa las oraciones. Usa el banco de palabras.

They are equivalent because distributing 2(n + 4) gives ___.Son equivalentes porque distribuir 2(n + 4) da ___.
I can also check by substituting n = ___ and getting ___.También puedo comprobar sustituyendo n = ___ y obteniendo ___.

Build

Some language support

Write two connected sentences. Use because, so, or but.Escribe dos oraciones conectadas. Usa porque, entonces o pero.

My claim is ___.Mi afirmación es ___.
I know because ___.Lo sé porque ___.
So ___.Entonces ___.

Explain

Light language support

Write a claim, give math evidence, and explain your reasoning.Escribe una afirmación, da evidencia matemática y explica tu razonamiento.

My claim is ___.Mi afirmación es ___.
My math evidence is ___.Mi evidencia matemática es ___.
This proves ___ because ___.Esto demuestra ___ porque ___.

4. Check Your Explanation

I answered the question.Respondí la pregunta. I used math evidence: numbers, an equation, a model, or a comparison.Usé evidencia matemática: números, una ecuación, un modelo o una comparación. I explained how the evidence proves my answer.Expliqué cómo la evidencia demuestra mi respuesta. I used at least two math words.Usé por lo menos dos palabras matemáticas. I reread complete sentences and punctuation.Volví a leer mis oraciones completas y la puntuación.