Equivalent Ratios — Notes Packet

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

Content Objective: I can find and check equivalent ratios using multiplication and division.

Language Objective: I can explain my reasoning using the words equivalent ratios, rate, proportion, and simplify.

📖 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.

1A comparison of two quantities is a .
2 — Two ratios that mean the same thing.
3A ratio that compares two quantities with different units, like miles per hour, is a .
4An equation showing that two ratios are equal is a .
5Writing a ratio in its smallest equal form, like 6:9 = 2:3, is to it.

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

Looking at the tomatoes-to-broth table (3:2, 6:4, 9:6, 12:8), how can you PROVE these ratios are all equivalent?

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 ratios — Two ratios that mean the same thing.Razones equivalentes — Dos razones que significan lo mismo. Rate — A ratio comparing two amounts with different units, like miles per hour.Tasa — Una razón que compara dos cantidades con unidades distintas, como millas por hora. Proportion — A math sentence saying two ratios are equal.Proporción — Una oración matemática que dice que dos razones son iguales. Simplify — To make a ratio smaller while keeping the same comparison.Simplificar — Hacer una razón más pequeña sin cambiar la comparación. Ratio — A way to compare two amounts.Razón — Una manera de comparar dos cantidades.

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.

These ratios are equivalent because each is ___ times ___.Estas razones son equivalentes porque cada una es ___ veces ___.

3. Build Your Explanation

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

Claim: 32 is 4 times 8, so she multiplies both ingredients by 4.

Evidence: A strong answer finds the scale factor 4 (32 ÷ 8) and explains both ingredients must be multiplied by 4 to make equivalent ratios.

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

Start

Most language support

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

These ratios are equivalent because each is ___ times ___.Estas razones son equivalentes porque cada una es ___ veces ___.
I checked by ___ both numbers.Lo comprobé al ___ ambos números.

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.