Use Ratio Reasoning — Notes Packet

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

Content Objective: I can use ratio reasoning to solve problems with proportions and scaling.

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

📖 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.

1An equation that states two ratios are equal is a .
2Multiplying the numerator of one ratio by the denominator of the other to check a proportion is to .
3To multiply a ratio up or down by the same factor is to it.
4Two ratios that show the same comparison are .
5The amount for exactly one unit is the .

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

You sorted ratio pairs into equivalent and not equivalent. How does ratio reasoning, like cross-multiplying, prove that 4:7 and 12:21 are 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.

Proportion — A math sentence saying two ratios are equal.Proporción — Una oración matemática que dice que dos razones son iguales. Cross-multiply — Multiplying across two ratios to check if they are equal.Multiplicación cruzada — Multiplicar en cruz dos razones para ver si son iguales. Scale — To multiply or divide both parts of a ratio by the same number.Escalar — Multiplicar o dividir ambas partes de una razón por el mismo número. Equivalent — Having the same value.Equivalente — Tener el mismo valor. Unit rate — A rate for just 1 of something. You find it by dividing.Tasa unitaria — Una tasa para solo 1 de algo. La encuentras al dividir.

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.

I reasoned that 4:7 and 12:21 are ___ because ___.Razoné que 4:7 y 12:21 son ___ porque ___.

3. Build Your Explanation

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

Claim: Find the scale factor (120 divided by 8 = 15), then multiply each ingredient by it.

Evidence: Students find the scale factor of 15 and explain that multiplying both ingredients by 15 keeps the recipe proportional (5 cups tomatoes becomes 75, 3 cups mozzarella becomes 45).

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

Start

Most language support

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

I reasoned that 4:7 and 12:21 are ___ because ___.Razoné que 4:7 y 12:21 son ___ porque ___.
Cross-multiplying gives ___ and ___, which are ___.La multiplicación cruzada da ___ y ___, que son ___.

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.