Ratio and Rate Problem Solving

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

Content Objective: I can solve real-world rate problems by finding and using unit rates.

Language Objective: I can explain my solution using the words rate, unit rate, per, and proportion.

📖 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 ratio comparing two quantities with different units is a .
2A rate for exactly one unit, like $3 per 1 pound, is a .
3The word that means 'for each' in a rate, like miles hour, is .
4Using a plan and math steps to find an answer to a real situation is .
5An equation that two ratios are equal 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

explain

Team 2 frosts 5 cupcakes every 4 minutes. How did you set up a rate or proportion to find how many cupcakes they frost in a longer time?

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.

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. Unit rate — A rate for just 1 of something, like cost for 1 item.Tasa unitaria — Una tasa para solo 1 de algo, como el precio de 1 artículo. Per — For each one. Example: 5 dollars per book.Por — Por cada uno. Ejemplo: 5 dólares por libro. Proportion — A math sentence saying two ratios are equal. It helps find a missing number.Proporción — Una oración matemática que dice que dos razones son iguales. Ayuda a hallar un número que falta. Problem solving — Using ratios and rates to find a missing amount.Resolución de problemas — Usar razones y tasas para encontrar una cantidad que falta.

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.

The rate is ___ cupcakes per ___ minutes.La tasa es ___ cupcakes por ___ minutos.

3. Build Your Explanation

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

Claim: Divide the total cost by the number of pounds to find the cost per 1 pound.

Evidence: Students divide $18 by 3 to get $6 per pound and explain the unit rate lets them find the cost of any number of pounds.

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

Start

Most language support

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

The rate is ___ cupcakes per ___ minutes.La tasa es ___ cupcakes por ___ minutos.
To find the total, I ___ the rate.Para hallar el total, ___ la tasa.

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.