Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 3, Lesson 2: Understand Rates and Unit Rates

Standard 6.AT.2

What students are learning Qué aprenden

Key idea: A rate compares two amounts with different units, like $12 for 3 pounds. A unit rate is the amount for just 1, like $4 for 1 pound. To find it, divide: $12 ÷ 3 = $4.Idea clave: Una tasa compara dos cantidades con unidades distintas, como $12 por 3 libras. Una tasa unitaria es la cantidad por solo 1, como $4 por 1 libra. Para hallarla, divide: $12 ÷ 3 = $4.

Words to know Palabras clave

Rates and Unit Rates Tasas y tasas unitarias
A rate compares two amounts. A unit rate is for 1.
Una tasa compara dos cantidades. Una tasa unitaria es por 1.
Rate Tasa
Two amounts compared, like miles for each hour.
Dos cantidades comparadas, como millas por cada hora.
Unit Rate Tasa unitaria
The amount for just 1 of something.
La cantidad para solo 1 de algo.
Per Por
For each one, as in 5 dollars for each book.
Por cada uno, como 5 dólares por cada libro.
Ratio Razón
A way to compare two amounts, like 3 to 2.
Una manera de comparar dos cantidades, como 3 a 2.
Unit price Precio unitario
The cost of just one item, like $0.60 a game.
El costo de un solo artículo, como $0.60 por juego.
Better Buy Mejor compra
The choice that costs less for each item.
La opción que cuesta menos por cada artículo.
Divide Dividir
Split a total into equal groups.
Repartir un total en grupos iguales.
Constant Constante
A number that stays the same.
Un número que se queda igual.
Total price Precio total
What the whole package costs.
Lo que cuesta todo el paquete.

Sentence starters Frases para empezar

I know ___ because ___.

First, I ___. Then, I ___.

The answer is ___, so ___.

How we did it in class today Cómo lo hicimos hoy en clase

  1. Booth A charges $3 for 5 games. I want the cost for just 1 game.
  2. I divide the cost by the games: $3 ÷ 5 = $0.60.
  3. So Booth A costs $0.60 per game. That is the unit rate.
  4. Because this unit rate is money for one item, it has its own name: it is the unit price.
  5. Now I can compare this booth's unit price fairly with any other booth's.

Play with today's math Jueguen con las matemáticas

Interactive Lesson Model — This is the exact same interactive tool your student used in class today. Change the numbers and watch what happens!

Modelo interactivo de la lección — Esta es la misma herramienta interactiva que su estudiante usó en clase hoy. ¡Cambie los números y observe qué sucede!

Works on a phone, a tablet, or a computer. Nothing to install, nothing to sign in to.

Try this together Inténtenlo juntos

Pick one question to talk about. You don't need to do them all!

A snack stand sells 4 juice boxes for $3.00 or 6 juice boxes for $4.20. Which deal is the better buy?

  1. 4 for $3.00 — $0.75 each
  2. 6 for $4.20 — $0.70 each
  3. They cost the same per juice box
  4. Not enough information
Check the answer

The answer is: 6 for $4.20 — $0.70 each

Take-home sheet Hoja para llevar a casa

Lesson 3.2: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 3.2: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

If they get stuck... Si se traban...

Watch out for this: A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y — Pack Y is actually the better buy). A second common mistake is dividing backwards — finding tokens ÷ cost instead of cost ÷ tokens — which turns 'dollars per token' into 'tokens per dollar' and gives an answer that looks reasonable but answers the wrong question. Always divide the total cost by the number of items, and check that your unit rate answers 'the cost for ONE item,' not the reverse.

Try asking: "Can you show me how you got that? Did we miss a step?"
Pregunte: «¿Puedes mostrarme cómo lo hiciste? ¿Nos saltamos algún paso?» Hablar de las matemáticas en voz alta ayuda mucho.

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