Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 9, Lesson 4: Apply Two-Variable Relationships to Solve Problems

Standard 6.AT.11

What students are learning Qué aprenden

Key idea: Use an equation to answer real questions: put in the number you know, solve for the one you don't, and check that the answer makes sense. If a car goes 50 miles each hour, d = 50h. To go 200 miles, 50h = 200, so h = 4 hours.Idea clave: Usa una ecuación para contestar preguntas reales: pon el número que sabes, resuelve para el que no sabes y comprueba que la respuesta tenga sentido. Si un carro recorre 50 millas cada hora, d = 50h. Para recorrer 200 millas, 50h = 200, así que h = 4 horas.

Words to know Palabras clave

solution solución
A value that makes the math sentence true.
Un valor que hace verdadera la oración matemática.
substitute sustituir
Put a number in place of a letter.
Poner un número en lugar de una letra.
at least al menos
That amount or more.
Esa cantidad o más.
predict predecir
Say what will happen before it happens.
Decir qué va a pasar antes de que pase.
justify justificar
Explain WHY your answer makes sense.
Explicar POR QUÉ tu respuesta tiene sentido.
Equation Ecuación
A math sentence with an equal sign.
Una oración matemática con un signo de igual.
Inverse operation Operación inversa
Two actions that undo each other, like × and ÷.
Dos acciones que se deshacen entre sí, como × y ÷.
Work backward Trabajar hacia atrás
Start at the end and undo each step.
Empezar por el final y deshacer cada paso.

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. The number of cars produced depends on the number of hours of operation. Every hour, the plant produces 2.5 cars.
  2. Let h = hours and c = cars. The equation is c = 2.5h. Check with the table: 8 hours gives 2.5 × 8 = 20 cars per shift.
  3. The order needs 1,000 cars, so substitute: 2.5h = 1,000.
  4. Divide both sides by 2.5: h = 1,000 ÷ 2.5 = 400 hours.
  5. Interpret it: 400 hours running 24 hours a day is about 17 days — about 2.5 weeks. That fits inside 3 weeks only if the plant runs 24 hours a day, 7 days a week.

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 printer prints 1.5 pages per second. Using 1.5s = 300, how many seconds does a 300-page job take?

  1. 450 seconds
  2. 20 seconds
  3. 200 seconds
  4. 298.5 seconds
Check the answer

The answer is: 200 seconds

Take-home sheet Hoja para llevar a casa

Lesson 9.4: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 9.4: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

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

Watch out for this: Adding the rate instead of multiplying — writing 2.5 + 8 = 10.5 cars for an 8-hour shift instead of 2.5 × 8 = 20. The rate applies to EVERY hour, so the total is always rate × amount.

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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