Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 9, Lesson 1: Explore Relationships Between Two Variables

Standard 6.AT.11

What students are learning Qué aprenden

Key idea: When two amounts change together, one depends on the other. The amount you choose or change is the independent variable, and the amount that responds is the dependent variable. Example: the cost of gas depends on how many gallons you buy, so gallons is the independent variable and cost is the dependent variable.Idea clave: Cuando dos cantidades cambian juntas, una depende de la otra. La cantidad que escoges o cambias es la variable independiente, y la cantidad que responde es la variable dependiente. Ejemplo: el costo de la gasolina depende de cuántos galones compras, así que los galones son la variable independiente y el costo es la variable dependiente.

Words to know Palabras clave

independent variable variable independiente
The amount you choose. The other amount depends on it.
La cantidad que eliges. La otra cantidad depende de ella.
dependent variable variable dependiente
The amount that changes when the other does.
La cantidad que cambia cuando cambia la otra.
depends on depende de
It changes when the other one changes.
Cambia cuando la otra cantidad cambia.
quantity cantidad
A number with a meaning, like 540 meters.
Un número con un significado, como 540 metros.
relationship relación
How two amounts are linked.
Cómo están conectadas dos cantidades.
Table of values Tabla de valores
A table that lists matching pairs of numbers.
Una tabla que muestra pares de números que se corresponden.
Input Entrada
The number you put in to start.
El número que pones para empezar.
Output Salida
The number that comes out.
El número que sale.

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 two quantities are hours of sunlight per day and average plant height after 3 weeks.
  2. Akela CHOSE where to put each tray, so she chose the sunlight. Sunlight is subject to choice — that makes it the independent variable.
  3. She did not choose how tall the plants got. Height responded. That makes height the dependent variable.
  4. Say it as a sentence: plant height depends on sunlight.

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 bakery sells muffins for the same price each. Which sentence is correct?

  1. Both quantities are independent variables.
  2. The total cost depends on the number of muffins bought, so the number of muffins is the independent variable.
  3. Neither quantity depends on the other.
  4. The number of muffins depends on the total cost, so the cost is the independent variable.
Check the answer

The answer is: The total cost depends on the number of muffins bought, so the number of muffins is the independent variable.

Take-home sheet Hoja para llevar a casa

Lesson 9.1: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 9.1: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

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

Watch out for this: Naming the variables backward — calling the responding quantity 'independent' because it is the one the question asks about.

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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