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Unit 9: Treasure Map Navigator Lesson 9-1 6.AT.11

Explore Relationships Between Two Variables

I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.

Speaking and writing goal: I can explain which quantity depends on the other using the words independent variable, dependent variable, and depends on.

What Your Child Is Learning

In this lesson, students practice how to recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable. They learn to show their thinking with numbers, pictures, words, or a model. The goal is not just getting an answer. Students should be able to explain why the answer makes sense.

Why This Matters

Expressions and equations help students describe patterns and missing numbers. This matters for planning, budgeting, games, coding, and solving everyday questions step by step.

What It May Look Like In Class

Your child may use the interactive lesson, guided notes, examples from the board, partner talk, and short practice problems. They may be asked to solve, draw a model, label important numbers, and explain their reasoning in a sentence.

How You Can Help At Home

You do not need to teach a new method. Ask your child to read the problem out loud, circle the important numbers, and explain what they tried first. Helpful questions include: What do you know? What are you trying to find? Does your answer make sense?

Apoyo para familias en español

Qué está aprendiendo su hijo/a

En esta lección, su hijo/a practica usar letras, números y reglas para resolver problemas. Puede usar dibujos, números, palabras o modelos para mostrar su pensamiento. Lo más importante es que pueda explicar por qué su respuesta tiene sentido.

Por qué es importante

Las expresiones y ecuaciones ayudan a describir patrones y números desconocidos. Son útiles para planear, presupuestar y resolver problemas paso a paso.

Cómo puede ayudar en casa

No necesita ser experto/a en matemáticas. Pídale a su hijo/a que lea el problema en voz alta, marque los números importantes y explique su primer paso. Puede preguntar: ¿Qué sabes? ¿Qué necesitas encontrar? ¿Tu respuesta tiene sentido?

Key Vocabulary

independent variable variable independiente

The quantity that is subject to choice. It does not depend on the other quantity.

Example: The hours of sunlight a tray receives — Akela chooses that.

dependent variable variable dependiente

The quantity that changes in response to the independent variable.

Example: The height the plants reach — it responds to the sunlight.

depends on depende de

One quantity depends on another when changing the first causes the second to change.

Example: Plant height depends on sunlight.

quantity cantidad

Something that can be counted or measured.

Example: Hours of sunlight, centimeters of height, minutes of jogging.

relationship relación

How two quantities change together.

Example: More sunlight goes with taller plants.

Try It Together

Pick one or two problems. Let your child explain the first step before opening the answer.

  1. Evaluate 3x + 2 when x = 4.
    Show answer

    14

  2. Solve x + 6 = 15.
    Show answer

    x = 9

  3. Write an expression for 5 more than a number n.
    Show answer

    n + 5

  4. Is y = 3 a solution to y + 4 = 7?
    Show answer

    Yes