6.EE.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

I can represent the quantities in a real-world problem using variables. I can write equations to show the relationships between dependent and independent variables in a real-world problem.

What Your Child Needs to Know

Understanding how variables interact in equations is fundamental in mathematics, especially as students begin to explore more complex algebraic concepts. In 6th grade, students are introduced to the idea of dependent and independent variables within real-world contexts. This helps them see the practical applications of math in everyday life and prepares them for more advanced studies. Learning to express relationships through equations and graphs not only enhances their analytical skills but also boosts their problem-solving abilities. By mastering this standard, students will be better equipped to handle more intricate mathematical challenges in the future.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Grocery Shopping Budget

Help your child create a simple equation to predict total cost based on the number of items bought at the grocery store. For example, if each item costs $3, the equation could be Total Cost = 3 × Number of Items.

2. Saving Up

Discuss a savings goal, like buying a new game or bicycle. Create an equation to determine how long it will take to reach that goal based on saving a certain amount each week. Use a simple graph to track progress over time.

3. Plant Growth Tracking

Measure and record the height of a plant over time. Use these measurements to create a table and graph. Write an equation that represents the plant's growth over time, identifying time as the independent variable and height as the dependent variable.

4. Classroom Book Tracker

If your child reads books over several weeks, help them create a graph to represent the total number of pages read per week. Develop an equation that predicts the total number of pages read based on the number of weeks.

5. Temperature and Clothing

Track daily temperatures and the type of outerwear chosen (e.g., coat, jacket, none). Create a table and a simple graph to show the relationship. Discuss how the choice of clothing depends on the temperature, establishing an equation to predict clothing based on temperature.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Using Concrete Examples

When your child struggles, use concrete examples from daily life to explain dependent and independent variables. Examples like cooking recipes or road trip durations make abstract concepts more relatable.

2. Step-by-Step Breakdown

Break down problems into smaller, manageable parts, focusing first on identifying variables, then on setting up equations. Simplify complex problems to build confidence.

3. Graphical Representation

Encourage drawing graphs to visually understand the relationship between variables. This can often make the connection clearer than equations alone.

4. Peer Discussion

Arrange for discussions with classmates or friends who are also learning the same concepts. Explaining their thoughts to others can help clarify their own understanding.

5-Minute Activities

Activity 1: Quick Variable Quiz

Ask your child to identify variables in different scenarios during a car ride or meal time. Quick, informal quizzes can reinforce their understanding.

Activity 2: Flashcard Challenge

Create flashcards with different variables and equations. Use these for quick review sessions.

Activity 3: Real-Life Equation Setup

During household activities, challenge your child to come up with an equation that might relate two variables (e.g., cooking time and number of servings).

Activity 4: Graph the Day

Ask your child to graph simple relationships they observe throughout the day, such as time spent on homework versus number of assignments completed.

Check Progress

Track improvement

Mid-Year Expectations

By the middle of 6th grade, your child should be able to:

  • Students should be able to identify independent and dependent variables in simple contexts.
  • Students should begin to graph relationships between two variables with guidance.

End-of-Year Expectations

By the end of 6th grade, your child should be able to:

  • Students can independently construct graphs showing relationships between variables.
  • Students can write and solve simple equations for one variable in terms of another.

Mastery Signs

Your child has mastered this standard when they can:

  • Student can explain the difference between dependent and independent variables.
  • Student can create equations and graphs from real-world scenarios without assistance.

Questions to Ask:

Ask your child to solve these problems and explain their process:

  • What is the dependent variable in an equation where y = 2x + 5, and what does it represent?
  • Create a graph to show the relationship between hours studied (x) and test scores (y) if y = 10x.
  • If you have 4 apples and buy x more, write an equation for the total number of apples.
  • Given the equation y = 3x - 7, predict the value of y when x is 10.