8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Hands-on Activities

1. Graph to Table Conversion

Give your child a simple linear function graph. Ask them to create a data table that corresponds to the graph, identifying key points like the y-intercept and slope.

2. Verbal to Algebraic

Describe a real-life situation, such as saving money over time. Have your child write an algebraic function that models the situation and discuss the rate of change.

3. Matching Game

Create cards with different representations of the same function (graph, table, equation, description). Have your child match the cards that represent the same function.

4. Function Detective

Provide descriptions of two functions (like a water tank filling and draining). Your child should graph each function and compare their rates, intercepts, and overall behavior.

5. Online Simulation

Use math software or online graphing tools to explore how changes in an algebraic equation affect the graph. Compare the numerical data from the table view and the graph view.

Strategies When Your Child Struggles

1. Visual Aids

Use color-coding for different functions when comparing them on the same graph or in a table to help distinguish their properties.

2. Step-by-Step Breakdown

Break down each function representation into simpler parts and discuss what each part represents.

3. Real-Life Analogies

Relate functions to everyday situations to make the abstract concepts more tangible.

4. Peer Explaining

Encourage your child to explain their understanding of the function comparisons to a sibling or friend, which can reinforce their learning.

5-Minute Activities

Activity 1: Daily Function

Each day, ask your child to describe a daily activity using a function (e.g., time spent on homework versus number of assignments).

Activity 2: Function Flashcards

Create flashcards with different function representations and have quick review sessions.

Activity 3: Graph Sketching

Quickly sketch a graph based on a given table of values and discuss the key features.

Activity 4: Rate Comparison

Discuss the rate of change in different scenarios, like biking vs. walking, and represent these rates graphically or numerically.

Mid-Year Expectations

By the middle of 8th grade, your child should be able to:

• Students should be able to identify and describe key properties of a function represented in a table or graph.
• Students should start to make connections between different representations of the same function.

End-of-Year Expectations

By the end of 8th grade, your child should be able to:

• Students should confidently compare and contrast functions represented in different forms.
• Students should use proper terminology to describe function properties and relationships between different representations.

Mastery Signs

Your child has mastered this standard when they can:

• Ability to switch between function representations without errors.
• Can verbally explain how one representation of a function relates to another.
• Correctly identifies rates of change and intercepts from graphs and tables.

Questions to Ask:

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

• Compare the rate of change in the functions given by the equations y = 3x + 5 and y = 3x - 2.
• Describe how the graph of y = x^2 differs from the graph of y = 2x^2.
• Given a table of values for a quadratic function, sketch its graph.
• Explain how the verbal description 'The temperature decreases by 2 degrees every hour' can be represented algebraically and graphically.