8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Hands-on Activities

1. Grocery Shopping on a Budget

Give your child a budget and a list of prices for items at a store. Ask them to plot the total cost against the number of items and identify the rate of change and initial cost.

2. Track Your Savings

Encourage your child to track their weekly savings and create a function to represent their total savings over time. They can determine the rate at which their savings are growing.

3. Distance vs Time Graph

Create a simple distance vs. time scenario, like walking at a constant speed. Have your child plot the data on a graph and determine the slope and starting point.

4. Temperature Change

Chart the temperature at various times during a day and have your child develop a function to model the linear relationship, if applicable, and discuss the rate of change.

5. Video Game Scores

Use the scores from different levels of a video game to plot points on a graph. Have your child determine if there's a linear relationship, the rate of change, and the initial value.

Strategies When Your Child Struggles

1. Visual Aids

Use graph paper or digital tools to help visualize problems and solutions. Seeing the graph can help understand the linear relationship better.

2. Step-by-Step Examples

Work through problems together, explaining each step to find the rate of change and initial value.

3. Real-Life Connections

Make connections to everyday life scenarios to make the concepts more relatable and easier to understand.

4. Practice with Feedback

Allow your child to practice and provide immediate feedback to help them understand mistakes and correct them in real-time.

5-Minute Activities

Activity 1: Quick Graphs

Draw quick sketches of linear graphs and ask your child to identify the rate of change and initial value.

Activity 2: Flashcard Quiz

Create flashcards with different linear equations and scenarios for quick reviews.

Activity 3: Table to Graph

Provide a table of values and ask your child to plot them on a graph and then derive the linear function.

Activity 4: Function Match

Write down different linear functions on cards and various scenarios or stories on others. Have your child match the function to the scenario.

Mid-Year Expectations

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

• Students should be able to identify linear relationships in tables and graphs.
• Students should understand and calculate the rate of change from a graph.

End-of-Year Expectations

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

• Students will construct linear functions from real-world data.
• Students will interpret the meaning of the rate of change and initial value in context.

Mastery Signs

Your child has mastered this standard when they can:

• Ability to create accurate graphs from a linear equation.
• Confident in explaining the relationship between rate of change, initial value, and the scenario modeled.

Questions to Ask:

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

• Graph the equation y = 2x + 3 and identify the rate of change and initial value.
• Given a table of values, determine if the relationship is linear and explain your reasoning.
• From the description 'A taxi charges a flat fee plus a per mile rate', write the linear function representing the total cost as a function of miles traveled.
• If a coffee shop charges $1.50 per coffee and a one-time membership fee of $5, write the function representing total cost and identify the rate of change and initial value.