8.F.3: Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Hands-on Activities

1. Graphing Grocery Costs

Help your child create a graph of the cost of a grocery list where each item is the same price, showing how the total cost increases with the number of items. Discuss how this represents a linear function.

2. Temperature Time Tracking

Track temperatures at several consistent times throughout the day and graph the results. Analyze whether the change in temperature forms a straight line (linear) or not.

3. Road Trip Readiness

Calculate the total travel time for a trip where you stop every hour for a break, adding a fixed amount of break time each hour. Graph travel time against the number of stops to see if the function is linear.

4. Savings Plan Projection

Create a simple savings plan where your child saves a fixed amount of their allowance each week. Graph the total savings over time to show a linear increase in savings.

5. Cell Phone Plan Comparison

Compare different cell phone plans by plotting the cost versus data provided. Identify which plans offer linear pricing and which do not.

Strategies When Your Child Struggles

1. Graphing Refresher

Review how to plot points on a graph and draw lines. Reinforce the concepts of slope and y-intercept.

2. Real-Life Linear Functions

Discuss and identify real-life examples of linear functions, such as speed or constant spending to solidify understanding.

3. Non-Linear Exploration

Experiment with equations that include squares or cubes (like y = x^2) to visualize how these graphs differ from linear graphs.

4. Interactive Online Resources

Use online graphing tools and interactive websites to create and manipulate linear and non-linear functions easily.

5-Minute Activities

Activity 1: Daily Temperature Log

Record the high temperature each day for a week and plot the points to see if they form a linear pattern.

Activity 2: Weekly Spending Chart

Track spending on snacks over a week and graph the results to determine if the spending is linear.

Activity 3: Stair Step Count

Count steps walked up in a day and graph against the day of the week to explore linearity.

Activity 4: Homework Time Tracking

Monitor and graph the time spent on homework each night to observe if the times are consistent (linear).

Mid-Year Expectations

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

• Students should be able to identify and graph linear functions using the slope-intercept form.
• Students will understand and explain the role of 'm' (slope) and 'b' (y-intercept) in the equation y = mx + b.

End-of-Year Expectations

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

• Students can distinguish between linear and non-linear functions both graphically and algebraically.
• Students will be capable of applying the concept of linear functions to solve real-world problems.

Mastery Signs

Your child has mastered this standard when they can:

• Consistently identifies linear functions and graphs them accurately.
• Demonstrates the ability to explain why a function is linear or non-linear using mathematical vocabulary.

Questions to Ask:

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

• What is the slope and y-intercept of the line represented by the equation y = 5x + 3?
• Graph the equation y = -2x + 7 and describe its slope and y-intercept.
• Given the function y = x^2, explain why this function is not linear.
• Compare the graphs of y = 3x + 1 and y = 3x^2 - 1. Which is linear and why?