8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Hands-on Activities

1. Graph the Weather

Track the daily high temperatures for a week and plot them on a graph. Discuss whether the temperature trend is increasing or decreasing and predict the next day's temperature based on the graph.

2. Budget Balancing

Create a graph based on a weekly allowance and spending. Identify periods where spending is faster than saving and discuss ways to balance or improve the budget.

3. Walk and Graph

Measure and record the time it takes to walk specific distances. Graph these times against the distances and analyze the shape of the graph to determine if the relationship is linear or nonlinear.

4. Science Experiment Observations

Conduct a simple science experiment, such as observing plant growth under different light conditions. Graph the growth over time and describe the relationship between light exposure and growth rate.

5. Classroom Polls

Conduct a poll in class about favorite books or sports and graph the results. Discuss how the graph's shape changes with different types of questions and answer choices.

Strategies When Your Child Struggles

1. Graph Reading Nightly

Encourage your child to describe graphs from newspapers or magazines each night to build familiarity and comfort with different types of graphs.

2. Use Manipulatives

Use physical objects like coins or blocks to create a visual representation of quantities and their changes, helping to conceptualize the graphing of these quantities.

3. Drawing Descriptions

Have your child listen to a verbal description of a scenario and then draw a graph to represent it, helping them visualize verbal information.

4. Graph Vocabulary Flashcards

Create flashcards with key vocabulary such as 'increasing', 'decreasing', 'linear', 'nonlinear', and use them regularly to reinforce understanding.

5-Minute Activities

Activity 1: Graph Sketch Relay

Give a verbal description of a function, and have your child quickly sketch a graph to match. Time them and make it a fun challenge.

Activity 2: Daily Graph Insights

Ask your child to describe one graph a day from different media sources, focusing on the type of relationship shown.

Activity 3: Function Story Game

Make up stories or situations and ask your child to sketch a graph that could represent that situation.

Activity 4: Graph Matching Game

Create cards with graphs and separate cards with descriptions of the graphs. Mix them up and have your child match each graph to its correct description.

Mid-Year Expectations

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

• Students should be able to identify whether a graph shows an increasing or decreasing trend.
• Students should begin to differentiate between linear and nonlinear relationships in simple graphs.

End-of-Year Expectations

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

• Students should be capable of sketching a graph from a verbal description of a relationship between two quantities.
• Students should confidently analyze complex graphs and describe the type of relationship they represent.

Mastery Signs

Your child has mastered this standard when they can:

• Can accurately sketch and interpret both linear and nonlinear graphs.
• Can verbally describe the features of a graph without seeing it, based on a description of the function.

Questions to Ask:

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

• Describe the relationship shown in the graph of a car’s speed over time.
• Sketch a graph that would represent a balloon’s height above the ground after it is released.
• Identify whether the graph of temperature versus time of day is linear or nonlinear, and explain why.
• Given a story about a runner’s speed during a race, draw a graph that could represent their speed over time.