8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

I can graph proportional relationships. I can interpret the unit rate as the slope of a graph. I can compare two proportional relationships that are shown in different ways.

What Your Child Needs to Know

Understanding proportional relationships and their graphical representations is vital in 8th grade as it lays the groundwork for more advanced algebraic concepts. Proportional relationships are a cornerstone in mathematics, serving as a bridge between arithmetic and algebra. By learning to graph these relationships, students gain insight into how variables interact and influence each other, which is crucial for solving real-world problems. Mastering this standard helps students interpret the unit rate as the slope of a graph, a key concept in understanding how different quantities compare and scale. This knowledge is not only fundamental in high school mathematics but also in everyday decision-making processes, where comparisons and rates are prevalent.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Grocery Shopping

Have your child compare prices of bulk items to single items to see which has a better unit rate, then graph these rates to visualize which is more cost-effective.

2. Fuel Efficiency

Track the family car's fuel efficiency over different trips. Graph the miles per gallon against the length of the trip to see if longer trips are more fuel-efficient.

3. Recipe Conversion

Convert a recipe's ingredients to serve different numbers of people and graph the relationship between the number of servings and each ingredient quantity.

4. Weather Temperature

Graph the relationship between hours of daylight and average daily temperatures over a month. Interpret the slope of the graph.

5. Cell Phone Plans

Compare two different cell phone plans by graphing the total cost against the number of data gigabytes included, then analyze which plan is more cost-effective based on the slope.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Simplifying Concepts

Break down the concepts by using simpler numbers or ratios to help the child understand the relationship and its graphical representation.

2. Using Visual Aids

Incorporate colored pencils and graph paper to make the activity more engaging and visually clear.

3. Relate to Interests

Connect graphing and proportional relationships to areas of the child's interest, such as sports statistics or gaming stats.

4. Incremental Difficulty

Start with easier examples and gradually increase the complexity as the child becomes more comfortable with the concepts.

5-Minute Activities

Activity 1: Rate of Speed

Discuss and graph the speed of different family members walking or running a fixed distance.

Activity 2: Price per Unit

At the store, quickly calculate and compare the unit price of two similar products and discuss which is the better buy.

Activity 3: Temperature Change

Graph the change in temperature from morning to evening and discuss the rate of change.

Activity 4: Video Game Stats

Use statistics from a video game (e.g., points per minute) to create a simple graph and discuss its slope.

Check Progress

Track improvement

Mid-Year Expectations

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

  • Students should be able to identify proportional relationships in tables and graphs.
  • Students should understand and calculate unit rates from real-world scenarios.

End-of-Year Expectations

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

  • Students can independently graph proportional relationships and interpret the slope as the unit rate.
  • Students can compare and analyze two different proportional relationships accurately.

Mastery Signs

Your child has mastered this standard when they can:

  • Student can explain what a slope of a graph tells us about the relationship between variables.
  • Student can use the slope to make predictions about values not shown in the graph.
  • Student can choose the more economical or efficient option based on graphical data.

Questions to Ask:

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

  • Graph the relationship between the cost of 3, 5, and 7 movie tickets. What does the slope represent?
  • Given a graph showing the relationship between hours studied and test scores, interpret the unit rate.
  • Compare the slopes of two graphs showing different phone plans. Which plan is more cost-effective per gigabyte?
  • Create a graph for a recipe that doubles and triples ingredient amounts. What does the slope tell you about the relationship between servings and ingredient quantities?