7.RP.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

I can find the unit rate in tables, graphs, equations, diagrams, and verbal descriptions.

What Your Child Needs to Know

The concept of the constant of proportionality, or unit rate, is a crucial part of understanding proportional relationships in mathematics. This standard, 7.RP.2.b, focuses on identifying the constant of proportionality across various representations including tables, graphs, equations, diagrams, and verbal descriptions. Understanding this concept will enhance your child's ability to solve real-world problems involving ratios and proportional reasoning, such as calculating speeds, determining costs, or analyzing data. Mastering this skill will not only aid in their current math courses but also build a foundation for more advanced topics in algebra and beyond.

Real World Practice

Visual models and hands-on activities

Hands-on Activities

1. Grocery Shopping

Have your child calculate the unit price of various items (price per ounce or per item) to determine the best buy during grocery shopping.

2. Cooking Conversion

While cooking, ask your child to convert measurements using different units (e.g., cups to tablespoons) to find the unit rates, enhancing their understanding of ratios in recipes.

3. Road Trip Planning

Involve your child in planning a road trip by calculating the fuel efficiency of your vehicle (miles per gallon) based on the distance traveled and fuel used.

4. Sports Statistics

Use sports statistics like points per game or goals per match to analyze players’ performances and discuss the concept of unit rates in sports.

5. Data Comparison

Encourage your child to compare mobile data plans or internet service providers based on cost per GB or Mbps to understand how unit rates apply in everyday decisions.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Visual Aids

Use colored pencils or markers to highlight different parts of tables or graphs, making it easier to identify and understand the constant of proportionality.

2. Real-Life Contexts

Discuss real-life scenarios where unit rates are used, such as speed limits or cost per unit in stores, to make the concept more tangible.

3. Step-by-Step Breakdown

Break down problems into smaller, manageable steps and go through each step with your child to ensure understanding.

4. Peer Study Groups

Encourage your child to study with peers, allowing them to explain concepts to each other, which reinforces their understanding.

5-Minute Activities

Activity 1: Unit Rate Flashcards

Create flashcards with different scenarios requiring unit rate calculations for quick practice.

Activity 2: Graph Interpretation

Spend 5 minutes analyzing a graph together, identifying the rate of change and discussing its significance.

Activity 3: Table Challenge

Quickly create a simple table with proportional values and have your child calculate the unit rate.

Activity 4: Verbal Quiz

Pose quick verbal problems related to unit rates, such as 'If 3 apples cost $1.50, what is the cost of one apple?'

Check Progress

Track improvement

Mid-Year Expectations

By the middle of 7th grade, your child should be able to:

  • Students should be able to identify the constant of proportionality in simple tables and graphs.
  • Students should understand the concept of unit rate and be able to explain it verbally.

End-of-Year Expectations

By the end of 7th grade, your child should be able to:

  • Students should confidently find the unit rate across various mediums including complex diagrams and multi-step verbal descriptions.
  • Students should apply their understanding of unit rates to solve real-world problems independently.

Mastery Signs

Your child has mastered this standard when they can:

  • Ability to calculate and explain the unit rate without errors consistently.
  • Can interrelate the constant of proportionality found in tables, graphs, and equations effectively.

Questions to Ask:

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

  • Find the unit rate: If 8 gallons of paint cover 360 square feet, how many square feet does one gallon cover?
  • Determine the constant of proportionality from the graph where 3 hours correspond to 150 pages read.
  • A recipe uses 4 cups of flour to make 24 cookies. What is the unit rate of cups per cookie?
  • Given a table showing the cost of multiple items, calculate the unit price for each item.