7.RP.2.a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Hands-on Activities

1. Recipe Adjustment

Ask the student to adjust a recipe's ingredients to serve different numbers of people and check if the ingredient ratios remain consistent.

2. Map Scaling

Use a map's scale to calculate actual distances between locations and determine if the scale provides a proportional representation of real-world distances.

3. Budget Planning

Help your child create a simple budget for a family event, checking if the costs of items are proportional to the number of guests.

4. Speed Analysis

Record times and distances for different trips in a vehicle. Create a table and graph these values to see if they form a straight line through the origin, indicating proportionality.

5. Art Project

Create a scale drawing of a household object. Use measurements from the object and the drawing to see if they hold a proportional relationship.

Strategies When Your Child Struggles

1. Visual Aids

Use colored pens to highlight different parts of a table or graph, making it easier for the student to see patterns and relationships.

2. Step-by-Step Guidance

Break down the process into smaller, manageable steps and guide the student through each phase of setting up tables and plotting graphs.

3. Real-Life Connection

Relate problems to real-life contexts the student is familiar with, such as comparing amounts of ingredients in recipes or prices in shopping.

4. Peer Learning

Encourage the student to explain their reasoning and methods to a classmate, which can reinforce their understanding and uncover any misconceptions.

5-Minute Activities

Activity 1: Quick Table Quiz

Create a quick quiz with different tables of values and ask the student to identify which ones represent proportional relationships.

Activity 2: Graph Point Plotting

Have the student plot points given in a table onto graph paper quickly to see if they align in a straight line through the origin.

Activity 3: Ratio Check

Present pairs of numbers and have the student quickly determine if they form a ratio equivalent to another pair.

Activity 4: Flashcard Challenge

Use flashcards with different scenarios and ask the student to decide if they depict proportional relationships or not.

Mid-Year Expectations

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

• Students should be able to identify proportional relationships in tables.
• Students should begin to feel comfortable graphing pairs of values on a coordinate plane.

End-of-Year Expectations

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

• Students can independently set up and interpret graphs to decide if a relationship is proportional.
• Students can explain why a relationship is or is not proportional using mathematical vocabulary.

Mastery Signs

Your child has mastered this standard when they can:

• Confidently identifies proportional relationships in various formats (tables, graphs).
• Can articulate reasoning behind the proportionality or lack thereof in a given scenario.

Questions to Ask:

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

• Is the relationship between the number of cups of flour and cookies produced proportional? Explain your reasoning.
• Graph the following pairs on a coordinate plane and determine if they show a proportional relationship: (2,4), (3,6), (4,8).
• Given a table showing the distance traveled over time, explain if the relationship is proportional.
• Why does a graph that is a straight line through the origin represent a proportional relationship?