Ratio Test

This worksheet goes one step deeper by asking students to calculate y/x for every pair in a table, record those values, and then decide whether the ratio is constant. If it is, students also write the constant of proportionality, k. This makes the worksheet especially useful because students are not just labeling a relationship proportional or non-proportional-they are identifying the exact number that explains how x and y are connected.

For a parent, the constant of proportionality is simply the number you multiply x by to get y. If y is always 3 times x, then k = 3. If y is always 1/2 of x, then k = 1/2. The worksheet has students verify that by calculating y/x across the entire table.

Key Learning Objectives

• Calculate y/x: Students find the ratio for each ordered pair.
• Determine Whether the Ratio Is Constant: Learners compare all calculated values.
• Identify k: Students write the constant of proportionality when the relationship is proportional.
• Connect Tables to Equations: Learners prepare to understand equations of the form y = kx.
• Distinguish Constant and Changing Relationships: Students see exactly why some tables are proportional and others are not.

Parent-Friendly Explanation

Suppose a table shows:

x: 2, 4, 6, 8
y: 6, 12, 18, 24

Calculate:

6/2 = 3
12/4 = 3
18/6 = 3
24/8 = 3

Since the ratio stays the same:

Constant? Yes
k = 3

That means the relationship can be described by:

y = 3x

But if the ratios come out 5, 4, 3.7, and 3.5, there is no constant k, so the relationship is not proportional.

Why This Worksheet Helps

• Makes k Meaningful: Students see where the constant of proportionality actually comes from.
• Builds a Bridge to Algebra: The ratio y/x becomes the coefficient in y = kx.
• Encourages Organized Checking: Students calculate every pair instead of assuming a pattern.
• Strengthens Fraction and Division Skills: The worksheet gives repeated practice computing ratios.
• Supports Graphing Later: The value of k will also connect to slope in proportional graphs.

Classroom & Home Use

• Great for Guided Practice: Parents or teachers can work through one table slowly before students continue.
• Useful for Intervention: The y/x row makes the thinking visible.
• Good for Assessment: Teachers can see whether a mistake happened in division or in the final classification.
• Strong for Algebra Readiness: Students begin connecting tables, ratios, and equations.
• Helpful for Homeschooling: The repeated structure makes the process easy to reinforce.

The real value of this worksheet is that it helps students understand that proportional relationships are controlled by one constant number. Tables, ratios, division, k, and equations all connect. For parents, the best coaching question is: “Does y divided by x stay the same every time?” If it does, that repeated answer is the constant of proportionality.