Proportional Or Not

This worksheet helps students decide whether a table shows a proportional or non-proportional relationship by checking whether the ratio y/x stays the same for every pair of values. Each problem gives a small table with x-values and y-values, and students compare the relationship between the two rows. If the ratio is constant all the way across the table, the relationship is proportional. If the ratio changes, the relationship is non-proportional. This activity strengthens ratio reasoning, division, table interpretation, and the idea of a constant of proportionality.

For a parent who may not remember this topic, the easiest way to think about it is this: in a proportional relationship, y is always the same multiple of x. For example, if x = 2 gives y = 6, x = 4 gives y = 12, and x = 6 gives y = 18, then y is always 3 times x. That means the relationship is proportional. But if one pair breaks that pattern, then the relationship is non-proportional.

Learning Goals

• Read x-y Tables: Students interpret paired values from a table.
• Calculate y/x: Learners divide y by x for each pair.
• Recognize a Constant Ratio: Students determine whether the quotient stays the same.
• Classify Relationships: Learners write Proportional or Non-Proportional.
• Build Constant-of-Proportionality Understanding: Students begin seeing the fixed multiplier that connects x to y.

Parent-Friendly Teaching Tips

A simple routine is:

1. Take one x-y pair.
2. Divide y by x.
3. Do the same for the next pair.
4. Compare the answers.
5. If every quotient is the same, the relationship is proportional.

For example:

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

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

The ratio stays 3, so the relationship is Proportional.

If even one quotient changes, it is Non-Proportional.

Why This Worksheet Helps

• Makes Proportionality Testable: Students have a clear numerical method instead of guessing.
• Connects Ratios to Tables: Learners see how proportional relationships appear in organized data.
• Prepares for y = kx: The constant ratio becomes the value of k later.
• Strengthens Division Skills: Students repeatedly calculate y/x.
• Builds Error Detection: One inconsistent pair is enough to show that the relationship is not proportional.

The main value of this worksheet is that it teaches students to look for a constant multiplicative relationship. Tables, ratios, division, and proportional reasoning all work together. For parents, the best question is: “Is y always the same multiple of x?” If yes, the relationship is proportional. If not, it is non-proportional.