Comparing ratios using tables helps Grade 6 math students answer an important question: which ratio represents more of one quantity relative to another? This printable worksheet develops that skill through equivalent ratio tables, visual comparisons, and real-world situations where simply comparing the original numbers can lead to an incorrect conclusion.

Students practise making one quantity equal in two relationships before comparing the other. For example, they investigate paint mixtures with blue-to-yellow ratios of 2:3 and 3:4. By constructing equivalent ratios using 6 cups of blue paint, they can determine which mixture requires more yellow paint. This gives students a clear mathematical method for comparing quantities fairly.

Practice That Goes Beyond Filling in Tables

The worksheet combines numerical calculations with visual models and mathematical reasoning. Students encounter the following activities:

• Equivalent ratio table comparisons: Complete missing values and identify whether relationship A, relationship B, or neither has the greater relative quantity.
• Paint-mixture table: Extend a blue-to-yellow paint ratio through multiplication and division, then compare it with a different mixture.
• Double tape diagrams: Compare ratios represented by flour and water, juice mixtures, rose and daisy plants, colored shirts, and bracelet beads.
• Error analysis: Find an incorrect multiplication result and correct the misconception that larger starting numbers always represent a greater ratio.
• Real-world short answers: Explain comparisons involving fruit drinks, students travelling to school, flower arrangements, and recycling collections.
• Multiple-choice questions: Check whether students can identify equivalent ratios and distinguish greater from smaller relationships.

Why Matching Quantities Matters

The central idea is proportional comparison. Two ratios can be compared by multiplying or dividing their quantities to produce a shared value. When the first quantities match, students compare the second quantities. When the second quantities match, they compare the first.

This distinction is especially important when ratios look different but are actually equivalent. A garden with 2 roses for every 5 daisies has the same roses-to-daisies relationship as one with 4 roses for every 10 daisies. Students use scaling to demonstrate that equivalence rather than making assumptions from the original totals.

The error-analysis section provides a further opportunity to examine mathematical thinking. Students consider why an incorrect product changes a comparison and why two relationships should not be judged solely by their starting numbers.

What Teachers Can Expect

The printable resource includes a brief lesson introduction, ratio comparison questions, numerical tables, tape diagrams, written explanations, and multiple-choice checks. Student Notes lines at the bottom of the worksheet provide space to record methods or reminders.

Teachers can use the introductory example during a lesson, assign the numerical comparisons as independent practice, or discuss the tape diagrams in pairs or small groups. The written explanations can help reveal whether students understand why their comparisons are valid, making the resource useful for homework, classroom practice, or formative assessment.

Developed for Grade 6 Common Core Mathematics standard 6.RP.A.3, this resource concentrates on constructing equivalent ratios and comparing their relative quantities. Its combination of computation and explanation helps teachers assess both calculation skills and proportional reasoning.