Equivalent Ratios Tables

Objective

By the end of this 30-minute lesson, students will be able to:

• Create and complete tables of equivalent ratios.
• Understand and explain why ratios in the tables are equivalent.
• Solve problems by finding missing values in tables of equivalent ratios.

Common Core State Standard:

• CCSS.MATH.CONTENT.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
• CCSS.MATH.CONTENT.6.RP.A.3.D: Use ratio reasoning to find the missing value in tables of equivalent ratios.

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Materials

• Whiteboard and markers
• Printed worksheets with ratio table templates (one per student)
• Colored markers or pencils
• Small manipulatives (e.g., counters or colored blocks)
• Calculators (optional)

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Lesson Breakdown

1. Introduction & Motivation (5 minutes)

• Start with a relatable scenario: "Imagine you are painting a fence and the paint mixture recipe has a ratio of 1 part blue paint to 3 parts white paint. How much paint do you need if you want to paint a bigger fence?"
• Write the ratio 1:3 on the board.
• Ask students what equivalent ratios they might get if they double, triple, or quadruple the parts.
• Briefly introduce the term tables of equivalent ratios as a way to organize these equivalent pairs.

2. Direct Instruction (7 minutes)

• Demonstrate a completed table of equivalent ratios using the 1:3 example:

Blue Paint	White Paint
1	3
2	6
3	9
4	12

• Explain each row represents the same ratio.
• Show the method to find missing values by multiplying or dividing both parts of the ratio by the same number.
• Emphasize that the ratios represent a constant relationship.

3. Guided Practice (8 minutes)

• Distribute worksheets with a blank table and a given ratio. Example: 2:5.
• Students fill out the next few rows to find equivalent ratios (e.g., 4:10, 6:15, 8:20).
• Circulate and provide help as necessary.
• Encourage students to explain their reasoning aloud or to each other—verbalizing understanding solidifies learning.

4. Hands-On Exploration (5 minutes)

• Give each student small colored blocks or counters representing the two quantities.
• Assign a ratio (e.g., 3:4) and ask students to physically model equivalent ratios (e.g., 6:8, 9:12) by grouping blocks and filling in their ratio tables.
• This kinesthetic activity helps strengthen recognition and understanding of equivalent ratios.

5. Assessment & Reflection (5 minutes)

• Present a mixed problem on the board:

Part A	Part B
5	?
?	20
15	?

• Ask students to find missing values that maintain equivalent ratios.
• Review answers as a group and discuss how they found the missing numbers using ratio reasoning.
• Close by asking students to explain the importance of tables of equivalent ratios in real-life contexts.

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Extensions (Optional for Homework)

• Give students word problems that require creating and using tables of equivalent ratios, e.g., recipes, map scales, or speed/distance problems.
• Challenge advanced learners to simplify ratios and then build tables from the simplified form.

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Teacher Notes

• Encourage students to verbalize their reasoning during activities to deepen conceptual understanding.
• Use manipulatives especially for tactile learners and to build concrete understanding before moving fully abstract.
• Focus on process over speed; proficiency in ratio reasoning is key at this grade level.

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This lesson is designed to foster conceptual understanding combined with practical computation, adhering closely to 6th-grade Common Core standards for ratio reasoning. Teachers using this plan will engage students in multiple learning modalities and encourage clear communication about mathematical ideas.