Equivalent Ratios Exploration

Lesson 20 of 30: Comparing Ratios: Finding Equivalent Ratios

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Grade Level

6th Grade

Duration

30 minutes

Class Size

13 students

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Common Core State Standards Alignment

CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, including finding equivalent ratios.

CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.

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Learning Objectives ("I Can" Statements)

• I can find equivalent ratios by multiplying or dividing both terms by the same number.
• I can compare two ratios and determine if they are equivalent.
• I can explain why two ratios are or are not equivalent using reasoning or models.

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Success Criteria

• I can correctly create equivalent ratios from a given ratio.
• I can use multiplication or division to find new ratios equivalent to the original.
• I can compare two different ratios and decide if they represent the same relationship.
• I can explain my thinking clearly using words, numbers, or drawings.

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Materials Needed

• Whiteboard and markers
• Ratio cards (pre-made cards showing various ratios, e.g., 2:3, 4:6, 5:10, 3:5)
• Student whiteboards or notebooks
• Manipulatives (e.g., colored counters or fraction bars)
• Worksheets for practice and extension
• Dyslexia-friendly printed notes (clear fonts like OpenDyslexic or Arial, larger size, increased spacing)

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Lesson Procedure

1. Introduction (5 minutes)

• Engage: Start with a quick real-life scenario: "If you have 2 red marbles for every 3 blue marbles, what would be the same ratio if you had more marbles?"
• Write the ratio 2:3 on the board.
• Ask students: "If we double the marbles of each color, will the ratio stay the same?"
• Define equivalent ratios as ratios that express the same relationship between quantities.

2. Guided Practice (10 minutes)

• Using ratio cards, work with the class to find equivalent ratios for 2:3 by multiplying both parts by 2, 3, and 4. Example: 2×2:3×2 = 4:6, 2×3:3×3 = 6:9, etc.
• Display the new ratios on the board and discuss how they compare to the original ratio.
• Use manipulatives (colored counters) to visually show why 4:6 and 6:9 have the same relationship as 2:3.
• Ask students to use their mini whiteboards to write the equivalent ratios for 3:5 by multiplying both terms by different numbers.

3. Independent Practice (8 minutes)

• Distribute worksheets with several given ratios.
• Tasks:
  • Identify if pairs of ratios are equivalent or not by simplifying or finding a common multiplier.
  • Create two equivalent ratios for each given ratio.
• Allow students to use manipulatives or drawing to support their work.
• Circulate to provide support and challenge questions.

4. Check for Understanding & Discussion (5 minutes)

• Call on volunteers to explain how they know two ratios are equivalent.
• Encourage them to use "I can" statements during their explanation.
• Clarify misconceptions, emphasizing the importance of multiplying/dividing both terms by the same number.

5. Extension & Reflection (2 minutes)

• Extension for advanced learners:
  Challenge students to create real-world ratio problems where they need to find unknown quantities using equivalent ratios.

• Reflection prompt:
  Have students write one sentence using an “I can” statement about what they learned today.

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Differentiation Strategies

• For students needing extra support:
  Use visual aids and manipulatives extensively. Provide ratio cards with simple numbers and work through problems step-by-step. Include guided notes with dyslexia-friendly fonts and increased spacing.

• For English Language Learners (ELLs):
  Pair visuals with clear language. Use sentence stems like "The ratio ___ is equivalent to ___ because...".

• For advanced learners:
  Offer problems involving ratios with decimals or adding a third term to explore proportional relationships more deeply.

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Dyslexia-Friendly Reading Options

• Provide printed notes and worksheets in Arial or OpenDyslexic font, size 14-16pt.
• Use high contrast color schemes: white background with dark blue or black text.
• Break down instructions into shorter sentences.
• Include visual examples beside text to reinforce understanding.

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Assessment

• Formative assessment through observation during activities and discussions.
• Review worksheet answers for accuracy in identifying and creating equivalent ratios.
• Use student explanations (“I can” statements) to judge conceptual understanding.

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Summary

This 30-minute lesson encourages 6th graders to understand, create, and compare equivalent ratios through hands-on, visual, and verbal activities. By incorporating "I can" statements and success criteria, students build confidence in mastering ratios while the teacher uses differentiated strategies to meet all learners' needs according to the Common Core standards.