Introduction to Ratios: Comparing Quantities

Introduction to Ratios: Comparing Quantities

Grade 6 · Math · NYS NY-6.RP.1 · 50 Minutes

Math Teacher Review Pilot: This resource is eligible for review by a NYS-certified Mathematics teacher.

NYS-Aligned Standard

NY-6.RP.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. NYS Next Generation Mathematics Learning Standards (2017)

Learning Objectives — “I Can” Statements

• I can explain what a ratio is and what it compares.
• I can write a ratio three different ways: a:b, a/b, and “a to b.”
• I can use ratio language (“for every,” “to,” “out of”) to describe real-world comparisons.
• I can distinguish between part-to-part and part-to-whole ratios.

Essential Question

When we compare two quantities, why does it matter HOW we express the comparison?

Lesson Sequence

Hook / Warm-Up (8 minutes)

1. Show a bowl of 8 red marbles and 4 blue marbles. “How many red? Blue? Which way can we compare them?”
2. Students suggest: “Subtract?” “Divide?” “Write a fraction?”
3. Introduce: “We can write a ratio: 8 to 4, or 8:4, or 8/4. All three mean the same thing.”
4. Simplify: 8:4 = 2:1. “For every 2 red marbles, there is 1 blue marble.”

Direct Instruction (12 minutes)

1. Ratio notation: introduce all three forms — 8:4, 8/4, “8 to 4”
2. Part-to-part vs. part-to-whole: “8 red : 4 blue is part-to-part. 8 red out of 12 total is part-to-whole.”
3. Ratio language: “for every,” “for each,” “out of,” “to,” “per”
4. Model 3 real-world examples with context sentences (recipe, classroom count, sports stats)
5. Simplify ratios: “6:9 = 2:3 (divide both by 3)“

Guided Practice (12 minutes)

1. Show a scenario: A classroom has 12 boys and 15 girls.
   • Write the boy:girl ratio three ways
   • Write the girl:total ratio
   • Simplify each
   • Describe in words: “For every 4 boys, there are 5 girls.”
2. Partners work through 2 additional scenarios.

Independent Practice (12 minutes)

Students complete the Ratio Practice Worksheet (6 problems covering: writing ratios 3 ways, part-to-part, part-to-whole, ratio language sentences, simplifying).

Closure (6 minutes)

1. Exit ticket: “A bag has 6 oranges and 9 apples. Write the orange:total ratio three ways and simplify.”
2. Discussion: “Why might a coach care about a win:loss ratio? A chef about ingredient ratios?”

SDI & Differentiation Block

Supports for MLLs/ELLs

Entering/Emerging (NYSESLAT Levels 1–2):

• Use physical objects (colored cubes) for all comparisons; students arrange before writing
• Vocabulary card: ratio, compare, part, whole, total — with visual examples
• Sentence frame: “For every ___ [object], there are ___ [object]. The ratio is :.”
• Allow student to draw the ratio before writing it in notation

Transitioning/Expanding (NYSESLAT Levels 3–4):

• Pre-teach ratio language phrases with visual examples
• Allow student to complete part of the practice in L1 as notes, then translate
• Provide worked example at desk for reference

Supports for Students with IEPs

SDI Adaptation Dimensions: content, methodology, delivery

• Content: Focus on writing ratios two ways (a:b and “a to b”) — skip a/b fraction notation; eliminate simplifying ratios if the student hasn’t solidified GCF skills
• Methodology: Use color-coded counters throughout; provide a ratio “frame” template with blanks: : (part to part) and : (part to whole)
• Delivery: One problem at a time on separate cards; allow extended time; allow verbal description of ratio instead of all three notation forms

Suggested Placement: ICT, Resource Room

Extensions for Advanced Learners

• Equivalent ratios: “What other ratios are equivalent to 2:3?”
• Connect to percents: “8 out of 20 — write as a ratio, a fraction, and a percent.”
• Real-world data: use a sports statistics table to identify and compare multiple ratios

Answer Key

Exit ticket: oranges:total = 6:15 = 2:5; or “6 to 15” or “6/15” simplified to 2/5 or 2:5. “For every 2 oranges, there are 5 pieces of fruit total.”

Alignment Record