Ratio Two-Way Comparison

Overview

Today students learn how to describe and compare quantities using ratios in two different ways, then practice ratio and unit-rate reasoning with worked examples. The lesson builds from understanding ratios as comparisons and moves toward unit rate language and solving problems using ratio reasoning.

Learning intentions

Students will be able to:

• Understand a ratio as a comparison of two quantities using ratio language.
• Compare quantities using a ratio expressed as a:b (with b ≠ 0).
• Describe a unit rate associated with a ratio and use unit-rate language in context.
• Use tables of equivalent ratios (and ratio reasoning) to solve real-world problems.

Success criteria

“I can…”

• Identify the two quantities in a situation and write the correct ratio (a:b).
• Explain what a ratio means using words (for every a there are b).
• Find and interpret a unit rate (e.g., dollars per hamburger; cups per cup).
• Complete a table of equivalent ratios and use it to answer questions correctly.

Curriculum links

• Ratios: understand ratio and use ratio language to describe ratio relationships (6.RP.A.1).
• Unit rate: understand unit rate a/b associated with a ratio a:b and use rate language (6.RP.A.2).
• Ratio tables: make tables of equivalent ratios, find missing values, plot pairs, and compare ratios (6.RP.A.3a).
• Ratio and rate reasoning: solve real-world problems using tables, diagrams, or equations (6.RP.A.3).
• Unit rate problems: solve unit rate problems including unit pricing and constant speed (6.RP.A.3b).

Lesson structure (60 minutes)

1. 0–8 min · Introduction (situation + ratio language). Teacher displays a scenario: “At a school store, each combo includes 3 hot dogs and 2 bottles of water.” Teacher asks: “What does the ratio 3:2 mean in words?” Students turn-and-talk, then share ratio meanings; teacher records correct phrasing: “for every 3 hot dogs there are 2 bottles of water.”

2. 8–18 min · Guided comparison in two ways. Teacher introduces “two ways” to compare the same relationship:

• Way 1: ratio of hot dogs to water = 3:2
• Way 2: ratio of water to hot dogs = 2:3 Teacher emphasizes that the quantities swap positions, so the ratio values change. Students complete a quick “two-way” rewrite: “If the hot dog to water ratio is 3:2, what is the water to hot dogs ratio?”

3. 18–28 min · Direct teach: unit rate from a ratio. Teacher connects ratios to unit rate: from 3 hot dogs to 2 water bottles, create a “per 1 hot dog” or “per 1 bottle” comparison. Example: “2 bottles for 3 hot dogs means 1 bottle for 1.5 hot dogs, or better use per hot dog: water per hot dog = 2/3 bottle per hot dog.” Teacher models reading: “We have 2/3 bottle of water for each hot dog.” Students practice with a second example shown on the board: “A recipe uses 4 cups flour to 6 cups sugar.” Teacher prompts: “What is the ratio flour:sugar? What is the unit rate sugar per cup flour?”

4. 28–42 min · Worked examples using ratio tables. Teacher presents a worked example with a table: “A rideshare charges the same rate: $75 for 15 hamburgers.”

• Step A: Identify ratio: cost:burgers = 75:15
• Step B: Find unit rate using reasoning: 75 ÷ 15 = 5 dollars per hamburger
• Step C: Use equivalent ratios in a table to fill missing values:
• If cost:burgers is 75:15, then 150:30, 25:5, 375:75, etc. Teacher guides students to compare how the ratios remain equivalent when scaled. Students copy the table structure and complete 2 missing entries independently while teacher circulates.

5. 42–52 min · Independent practice (multi-step). Teacher gives a 6-question set (or 2–3 longer tasks) with the following types:

• Write ratios in two ways for the same situation.
• Identify the unit rate and write it using correct rate language.
• Use a completed ratio table to answer a question about “for every…” or “how many if…” Students work independently; teacher provides a simple “ratio checklist” at their desk (quantities identified, correct order, simplified unit rate, table equivalence).

6. 52–60 min · Assessment (exit ticket + share-out). Teacher collects an exit ticket:

• Part A: “A class mix has 5 red beads and 3 blue beads. Write the ratio red:blue and blue:red.”
• Part B: “At the same rate, how many blue beads for 10 red beads? Show how you know using a ratio table or equivalent ratios.” Students submit. Teacher uses responses to plan next steps.

Resources

• Scenario cards or slide for examples (hot dogs/water, flour/sugar, $75 for 15 hamburgers)
• Student ratio note-catcher (2-column: ratio in words, unit rate statement)
• Blank ratio table templates (2–4 rows)
• Independent practice worksheet or task cards
• Exit ticket (ratio two ways + table-based comparison)
• Dry-erase boards or digital whiteboard for quick checks

Assessment

• Formative: listen for correct “for every a there are b” ratio language during turn-and-talk.
• Formative: during guided practice, check students’ ability to swap ratio order correctly (3:2 vs 2:3).
• Formative: review completed table entries in worked example and provide immediate feedback.
• Exit ticket: accuracy with two-way ratios and using equivalent ratios/table reasoning to find missing quantity.

Differentiation

• Support: provide sentence frames for ratio language (“For every ___, there are ___.”) and unit-rate language (“There are ___ per ___.”).
• Support: include a ratio-table scaffold showing how to scale from one row to the next (multiplying both quantities by the same factor).
• Extension: include a challenge question asking students to justify which comparison is “better” for a given question (e.g., compare using unit rate vs using the original ratio).
• EAL/SEN: allow use of drawings/tape diagrams; ensure word problems highlight the two quantities and the rate context; permit partner work during independent practice with clear roles (one writes ratio, one computes unit rate, one checks table equivalence).