Ratio Foundations

Overview

Students will build understanding of ratios as multiplicative comparisons between two quantities. They will identify ratios vs. non-examples, compare quantities using ratio language, and practice writing equivalent ratios in both fractional form and colon form.

Learning intentions

Students will be able to:

• Explain what a ratio is and use ratio language to compare two quantities.
• Determine whether a statement is a ratio (vs. a different type of comparison).
• Write ratios in colon form and as fractions.
• Use ratio language to compare quantities in real-world contexts.

Success criteria

“I can…”

• Describe a ratio as “for every A, there are B” using correct ratio language.
• Distinguish ratio examples from non-examples using reasoning, not memorization.
• Write a ratio from a situation in both colon form (a:b) and fractional form (a/b).
• Compare two ratios using the quantities in the situation or table.

Curriculum links

• Ratios and Proportional Relationships: Understand the concept of a ratio and use ratio language to describe a ratio relationship.
• Ratios and Proportional Relationships: Use ratio and rate reasoning to solve real-world problems (introductory reasoning with writing ratios).
• Ratios and Proportional Relationships: Make tables of equivalent ratios and use tables to compare ratios (preview through today’s ratio comparison tasks).

Lesson structure (60 minutes)

1. 0–7 min · Hook with a real situation. Teacher displays: “For every 2 wings, there is 1 beak” and asks: “What stays the same relationship-wise? What does ‘for every’ hint at?” Students think-pair-share and record their best explanation.

2. 7–18 min · Mini-lesson: What ratios mean. Teacher models how a ratio compares two quantities in the same context (Example: wings to beaks = 2:1), emphasizing “for every A, there is B.” Students complete two guided items:

• “If there are 3 blue marbles and 5 red marbles…” Students write the ratio in colon form and in fractional form (3/5 or 3:5 depending on prompt wording).
• “If there are 8 students and 2 teachers…” Students write the ratio of students to teachers and label what each number represents.

3. 18–28 min · Ratio vs. non-example sort. Teacher gives cards or displays statements like:

• “2 to 5” (ratio)
• “2 + 5” (not a ratio)
• “2 is 5 more than…” (not a ratio)
• “For every 2 cups, there are 5 cups…” (ratio) Students work in pairs to sort into “Ratio” and “Not a ratio,” then justify using the phrase “for every… there is…”.

4. 28–40 min · Guided practice: Writing ratios from pictures and tables. Teacher shows a simple context with discrete items (e.g., classroom lanyards: 4 green, 6 yellow) and a small table template:

• Row A: Green count and Yellow count
• Students fill in ratio statements in two forms: green:yellow and green/yellow. Next, teacher adds a second situation and students compare which ratio is larger (without needing cross-multiplication yet—just interpret “how many for every 1” using the counts).

5. 40–52 min · Interactive activity: Ratio scavenger. Teacher posts 4 stations around the room with short prompts (recipes, vote counts, animal features, sports stats). Each station has one task: “Write the ratio A to B in colon form. Then write it as a fraction A/B. Finally, describe it using ‘for every A, there is…’.” Students rotate every ~3 minutes, recording answers on a station sheet.

6. 52–60 min · Exit ticket and closure. Teacher collects an exit ticket with 3 questions:

• Q1: Write the ratio of ___ to ___ in colon form.
• Q2: Write the same ratio in fractional form.
• Q3: Circle the sentence that is a ratio and explain why in one sentence using “for every…”. Students submit before leaving.

Resources

• Ratio example/non-example cards or projected slides
• Station prompt sheets (4 stations) and recording sheet
• Small manipulatives or pictures (marbles, colored counters, animal-feature diagrams) for quick reference
• Whiteboards or mini-slate materials for quick student writing
• Timer for station rotation
• Exit ticket slips

Assessment

• Formative checks during pair work: teacher circulates and listens for correct use of “for every A, there is B.”
• Ratio sort justification: students must explain why it is or is not a ratio.
• Exit ticket: checks accurate writing of ratios in both colon and fractional forms and correct identification of ratio vs. non-ratio.

Differentiation

• Support: Provide sentence starters such as “The ratio of ___ to ___ is :. For every ___, there are ___.” Offer a worked example on the board for reference during practice.
• Support: Offer a partially completed table template with columns labeled “A” and “B” so students only fill in numbers and ratio expressions.
• Extension: Challenge students to create their own ratio example from a familiar context (e.g., snacks, classroom jobs) and also provide one non-example (“not a ratio”) with a one-sentence explanation.
• EAL/SEN: Allow students to respond with drawings alongside writing; provide a word bank (ratio, for every, there is, to, per).