Equivalent Ratios: Scale Both Quantities

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Use complete groups and a ratio table to explain equivalent ratios, challenge a same-addend error, and choose a focused follow-up. Begin with a separate readiness task and a short introduction to ratio language. The kit includes a model, three guided tasks, three independent tasks, two supplied reteaching routes, two later tasks, and an extension.

All files are free. No email address, account, payment, trial or subscription is required.

Who it is for

Grade 6 mathematics; check prerequisites and local curriculum fit.

Preparation

About 4–6 minutes, estimated.

Teaching time

Full lesson about 35–45 minutes; independent check about 4–6 minutes; selected follow-up about 8–12 minutes. These are planning estimates, not classroom-timed results.

Materials

Ordinary paper and pencil. Counters are optional; learners can sketch groups.

Version and review

v0.1.7. Independently AI checked and AI instructional audit completed. No human mathematics review or classroom-use trial has occurred.

Choose what to print

1. Teach the full lesson: give the separate Readiness page first, before showing the introduction. Then use Teach the Lesson pages 1–6. The first page explains “for every” and colon notation; later pages contain the model, guided work, and independent tasks.
2. Use a short check: print Check-only pages 1–3. These repeat the lesson's three independent tasks, so use one copy or the other.
3. Teach one follow-up: use Follow-up page 1 for complete matched groups after same-addend reasoning, or page 2 to explain a valid ratio when the known quantity is second.
4. Look again later: use Later Revisit pages 1–2 after another learning opportunity. The tasks are fresh, but they are not validated equivalent test forms.

Use the Start Here guide in HTML for the complete route and page selection. The representation glossary and optional local planning record are also available as HTML. Keep any student notes local; the site does not collect student responses.

Preview the student check

Read the three independent tasks as HTML. Answers and routing guidance are in the separate teacher guide.

Student files

• Readiness page — Printable PDF (24 KB)
• Readiness page — Editable Word file (37 KB)
• Readiness page — HTML text (3 KB)
• Full lesson — Printable PDF (51 KB)
• Full lesson — Editable Word file (38 KB)
• Full lesson — HTML text (8 KB)
• Independent check only — Printable PDF (29 KB)
• Independent check only — Editable Word file (37 KB)
• Independent check only — HTML text (4 KB)
• Two focused follow-up routes — Printable PDF (28 KB)
• Two focused follow-up routes — Editable Word file (37 KB)
• Two focused follow-up routes — HTML text (3 KB)
• Later revisit tasks — Printable PDF (26 KB)
• Later revisit tasks — Editable Word file (37 KB)
• Later revisit tasks — HTML text (3 KB)

Teacher files and shared tools

• Teacher guide and complete key — Printable PDF (86 KB)
• Teacher guide and complete key — Editable Word file (41 KB)
• Teacher guide and complete key — HTML text (17 KB)
• Start Here guide — Printable PDF (29 KB)
• Start Here guide — Editable Word file (37 KB)
• Start Here guide — HTML text (3 KB)
• Representation glossary — Printable PDF (31 KB)
• Representation glossary — Editable Word file (37 KB)
• Representation glossary — HTML text (3 KB)
• Optional local planning record — Printable PDF (26 KB)
• Optional local planning record — Editable Word file (37 KB)
• Optional local planning record — HTML text (3 KB)

Use the response cautiously

Look separately at quantity order, complete groups or a shared factor, arithmetic, units, and explanation. A blank or unclear response calls for clarification before a content reteach. A short correct response does not establish broad ratio mastery. The later tasks change context; one also asks learners to scale down.

This kit addresses part of the equivalent-ratio work in 6.RP.A.3a. It does not cover coordinate plotting or the complete Grade 6 ratios domain. Grade 6 is an authoring target, not a tested placement level.

Review and use

The v0.1.7 answer-bearing content passed a blind AI review, a separate AI instructional audit, and a fresh independent AI release review. The PDFs were rendered and inspected. Human mathematics review, teacher-use testing, assistive-technology testing, physical printing, and Microsoft Word or Google Docs rendering have not been completed. The PDF and DOCX contain separate student and teacher material; Word files have editable text and tables.

You may print, copy and adapt the resource for your planning and classroom use under our Terms of Use. Report a resource issue.