Free Grade 6 mathematics teaching kit

Equivalent Ratios: Scale Both Quantities

Is this the right resource?

Audience / fit: Grade 6 math
Teaching or planning target: Use complete groups and a ratio table to explain equivalent ratios, challenge a same-addend error, and choose a focused follow-up.
Essential prerequisites: Count and name the two quantities in a ratio, preserve their order, and use equal groups or whole-number multiplication and division. The lesson introduces “for every” and colon notation.
Preparation: About 4–6 minutes, estimated.
Use 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.
What to print: Use the stage-specific student choices below and the matching teacher guide. Give independent, new-evidence and later-assessment pages only at their intended stage.

Start teaching

Model and guided practice · PDF (2 pages)

Read the teacher guide and answers · PDF (8 pages)

Start with the one-page readiness check if needed, then teach using the separate model and guided-practice pages. Give the independent check afterward. The original six-page lesson combines teaching, independent tasks and an extension; keep that complete reference packet with the teacher. The later-revisit tasks are separate.

Editable Word, browser copies and other files

Print and adapt for your own planning and classroom use; printed copies may be shared within your classroom or school team, provided the source is not sold. Keep attribution and resource-specific notices. For redistribution and third-party materials, read the Terms of Use. Recommend this resource using its page link.

Choose a stage and format

Give only the stage being used. Keep later tasks and all teacher keys with the teacher until needed.

Formats and all files

Complete reference files may include teaching, independent tasks, later evidence or teacher answers. Keep them with the teacher; use the separate stage selections above for handouts.

Browse free resources

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.
What’s included: Printable student materials and editable files are supplied with separate teacher guidance.

Choose what to print

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.
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.
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.
Look again later: use Later Revisit pages 1–2 after another learning opportunity. The tasks are fresh, but compare the reasoning students show in each context.

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.

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. Check the prerequisites for your class.

About the materials

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

Use familiar practice beyond the lesson

Keep this lesson’s target when preparing familiar practice beyond the lesson. Prepare a substitute handoff with the exact student pages and return instructions. Plan neutral directions and representation supports that preserve the mathematics. Offer a brief family conversation about practice already taught.

Keep teacher keys and later checks with the teacher. Previously shown or helped work is practice; record the support before interpreting a response.

Choose a next move

Choose a route that fits the response and your teaching goal. These are links to materials already supplied, not a prescribed sequence or a placement decision.

Objective-to-Assessment Alignment Pack — Check that the mathematics task and criterion require both quantities to change together; use the blank planner.
Check for Understanding and Choose the Next Step — Record observed ratio reasoning using the equivalent-ratio lesson’s criteria and next tasks. The planning tool’s worked inference example is not a mathematics key.
Find and Interpret “Per One” — When labeled equivalent-ratio reasoning is secure, interpret a requested per-one rate and its units.
Unit Rates and Fair Comparisons — Choose the entry point in the connected equivalent-ratio and unit-rate collection.
Substitute Handoff and Independent-Work Pack — Prepare familiar ratio or rate practice with complete student pages, established routines and a return route.
Clear Directions and Language-Support Pack — Plan neutral directions and representations while keeping quantity labels, rate direction and explanation visible.
Practical Family-Communication Templates — Invite a short conversation about familiar mathematics; keep later classroom checks and teacher keys at school.

Save follow-up tasks until students are ready to try them on their own. Once a task has been shown, modeled or practiced, use it for practice. Keep answer keys with the teacher and use each resource’s own learning target and criteria.

When quantity meanings need first teaching

Explain Equal Groups, Comparisons and Shares — Before paired ratios, teach one-quantity group roles and distinguish copies from an additive difference when those meanings are unclear.

Move from a supplied rate to testing a relationship

When paired-ratio and per-one reasoning are secure, the selected Grade 7 Proportional Relationships collection teaches multi-row tests, tables, rules, graphs, starting amounts and model limits. It supplies actual response lessons, different independent checks, transfer and complete keys. This adds a new reasoning target; keep this resource’s own tasks and exposure records for their original purpose.

Editable Word files

Choose the editable files for this resource and keep teacher guidance separate.