Start Here · Unit rates and fair comparisons
Equivalent ratios, unit rates and fair comparisons
A short U.S. Grade 6 supplement on equivalent ratios, unit rates and fair comparisons. Choose the starting point from the guidance below.
Choose the entry
Equivalent ratios introduces ratio language and matching groups. Open its Start Here guide for page selections. Find and interpret per one teaches unit-rate meaning. Compare unit rates teaches comparisons on a shared basis; begin there when students understand per one and the quantity labels.
Equivalent ratios classroom resource
Included prerequisite guide: Equivalent ratios — Start Here
Teach, check, respond, revisit
1. Begin with Equivalent ratios for prerequisite work, then Find and interpret per one, then Compare unit rates. Begin with comparisons only when students already understand per one and quantity units.
2. Give Readiness alone before any model, glossary or lesson. If prerequisite reasoning is unclear, use Equivalent ratios or Find and interpret per one as needed. Use the response to choose where to begin teaching.
3. Teach the model and guided page. Then give the separate Independent check file without the answer key. Lesson and check use different tasks.
4. Use the teacher guidance to choose one follow-up from the student’s response. Note why you chose it and give only that follow-up page.
5. Save the follow-up check, later revisit and application tasks until students are ready to try on their own. Their contexts and data differ, so the tasks may have different demands. If students have seen a task before, treat the response as practice.
6. Use the follow-up check after teaching, the later revisit after another learning opportunity, then the application task. Keep local notes on tasks already seen, tools and other support.
Stop within the boundary
Interpret per one, preserve direction and units, compare on the same basis, explain ties and missing information, and apply a stated constant rate. No percent, measurement conversion, coordinate graphing, complex fractions or complete proportionality course.
Free classroom use
Paper and pencil. Optional counters for equal groups. No device, purchase, account or email is needed.
The complete ZIP contains teacher answer keys and all student tasks. Keep it for teacher use. Give students only the pages you have chosen. HTML, PDF and editable Word files contain the same teaching text.
File and page selections
| File | Pages | When to use |
|---|---|---|
| Readiness | 1 | First; before any teaching aid |
| Teach the lesson | 1–2 | Model/Worked example then Guided task 1/Guided task 2 |
| Independent check | 1–2 | Independent task 1/Independent task 2; no visible model/key |
| Continue file | 1 | Continue task only after route choice |
| Clarify file | 1 | Clarify task only after route choice |
| Reteach file | 1 | Follow-up task 1 only after route choice |
| Extend file | 1 | Extension task only after route choice |
| Follow-up check | 1–2 | Follow-up check task 1/Follow-up check task 2 after selected move |
| Later revisit | 1–2 | Later task 1/Later task 2 after another opportunity |
| Apply in a new setting | 1 | Apply task after taught work |
| Teacher guide | 1–16 | Teacher-only: criteria, routes, all keys |
| Representation glossary | 1–2 | Teaching aid; after readiness |
| Local decision record | 1 | Teacher record kept locally |
Each unit-rate lesson has separate student files and a teacher guide. Shared guides are provided with the collection. Each file is available as PDF, editable Word and HTML. In each two-page check file, page 1 is the first task and page 2 is the second. Use the PDF for the page selections listed here; Word pagination may change with local software.
Teacher guide map
Page 1 quick start; page 2 printing and task selection and criteria; pages 3–6 routes (continue, clarify, reteach, extend); pages 7–14 all 15 task keys in task order (two per page, last one alone); page 15 supports/standards; page 16 classroom use and limits.
Local conditions
Record prior exposure, response mode, neutral reading assistance, calculators and other support. Brief checks guide a tentative teaching move; they do not establish stable ability, assessment equivalence, or classroom effectiveness.