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Selected Grade 7 mathematics

Test and Explain Proportional Relationships

Current teacher guidance: 2 November 2026. Student tasks retain their stated core editions. Use the current stage choices and matching guide below.

Changes in the current files · 2 November 2026
  • The teacher guide includes annotated fictional sound, partial and error responses, with concrete teaching actions and evidence to seek next.

Prepare the materials

Prepare this lesson or activity

Recommended selection edition 1.0.0. Original source files retain their displayed editions.

Use the matching guide to choose a response to the work you observe. Clarify access and task wording first; one response is not a diagnosis. Keep independent work, later tasks and answers aside until their intended use.

Current teacher guidance: 2 November 2026. Student tasks retain their stated core edition; use the matching current guide linked here. Earlier files are kept separately in the archive.

Audience / fit
Selected Grade 7 math
Teaching or planning target
Teach selected Grade 7 learners to test proportional relationships across tables, rules and graphs, respond to one-pair or starting-value shortcuts, then use different checks and transfer.
Essential prerequisites
Students can name paired quantities in order and interpret a requested unit rate. Use the linked ratio and per-one lessons first when needed; coordinates and model limits are taught in this kit.
Preparation
Read the Start Here selections; preparation time depends on the selected route.
Use time
Use the teacher guide to plan the selected route
Materials
Selected student pages, paper and pencil or an established response method, and the separate teacher guide.
What to print
Print the chosen activity. Follow the source or reveal instructions beside it.

Evidence to notice: Look across all displayed pairs, the starting value and the connections among table, rule and graph; one pair alone is limited evidence.

Preview the actual student page
Student page 1: Starting task
Actual student PDF page 1 of 2: Starting task. This page belongs to the named task; a teaching stage may intentionally show a model. Keep the matching teacher answers and reserved tasks separate.

Start with the selected task

Matching teacher guide and answers — keep separate: Matching teacher guide and answers · 13 pages.

Compare the observed response with the guide’s criteria. Clarify access and wording, then use its conditional directions to choose an activity below. Follow-up and later tasks are not interchangeable test forms.

Teaching stages, response practice and later checks

Starting tasks

Teaching and guided practice

Independent responses

Focused teaching responses

Follow-up checks

Later tasks — reserve for another occasion

Teacher files — separately

Archived page guidance and source files · Write a local teaching plan

Choose a teaching move from the response

Current print and editable package

Library package prepared 2 November 2026. Revised guides are marked with that date; other files retain their stated editions. Keep this package with the teacher. Read START-HERE, choose one stage, and retain teacher keys and checks for later use in their separate folders. Online browser versions are linked from the preparation pages.

Test and Explain Proportional Relationships · current ZIP · 1.3 MB

Choose from the response

Choose the next teaching move

Describe what the learner said, wrote or showed. Check access, wording, prerequisites and calculation before interpreting it. A single response is not a diagnosis. Record support and prior exposure; a helped or rehearsed task is practice.

Check ratio and per-one prerequisites first. Teach the three supplied model/practice files in order. Give only the chosen response task, then an unused follow-up after another opportunity. Later transfer has a different demand, not equivalent difficulty.

Start with the supplied materials

Observe, clarify and select one response

One pair is checked although another displayed pair contradicts it.

Teaching move: Test Every Displayed Pair: use the model and different practice.

Read the matching teacher directions; keep answers with the teacher.

Equal increases are treated as enough and a nonzero start is ignored.

Teaching move: Check the Starting Value: compare totals, ratios and the zero-input pair.

Read the matching teacher directions; keep answers with the teacher.

Quantity labels, coordinate order or the meaning of one are unclear.

Teaching move: Name the Quantities and Points; revisit per-one foundations if needed.

Read the matching teacher directions; keep answers with the teacher.

Table, rule and points agree but explanation is thin.

Teaching move: Connect Your Representations; explain the constant and domain.

Read the matching teacher directions; keep answers with the teacher.

A finite table or one point is treated as proof of every later value.

Teaching move: One Pair, Two Possible Rules: compare claims and state the missing condition.

Read the matching teacher directions; keep answers with the teacher.

Look again after teaching

After the supplied teaching and guided practice, give the selected independent task without its answers. Use its explanation to choose a response above.

After selected response teaching and another learning opportunity, use the unused follow-up task.

Return on a later occasion

Reserve these tasks until their intended use. They have different demands; do not treat them as equivalent tests or proof of broad mastery.

Return to preparation and all formats · Complete teacher guide and answers

Archive: Additional formats, earlier editions and teaching guidance

Earlier guidance and source files are retained as historical records. For classroom teaching and printing, use the current stage files and matching guides above. Older guidance, timing and layouts are superseded; some retained browser/Word files have limited writing space or sparse extra pages. Keep historical student files with their historical keys and do not mix editions.

Is this the right resource?

Audience / fit
Selected Grade 7 math
Teaching or planning target
Teach selected Grade 7 learners to test proportional relationships across tables, rules and graphs, respond to one-pair or starting-value shortcuts, then use different checks and transfer.
Essential prerequisites
Students can name paired quantities in order and interpret a requested unit rate. Use the linked ratio and per-one lessons first when needed; coordinates and model limits are taught in this kit.
Preparation
Read the Start Here selections; preparation time depends on the selected route.
Use time
Use the teacher guide to plan the selected route
Materials
Selected student pages, paper and pencil or an established response method, and the separate teacher guide.
What to print
Use the primary PDF choice below and its matching adult guide. Print only the phase/task being used; keep complete keys and later checks with the teacher.

Start teaching

Starting task: test a relationship · PDF (2 pages)

Read the starting and print guide · PDF (2 pages)

Complete teacher guide, answers and alternatives · PDF (10 pages)

Print only the student pages you plan to use. Keep teacher answers and later checks with the teacher until their intended use.

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.

Archive: Formats and all files

Earlier guidance and source files are retained as historical records. For classroom teaching and printing, use the current stage files and matching guides above. Older guidance, timing and layouts are superseded; some retained browser/Word files have limited writing space or sparse extra pages. Keep historical student files with their historical keys and do not mix editions.

Browse free resources · Collection and entry route

Teach selected Grade 7 learners to test proportional relationships across tables, rules and graphs, respond to one-pair or starting-value shortcuts, then use different checks and transfer.

Start from what is already secure

If ratio order or per-one meaning needs teaching, begin with Equivalent Ratios and Find and Interpret Per One. Their original checks and keys remain available. This collection changes the task from applying a supplied constant rate to deciding what a whole relationship and its evidence establish.

Teach the relationship rather than one calculation

A learner can find a unit rate correctly from one pair and still overstate what it proves. The supplied teaching compares every relevant positive-input pair, handles the zero pair separately, and connects those judgments to the rule, graph and quantities. A straight line with a starting amount can have equal increases without proportional totals. A curve may pass through the origin and still fail the common-multiplier test.

The model lessons provide actual tables, contrasting examples, teacher language, guided tasks and individual practice. They introduce coordinates and the meaning of the origin and one-unit point. Whole-number piece counts remain discrete; a time model can permit a continuous line segment. No division by zero is needed.

Choose teaching from the explanation

  • Only one pair is tested: use Test Every Displayed Pair to challenge a candidate rule with a different row.
  • Equal changes settle the claim: use Check the Starting Value to distinguish total output from output added.
  • Units or coordinates are unclear: use Name the Quantities and Points and return to per-one foundations if needed.
  • Representations agree but meaning is thin: use Connect Your Representations to explain the constant, one-unit point and domain.
  • A small record becomes an unrestricted prediction: use What a Model Establishes and One Pair Two Possible Rules to state what further condition is needed.

The teacher guide includes the models, task-specific answers, exact fractions or decimals, defensible alternatives and questions that investigate uncertainty before selecting teaching. Do not infer a lasting misconception from one missing response.

Teacher preparation and complete answers

Student files to select

Keep checks and transfer useful

Use Starting Task before showing its discussion or key. Teach the three main lessons, then give Independent Check alone. After a selected response lesson and another learning opportunity, use the different Follow-Up Check. Save Later Transfer for a later occasion: it changes to ribbon mass with a bag and square side versus area. The checks use different numerical data; they have not been calibrated to equal difficulty.

Record previous exposure, help, calculator or model use, response method and any target change on the local decision record. A shown or supported task is practice. A finite set of matching ratios permits a conditional prediction; it does not prove all unseen readings or behavior beyond the stated domain.

Complete classroom download

Archive: ZIP files · teacher preparation only

Earlier guidance and source files are retained as historical records. For classroom teaching and printing, use the current stage files and matching guides above. Older guidance, timing and layouts are superseded; some retained browser/Word files have limited writing space or sparse extra pages. Keep historical student files with their historical keys and do not mix editions.

This archive may combine teaching, later tasks and answers. Choose the individual resource and its stage-specific pages before making student handouts.

Download the complete classroom collection: fifteen document sets in PDF, editable Word and HTML, two labeled graph images and the unchanged per-one lesson and teacher guide. Thirty-four planned print pages cover the new teaching. Browse the individual files. The ZIP contains answers and unused later tasks, so give learners only the selected student pages.

Teacher starting guide for proportional relationship teaching
Teacher preparation preview. Later task answers remain separate.

Preparation and classroom use

Read Start Here and the teacher guide, select the student pages, and use ordinary paper and pencils. Read-aloud, enlarged text, extra processing time or an agreed oral, drawn or labeled-table explanation can preserve the reasoning target. Every graph has numerical descriptions and labeled tables. Quarter values can be placed between integer grid lines; exact fractions or decimals are accepted. Supplying a classification, ratio, rule or point changes the evidence collected.

This is a selected Grade 7 supplement after labeled equivalent-ratio and per-one reasoning. It references recognition and representation in CCSS 7.RP.A.2; it does not cover the full standard, grade or course. All numerical situations and example responses are original constructed teaching material. Classroom effectiveness has not been established.

No account, payment or student upload is needed. Print or adapt the original material under the Terms of Use; keep attribution, identify local changes and check Word print preview after editing. Report a resource issue.

Find the rate when it is not supplied

When quantity, coordinate and proportional reasoning are secure, continue to the selected Grade 8 Linear Relationships collection. It teaches change per input unit from unequal intervals, initial-value recovery, signed and zero cases, representations and rate versus output comparisons. Use its new entry task and record the added arithmetic demands; keep this collection’s later checks and exposure records for their original target.

Editable Word files

Archive: ZIP files · teacher preparation only

Earlier guidance and source files are retained as historical records. For classroom teaching and printing, use the current stage files and matching guides above. Older guidance, timing and layouts are superseded; some retained browser/Word files have limited writing space or sparse extra pages. Keep historical student files with their historical keys and do not mix editions.

This archive may combine teaching, later tasks and answers. Choose the individual resource and its stage-specific pages before making student handouts.

Per-one foundation guide (ZIP). Choose the editable files that match the task you will use. Use the full classroom collection for PDFs, HTML and other materials. The complete classroom collection includes these Word editions. Keep the bundles with the teacher and share only selected student tasks.

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Report a resource issue · Open an issue email

Do not include student names or identifiable work in an issue report. Page revision: 2 November 2026; classroom files retain their own editions.