MTMentor Teaching

Selected Grade 7 mathematics

Test and Explain Proportional Relationships

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

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

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.