Teacher's Guide

Learning objectives

• Explain Premise and Counterexample in the context of this lesson.
• Use the worked example to answer the three practice questions with supporting reasoning.
• Complete the activity, evaluate its result, and identify one limitation or possible improvement.

Prerequisites: Basic reading and arithmetic; no previous subject study is assumed.

Suggested time: Three to five 45-minute sessions, including activity development and review. Language units need brief repeated spoken practice between sessions.

Teaching sequence

1. Introduce: Present the title as a question or problem. Ask learners what they notice and record two initial ideas without treating them as established facts.
2. Explain: Read the concept section and teach the two vocabulary items. Ask learners to paraphrase the distinction between them using a concrete example.
3. Model: Work through the example. Identify given information, assumptions, and the reason for the result or interpretation. Use a teacher's spoken model for language pronunciation.
4. Apply: Complete the activity individually or in pairs. Require a draft, a check against the task, and a brief revision. Discuss why different justified responses may be acceptable.
5. Retrieve and evaluate: Answer practice and vocabulary questions independently; use the answer key for feedback. Finish with the reflection and an activity rubric.

Assessment and differentiation

The companion CSV contains five retrieval entries: two vocabulary questions and three practice questions. Award one point per accurate answer, accepting equivalent wording that preserves the meaning. Language answers may be oral or written according to the goal. Revisit missed concepts rather than using the score as the only measure of learning.

Assess the activity separately with four criteria, each scored 0-2: correct use of lesson concepts; clear evidence or reasoning; completion of the task requirements; and a useful revision or acknowledged limitation. A 0 indicates missing or unsupported work, 1 indicates partial achievement, and 2 indicates clear achievement. Accept multiple designs, interpretations, and decisions when their reasons meet the criteria.

Support learners with a word bank, annotated example, smaller first step, or partner rehearsal. Extend by changing one assumption or constraint and asking how the result would change. Use invented personal details in financial and social tasks. Optional school character discussion can connect honesty, respect, cooperation, and stewardship to the activity; assess the subject knowledge and reasoning separately.

Student Worksheet

Concept and helping material

An argument connects premises to a conclusion. A premise is a supporting statement; a conclusion is what the argument seeks to establish. A counterexample can challenge a universal claim. One example consistent with a universal claim does not prove that every case fits.

Vocabulary

• Premise: A statement used to support a conclusion.
• Counterexample: A case that contradicts a general claim.

Worked example

The claim all useful objects are expensive is challenged by a useful inexpensive pencil. The pencil need not show that expensive objects are never useful.

Investigation or design task

Write a universal claim about learning tools, identify its premise and conclusion, and test it with a counterexample. Revise the claim to fit the evidence.

Record your work: State the goal; show your drawing, dialogue, calculation, data, or argument; explain one choice; and describe one check or revision. Identify a limitation rather than claiming your work proves more than it does.

Practice

1. What is enough to refute all useful objects are expensive?
2. Do three expensive useful objects prove the universal claim?
3. Does the counterexample show expensive objects cannot be useful?

Vocabulary retrieval

1. Define Premise.
2. Define Counterexample.

Reflection

Choose one answer or activity decision. Explain the evidence, calculation, language pattern, or reasoning that supports it. Describe one change of context or assumption that could change your conclusion.

Answer Key

1. One useful object that is not expensive.
2. No.
3. No. It only challenges the all claim.

Vocabulary answers are the definitions above and appear in the CSV. Activity and reflection responses vary; use the teacher rubric and require specific reasoning tied to the task. A different supported interpretation is acceptable where the question allows it.

Source Reference

Original teaching material. No directly matching, age-appropriate lesson reference was identified in the supplied G7-12 PDF collection. No external research is claimed.

Companion question CSV | Grade guide