Mathematics · Class 11

Active learning ideas

Statements (Propositions)

Let's begin our journey into mathematical reasoning by learning the special language mathematicians use. We will discover what makes a simple sentence powerful enough to be called a 'statement'.

• CBSE Learning Outcomes
• NCERT Class 11: Chapter 14 - Mathematical Reasoning

• 10–20 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 20 min · Small Groups

Statement or Not? Card Sort

Prepare cards with various sentences (commands, questions, opinions, facts, paradoxes). In small groups, students sort these cards into three piles: 'Is a Statement', 'Not a Statement', and 'Unsure/Debatable'.

Explain the criteria that a sentence must meet to be considered a mathematical statement.

Facilitation Tip

Encourage groups to present their most debated card to the class to spark a wider discussion.

What to look for

Use an exit ticket: provide three sentences (e.g., a question, an opinion, and a statement) and ask students to identify the statement and briefly explain why the other two are not.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Truth Value Hunt

Provide a list of valid mathematical statements. In pairs, students must determine the truth value (True or False) of each statement, providing a brief justification for their answer.

Analyse the sentence 'Mathematics is fun' and justify why it is not a valid mathematical statement.

Facilitation Tip

Include some statements whose truth value is not immediately obvious to encourage quick research or discussion.

What to look for

During class discussion, use targeted questioning. Ask 'Why is this not a statement?' or 'How could we change this question into a statement?' to check for understanding.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 10 min · Individual

Write and Swap

Each student writes three sentences: one that is a true statement, one that is a false statement, and one that is not a statement. They then swap with a partner who must correctly identify each one.

Compare the sentences 'The sum of two even numbers is even' and 'Close the door' in terms of logical reasoning.

Facilitation Tip

Circulate and check if students are correctly distinguishing between false statements and non-statements.

What to look for

A short quiz containing a mix of sentences where students must identify which are statements. For those that are statements, they must also assign a truth value (True/False/Cannot be determined).

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Start with clear, contrasting examples on the board: 'The capital of India is New Delhi' versus 'Where is the capital of India?'. Ask students which one can be labelled 'true'. Use this to build the definition of a statement: it must be declarative and have a clear true or false value. Reinforce with non-examples like commands ('Do your homework') and opinions ('Cricket is the best sport').

After this lesson, you will be able to look at any sentence and confidently decide if it meets the strict criteria to be a mathematical statement.

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Watch Out for These Misconceptions

• If a sentence is false, it cannot be a mathematical statement.

  A mathematical statement is any declarative sentence that has a definite truth value. This value can be either 'true' OR 'false'. For example, 'The Earth is flat' is a perfectly valid statement; its truth value is false.

• Any sentence containing numbers or variables is a mathematical statement.

  A sentence must be declarative. 'Is 5 greater than 2?' is a question, not a statement. Also, a sentence with a variable like 'x + 2 = 5' is an 'open sentence', not a statement, because its truth depends on the value of x.

• Opinions or subjective sentences can be statements if I believe them to be true.

  A statement's truth value must be objective and not depend on personal opinion. 'Mathematics is a difficult subject' is not a statement because its truth varies from person to person.

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Methods used in this brief

• Think-Pair-Share