Mathematics · Class 7

Active learning ideas

Multiplying and Dividing Powers with the Same Base

Get ready to unlock a mathematical superpower! We will learn the secret rules for multiplying and dividing powers that make handling very large numbers incredibly easy.

• CBSE Learning Outcomes
• NCERT Class 7: Chapter 13 - Exponents and Powers

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

Activity 01

• Inquiry-Based Learning
• 15 min · Pairs

Exponent Card Match

Create two sets of cards: one with expressions like 'x^5 * x^3' and the other with their simplified forms like 'x^8'. Students work in pairs to match the expression card with the correct simplified card.

Explain the rule for multiplying two powers with the same base, using the example of 3^2 * 3^4.

Facilitation Tip

Ask students to explain to their partner why their chosen pair is a correct match.

What to look for

Exit Slip: Ask students to simplify two expressions, one for multiplication (e.g., p^9 * p^2) and one for division (e.g., 8^11 / 8^5), before they leave the classroom.

• Apply
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 02

• Inquiry-Based Learning
• 20 min · Individual

Rule Discovery Worksheet

Provide a worksheet with the first column showing an expression (e.g., 2^4 * 2^3), the second asking for its expanded form, and the third for the final answer in exponential form. After a few examples, students will see the pattern and discover the rule themselves.

Justify why a^m / a^n = a^(m-n) by expanding the terms.

Facilitation Tip

Circulate and ask guiding questions like 'What is the connection between the exponents in the first column and the exponent in the last column?'

What to look for

Whiteboard Check: Give a problem to the class. Have every student solve it on a small whiteboard or in their notebook and show you their answer at the same time for a quick check of understanding.

• Apply
• Analyze
• Evaluate
• Self-Management
• Social Awareness

Activity 03

• Inquiry-Based Learning
• 10 min · Whole Class

Human Exponents

Assign a base number to the whole class, for example, '5'. Call up 3 students to represent 5^3 and another 2 students for 5^2. Ask them to combine to show 5^3 * 5^2, demonstrating that there are now 5 students, representing 5^5.

Analyse the expression 5^7 / 5^3 and simplify it using the law of exponents.

Facilitation Tip

This kinesthetic activity helps make the abstract concept of adding exponents very concrete.

What to look for

A short quiz section with a mix of numerical and variable-based problems that require simplification using the laws of exponents for multiplication and division.

• Apply
• Analyze
• Evaluate
• Self-Management
• Social Awareness

A few notes on teaching this unit

Begin by reinforcing the meaning of exponents through expansion. For 3^2 * 3^4, write out (3*3) * (3*3*3*3) and ask students to count the total number of 3s. Let them discover the pattern of adding exponents. Use the same discovery approach for division, showing cancellation of terms in a fraction to establish the subtraction rule.

After this lesson, students will be able to look at a problem like (7^10 * 7^5) / 7^3 and simplify it in seconds, without needing a calculator.

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Watch Out for These Misconceptions

• When multiplying powers, the exponents should be multiplied. For instance, 4^2 * 4^3 = 4^6.

  The rule is to add the exponents. Expanding it shows why: (4*4) * (4*4*4) gives us a total of five 4s being multiplied, so the answer is 4^(2+3) = 4^5.

• The base numbers should also be multiplied. For example, 5^2 * 5^4 = 25^6.

  The base remains the same because it is the number being repeatedly multiplied. We are only changing the count of how many times it is multiplied, which is what the exponent tells us.

• When dividing powers, the exponents should be divided. For example, 10^8 / 10^2 = 10^4.

  Division involves cancelling common factors. We start with eight 10s on top and two 10s at the bottom. After cancelling, we are left with 8-2=6 tens on top. So, the rule is to subtract the exponents: 10^(8-2) = 10^6.

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Methods used in this brief

• Inquiry-Based Learning