Multiplication & Division of Whole Numbers and Decimals

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Subject: Mathematics

Semester: 1

Period: 1

Week: 2

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School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 2
Lesson Duration: 45 minutes
Week & Period: Week 2, Period 1
Topic: Multiplication & Division of Whole Numbers and Decimals
Sub-topic: Solving with Whole Numbers and Decimals

Learning Objectives
By the end of the lesson, students should be able to:

1. Multiply and divide whole numbers accurately.
2. Multiply and divide decimals by whole numbers and decimals.
3. Solve real-life word problems involving money, prices, and measurements.

Previous Knowledge
Students already know multiplication tables and basic division.

Instructional Materials
Mathematics textbook, abacus, place value chart, money notes

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
The teacher gives oral multiplication drills: 7 × 8, 12 ÷ 3, etc.

B – Building Knowledge (Main Lesson Body)

Topic: Multiplication & Division of Whole Numbers and Decimals
Time: 25–30 minutes
🧠 Definitions and Explanations

1. Multiplication (Whole Numbers)
   Multiplication is repeated addition. When you multiply a whole number by another whole number, you are adding one number as many times as the other number says.
   • For example, 4×3=3+3+3+3=12
2. Long Division (Whole Numbers)
   Division is splitting a whole into equal parts. Long division is a method for dividing larger whole numbers (when the divisor has more than one digit or the dividend is large) by a one‑ or multi‑digit divisor, using steps of divide, multiply, subtract, bring down, repeat.
3. Decimals
   A decimal is a way of writing fractions in a base‑10 system, using a decimal point to separate whole parts from fractional parts (tenths, hundredths, thousandths, etc.).
4. Multiplying Decimals
   When multiplying decimals:
   • Treat them as whole numbers first (ignore decimal points), multiply.
   • Then count the total number of decimal places in the factors to place the decimal point in the product.
5. Dividing Decimals
   When dividing decimals by whole numbers or by decimals:
   • If divisor is a whole number, divide normally and place the decimal point properly in the quotient.
   • If divisor is decimal, shift the decimal in divisor to make it a whole number (multiply both divisor and dividend by the same power of 10), then divide.

 

More Examples

Whole Number Multiplication & Division

• 47×6=282
• 125×12=1,500
• Long Division: 345÷5=69
• Long Division: 1,234÷7=176 (if applicable, or decimal continuation)

Decimal Multiplication & Division

• 3.2×4.5=
  Multiply as 32×45=1,440
• Total decimal places: 1 + 1 = 2 → Product = 14.40 or 14.4
• 0.75×0.2=
  75×2=150,

decimal places = 2 + 1 = 3 → 0.150 or 0.15

• Decimal Division: 7.2÷3=2.4
• Division by Decimal: 4.8÷0.6. Multiply numerator & denominator by 10 → 48÷6=8.0→8

 

⚙️ Practical / Word Problem Examples

1. Books purchase
   A book costs L$245. If 6 books are bought, how much is paid?
   → 245×6=1,470
2. Dividing rope (whole parts)
   A rope is 25.6 m long. If divided equally among 4 children, how many meters does each get?
   → 25.6÷4=6.4
3. Decimal × decimal, money situation
   If 1.25 liters of oil cost L$320 per liter, how much is 0.75 liters?
   → 320×0.75=320×(75/100)=(320×75)÷100=24,000÷100=L$240 Division with remainder or decimal
   If you have L$500 and the price of one pen is L$39.75, how many pens can you buy, and what is the leftover (change)?
4. Measurement example
   A carpet is 3.5 m long and 2.2 m wide. What is the area? (Though this edges into area, but uses decimal multiplication) → 3.5×2.2=7.70  m²

🧍 Learners’ Activities (Expanded & Interactive)

1. Place‑Value Decimal Boards
   Students use place‑value charts to multiply decimals. E.g., multiply 2.34 × 5 by placing digits in columns, performing whole‐number multiplication, then placing decimal.
2. Money Word Problems in Pairs
   Given prices (with decimals), students compute totals, change, cost for multiple items. E.g., cost of 3.75 kg of rice at L$155.30 per kg.
3. Division Relay Game
   Groups take turns solving decimal division problems and writing steps on board: e.g., 8.4 ÷ 2.5, 6.72 ÷ 0.8, etc.
4. Real Measurement & Sharing Activity
   Use rope, string, or measuring tape: measure a length and divide equally among groups, express answer in decimals.
5. Error‑Spotting Activity
   Present worked‑out multiplication/division problems with mistakes in decimal placement or algorithm steps; students identify and correct.

 

✅ Assessment Checks (Formative)

• Teacher asks:

1. Explain the steps of multiplying 2.5 × 3.2, including how many decimal places will be in the answer.
2. What is 128 ÷ 4? Explain how you divide a multi‑digit whole number using long division.
3. Divide 6.4 ÷ 0.2 on the board. Walk through shifting the decimal.
4. Multiply a decimal by a whole number: 5.75 × 8.
5. Word problem: If 4 notebooks cost L$275.50 each, how much do 7 notebooks cost?

• Also have a mini‑quiz:

Problem	Student solves, shows working
a) 123 × 9
b) 1.2 × 3.4
c) 72 ÷ 8
d) 5.5 ÷ 0.5

 

📝 Notes (Expanded & Detailed)

• Multiplication and division are inverse operations:
  Knowing multiplication helps checking division, and vice versa (e.g. if a×b=c, then c÷b=a ).
• Decimals follow same rules as whole numbers, but correctness of decimal point placement is crucial. A misplace makes large errors.
• Place value understanding is key: tenths, hundredths, thousandths; moving decimals right/left when multiplying/dividing by 10, 100, etc.
• Emphasize estimating first: before computing, students estimate what the answer should roughly be (helps detect major errors).
• Use realistic contexts (money, measurements) so students see usefulness.

 

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews key steps for multiplication and division of decimals.

Evaluation Method (Expanded):
Exit slip/quiz: Solve 2.3 × 2, 15.6 ÷ 3, 7 × 245.

Assignment (Expanded):
Textbook practice questions on decimals and division.

Follow-up Activity:
Learners record daily prices of items and calculate costs using multiplication.

Differentiation / Inclusive Strategies
Support weaker learners with step-by-step guides.

Teacher’s Reflection (After Class)
• What worked well? ___________________________________________
• What needs improvement? ____________________________________
• Students’ engagement level: ☑ High ☑ Medium ☑ Low