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Subject: Mathematics
Semester: 1
Period: 3
Week: 15
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 15
Lesson Duration: 45 minutes
Week & Period: Week 15, Period 3
Topic: Fractions
Sub-topic: Multiplying & Dividing Fractions and Mixed Numbers
Learning Objectives
By the end of the lesson, students should be able to:
- Multiply fractions by fractions and whole numbers
- Multiply mixed numbers
- Divide fractions using reciprocal method
- Divide mixed numbers
Previous Knowledge
Students already know addition and subtraction of fractions
Instructional Materials
Mathematics textbook for Grade 5
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: “What is 2 × 3/4?” Learners try and share their thinking.
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition:
Multiplying fractions means multiplying the numerators (top numbers) together and then the denominators (bottom numbers) together.
Formula: a/b×c/d=(a×c)/(b×d)
Multiplying a whole number by a fraction: Write the whole number as a fraction over 1, then multiply normally.
Multiplying mixed numbers: Convert each mixed number into an improper fraction before multiplying.
Dividing fractions means multiplying the first fraction by the reciprocal (flip) of the second fraction.
Formula: a/b÷c/d=a/b×d/c
Dividing mixed numbers: Convert all mixed numbers to improper fractions, then multiply by the reciprocal of the divisor.
Examples:
1. 2/5×3/4=6/20=3/102.
- 3/8×2=3/8×2/1=6/8=3/4
3. 1 1/2×2/3=3/2×2/3=6/6=1
4. 5/6÷2/3=5/6×3/2=15/12=1 1/4
5. 2 1/3÷3/5=7/3÷3/5=7/3×5/3=35/9=3 8/9
Learners’ Activities (Expanded):
Learners use fraction tiles or strips to visually represent multiplication. For example, using three 1/4 tiles and repeating them 2 times to represent 3/4×2.
They draw arrays or rectangles on graph paper to show fractional parts shaded for multiplication (e.g., 2 rows of 3/5 each).
Pairs are given task cards where they flip the second fraction in a division problem and multiply. They write each step clearly and simplify.
Students work in groups to convert mixed numbers to improper fractions, multiply/divide, and convert back to mixed numbers.
An interactive game ("Flip & Multiply") is played where one student gives a division question and another must respond with the reciprocal and final answer.
Assessment Checks:
The teacher poses oral and board questions such as:
– "What is 3/7×4/5?" → Answer: 12/35
– "Solve: 2/3÷3/4" → Flip second: 2/3×4/3=8/9
– "Convert and multiply: 1 2/3×2 1/2" → 5/3×5/2=25/6=4 1/6
Quick written quiz:
1. Multiply: 5/8×2/3
2. Divide: 7/10÷2/5
3. Word Problem: If a container holds 2/3 of a liter and you pour 3/4 of it, how much did you pour? → 2/3×3/4=6/12=1/2
Notes (Expanded & Detailed):
Multiplying fractions is one of the simplest operations—learners must remember that they do not need to find common denominators. Simply multiply the tops (numerators), then the bottoms (denominators), and simplify.
Mixed numbers must always be converted to improper fractions before multiplying or dividing, or else the operation will be incorrect.
For division, the reciprocal rule is crucial: the second fraction is flipped and the operation changes to multiplication.
This is often summarized as “Keep, Change, Flip”:
– Keep the first fraction
– Change division to multiplication
– Flip the second fraction (find reciprocal)
This topic is foundational for real-life problem solving involving parts of a whole—such as cooking (e.g., using half of 2/3 cup), measuring, or splitting materials.
Mastering this also prepares students for working with ratios, algebraic fractions, and proportional reasoning in higher math.
Students should also be encouraged to check their answers by estimating or using visual aids (e.g., asking: “Is your answer greater or smaller than 1?”).C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Multiplication is numerator × numerator, denominator × denominator. Division is multiplying by reciprocal.
Evaluation Method (Expanded):
Exit slip/quiz:
Multiply: 2/3 × 5/9
Divide: 7/8 ÷ 1/4
Assignment (Expanded):
Solve:
3/5 × 2/7
2 1/4 × 3/8
4/9 ÷ 2/3
Follow-up Activity:
Learners create word problems for fraction multiplication and division.
Differentiation / Inclusive Strategies
Provide manipulatives for struggling learners. Enrich advanced learners with larger mixed numbers.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low