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Subject: Mathematics
Semester: 1
Period: 3
Week: 16
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 16
Lesson Duration: 45 minutes
Week & Period: Week 16, Period 3
Topic: Fractions and Decimals
Sub-topic: Comparing, Ordering & Converting Fractions
Learning Objectives
By the end of the lesson, students should be able to:
- Compare fractions with same and different denominators
- Order fractions from least to greatest or vice versa
- Convert fractions to decimals
- Convert decimals to fractions
Previous Knowledge
Students already know place value of decimals and basic fraction operations
Instructional Materials
Mathematics textbook for Grade 5, base-10 models, number lines
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher writes 2/5 and 3/5 on the board. Asks which is greater and why.
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definitions and Explanations:
Comparing Fractions with Like Denominators: When two fractions have the same denominator, compare the numerators directly. The larger numerator indicates the larger fraction. Example: 4/9<5/9 because 5 > 4.
Comparing Fractions with Unlike Denominators: When denominators are different, use cross multiplication or find the Least Common Denominator (LCD) to make equivalent fractions.
– Cross Multiply: Multiply the numerator of the first fraction by the denominator of the second and vice versa. Compare the results.
Example: Compare 2/3 and 3/5
→ Cross multiply: 2×5=10, 3×3=9. Since 10 > 9, 2/3>3/5.
– LCD Method: Find a common denominator, convert both fractions, and compare numerators.
Example: 1/4 and 2/5
→ LCD of 4 and 5 = 20
→ 1/4=5/20, 2/5=8/20 → 2/5>1/4
Ordering Fractions: Arrange from least to greatest or greatest to least using LCD or cross multiplication.
Example: Order 3/8,1/2,5/6
→ Convert to common denominator or decimals: 3/8=0.375, 1/2=0.5, 5/6≈0.833
→ Ordered: 3/8<1/2<5/6
Converting Fractions to Decimals: Divide the numerator by the denominator.
Example: 3/4=3÷4=0.75, 2/5=0.4
Converting Decimals to Fractions: For terminating decimals, write the decimal as a fraction over 10, 100, 1000, etc., then simplify.
Example:
→ 0.6 = 6/10=3/5
→ 0.125 = 125/1000=1/8
Examples:
- Compare 4/9 and 5/9: Same denominator → 5 > 4 → 5/9>4/9
- Compare 2/3: Cross multiplication → 10 > 9 → 2/3>3/5
- Order 1/3,3/5,2/7:
Convert to decimals: 1/3=0.333, 3/5=0.6, 2/7≈0.286
→ Ordered: 2/7<1/3<3/5
- Convert ¾ to decimal → 0.75
- Convert 0.6 to fraction → 6/10=3/5
Learners’ Activities (Expanded):
Students work in pairs to compare fractions using cross multiplication cards. Each card shows two fractions; learners cross multiply and circle the larger result.
In groups, learners use number lines to arrange fractions from least to greatest. Each student places a fraction card in the correct spot along a drawn number line (0 to 1).
Pairs are given a set of mixed decimals and fractions, and they must convert all to one form (either decimals or fractions), then sort them in order.
Learners convert real-life decimal prices (like 0.25, 0.75) into fractions and explain how they did it.
Assessment Checks:
- Teacher writes on the board: Compare 3/5 and 4/7. Ask: “Which is greater?”
→ Solution: 3×7=21, 4×5=20
→ 3/5>4/7
- Order the following fractions: 2/3,4/6,3/4
→ Convert to decimals: 0.666,0.666,0.75
→ Order: 2/3=4/6<3/4
- Convert 2/5 to a decimal: 2÷5=0.4
- Convert 0.75 into a fraction: 75/100=3/4
- Compare: Which is larger: 5/8 or 7/12?
→ Cross multiply: 5×12=60, 7×8=56
→ 5/8>7/12
Notes (Expanded & Detailed):
Understanding how to compare, order, and convert fractions and decimals is essential for real-life decision-making such as budgeting, cooking, and interpreting data.
Fractions with the same denominator are straightforward—compare numerators directly.
Fractions with different denominators require more reasoning—cross multiplication is a quick and visual method, while the LCD method builds foundational skills for algebra.
Decimals and fractions are just different forms of the same value; being able to convert between them helps learners in higher math, measurement, and data interpretation.
Use of visual tools like number lines and base-10 blocks reinforces understanding, especially when comparing or converting.
Teachers should emphasize estimation and reasoning. For example, “Is 0.6 more or less than ½?” encourages learners to think beyond rules and understand value.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Fractions can be compared using denominators or cross multiplication. They can also be changed to decimals for easier comparison.
Evaluation Method (Expanded):
Exit slip/quiz:
Order: 1/2, 3/8, 5/6
Convert: 0.25 to fraction
Assignment (Expanded):
Convert 7/10 to decimal
Convert 0.125 to fraction
Order: 2/3, 3/4, 5/12
Follow-up Activity:
Learners create a chart comparing fractions and decimals from 0–1.
Differentiation / Inclusive Strategies
Use number lines for visual learners. Give advanced learners word problems involving comparisons in context.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low