Lesson Plan
Comparing Commanders
Students will be able to compare and order fractions with different denominators by finding common denominators or using benchmarks.
Mastering fraction comparison is crucial for solving real-world problems involving quantities and laying a strong foundation for future math concepts.
Audience
4th Grade Small Groups
Time
45 minutes
Approach
Interactive instruction, card game, and practice worksheet.
Materials
Whiteboard or projector, Order Up Fractions Slide Deck, Fraction War Card Deck, Greater Than Less Than Practice Worksheet, Pencils, and Scratch paper
Prep
Teacher Preparation
15 minutes
- Review the Order Up Fractions Slide Deck and discussion points.
- Print and cut out the Fraction War Card Deck (one set per small group).
- Print copies of the Greater Than Less Than Practice Worksheet (one per student).
- Ensure whiteboard or projector is ready for display.
- Review all generated materials as needed.
Step 1
Introduction: Fraction Face-Off (5 minutes)
5 minutes
- Display the first slide of the Order Up Fractions Slide Deck.
- Begin by asking students: "When do we use fractions in our daily lives?" (e.g., cooking, sharing food, measuring).
- Introduce the concept of comparing fractions: "Today, we're going to become 'Comparing Commanders' and learn how to determine which fraction is bigger or smaller, even when they look tricky!"
Step 2
Direct Instruction: Mastering Comparison (15 minutes)
15 minutes
- Use the Order Up Fractions Slide Deck to guide the instruction.
- Slide 2: Same Numerator, Different Denominator. Explain that when numerators are the same, the fraction with the smaller denominator is larger (think of pizza slices). Provide examples.
- Slide 3: Same Denominator, Different Numerator. Explain that when denominators are the same, the fraction with the larger numerator is larger. Provide examples.
- Slide 4: Different Numerators and Denominators. Introduce strategies:
- Finding a Common Denominator: Demonstrate how to find a common denominator and create equivalent fractions.
- Using Benchmarks (0, 1/2, 1): Show how to compare fractions to 0, 1/2, and 1 to quickly determine relative size.
- Engage students with questions throughout: "Can anyone give me an example of two fractions with the same numerator? Which one is bigger?"
Step 3
Activity: Fraction War (15 minutes)
15 minutes
- Distribute one Fraction War Card Deck to each small group.
- Explain the rules of Fraction War: Students play in pairs. They each draw a card, compare their fractions using the strategies learned, and the student with the larger fraction wins both cards. In case of a tie, they draw again (War!).
- Circulate among groups, providing support and asking guiding questions: "How did you decide which fraction was larger? What strategy did you use?"
Step 4
Independent Practice: Greater Than, Less Than (8 minutes)
8 minutes
- Distribute the Greater Than Less Than Practice Worksheet to each student.
- Instruct students to complete the worksheet independently, applying the strategies they've learned.
- Provide individual assistance as needed.
Step 5
Conclusion: Review and Share (2 minutes)
2 minutes
- Briefly review a few problems from the Greater Than Less Than Practice Worksheet as a group.
- Ask students to share one new thing they learned or one strategy they found most helpful.
- Conclude by reiterating the importance of comparing fractions in everyday life.
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Slide Deck
Order Up Fractions!
Become a Comparing Commander!
Get ready to master comparing and ordering fractions!
Greet students and introduce the exciting journey of comparing fractions. Emphasize the real-world relevance.
Why Compare Fractions?
- Cooking: Which recipe uses more flour: 1/2 cup or 1/4 cup?
- Sharing: Is it fair if you get 1/3 of the pizza and your friend gets 1/2?
- Building: Which plank is longer: 3/4 foot or 7/8 foot?
It's all about knowing which amount is bigger or smaller!
Ask students to share their initial thoughts on where they encounter fractions. Connect it to the lesson's goal.
Same Numerator, Different Denominator
The Rule:
When the numerators are the same, the fraction with the smaller denominator is the larger fraction.
Think: Pizza Slices!
1/2 of a pizza is more than 1/4 of a pizza.
Examples:
- 1/3 vs. 1/5 (1/3 is larger)
- 2/7 vs. 2/9 (2/7 is larger)
Explain the rule clearly. Use visual aids or draw on the board if possible. Ask for student examples.
Same Denominator, Different Numerator
The Rule:
When the denominators are the same, the fraction with the larger numerator is the larger fraction.
Think: Counting Parts!
3/4 of a cake is more than 1/4 of a cake.
Examples:
- 3/8 vs. 5/8 (5/8 is larger)
- 2/6 vs. 1/6 (2/6 is larger)
Explain this rule, perhaps by relating it to counting. Provide more examples and check for understanding.
Different Denominators & Numerators
Strategy 1: Find a Common Denominator
- Example: Compare 1/3 and 2/5
- Find the least common multiple of 3 and 5 (which is 15).
- Convert: 1/3 = 5/15, and 2/5 = 6/15
- Now compare: 5/15 vs. 6/15 (6/15 is larger, so 2/5 is larger)
Strategy 2: Use Benchmarks (0, 1/2, 1)
- Example: Compare 3/8 and 4/5
- 3/8 is less than 1/2 (because 4/8 would be 1/2)
- 4/5 is greater than 1/2 (because 2.5/5 would be 1/2)
- So, 4/5 is larger than 3/8!
This is the trickiest part. Walk through both strategies. Emphasize that finding a common denominator makes them 'speak the same language'. Benchmarks are a quicker mental math tool.
Time to Practice!
Let's Compare:
- Which is greater: 2/3 or 3/4?
- Which is smaller: 1/6 or 2/5?
- Order from least to greatest: 1/2, 1/3, 3/4
Pose these questions and encourage students to explain their reasoning using the strategies taught. Facilitate a brief discussion.
Fraction War!
Get Ready to Play!
- You will play in pairs.
- Each of you will draw a fraction card.
- Compare your fractions!
- The player with the LARGER fraction wins both cards.
- If it's a tie, declare "WAR!" and draw again.
Good luck, Comparing Commanders!
Introduce the game! Get students excited about applying their new skills in a fun way.
Game
Fraction War Card Deck
Objective: Practice comparing fractions with different numerators and denominators.
Instructions:
- Print out this document and cut along the lines to create individual fraction cards.
- You will need one deck per pair or small group of students.
Fraction Cards
Cut out each rectangle below to create your cards.
| Card 1 | Card 2 | Card 3 | Card 4 | Card 5 |
|---|---|---|---|---|
| 1/2 | 1/3 | 1/4 | 2/3 | 3/4 |
| 1/5 | 2/5 | 3/5 | 4/5 | 1/6 |
| 5/6 | 1/8 | 3/8 | 5/8 | 7/8 |
| 2/7 | 3/7 | 4/7 | 5/7 | 1/9 |
| 2/9 | 4/9 | 5/9 | 7/9 | 8/9 |
| 1/10 | 3/10 | 7/10 | 9/10 | 1/12 |
| 5/12 | 7/12 | 11/12 | 2/3 | 4/5 |
| 1/2 | 3/4 | 2/5 | 5/6 | 1/3 |
| 3/8 | 7/10 | 1/4 | 2/9 | 5/12 |
| 1/7 | 2/11 | 3/10 | 4/6 | 6/7 |
Worksheet
Greater Than, Less Than, or Equal To?
Instructions: Compare the fractions below. Write > (greater than), < (less than), or = (equal to) in the circle to make each statement true. Show your work or explain your reasoning for each comparison.
-
1/2
3/8Show your work or explain:
-
2/3
5/6Show your work or explain:
-
1/4
2/8Show your work or explain:
-
4/5
7/10Show your work or explain:
-
3/7
1/3Show your work or explain:
-
5/9
2/4Show your work or explain:
-
1/6
2/12Show your work or explain:
-
3/5
6/10Show your work or explain:
Challenge Question!
Order the following fractions from least to greatest: 2/3, 1/2, 5/6, 3/4