Grade 4 · Mathematics
Quarter 2 · Week 4 · TEKS
This text lesson has a separate video watch page so search engines and learners can treat the written lesson and the video lesson as distinct resources.
This Grade 4 mathematics lesson focuses on comparing two fractions that have different numerators and different denominators. Students will learn to represent these comparisons using the symbols >, =, or <. The lesson also integrates addition and subtraction of fractions with equal denominators and evaluating sums and differences using benchmark fractions. The lesson is grounded in TEKS standards and designed to develop students' conceptual understanding through concrete models, pictorial representations, and number lines, preparing them to reason about fractions and communicate their mathematical thinking effectively.
Students should understand what fractions represent as parts of a whole, be familiar with numerator and denominator terms, and know how to identify fractions on a number line. They should also have experience with basic fraction addition and subtraction when denominators are the same.
A fraction represents a part of a whole and is written as numerator over denominator. When comparing fractions with different numerators and denominators, we cannot simply compare the numerators or denominators alone. Instead, we must find a way to compare their sizes relative to the same whole. For example, 2/3 and 3/4 have different numerators and denominators, so we need strategies to determine which is larger.
1. Using Common Denominators: Find equivalent fractions with the same denominator and then compare numerators. For example, to compare 2/3 and 3/4, convert to 8/12 and 9/12 respectively. Since 9/12 > 8/12, 3/4 > 2/3. 2. Using Common Numerators: Find equivalent fractions with the same numerator and compare denominators. For example, 2/3 and 2/5 can be compared by converting to 10/15 and 6/15. Since 10/15 > 6/15, 2/3 > 2/5. 3. Using Benchmark Fractions: Compare fractions to known benchmarks like 1/2 to estimate which is larger. 4. Using Visual Models: Use fraction strips, circles, or number lines to visually compare sizes.
Once students determine which fraction is larger or if they are equal, they use the symbols > (greater than), < (less than), or = (equal to) to represent the comparison. For example, if 3/4 is larger than 2/3, write 3/4 > 2/3.
Students also represent and solve addition and subtraction problems involving fractions with the same denominator. For example, 1/4 + 2/4 can be represented using fraction strips or number lines, showing the sum as 3/4. Understanding the denominator as the size of each part and adding or subtracting numerators helps students compute sums and differences.
Students learn to check if their answers to fraction addition or subtraction problems are reasonable by comparing results to benchmark fractions such as 0, 1/4, 1/2, 3/4, and 1. For example, if adding 1/4 + 1/4, the sum should be close to 1/2, which helps confirm the answer is reasonable.
Compare the fractions 3/5 and 2/3. Which is greater? Represent the comparison using >, =, or <.
To compare 3/5 and 2/3, find a common denominator. The least common denominator of 5 and 3 is 15. Convert each fraction: 3/5 = 9/15 (because 3 × 3 = 9 and 5 × 3 = 15) 2/3 = 10/15 (because 2 × 5 = 10 and 3 × 5 = 15) Now compare numerators: 9 < 10, so 9/15 < 10/15. Therefore, 3/5 < 2/3.
3/5 < 2/3
Add the fractions 1/4 and 2/4 using a pictorial model or number line.
Since the denominators are the same (4), add the numerators: 1 + 2 = 3. So, 1/4 + 2/4 = 3/4. Using a number line, start at 0, move 1/4 units, then move 2/4 units more, landing at 3/4.
1/4 + 2/4 = 3/4
Evaluate if the sum of 1/4 + 3/4 is reasonable by comparing it to benchmark fractions.
1/4 + 3/4 = 4/4, which equals 1 (the whole). Benchmark fractions 0, 1/4, 1/2, 3/4, and 1 help us see that the sum is exactly 1, which is reasonable since the parts add up to the whole.
The sum 1 is reasonable because it equals the whole, matching the benchmark fraction 1.
Begin by showing two different fractions with different numerators and denominators, such as 2/3 and 3/4, using fraction strips or drawings. Ask students which fraction they think is larger and why.
Students share their initial thoughts and guesses about which fraction is larger and explain their reasoning.
This activity activates prior knowledge about fractions and encourages students to think about comparing fractions that are not immediately obvious.
Provide students with fraction strips or circles and pairs of fractions with different numerators and denominators. Guide them to find equivalent fractions with common denominators or use visual models to compare the fractions.
Students use fraction strips or drawings to find common denominators or visually compare the fractions. They record their comparisons using >, =, or < symbols.
Hands-on exploration helps students concretely understand how to compare fractions by finding common denominators or using visual models.
Demonstrate step-by-step how to compare fractions with different numerators and denominators by finding common denominators and then comparing numerators. Show how to write the comparison using >, =, or <. Also, explain how to add and subtract fractions with equal denominators using pictorial models and number lines.
Students observe the teacher’s demonstration and take notes. They ask questions to clarify the process of comparing fractions and adding/subtracting fractions with equal denominators.
Explicit teaching clarifies the procedures and reasoning behind comparing fractions and performing operations with fractions having equal denominators.
Present real-world problems involving comparing fractions with different numerators and denominators and adding or subtracting fractions with equal denominators. Guide students to solve these problems using the strategies learned.
Students solve problems such as comparing the amount of juice in two different containers (fractions with different numerators and denominators) and adding fractions of a recipe ingredient (fractions with equal denominators). They explain their reasoning to peers or the teacher.
Applying skills to real-world contexts deepens understanding and shows the usefulness of comparing and operating with fractions.
Ask students to complete a short task comparing pairs of fractions with different numerators and denominators, representing the comparison with >, =, or <. Include addition and subtraction problems with equal denominators and a question evaluating the reasonableness of their answers using benchmark fractions.
Students complete the task independently and explain their reasoning either orally or in writing.
This assessment checks students’ mastery of comparing fractions, performing operations with fractions, and evaluating answers for reasonableness.
Students use fraction strips or drawings to find common denominators or visually compare the fractions. They record their comparisons using >, =, or < symbols.
Which fraction is greater: 1/3 or 1/4? Use >, =, or < to show your answer.
1/3 > 1/4 because one-third is larger than one-fourth.
Compare 2/5 and 3/7 by finding a common denominator and write the comparison using >, =, or <.
2/5 < 3/7 because 14/35 < 15/35.
Add 3/8 and 4/8 using a number line or pictorial model. What is the sum?
3/8 + 4/8 = 7/8.
Compare 5/6 and 4/5 by converting to equivalent fractions with a common denominator. Which is greater?
5/6 > 4/5 because 25/30 > 24/30.
If you add 1/4 and 2/4, then subtract 1/2, is the result reasonable? Use benchmark fractions to explain your answer.
Yes, the result is 1/4, which is a benchmark fraction, so it is reasonable.
Use fraction strips and visual models to support understanding. Provide step-by-step guided practice with common denominators. Use simpler fractions for initial comparisons.
Use visual aids and gestures to explain fraction parts. Provide vocabulary cards with fraction terms and symbols. Encourage peer discussion to practice mathematical language.
Challenge students with comparing improper fractions or mixed numbers. Introduce adding and subtracting fractions with unlike denominators. Have students create their own fraction comparison problems and explain their reasoning.
Encourage students to find examples of fractions at home, such as in cooking recipes or measuring objects, and compare them using >, =, or < symbols. They can bring examples or drawings to share with the class.
In this lesson, students learned how to compare two fractions with different numerators and denominators by finding common denominators, using visual models, and representing comparisons with the symbols >, =, or <. They also practiced adding and subtracting fractions with equal denominators using pictorial models and number lines. Finally, students evaluated the reasonableness of their answers using benchmark fractions like 0, 1/4, 1/2, 3/4, and 1. These skills build a strong foundation for understanding fractions and their relationships.
Use the exact standards alignment and retrieved-source provenance stored with this enrichment.