Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
4th Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of number, fraction, and decimal concepts.
3rd Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of number and fraction concepts.
Learning Targets
Explain that when comparing fractions they must refer to the same whole.
Compare fractions using benchmarks (7/8 > 3/10).
Compare fractions by reasoning about their size and relationship (7/8 > 3/10)
Compare fractions by reasoning about their size when there are the same number of pieces (common numerator, 3/6 > 3/10).
Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).
Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).
Create equivalent fractions to compare using common denominators (if needed, 3rd quarter)).
Record comparison using >, <, or =.
Explain how fractions are compared.
About the Math
There are several ways to compare fractions. Before moving to the procedure of finding a common denominator, fraction sense, and reasoning should be the focus.
Explain that when comparing fractions they must refer to the same whole.
Students must demonstrate an understanding that comparison of fractions is grounded in the same whole be referred to in the comparison. Students should have opportunities to explore this. They can use real-world contexts such as the comparison of half of small pizza and half of a large pizza.
Compare fractions using benchmarks (7/8 > 3/10).
One way of comparing fractions is to look at benchmark fractions. Benchmark fractions are fractions that are easy to visualize such as ¼, ½ , ¾. So you look at fractions in relation to ½. When comparing the two fractions 7/9 and 3/8, students should think 7/9 is greater than ½ and 3/8 is less than ½ so 7/9 is greater than 3/8.
Compare fractions by reasoning about their size and relationship (7/8 > 3/10)
Sometimes we can compare fractions by their benchmarks. Other times we can compare fractions, with unlike denominators, by thinking about their distance from 0 or 1 or other familiar fractions. 7/8 is almost one whole. 3/10 is between 0 and 1/2. 7/8 is greater than 3/10. Note that this is similar to benchmark comparisons and that students do not have to differentiate between the strategies.
Compare fractions by reasoning about their size when there is the same number of pieces (common numerator, 3/5 > 3/10).
When comparing fractions with the same numerators, such as 3/5 and 3/10, it should be obvious to the students which is greater because they have the same number of parts. Knowing this, they can think about the relative size of denominators. Here, fifths are larger than tenths so three of them is larger than three tenths.
Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).
We can think about the number of missing pieces to compare fractions. 4/5 and 9/10 are both missing one piece. Fifths are greater than tenths. Therefore, 9/10 is close to one whole than 4/5. 9/10 is greater than 4/5.
Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).
This strategy is the same as common denominators. Simply, we can compare two fractions with the same sized pieces by counting the number of pieces.
Create equivalent fractions to compare using common denominators (if needed, 3rd quarter).
Students should be able to create equivalent fractions to compare fractions with unlike denominators. This should occur have other strategies and understandings have been developed.
Record comparison using >, <, or =.
Fractions can be compared using the same symbols we use to compare whole numbers.
Explain how fractions are compared.
Students should understand the fundamental concepts of what fractions are and how they are related. Students should understand that counting pieces or that the number of parts in the whole do not determine which fraction is greater.
Essential vocabulary for this standard includes numerator, denominator, fraction, greater than, less than, and equal.
Math in Minutes
The video links below demonstrate the way your student will learn specific concepts.
These tasks can be used with small group or whole group instruction.
Distribute fraction manipulatives to each student. Write the following fractions on the board: 1/6, 1/3, 3/4. Ask students to use their materials to represent the three fractions. The discussion should then be about how these fractions compare. Which is the largest and why? Could you order the fractions least to greatest? Repeat with other fractions. This is an introduction and provides students an opportunity to see the physical size of the fraction pieces and why one fraction is larger than another even when the digit is opposite, for example 1/6 is less than 1/3 even though 6 is bigger than 3.
Distribute fraction manipulatives to each student and ask them to build 3/8 and 5/8. Discuss which is greater/least and why. Guide the conversation to same size parts (denominator) but one fraction has more of those parts. Ask students to build 3/8 and 3/4. Discuss which is greater/least and why. Guide the conversation to same number of parts under consideration (numerator) but different sized parts and what that means. (fourths are larger than eighths so if I have the same number of each, 3/4 will be larger) The goal is for students to reason about fractions using these two strategies without the manipulatives, but you start here with them and then remove them.
Write three fractions between ½ and 1 whole.
With a partner, list five fractions between 0 and ⅘?
If two fractions have the same numerator, how will this help you compare the fractions? Explain.
How do benchmark fractions help you compare fractions?
If you were hungry and you offered your friend a choice between ⅗ of a cookie and 7/10 of a cookie, which fraction of a cookie would you hope she took? Explain.
What strategies could you use to compare ¾ and 2/12?
Think of a real-world example when ¾ would be smaller than ½. (Students should think of examples where the whole is different. For example, ¾ of a cupcake is less than ½ of an entire cake.
Two students were asked to write a sentence using the fractions ⅔ and 2/6. Damian wrote “The numerators of ⅔ and 2/6 are equal, so the fractions are equal.” Devon wrote “2/6 is greater than ⅔ because 6 is greater than 3.” Do you agree with Damian, Devon, or neither? Explain why.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
3-5
Zero, One-Half, or Half, Activity 5.7, Page 145 Close Fractions, Activity 5.8, Page 145 About How Much, Activity 5.9, Page 145 Ordering Unit Fractions, Activity 5.10, Page 146 Choose, Explain, Test, Activity 5.11, Page 148 Line 'Em Up, Activity 5.12, Page 148
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
