Getting Started 
Misconception/Error The student does not have an effective strategy for using benchmark fractions to locate and compare the fractions. 
Examples of Student Work at this Level The student does not anchor the number line with zero and makes significant errors when placing Â and Â on the number line.
The student disregards the numerators in the fractions and places the fractions on the number line based on the size of the denominator.

Questions Eliciting Thinking How many parts should be in the whole if the fraction is ? What does the denominator tell you? What does the numerator tell you?
What fraction with a denominator of six is equivalent to ? So if Â is equivalent to , where would Â be placed on the number line? Would Â be placed before or after Â on the number line?
What fraction with a denominator of eight is equivalent to ? So if Â is equivalent to , where would Â be placed on the number line? Would Â be placed before or after Â on the number line? 
Instructional Implications Provide direct instruction on the meaning of fractions (between zero and one). Explicitly describe the meaning of the numerator and the denominator in fractions. Use number lines as a context for understanding fractions and their relative sizes.
Use fraction tiles to demonstrate for the student that the larger the denominator, the smaller the part of the whole. Line up the tiles representing , , , , , , and . Ask the student, â€śHow does the size of the part change as the denominator increases?â€ť
Consider using the MFAS task Comparing Fractions (3.NF.1.3).
Guide the student to scale a number line and place fractions on a number line. Once the student is able to correctly scale a number line, have the student use the number line to compare fractions. 
Moving Forward 
Misconception/Error The student attempts to use the number line to locate and compare the fractions, but makes errors and does not correct despite prompting. 
Examples of Student Work at this Level The student attempts to scale the number line, but makes significant errors and incorrectly places Â and Â on the number line.
The student draws an additional number line and places each fraction on a separate number line but does not consider Â when placing one or both of the fractions.
The student uses a strategy other than benchmark fractions (e.g., common denominators or visual fraction model) to compare but is unable to justify his or her comparison by using benchmark fractions.
The student attempts to use benchmark fractions but makes mistakes when locating the fractions on the number line.
The student crossmultiplies and correctly determines that Â is greater than . However, the student is not able to say that by crossmultiplying he or she is making common denominators, which is why the â€śtrickâ€ť works. When asked to place the fractions on the number line to prove that Â is greater than , the student makes significant errors.

Questions Eliciting Thinking How can you use the same number line to show two different fractions? Can you label the top of the number line with one fraction and the bottom of the number line with the other fraction?
What fraction with a denominator of six is equivalent to ? So if Â is equivalent to , where would Â be placed on the number line? Would Â be placed before or after Â on the number line?
What fraction with a denominator of eight is equivalent to ? So if Â is equivalent to , where would Â be placed on the number line? Would Â be placed before or after Â on the number line?
You correctly compared the fractions using common denominators. Can you now use the number line to prove to me that Â is greater than ? Where would you place each of the fractions? 
Instructional Implications Model how to represent two fractions with different denominators on a number line. Explain to the student how to use benchmark fractions to help in locating fractions on a number line.
Consider using the MFAS task FiveEighths on a Number Line (3.NF.1.2).
Provide opportunities for the student to locate multiple fractions with different denominators on a number line using benchmark fractions. 
Almost There 
Misconception/Error The student correctly locates and compares the fractions on a number line, but does not use benchmark fractions. 
Examples of Student Work at this Level The student correctly determines that Â is greater than Â by using a strategy other than using benchmark fractions. When asked to locate Â and Â on the number line, the student is only able to do so by scaling the entire number line instead of thinking of the relative size of the fractions in relation to benchmark fractions. Despite prompting, the student is unable to clearly articulate how Â can help determine that Â is greater than .
Â

Questions Eliciting Thinking How can you use benchmark fractions to compare Â and ?
What is a benchmark fraction? How can you use Â to help you locate Â on the number line? How about ?
Is it necessary to scale the entire number line to know where to place ? What about ? 
Instructional Implications Guide the student to compare fractions by reasoning about their numerators and denominators using a number line and benchmark fractions rather than drawing area model representations.
Model how to show equivalent fractions for . Assist the student in determining where Â and Â are on a number line in relation to .
Provide the student with matching fraction card sets. Half of the cards should show a fraction on a number line. The other half should have benchmark fractions. The student should match the benchmark fraction card to the fraction on the number line. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly labels the number line with both fractions and benchmark fractions without scaling the entire number line. The student correctly writes .
Â

Questions Eliciting Thinking How would you compare Â and Â by using common denominators?
How would you compare the fractions Â and ? Would drawing an area model be the most efficient way to compare the fractions? What would be an efficient way to compare the fractions?
Can you use benchmark fractions to compare two fractions in any situation?
What is an example of when using benchmark fractions might not be an effective strategy? What other strategy could you use instead of benchmark fractions? 
Instructional Implications Provide the student with opportunities to compare fractions greater than one (e.g., Â and ) using a number line.
Consider using the MFAS task Comparing FourFifths And ThreeFourths (4.NF.1.2) which has students considering different wholes when comparing fractions.
Help the student to see that different strategies can be used to compare fractions based on the fractions being compared. Guide the student to be flexible in his or her choice of strategies instead of only using just one strategy to compare fractions. 