Using Materials

Problem: "?/4 is a number between 2 and 4. What numbers could go in the box?"
Get the students to draw and mark a double number line in both mixed fractions and common fractions.

(Answer: 9/4, 10/4, 11/4, 12/4, 13/4, 14/4, 15/4, are all between 2 and 4.)
Example: “?/3 is a number between 3 and 5. What numbers could go in the box?”

Using Imaging

Problem: “?/5 is a number between 3 and 3 . Imagine which number could go in the box.” Fold back to drawing the number line if necessary.

(Answer: Only 3 3/5 fits between 3 2/5 and 3 4/5. And 3 3/5 = 18/5. So 18 goes in the box.)

Examples: Find the number that can go in the box:
?/5 is between 2 1/2 and 2 3/5
?/7 is between 1 4/7 and 1 6/7

Using Number Properties

Examples: Find the number that goes in the box: 

?/5 is between 3 3/5 and 4
?/3 is between 8 and 8 2/3.
3 ?/6 is between and 20/6 and 22/6
3 ?/6 is between 21/6 and 23/6.