Directions: Using the digits 1 to 9 exactly once, fill in the boxes to create and place 4 fractions on the number line in the correct order. (fractions B & C are equal)

### Hint

### Hint

The sum of the equivalent fractions is greater than a half and greater than a quarter separate. How do you know if two fractions are equivalent? How do you know if fractions are less than or greater than another fraction?

### Answer

### Answer

There are many possible answers. Here are a couple: A = 1/7, B = 3/8, C = 9/24, D = 5/6; Another possibility is A = 1/5, B = 3/9, C = 8/24, D = 6/7; yet another possibility is A = 5/8, B = 3/4, C = 9/12 and D = 6/7. (or D could be 7/6)

Source: Graham Fletcher, Bowen Kerins, Kate Nowak

Here is another answer a student found A = 5/8, B = 3/4, C = 9/12 and D = 6/7. (or D could be 7/6)

Thank you for your contribution Erick! Your student’s solution has been added to the problem.

B and C are not equivalent in your first possible answer. (3/6 > 9/27)

Thank you for catching that Gina, the answer set has been updated.

This is so much fun! My students and I are wondering about A= 3/7, B=4/8, C=6/12 and D=9/5 and A= 2/7, B=3/6, C=9/18 and D=5/4 Thanks for sharing your work with us!

A group of students worked on this yesterday as they reviewed equivalent fractions and ordering…and they/we had so much fun doing! It was their first “open-middle” task with the recording sheet. I am so excited about this task. There were so many great discussions, mistakes, revisions…

Another possibility…I got 3/7, 2/4, 9/18, and 5/6.

My son spent a few hours seeking to find the most optimal answer based on the partitioning of the number line. He makes a case for 2/5, 3/6,7/14, 8/9. The difference or distance between 3/6 and 8/9 is approx. 4 times the distance between 2/5 and 3/6.

What fun. Today we were comparing fractions to 1/2. I wanted to test this out myself before I introduced it to the class. I thought, if I make B 1/2 or its equivalent, than I can use the left over digits to create a fraction less than 1/2, and another greater than 1/2. I came up with a = 3/9, b = 2/4 = 8/16, and d = 5/7. I wonder if any of my students will think this way.