Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to create five fractions and place them all on a number line with the correct order and spacing.

### Hint

What will be your benchmark fractions?

Which fraction denominators will be more challenging to place?

Which fraction denominators will be more challenging to place?

### Answer

There are many correct answers. One answer involves using 0/6 to represent 0, 8/4 to represent 2, and then placing the other fractions accordingly, for example, 9/3, 7/2, and 1/5.

Source: Robert Kaplinsky

It seems like you all have developed a very well-specified theory of open middle task design. I can see you guys spinning that template out into a number of very interesting tasks. What’s missing here, I think, is a sense of how students react to the template. Any plans to get these in front of students?

Currently I am working through a group of problems for 8th grade to use this upcoming school year. I am going to field test some of the K-1 problems on my son however.

My concern with your example is related to the standard. Third graders are limited in the numbers they use for the denominator. How can you present 0/9 when 9ths in not acceptable fractions for 3rd grade per common core?

Good catch Jad, I have altered the wording in the solution set to avoid that. Thank you for contributing to the discussion.

Jad, the standard states: “Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.” Where are you seeing that 9ths can’t be a denominator?

Here is the other standard that we use along with the standard that Jad mentioned: 3MA.C.19: recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8. (e.g., 1/2 = 2/4, 4/6 = 2/3); explain why the fractions are equivalent by using a visual fraction model. In our analyzing the standards book it mentions that 3rd grade students are only required to know fractions with the above mentioned denominators. This activity that you presented seems more of a challenging extension to fractions and not one the should realistically be taught in 3rd grade. If we are suppose to teach to this level, then someone needs to tell all of the 3rd grade teachers in the county and students will have this expectation.

Hi Beth. Can you provide a link to where standard “3MA.C.19” is? Is that a Common Core Math Standard?

Looking forward to offering this task to my 3rd grade team as they develop fraction sense in their students. The denominators are noted as a footnote at the Domain level. http://www.corestandards.org/Math/Content/3/NF/ Note the tiny font at the foot of the page here.

Regardless, I look forward to offering it up and seeing how students grapple with it.

Beth, would 2/9 or 3/9 be in grade 3?

That was suppose to be 9/2 or 9/3

Good question. I actually have tried several out with students. It was a very humbling experience in terms of dealing with lack of perseverance and content knowledge. I have some great student work samples I’ve already scanned. I just haven’t gotten around to blogging about it but will put it back on my radar.

Wanted to share this tweet from Joe Schwartz. https://twitter.com/JSchwartz10a/status/562733071678849025

I know I’m late to the party, but….My thought is if they don’t feel comfortable with 9 in the denominator they can use it in the numerator. I’m excited to try this with my third graders. We’ll see how it goes. If it causes too much trouble, maybe I’ll alter the numbers to choose from…excluding two of the choices perhaps. That would still leave a lot of room for some fun!