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Assessing the Common Core Standards: Real Life Mathematics

Andrew Miller

Instructional Coach at Shanghai American School
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Another buzzword that permeates the conversation around education is relevancy, and rightfully so. We want our students not only to make connections to real-world problems but also to do these activities.

However, it is not simply in the task that we want students to mimic real world connections. Students are already conditioned to do this. They are used to sitting and completing tasks. Even when the task might have great connection to the real world, it can still just be that: a task to complete. We need to keep this in mind when we ask students to perform real world math, just as the Math Common Core dictates.

Taking a Closer Look

The following Common Core standard gives a great example and sets a solid tone for what can be targeted in math instruction:


In a previous blog discussing Math PBL Project Design, I wrote about reframing the word "problem," and pointed to this standard. For many of us, there is a very traditional meaning that is activated: a word problem in the text book, or simply a calculation to be made. In fact, the Common Core gives it as an example.

We can do better. We can assess learning in a much more relevant and engaging way. For instance, how do we assess this Common Core standard related to area and volume?


This standard is much less specific about what this might "look like" in the classroom, which leaves it ripe for innovation. There are a variety of products and contexts that could assess this standard. The major assessment, or culminating product in PBL terms, could take on the form of a podcast, presentation, marketing plan, or even a short story.

Other ways to assess this standard in imaginative, real-world scenarios:

  • High school students are creating a swimming pool that can meet the needs of all people who want to use it -- from those who have special needs to children -- and at the same time needs, it meets certain criteria in terms of standard amounts of water and size.
  • Middle school students are in charge of designing a new and improved pyramid to be presented to the pharaoh, complete with a variety of antechambers.
  • Elementary students are in charge of creating an organic garden to sell certain products at the local farmer's market.



Criteria and Rubrics

A word of caution, don't give students the exact criteria, instead make them research and make decisions on what the criteria should be.) Again the genre is not as important as the rubric that demands specific criteria. As long as the rubric is clear and transparent where students must demonstrate math skills, include examples, etc., then we know that students are in fact learning and applying the Common Core standard.

If you as the teacher need a specific graph, then make sure to include in the rubric. If you need written explanation around the mathematical calculations, then demand it. If you need diagrams and measurements, then make sure the rubric demands it. Grading is not a surprise anymore. It is clear and transparent.

When looking at the potential for work with this Math Common core, make sure you have high expectations for the level of work your students can do. The old definition of the word "problem" is not rigorous. Redefining the word "problem" within the frame of Problem or Project-Based Learning is rigorous, and still demands real world connections in an authentic way.

If we want our students to really wrestle with math concepts, then we must create space for this work to happen, and create assessments that mirror this complex work.

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Jen's picture
High School Math Teacher, Minnesota

I absolutely love the idea of having my students work through problems. As individuals or as teams, they seem to understand the concepts and think through the material at a much deeper level. My struggle is, as always, time. If we are going to do a project in class, or work on a problem, I need to take the time to decide which standards it covers, what parts of the traditional curriculum (text book) I can cut out and replace, where it fits in our curriculum map, plan and organize the problem we are going to work on, get my other colleagues on board with the change (consistency in what we cover is required), etc.
For those of you who do these "problems" in your classrooms - where do you start?? How do you find time?

Ryan Spencer's picture
Ryan Spencer
6th grade math teacher in Anoka, Minnesota.

The middle school pyramid project would be perfect for my 6th grade math classes because social studies does ancient Egypt in 6th grade. This would be a great opportunity to team up with social studies for an integrated project.

amy v's picture
amy v
Elementary Teacher, 3rd Grade, Atlanta, GA

There are a multitude of activities for this- many come to mind using pattern blocks. Middle school can design a stained glass replica using the various shapes. They then determine cost for the glass based on the area used to cover a certain size window. The volume is incorporated into determining the space needed to be filled: how thick is the glass? Another measurement is weight- how much glass can be used, and if the different colors of glass are given specific wight amounts, then proportion can be tied in.

More and more ideas of this project are developing as I type this up. I am sure any one else reading this understands where this can go. What fun!!

Kondrik's picture

I TOTALLY agree with you around who is being asked to justify good practice ! It's backwards and upside down. Why ?!?!?

Vincent's picture
Curriculum developer; Education and Media blogger

Hi Andrew,

I came across your post Googling around for materials for a proposal I am working on. Totally agree about Project Based Learning and like your suggestion to redefine "word problem." I have often felt that the goal of teaching is to nurture positive habits in reading and math.

Sue Boudreau's picture
Sue Boudreau
Seventh Grade science teacher from Orinda, California

and project based learning at least implied in the new common core standards. It will mean that science teachers like me will have to *gasp* collaborate with our math colleagues to a. re-learn rusty math skills in the way our shared students are taught and b. think about how and where we can incorporate those skills within science pbl. Last year, I had kids figure out their carbon footprints, make a change in their lifestyle and calculate how much carbon they saved. Lots of math there.

Same collaboration will be needed for full implementation of the ELA common core standards which demand scientific literacy and writing across the curriculum.

I'm looking forward to all this. Love the innovation that almost always happens at edges and overlaps.

Kevin's picture
High School Math Teacher from Cleveland, Ohio

My school district is going through the process of changing our curriculum over to the common core. This blog helped me understand the important changes going on and the shifts in the depth understanding we want our students to have.

Danibelle0606's picture
Middle School Math Teacher from Ohio

Thank you for sharing. My school is shifting to the common core and this really helped me understand what the purpose of the broad ideas in the standards are for.

Wowzers's picture
Wowzers offers online Game-based Math curriculum for Grades 3-8

This article brings up some great points. How do ask teachers to develop higher-level thought and deeper understanding if have no means to assess these skills?

According to a recent study, it seems PAARC and Smarter Balanced may be on the right track in assessing 'deeper understanding'. Check out this link to learn more about the study's findings -

Jaimin Patel's picture

Very nice article explaining underlying meaning. Surprised How did I missed this one earlier.

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