Authentic Math Modeling in Middle School

Modeling with Mathematics: Authentic Problem Solving in Middle School
By Nancy Butler Wolf
(Heinemann, 2015 – Learn more)

m fastabend 120Reviewed by Maia Fastabend

Are you left wondering what so many people are talking about when they speak of open ended tasks, Dan Meyer, MARS Tasks, NCTM Illuminations, high low ceilings, and modeling in mathematics? Good news. The author of Modeling with Mathematics, Nancy Butler Wolf, addresses all of these issues and then some in her book.

Wolf has taken many of the top names and topics in mathematics and has applied their work to the Common Core Mathematical Practice Standard “Modeling in Mathematics” (MP4). She also touches on Constructing Viable Arguments and Critiquing the Reasoning of Others.

modeling with math fastabendThe book takes on two large topics. Topic One is looking at rich tasks. Wolf identifies rich tasks as 1) Accessibility to All Learners; 2) Real Life Tasks; 3) Multiple Approaches and Representations; 4) Collaboration and Discussion; 5) Engagement, Curiosity, and Creativity; and 6) Opportunities for Extension. Here her point with accessibility aligns well to the work of Jo Boaler and providing students with problems that are low entrance and high ceiling which provide the opportunities for extension.

Wolf’s work could act as a strong extension for teachers who are trying to build steps towards understanding problems and topics presented by Boaler. Wolf touches on engagement with a strong section on helping teachers deal with the dreaded IDK response when students are tasked with open ended problems or problems which, simply put, just involve words.

Wolf also does a good job with her second topic: taking textbook problems and transitioning them into problems that are rich tasks and useful for mathematical modeling.

An example she gives includes a problem with Distance = Rate x Times. She transitions this basic formula problem into a scenario where students design a route with stops using a set of criteria, and where (Distance = Rate x Times) would be helpful and build into a quicker way to come up with a given route for the individual who needed help with his schedule.

The discussion of transitioning textbook problems to rich tasks is Wolf’s extension of ideas that have been spoken of by Dan Meyer, who is currently prominent in K-12 education.

A good resource for new math teachers

The strong points in Wolf’s Modeling with Mathematics include student/teacher discussion examples, problem examples, and some great ideas/examples on using rubrics to grade rich tasks. I was a little frustrated that so many examples were from sources I was already familiar with. These include resources from NCTM Illuminations, Dan Meyer’s 3-Act Math, and MARS Tasks, to name a few. These are all great resources, but the book’s content wasn’t anything “new” per se, at least from my perspective as an active professional learner in the math sphere.

Wolf’s book might be best suited for an audience that may not yet be deeply immersed in math or math coaching, or someone who is trying to wrap their head around the topics above or see them in another light. She excels at offering clear explanations.

Maia Fastabend is a 6th year teacher from Southern Oregon who when not teaching can be found whitewater kayaking or trail running. She has experience teaching 6th-8th grade general math and advanced math, some district coaching/speaking (including NW Math Conference 2014 and the Southern Oregon Tech Conference 2015), and recently has found her niche teaching remedial/support. Musings about her teaching and current topics can be found at


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