Numbers & Operations for Advanced Students

Advanced Common Core Math Explorations: Numbers and Operations (5-8)
By Jerry Burkhart
(Prufrock Press Inc., 2014 – Learn more)

m fastabend 120Reviewed by Maia Fastabend

In Advanced Common Core Math Explorations, Jerry Burkhart structures the content into three sections. Each section includes an introduction for teachers, a student handout, a teachers guide, and a wrap-up. The introduction lists the materials, prior knowledge, learning goals, and how to start the activity.

The student handout is composed of three stages with between 8 and 11 questions. The teachers guide contains an answer key and some helpful hints to give students who may be stuck, and the wrap-up includes how to share, summarize, and build upon what was learned.

advance cc math burkhart fastabendEvery activity in the book centers around the Common Core strand Numbers and Operations with emphasis on students using the CCSS mathematical practice standards. Within the CCSS strand Numbers and Operations, Burkhart uses a fifth and an eighth grade standard: 5.NBT.A and 8.EE.A.

Despite a focus on these two standards, the activities are geared towards advanced students as the book’s title suggests.

Best for truly advanced students

I found these activities would be best suited for truly advanced students and are more geared towards those in grades 7-9; this is mostly due to the “wordiness” of every activity, all are geared towards high level readers, and to each activity’s three stages that build upon each other, getting progressively harder.

The exercises are modeled similarly to Inside Mathematics – Problems of the Month, but with much more guidance and far fewer entry level tasks for all students to be involved. For example, activities include titles such as “Discovering Divisibility Tests,” “Multiplication Slide Rules,” and “Factor Blocks and Radicals.”

Within many of these activities Burkhart uses language that may be unfamiliar to students and will need pre-teaching. These words included longs, flats, smalls, multiplication scales, and block diagrams to name a few. Lastly, it is important to know that many of Burkhart’s activities need to be done in order, meaning one can’t try an activity on divisibility without having completed an earlier task in the book, due to the building of terms and certain problems surrounding a “Torran Planet.”

The book’s place in a series

In addition, Burkhart’s three books in the 5-8 series build on each other. The other strands have exercises that do a better job of introducing block diagrams, but in this book Burkhart does provide an appendix with additional information on block diagrams to help an educator teach and understand them.

As an educator who teaches 6th-8th grade in a public school setting with no advanced classes, I see myself using maybe one or two of the activities, but due to the in-depth exploration of standards 5.NBT.A and 8.EE.A, it will be hard to include the activities in an already lengthy curriculum.

The activities I did like could be used on substitute days because of the structure of having 8-11 questions where students are told what to find. The activities that were most geared towards my use in classes of 6th-8th grade students include looking at divisibility rules, triangle sums, and number line magnifiers (decimals).

Maia Fastabend is a 5th 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, and has recently found her niche teaching remedial/support. Musings about her teaching and current topics can be found at


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