Mathematical Explorations to Support Common Core

...going beyond numbers to mathematical thinking


An overarching value that infuses the Common Core Mathematics Standards is to introduce what it means to think like a mathematician.  The lessons described below were developed specifically to meet this objective.  Each lesson introduces mathematical concepts generally not part of the regular classroom instructional curriculum, but that are ideas young people can explore and develop just as if they were a mathematicians.  The focus in each lesson is on the process of discovery vs. the specific mathematical content. While the lessons have math content they are more about thinking processes. 

This project is a work-in-progress.  Additional lesson will be posted after they are classroom tested.  Your feedback, positive and negative, is greatly appreciated.  Please feel free to email me.

Lesson Descriptions

Below are lesson description in terms of key questions the lesson explores.  All the lessons and accompanying handouts are in a dropbox which is accessed by clicking here.

big numbers  counting  
How big is a big number?  Is there a biggest?  What does a million look like?  What does a googol look like?
big numbers calculating (handout only;  no lesson plan) How fast is the earth moving?  How far does the Earth (with us onboard) travel in a year?  How fast is light?
happy-sad arithmetic  
What do you get when you add a happy and sad face?  A Sappy?  Playing with picture numbers (but really an introduction to integers).
math art fractals  
How can you construct a picture of a tree with a mathematics rule?   Can math describe nature?
math art polygrams 
What do you get inside a pentagon when you draw some diagonals?   Do you always get a star when you draw the diagonals of a polygon?
patterns in our number system Patterns, patterns and more patterns (exploring our fabulous number systems):  Can you find any vertical patterns?  Can you find any diagonal patterns? Can you find any patterns when you add the digits of a number?
topology 1 curves  
Is that an open or close curve?  Are those points inside or out?
topology 2 traceability Can you trace that curve without lifting your pencil? What does it mean that the letters A and R are topologically equivalent? 
topology 3 networks Can you discover a rule for when a curve is traceable?
topology 4 map problem    What is the smallest number of colors you need to color a map?
topology 5 Mobius Strip How can a paper strip have just one side?


Objective in creating these lessons

The goal of these enrichment activities is to address the eight Common Core Standards for Mathematical Practice:
  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.
These lesson plans are designed to provide the teacher with a handouts and accompanying questions that enable the student to make discoveries about mathematics.  They should not be thought of as didactic materials to be presented in a lecture format. 

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Please feel free to email me with questions and suggestions.

Jason Frand, PhD.
Math Olympiad Coach and
Los Angeles County-wide Math Olympiad Tournament Chairperson
Linwood Howe Elementary School
Culver City Unified School District
Adjunct Assistant Professor, Retired
Assistant Dean and Director, Retired
UCLA Anderson School of Management
Created July 20, 2014
Updated May 13, 2015