Advanced Common Core Math Explorations: Factors and Multiples
The Advanced Common Core Math Explorations series creates and nurtures mathematical adventurers! Students engage in challenging activities that deepen and extend their understanding of concepts from the Common Core State Standards for Mathematics. They stretch their mathematical imaginations to the limit as they explore mystifying patterns of colored blocks, analyze paths of pool balls, solve mathematical word puzzles, and unravel a baffling mathematical code. Each activity comes with extensive support for teachers including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigations. There is also a free supplemental ebook offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.
Exploration 1: Building Blocks
Explore prime number patterns by decoding a complex design of colored blocks.
- A larger copy of the grid from Problem #1
- The completed and numbered grid (I give this to students after they solve the problem. We use it all year long!)
- "Building Numbers from Primes" (an article of mine from NCTM's Mathematics Teaching in the Middle School journal)
- Comments (some thoughts and ideas that didn't make it into the book)
Exploration 2: 1000 Lockers
As you explore a classic problem about taking turns opening and closing a set of 1000 lockers, you will learn to solve challenging problems by making them simpler.
Exploration 3: Factoring Large Numbers
The best way to learn the ins and outs of factoring is to play with large numbers. In this exploration, you will discover some of the tools and strategies that mathematicians use to make time-consuming factoring processes more efficient.
Exploration 4: Factor Scramble
What could be better than combining number puzzles with word puzzles? Learn how all the factors of a number are hiding in its prime factorization.
- byrdseed.tv has a video to accompany this exploration!
Exploration 5: How Many Factors?
Quick now - how many factors does the number 5000 have? If you know its prime factorization, you can find the answer in a flash.
Exploration 6: Differences and Greatest Common Factors
A fifth grade class of mine discovered a clever way to save time when they were simplifying fractions. Learn how they did it!
Exploration 7: A Measurement Dilemma
Suppose you were stranded on a desert island and all you had to measure with were a 5-cup and a 7-cup container... Okay, it's not very realistic, but it does have the ingredients of a fun and instructive math problem!
Exploration 8: Paper Pool
Can you imagine the paths that pool balls would take if they just kept on going? Learn about greatest common factors, least common multiples, ratios, similarity, algebra, and more as you explore this question.
Exploration 9: The GCF-LCM Connection
Math is full of surprising connections. For example, did you know that you can use GCFs to help you find LCMs - or vice versa? The strategies that you discover will prepare you to tackle future algebra tasks.
Exploration 10: Mathematical Mystery Code
Every time you think you see a pattern in this mysterious code, it seems to fall apart -- that is, until you start thinking "outside the box"! Learn new ways to think about place value and exponents. There is also sneaky connection to Exploration 1. Can you find it?
Please look near the top of this page to find a link to an errata sheet containing corrections for errors on pages 76, 121, 145, and 151.