School math, multimedia, and technology tutorials.
[Photo by bumeister1 via flickr.]
Scattered between all the math blog links, I’ve included highlights from the Common Core Standards for Mathematical Practice, which describe the types of expertise that teachers at all levels — whether in traditional, experimental, or home schools — should seek to develop in their math students. Continue reading at Let’s Play Math.
In the Mathematical Palette, my mathematics appreciation blog, I wrote about mathematics being a science of patterns. The images below only affirm the beauty of these patterns. they also show the intuitive proof of the statement, or what some people call proof without words.
Do you think the number pattern will continue as the number of circles increase? What conjectures can you make from the pattern?
Exercise: Prove your conjecture.
This is the second part of the Introduction to Modular Systems Series. Please read the first part before proceeding.
Last Monday, we have learned a number system that uses numbers on the 12-hour analog clock. We have performed addition using these numbers and discovered that in that system, 12 behaves like 0. We have also observed that to add large numbers, we need to divide the number by 12 and get the remainder.
Recreating the table by replacing 12 with 0 gives us the second table in the figure above. As we can see, in this new number system, we have digits 0 through 11 as opposed 0 through 9 in the number system that we use everyday (the decimal number system).
In this new system, we have observed that there is a certain number where numbers wrap around. The wrap around number is called the modulo. The modulo of our “clock number system” is 12, so we call it modulo 12. » Read more