Mr. Ellis's 6th grade math

Fraction Concepts

Steven Ellis — Mon, 27 Oct 2008 05:12:51 -0500

We will spend considerable time on fractions concepts and computation with fractions. This is one of the critical concepts that students need for success in algebra. My goal is for kids to truly understand fractions and computation with them. Most of this will be done through drawings.

More later ..., although I have been have trouble keeping up with this Blog.

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The Sieve of Eratosthenes

Steven Ellis — Sun, 5 Oct 2008 09:42:06 -0500

We have been working with prime numbers. A very good way to introduce students to prime numbers and to see prime numbers in a larger context is to use an activity called, "The Sieve of Eratosthenes". This method was devised by Eratosthenes, who lived from 276 - 195 B.C. He also calculated the circumference of the earth at a time when most people thought that the earth was flat: http://www.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm

As for "the sieve",

http://hvms6math.atom5.com/the-sieve-of-erastot-2032.html

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The End of The First Three Weeks

Steven Ellis — Sat, 13 Sep 2008 07:55:48 -0500

We have finished the first three weeks of 6th grade. Every year two things jump out regarding students' math knowledge. The first is multiplication facts ... finish later

http://hvms6math.atom5.com/the-end-of-first-thr-1614.html

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The first questions: digits and base-ten

Steven Ellis — Sat, 23 Aug 2008 23:08:07 -0500

The first two questions for my sixth-graders:

1. How many digits do we have in our system of numbers and what are they?
2. What is the "main thing" about our numbering system?

A note about the awkward nature of this question.

    If I ask, "What is the basis of our system of numbers?" or, "On what is our numbering system based?"; students will not understand the use of the words "basis" and "based". So, I will use "main thing" and we will talk about what I mean:
            main idea
            the foundation
            main concept

Some examples from students' experience:
            something can sit on its "base"
            being "safe" in tag is touching a "base"
            being "safe" in baseball is being on "base"

Ultimately, students will understand that:
Our system of numbers is based on groups of ten. We work in a base-ten numbering system. Furthermore, each place value has a base of 10 with an exponent.
10^3 10^2 10^1 10^0
thousands hundreds tens ones or units
These are called "powers of 10". In other words, exponents all with a base of ten.

We have ten fingers called digits. Long ago, when people counted things, they counted on their fingers and kept track of groups of ten. Symbols were developed for each of the number of things. Ten symbols were developed: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When all their fingers, or digits, were used up, they recorded the number as 1 group of ten, or 10. Notice that the 1 moves to the next higher place value, which became the tens. I am not sure how much I will discuss zero as a place holder and a symbol for an empty set, but the invention of zero was a significant advancement in the development of number systems.

From this, our system of numbers was developed based on groups of ten. This became our base-ten system of numbers.

For years, teachers have used "base-ten blocks" or "base-ten drawings" to help students understand the idea of base-10 in our system, particularly how it is related to place-value. Each symbol represents a ten-fold (ten-times) difference in size or value. At this time, we will use the symbols for 100s, 10s, and 1s.

A couple of examples of base-ten drawings:

Homework is to make a base ten drawing for each of these eight numbers:

23
89
217
454
34
72
232
877

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The 2008-2009 School Year -- Welcome !!

Steven Ellis — Sat, 23 Aug 2008 06:42:23 -0500

This is the link to my website and my email address:

http://www.eusd4kids.org/Schools/hidden_valley/teacherfolders/sellis/website/index.html

sellis@eusd4kids.org

Hello and welcome to the 2008-2009 school year!

Several people have said that I should add a blog to my website, so here it is. I am not quite sure how this is going to work, but we will see. If you have not already, you will find that the teaching and learning of mathematics at the elementary and middle school levels is quite controversial. This is one place where some of those controversies can be discussed with all those involved rather than just reading my opinion. So, as you have questions or comments throughout the year, you can email me or post a comment, and I can respond and possibly start a new thread on which others can post their comments. Again, I am not quite sure how all this works, so this will be interesting.

Hopefully, we will all have some fun.

Mr. Ellis

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