Order of Operations

By Curtis Nichols(9-12 classroom)

Book 1
827K
Build a Tree
Evaluate

Book 2
2.93M
Build a Tree
Evaluate
Describe

These books are a work in progress. My students love them. Other books will be posted when they become available.

The idea of this work is to give students practice with the "algebraic" order of operations. We construct tree diagrams to facilitate this. The numbers in the expression become leaf nodes, the operations (which yield numbers) become non-leaf nodes (interesting fact: there are always 1 fewer non-leaf nodes than leaf nodes.) Later, students use the trees to create one-word descriptions of the expression (it breaks into two pieces at "the weakest link.") Book 3, already under construction, will expand on this idea to write word descriptions (noun phrases) of a variety of expressions. It turns out that word descriptions are tightly related to "pre-order" tree traversal. This got me to thinking that people who find it difficult to translate phrases into mathematical expressions are being asked to do something non-trivial. By working with trees, I hope to give them some tools to help do this. Interestingly, the approach seems to be a write-first, read-later kind of thing. Curious! Book 3 will be the "write it" book, book 4 will be for reading (which you write in mathematics, or infix-notation.) Don't be scared off by the technical terms! The children won't be.

Measuring the Height of a Tree

By Curtis Nichols (9-12 classroom)

I found this among a quantity of "Straight Arrow" cards. These were cardboard separators between layers of Shredded Wheat in packages dating from 1949 to 1952. It is a cute way to measure the height of a tree.

We modified the procedure so that we viewed objects using a ruler to sight. We walked backward or forward until the object took up the full 12 inches in our view. Then walk to the object (trees mostly) counting steps and you get the height of the object in feet. Later, we looked at the similar triangles involved to understand why the process works (we think of the process as involving a "scaling factor" by which the larger triangle is multiplied to obtain it from the smaller triangle.)

Algebra Equations Level 1 Books

by Curtis Nichols (9-12 classroom)


	Book_1 1-step 1-equ.		Book_2 2-step 1-equ.		Book_3 1-equ. combine like terms
	Book_4 1-equ. X's on both sides		Book_5 1-equ. distributive law		Get the album pages

Solve equations in a single unknown. Books are in MS Word format (need Word Viewer?).

Teacher-to-Teacher Sharing

Edited by
Curtis J. Nichols

Archives at: 04/27/2003 - 05/03/2003 05/04/2003 - 05/10/2003 05/18/2003 - 05/24/2003 05/25/2003 - 05/31/2003 06/01/2003 - 06/07/2003 06/15/2003 - 06/21/2003 06/22/2003 - 06/28/2003 08/31/2003 - 09/06/2003 09/28/2003 - 10/04/2003 08/15/2004 - 08/21/2004

Edited by Curtis J. Nichols

Edited by
Curtis J. Nichols