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1.17: Lesson Seventeen

Difficulty Level: At Grade Created by: CK-12

Matrixes

1. A matrix can help you sort out sounds and letters. A matrix looks like a big square divided up into smaller squares, like this:

2. A matrix has columns and rows. Columns run up and down on the page — like the stone columns in front of a big building. Rows run across the page — like a row of people on a bench. So we can label our matrix this way:

Left Column Right Column
Top Row
Bottom Row

3. We can also number the little squares:

Left Column Right Column
Top Row Square #1 Square #2
Bottom Row Square #4 Square #3

4. Squares #1 and #2 make up the top row. Which two squares make up the bottom row? #3 and #4

5. Squares #1 and #3 make up the left column. Which two squares make up the right column? #2 and #4

6. The left column and the top row overlap in Square #1. In what square do the left column and the bottom row overlap? Square #3

7. What column and row overlap in square #4? Right column and bottom row

Teaching Notes.

1. Two-dimensional matrixes like the four-square models introduced in this lesson are used extensively in upcoming lessons. They are a very powerful tool for helping students solve the kinds of problems posed for them in the Basic Speller. Nearly always in solving these problems the students must notice how two different conditions either do or do not occur together. Two-dimensional matrixes make that job easier.

Because matrixes are so important to upcoming lessons, it is crucial that the students understand the basic concepts introduced in this lesson: What a column is. What a row is. How a square is created when a column and a row overlap. Most students seem to catch on to the basic idea of matrixes very readily. If anyone is having trouble, you might find it useful to point out that they operate just like a multiplication table. In fact, a multiplication table is nothing but a two-dimensional matrix with a lot of rows and columns:

234562468101236912151848121620245101520253061218243036\begin{align*}& && 2 && 3 && 4 && 5 && 6\\ &2 && 4 && 6 && 8 && 10 && 12\\ &3 && 6 && 9 && 12 && 15 && 18\\ &4 && 8 && 12 && 16 && 20 && 24\\ &5 && 10 && 15 && 20 && 25 && 30\\ &6 && 12 && 18 && 24 && 30 && 36\end{align*}

You might point out that these matrixes are all over the place: Your attendance sheet is probably a two-dimensional matrix, so too any progress charts you may keep on the bulletin board. A monthly calendar is a two-dimensional matrix; it is just that we usually don't bother to label the rows. The columns are labeled with the days of the week.

An informal matrix hunt might turn up some surprising examples. And such hunts are quite powerful teaching and learning strategies since the ability to identify a new, and perhaps slightly different, instance is an excellent sign of mastery of the general concept.

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