Activity Set 2.2 PREP PPTX Visual Algebra for Teachers

Chapter 2 LINEAR EXPRESSIONS, EQUATIONS AND GRAPHS Visual Algebra for Teachers

Activity Set 2.2 Introduction To Tile Figure Sequences Visual Algebra for Teachers

PURPOSE To learn how to analyze sequences of tile figures numerically, in words and symbolically to see, define and explore an underlying algebraic pattern. To learn how to model algebraic patterns with black tiles and black n-strips and to represent the algebraic pattern graphically.

Black tiles and black n-strips MATERIALS

INTRODUCTION

Black n-Strips A Black n-Strip, represented by the variable n, represents a positive (output) number; n = 1, 2, 3 … The output value of a black n-strip is the same as the input number (n = 1, 2, 3 ….). The height of the black n-strip is fixed and is the same length as the edges of the black and red tiles (1 or -1) The length of the black n-strip is an arbitrary length. Since it is black, the dimensions of the black n-strip can be 1  n or -1  -n.

Using Black n-Strip Edge Pieces In Chapter 1, we used black and red edge pieces to measure lengths of 1 unit and -1 unit. In the same way, a thin piece of a black n-strip (black n- strip edge piece) measures a length of n units A a thin piece of a red n-strip (red n-strip edge piece) measures a length of -n units.

Black n-Strip Dimensions

Modeling with Black n-Strips A sequence of tile figures whose nth figure is modeled by a black n-strip might look like one of the following horizontal or vertical sets of tile figures:

Modeling with Black n-Strips

Modeling the nth Figure Using Black n-Strips to Model the nth Figure of a Tile Sequence The black n-strip can be all or part of the nth figure for a tile sequence and can be combined with other algebra pieces and black and red tiles. An nth figure might look like this:

Sketching Black n-Strips To sketch a black n-strip, you may wish to simply sketch an outline of the strip. In future activity sets you will also need to sketch red n-strips. To distinguish the black n-strip outline, label a black n- strip with a B for black.

Black and Red n-Strip Edges Sketching Black and Red n-Strip Edge Pieces To sketch a black or red n-strip edge piece, simply sketch an outline of the strip, label it B n or R –n or shade the strip and label it n or –n. The overall goal of this activity set is to think about and work with patterns and algebraic relationships. Develop a quick (but clear) sketch technique to use when recording your algebra piece models.

PREP Question #1 Use black and red tiles and model the following sequence, Tees, of black tile figures with black tiles:

PREP Question #1 Write in your coursepack, Activity Set 2.2 #1 Step One: Loop and number each figure and Numerically determine the total number of black tiles in each figure. Mark your number counts on the figures. Step Two: Convert your looping ideas into Words. Step Three: Convert your looping and word ideas into Symbols. Use n for the figure number and T for the total number of black tiles. Simplify your symbolic equation and check it for n = 1, 2, 3 and 4.

PREP Questions #2 - 4 Write in your coursepack, Activity Set 2.2 #2 - 4 Describe the 100th Tee figure. What does it look like? How many black tiles are in it? Which Tee figure will have 2002 black tiles? Describe the figure. What does the nth Tee figure look like? Use your black n- strips and tiles to model the figure; be sure to have the pieces oriented to look like the other tile figures in the Tee sequence

You are now ready for: PREP QUIZ 2.2 See Moodle Visual Algebra for Teachers