Visual Algebra for Teachers Activity Set 2.3 PREP PPTX

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

Visual Algebra for Teachers Activity Set 2.3 Tile Figures and Algebraic Equations

PURPOSE To learn how to use algebra piece models to answer questions about sequences of tile figures and to solve basic algebra problems. To learn how to use algebraic equations to build tile figure sequences. To learn how to connect the work with algebra piece models to their corresponding symbolic steps.

MATERIALS Black and red tiles and black n-strips

INTRODUCTION

Modeling an Equal Symbol Two black edge pieces make an excellent = symbol while working with algebra pieces and equations.

Using Algebra Pieces Using Algebra Pieces to Solve Problems When using algebra pieces to solve problems, set the pieces up on your table and use them, as you have been using black and red tiles, to work out the question you are considering. In many cases, there will be a large number involved that is impractical to model with black or red tiles. You may wish to keep track of these large numbers by jotting them on scraps of paper.

Example (using pieces to solve) For the equation T = 2n + 5, use your algebra piece representation of the nth T = 2n + 5 figure to determine which figure has 35 black tiles. Use a table to sketch your algebra piece work in the left column Include brief notes about what you are doing) Write the corresponding symbolic steps in the right column. Check your final solution.

Example (using pieces to solve) ALGEBRA PIECE WORK with notes CORRESPONDING SYMBOLIC WORK Set up pieces Set up equation 2n + 5 = 35 Add 5 red tiles to each side +-5 +-5

Example (using pieces to solve) ALGEBRA PIECE WORK with notes CORRESPONDING SYMBOLIC WORK Simplify 2n = 30 Divide each side into 2 (equally sized) groups

Example (using pieces to solve) ALGEBRA PIECE WORK with notes CORRESPONDING SYMBOLIC WORK Simplify CHECK 2(15) + 5 = 35

Modeling (n + 1)st Figures The (n + 1)st figure in a tile sequence is the next figure after the nth figure in a tile sequence. As you work with algebra piece models you will often be asked to model both the nth figure and the (n + 1)st figure (two arbitrary, consecutive figures) for a given tile sequence. Let’s look at a two examples to see how (n + 1)st figures are constructed.

Modeling (n + 1)st Figures To build a (n + 1)st figure from an nth figure, change all side dimensions n in the nth figure to a side dimensions n + 1 for the (n +1)st figure. Note fixed lengths such as 1 or 2 do not change. Edge pieces are shown here to emphasize the dimension changes from the nth figure to the (n + 1)st figure.

Symbolic Equation: T = 2n Modeling (n + 1)st Figures Symbolic Equation: T = 2n nth figure (n + 1)st figure Dimensions 2  n 2  (n + 1)

Symbolic Equation: T = n + 2 Modeling (n + 1)st Figures Symbolic Equation: T = n + 2 nth figure (n + 1)st figure Dimensions 1  (n + 2) 1  [(n + 1) + 2]

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

PREP Question #1 Write in your coursepack, Activity Set 2.3 #1 (This is the prep / set-up for the two-column lesson idea) 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 2.3 #2 - 4 Describe the 100th Rectangles figure. What does it look like? How many black tiles are in it? Which Rectangles figure will have 2002 black tiles? Describe the figure. What does the nth Rectangles 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 Rectangles sequence

Tripled and 10 more black tiles are added PREP Question #5 Question: If the collection of tiles in a certain Rectangle figure is: Tripled and 10 more black tiles are added There will be a total of 160 black tiles. Which Rectangle figure is this? Use a two column table and sketch your algebra piece work in the left column (include brief notes about what you are doing) and write the corresponding symbolic steps in the right column. Check your final solution. (Prep demo next slides)

PREP Question #5 (demo solution) ALGEBRA PIECE WORK with notes CORRESPONDING SYMBOLIC WORK Set up pieces Set up equation 3  2n + 10 = 160 Add 10 red tiles to each side 6n + 10 = 160 +-10 +-10

PREP Question #5 (demo solution) ALGEBRA PIECE WORK with notes CORRESPONDING SYMBOLIC WORK Simplify 6n = 150 Divide each side into 6 groups, each group: = 25 CHECK: 32(25) + 10 = 160 

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