Activity Set 1.1 CLASS PPTX Visual Algebra for Teachers

Chapter 1 INTEGERS AND INTEGER OPERATIONS Visual Algebra for Teachers

Activity Set 1.1 Modeling Integers with Black and Red Tiles Visual Algebra for Teachers

PURPOSE To learn how to model positive and negative integers with black and red tiles and how to determine the net value and opposite net value of collections of black and red tiles.

MATERIALS Black and red tiles Black and red tiles are black on one side and red on the other side. No calculators for this activity set

INTRODUCTION

Integers The set of Integers (Z) is the set of positive and negative counting numbers and zero and is denoted by the letter Z. Z = {0, ±1, ±2, ±3 …}

Black and Red Tiles One black tile has value +1 Two black tiles have value +2 One red tile has value -1 Two red tiles have value -2, etc.

Opposite Colors Black and red tiles are Opposite Colors and one black tile and one red tile cancel each other out. One black tile and one red tile = = 0

A Collection of black and red tiles is any set of black and red tiles. The Net Value of a collection of black and red tiles is the value of the remaining black or red tiles once all matching pairs of black and red tiles are removed. For example the net value of 1 black tile and 1 red tile is 0, the net value of 2 black tiles and 1 red tile is +1 and the net value of 2 black tiles and 5 red tiles is -3. Net value +1 Net value -3 Black and Red Tile Terms

An Opposite Collection of black and red tiles is a collection in which all of the tiles have been flipped to the opposite color. For example, the opposite collection of 2 black tiles and 1 red tile is 2 red tiles and 1 black tile. Net value +1 (opposite) Net value -1 The Opposite Net Value of a collection of black and red tiles is the net value of the opposite collection of the black and red tiles. Black and Red Tile Terms

Take a dozen or so black and red tiles and toss them on your table. Repeat as you fill out each row in the table; remove all matching black and red pairs before filling out the last two columns. As you toss, discuss your results. What observations can you make about black and red tiles? List all of your observations. Class Question #1 (coursepack)

Take a dozen or so black and red tiles and toss them on your table. Fill out the first row, and then flip over the tiles to form the opposite collection and fill out the second row. As you toss and flip, discuss your results. What observations can you make about collections, opposite collections, net value and opposite net value of collections of black and red tiles Repeat for 3 tosses Class Question #2 (coursepack)

Take turns filling out the shaded cells in each row of the table with numbers of your choice and have your partner determine how to fill out the rest of the row. Completely fill out the table on both partner’s pages. What observations can you make about collections of black and red tiles in this setting? Class Question #3 (coursepack)