CURS Nazanin Afshari Sep. 25, Alge Tiles

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1 CURS Alge Tiles

2 Description: Alge - Tiles Alge-Tiles is a set of manipulative materials which is designed to help students to make connection between their concrete experience and abstract mathematical concepts. Alge-Tiles is a set of different sized and colored rectangles and squares that allows students to explore and touch concrete concepts related to integers, equations, and algebraic expressions. A complete set of Alge-Tiles for 30 students contains: 15 x set :» 25 1 tiles (12 mm x 12 mm) red and white» 12 x tiles (12 mm x 65 mm) green and white» 6 x² tiles (65 mm x 65 mm ) green and white 15 y set :» 12 1 tiles (12 mm x 44 mm) orange and white» 12 y² tiles (44 mm x 44 mm) orange and white» 6 xy tiles (44 mm x 65 mm ) gray and white The resource binder:» Containing detailed information on how and when to use this material in your class.

3 Purpose: Alge - Tiles Research has shown the concepts that are introduced using hands on materials have greater chance of producing thorough understanding than concepts that are initially developed abstractly. If students are given extensive experience using the materials to learn abstract concepts such as: ratio, integers, and solving equations, they will be more confidant in their ability. This confidence will translate into greater success in Mathematics. Alge-Tiles can be used to teach the following concepts: Ratios Investigating and Equivalent ratios Integers Add, subtract, multiply and divide integers Polynomials Add, subtract, multiply and divide polynomials Factoring Common, Trinomials factoring Solving Equations Quadratic & Linear

4 Alge - Tiles Activity1: Introduction to Ratios Count and record the number of tiles shown. Type of Tile Total Use the result to compare the number of tiles: a) small squares tiles to large square tiles b) small squares tiles to large square tiles c) small square tiles to small square tiles

5 Alge - Tiles Activity2: Investigating Ratios 1) Study the pattern of tiles in each figure below. A B C 2) Repeat the above pattern using the tiles and complete the chart. Figure # of Rectangular tiles # of square tiles Rectangular : Square tile tile A : 2 B C D E Students can be asked to create their own pattern using the tiles and Investigate the existing ratios.

6 Alge - Tiles Activity 3 : The Zero Model Note! When there is an equal number of red and blue tiles, no color is dominant. When one red tile and one blue tile are combined, they make a model zero: = 0 Ex: What tiles must be added to (+2) to result in the zero model? integers like +2 and -2 are called 0 opposite integers Use the Zero model: a) Display +2 using 4 tiles: c) Display -1 using 5 tiles b) Display 1 using 5 tiles: d) Display -3 using 9 tiles Why is it impossible to display 0 using 5 tiles? Challenge students to come up with their own reasoning and come to a conclusion.

7 Alge - Tiles Activity 4: Subtracting Negative Integers Use the Alge Tiles to represent (-2) (-6) =? Step1: Count out 2 negative pieces to represent -2: Step 2: Subtract means to take away so take away six of the negative pieces. But you only have 2 negative pieces Zero Principle to the rescue! 0-2 Step 3: Take away (-6) and complete the number sentence. (-2) (-6) = +4 Now try:

8 Related Links: Alge - Tiles To order Exclusive Educational Products or catalogues visit: National Council of Teachers of Mathematics, has virtual manipulative materials including algebra tiles : Virtual Algebra tiles, showing the polynomials including the intermediate steps to find the factors: Basics introduction to Algebra tiles using several examples:

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