Using Manipulatives for Pattern Recognition in Mathematics

Helping students understand the relationship between patterns and algebra can be an abstract progression. Using manipulative to help students visualize the patterns can be an incredibly useful tool. If teachers can start getting students to visualize the progressions of certain patterns and develop their skills in visualization the transition into algebra will be much smoother.

The following pattern is an example of this type of relationship:

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When I look at this pattern it is easy to develop an algebraic expression to determine the relationship. The expression n+4, where n=term number represents this.  Although it is easy to develop this expression it is important to take the time to look at this relationship and see why this expression makes sense. If we can have students focus on the fundamentals of developing this expression. If we can have students look at the diagrams and determine which parts are growing and which parts are consistent they can easily see relationship. Recreating these patterns with manipulative gives students the opportunity to visualize the progressions. The green triangles remain constant at 4. The purple square increases by one for each term; starting at one. 

The exciting part of this is that with repetition and practice students will be able to identify more complex problems and how they relate to linear relationships. 

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After practicing pattern recognition and developing algebraic expressions students can begin to relate these activities to graphing linear relationships. Take the pattern to the right for example. While recreating the patterns students will be able to develop the algebraic expression to be 3n+4. The difficult part in this example would be seeing that the centre square is also part of the fixed triangles. It would be through the practice that students would become accustom solving this. 

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From here, students can use manipulatives from the patterns on graph paper to visualize the growth.  Next they can track the progressions and relate the this growth back to the algebraic equation. This lays the frame work for discussions surrounding graphs as well. The relation between term 0 and the y-intercept is is easily seen. Extrapolation is also evident while using this method.