Project M3 Level 3: Awesome Algebra: Looking for Patterns and Generalizations Student Mathematician’s Journal

Awesome Algebra: Looking for Patterns and GeneralizationsWe do not usually think of algebra as a topic for the elementary mathematics classroom. However, algebra is one of the five major content strands outlined by the National Council of Teachers of Mathematics (NCTM) in Principles and Standards for School Mathematics (2000). Looking for patterns, extending a pattern, making a generalization about a pattern — all are part of algebraic thinking. So we talk about algebraic thinking or reasoning as opposed to the formal study of algebra. In our Project M unit Awesome Algebra: Looking for Patterns and Generalizations, students are encouraged to study patterns and determine how they change, how they can be extended or repeated and/or how they grow. They then move beyond this to organize the information systematically and analyze it to develop generalizations about the mathematical relationships in the patterns. There is a strong focus on mathematical discourse revolving around how to verbalize a generalization. During Awesome Algebra: Looking for Patterns and Generalizations students will be encouraged to use the idea of a variable as they think about how to represent a rule. This will help them become aware of the usefulness of a variable when representing a generalization. Our emphasis on number patterns is designed to challenge mathematically talented students by encouraging them to take a new look at basic number concepts, that is, arithmetic from an algebraic perspective. Students will become better estimators and give have effective tools to perform computation mentally. We hope that the experiences and discussions in the unit will provide a rich context for introducing students to algebraic thinking and strengthen their reasoning and communication skills. Student Mathematician’s Journal The Student Mathematician’s Journal is a unique feature of every unit in the Project M: Mentoring Mathematical Minds series, encouraging students to communicate in writing. It includes the student worksheets from each lesson. In these journals we ask students to reflect on what they have learned and write about it; in effect, they are working and acting like real mathematicians when they do this. Components used to teach this module: Awesome Algebra Teacher Guide (0-7575-2331-5)Awesome Algebra Student Mathematician’s Journal

Awesome Algebra: Looking for Patterns and GeneralizationsWe do not usually think of algebra as a topic for the elementary mathematics classroom. However, algebra is one of the five major content strands outlined by the National Council of Teachers of Mathematics (NCTM) in Principles and Standards for School Mathematics (2000). Looking for patterns, extending a pattern, making a generalization about a pattern — all are part of algebraic thinking. So we talk about algebraic thinking or reasoning as opposed to the formal study of algebra. In our Project M unit Awesome Algebra: Looking for Patterns and Generalizations, students are encouraged to study patterns and determine how they change, how they can be extended or repeated and/or how they grow. They then move beyond this to organize the information systematically and analyze it to develop generalizations about the mathematical relationships in the patterns. There is a strong focus on mathematical discourse revolving around how to verbalize a generalization. During Awesome Algebra: Looking for Patterns and Generalizations students will be encouraged to use the idea of a variable as they think about how to represent a rule. This will help them become aware of the usefulness of a variable when representing a generalization. Our emphasis on number patterns is designed to challenge mathematically talented students by encouraging them to take a new look at basic number concepts, that is, arithmetic from an algebraic perspective. Students will become better estimators and give have effective tools to perform computation mentally. We hope that the experiences and dis