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Extending Understanding for Success in Pre-Algebra

Math: Grades 6-8



Brain research explains why adolescents often exhibit impulsive or thoughtless behaviors, why they seek novelty and thrive when learning is relevant and social. The challenges of engaging middle school students in the study of pre-algebra mathematics hones the roster of successful middle school math teachers to a special group. The critical years a student spends in middle school determine to a large degree his/her success in high school. It has been reported that nearly half of students entering 9th grade in many schools will not graduate and most dropouts cite failure to pass Algebra I as the primary catalyst. We know that students who pass Algebra I have a 95% graduation rate and the pre-algebra studies of grades 6-8 prepare them for that success.


Component One: One Number, Many Names. This component explores the different representations of rational numbers so a student can answer the important question, “What is the most useful name for 3 ½ in this situation?” The ability and confidence to answer this question provides flexibility that allows the young mathematician to participate in conversations about the best way to solve important problems.
Component Two: Numbers and Their Opposites. A second component focuses on integers and provides students the understanding to make sense of the algorithms for adding, subtracting, multiplying and dividing these positive and negative numbers.
Component Three: Multiplying and Dividing Fractions to Solve Problems. This component extends the study of parts and wholes from the 3-5th grade course (Building Blocks for Understanding Mathematics) and provides strategies to help students understand the why and how of multiplying and dividing fractions to solve important mathematics.
Component Four: Making Sense of Proportional Reasoning. The final component of this course addresses the relationship between numbers as displayed in ratios and proportions. Discussion will focus on the importance of developing proportional thinking and will offer strategies that relate proportional thinking to its many applications with percent, scale drawings and finding unit cost. The relationship between sets of numbers displayed in a data tables will be studied in preparation for the study of linear algebra.



Foundations For Understanding Mathematics: Grades K-2

Building Blocks For Understanding Mathematics: Grades 3-5

Algebraic Reasoning

Geometry: The Shape of Our World

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