Extending Understanding for Success in Pre-Algebra: Grades 6-8 course cover image

About this Course

Why success in pre-algebra matters
Brain research explains why adolescents often exhibit impulsive behaviors, why they seek novelty and thrive when learning is relevant and social. The challenges of engaging middle school students to study pre-algebra hones the roster of successful middle school math teachers to a special elite group. However, these critical middle school years determine to a large degree success in high school.

Studies show that nearly half of students entering 9th grade in many schools will not graduate and that most dropouts cite failure to pass Algebra I as the primary catalyst. Research also shows that students who pass Algebra I have a 95% graduation rate—making the pre-algebra studies of grades 6-8 even more important.


  • One Number, Many Names—Explore the different representations of rational numbers to provide the flexibility allowing young mathematicians to participate in conversations about the best ways to solve important problems.
  • Numbers and Their Opposites—Focus on integers and help students make sense of the algorithms for adding, subtracting, multiplying and dividing positive and negative numbers.
  • Multiplying and Dividing Fractions to Solve Problems—Help students understand the why and how of multiplying and dividing fractions.
  • Making Sense of Proportional Reasoning—Address the relationship between numbers as displayed in ratios and proportions. Focus on the importance of developing proportional thinking with strategies that relate it to its many applications with percent, scale drawings and finding unit cost. Also look at the relationship between sets of numbers in data tables in preparation for linear algebra.



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