This course examines topics that build on students’ firm foundation of counting and number sense, basic addition and subtraction, place value, and the ability and confidence to apply their knowledge to solve important problems. Along with a discussion of content topics essential for mastery in grades 3-5 and research-based strategies used by successful teachers to ensure that mastery, this course presents information about how the preadolescent brain learns and how this should influence instruction.
Component 1: Component One: Teaching Mathematics to the Preadolescent Brain. It seems reasonable that efforts to teach are consistent with how the brain learns. This first component uses what brain researchers are learning about the preadolescent brain to suggest guidelines for math instruction in grades 3-5.
Component Two: Understanding Our Number System. This component focuses on expanding students’ understanding of their number system, how numbers are composed and decomposed, and the relationships between numbers in their various equivalent forms.
Component Three: Using Multiplication and Division to Solve Problems. An understanding of multiplication and division as repeated addition and subtraction and skills that provide accuracy and efficiency in problem solving are the focus of component three. Strategies proven successful for initial instruction and interventions with those who struggle are presented.
Component Four: Parts and Wholes. Component 4 focuses on the part-whole relationships of fractions and decimals. Discussion begins at the concrete level to insure that each student understands how whole numbers can be broken into equal parts, how fractions expand our number system, and how equivalent fractions name the same value.
Component Five: Adding and Subtracting Fractions. This component uses students’ understanding of equivalent fractions as the foundation for teaching the algorithm of adding and subtraction fractions to solve problems.