Lessons and Tools for Teachers

#### Lessons for Complex Numbers

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• Let's Understand Multiplication of Positive and Negative Numbers - … the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades …
• Discovering How to Subtract Rational Numbers Using the Additive Inverse - … the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades …
• Jumping Beans: Adding with Open Number Lines - … how we decomposed the numbers. Which number would be easier to decompose? Why? Students should evaluate both numbers in the number sentence to determine … decomposing numbers. Students who are not fluent with decomposing numbers will need to practice using the open number line with less complex numbers. (Possibly using numbers up to 300 when adding.) Extensions: Students who are proficient with adding using the open number
• Stacking Squares - … number can be pulled in front of the radical sign. Then, decompose the number in front to various quantities. For instance, the number … ask students to compile other sets of numbers that will work for a given number of participants. Teacher Reflection How engaged were … Expectations Number & Operations 9-12 Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as …