Teaching Rational, Irrational, and Pythagorean Theorem online

Abstract

This unit consists of two parts. The first part is a study of the numbers system. The second part is a study of the Pythagorean Theorem. The central focus of this unit involves students deepening their understanding of rational and irrational numbers though simplifying and estimating numbers. In this unit, students must have the ability to identify what rational and irrational numbers are (NY-NS.1). Then students learn about perfect squares and cubes (NY-EE.2). Students are going to need that knowledge to estimate the value of non-perfect squares and cubes. Then to conclude the unit, students must place rational and irrational numbers on a number line (NY-NS.2). In the second half of the unit, we dive into the Pythagorean Theorem. The central focus for this half of the unit is for students to conceptually understand the Pythagorean Theorem and be able to use it in different situations. However, before we can talk about the Pythagorean Theorem, students need to have the ability to solve equations with ????2 and ????3(NY-EE.2). Then we can talk about the Pythagorean Theorem and how to find the length of the hypotenuse (NY-G.6). Then students must be able to explain what the converse of the Pythagorean Theorem is. This leads students to determine the length of the missing side. Students will then determine if a triangle is a right triangle given the side lengths (NY-G.6). Then students will use the Pythagorean Theorem to find the distance of a diagonal line in the coordinate plane (NY-G.8). Finally, students will use the knowledge of the Pythagorean Theorem to solve real-life problems (NY-G.7). The structure of the lesson