Work in this section prepares students to understand and apply the Pythagorean Theorem. First, students investigate properties of right and non-right triangles by looking for patterns between their side lengths and the squares of their side lengths. Some students may notice that for right triangles only, , where and are the legs of the right triangle and is the longest...

Work in this section explores different representations of rational numbers, further reinforcing the idea that rational numbers can be written as positive or negative fractions, or , while irrational numbers cannot. Yet both types of numbers still have a place on the number line. First, students find decimal representations of rational numbers using long division, building on skills learned in...

Work in this section begins with investigating square roots from a geometric perspective relating the areas and side lengths of squares and then transitions to working with square roots as numbers on the number line.

First, students find the areas of tilted squares using various strategies and estimate their side lengths by reasoning about the areas and side lengths of...

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

Work in this section connects the work with squares and square roots to the concept of cubes and cube roots. Students understand that represents the edge length of a cube with volume cubic units and is also the solution to equations of the form . Students approximate values of cube roots and plot those points on a number line, reinforcing...