Students practice choosing a method to find lengths of sides of triangles or angle measures using triangle theorems and formulas using this interactive resource. Decisions are made based on the information initially given.

Composing Transformations--This is part four of a four-part e-example from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math Investigations.

This lesson requires students to explore quadratic functions by examining the family of functions described by y = a (x - h)^2 + k. This lesson plan is based on the activity Tremain Nelson used in the video for Part I of this workshop.

This lesson teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases.

The purpose of this task is to have students create and analyze attributes of Venn diagrams, then make sense of the data. Students will add academic vocabulary (mutually exclusive, joint, disjoint) and will distinguish between conditional probability and using the addition rule. At the end of the task, students will be able to:
● Create Venn Diagrams that highlight specific data.
● Understand mutually exclusive, joint (intersection), and the Addition Rule using Venn diagrams.
● Distinguish between conditional probability and the Addition Rule.
● Get out vocabulary such as joint, disjoint, mutually exclusive, Addition Rule, and conditional probability.
● Analyzing data from a two way table and from probability notation to create various Venn Diagrams

In this lesson, students examine the geometric process known as triangulation and simulate the Global Positioning System by using triangulation to locate a target.

This task provides opportunity to extend the work of factoring and working with the area model for quadratics to those of the form !!! + !" + !, with an a-value other than one. Students will work to see how the area model connects with quadratics of this form and how both factored form and standard form connect with the area model. The task begins with expressions that have a common factor between terms, and continues to other expressions with ! ≠ 0. The distributive property will be used to verify the work and move to efficiency as combinations of the factors of a are considered with the combinations of the factors of c.

The purpose of this task is to practice working with the arithmetic of irrational and complex numbers and to make conjectures as to which of the sets of integers, rational numbers, irrational numbers, real numbers or complex numbers are closed under the operations of addition, subtraction and multiplication; that is, the sum or product of any two numbers from the set always produces another number in that set. Students also experiment with the closure of the set of polynomial functions under the operations of addition, subtraction and multiplication. From this perspective, the set of integers behave in the same way as the set of polynomials. Once polynomial division has been introduced in Mathematics III, it can be shown that neither set is closed under the operation of division—dividing two integers results in a rational number and dividing two polynomials results in a rational function.

The purpose of this task is for students to understand equivalent expressions obtained from factoring trinomials. In the task, students use area model diagrams to identify the sides of the rectangle, and thus, the factors. In the previous task, Factor Fixin’, students factored trinomials in which all of the terms are positive. This task builds on that work to include factoring expressions that have both positive and negative terms. The problems are carefully selected to help students see number patterns that they can use to become fluent with factoring. Students write expressions in both factored form and standard form.