#### Activity Overview

What is the probability that a randomly generated quadratic will factorise? This investigation looks at a significantly reduced set of quadratics using dice to generate the coefficients. The coefficient of x is the sum of two dice and the constant is the product of two dice. Simulation is used for predicting the probability followed by theoretical computations.

#### Objectives

- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
**(ACMNA213)**

- Expand binomial products and factorise monic quadratic expressions using a variety of strategies
**(ACMNA233)**

- Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
**(ACMNA239)**

- Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence
**(ACMSP246)**

#### Vocabulary

- Quadratic Equations,
- Distributivity,
- Monomials,
- Binomials,
- Probability,
- Experiments

#### About the Lesson

Students create a simulation using TI-nspire that produces four dice rolls simultaneously. The outcome from each is used to form a single quadratic equation. TI-nspire is then used to determine if the quadratic factorises, a simulation that is repeated by students to obtain an approximate answer to the questions "What is the probability that a randomly generated quadratic will factorise?" Students are then guided through a series of scaffolded questions to determine the theoretical probability.