# Activities

• • ##### Author Aust Senior

2 Hours

• ##### Device
• TI-Nspire™ CX

5.0

## Probable Factors #### Activity Overview

What is the probability a randomly generated quadratic will factorise? This investigation looks at a substantially reduced set of equations. Dice are used to determine the coefficients. The investigation starts by using a simulation and reducing the set further by considering integer factors. The activity is a wonderful mix of algebra and probability, with extension options available for sampling distributions. A great option for a Problem Solving and Modelling Task.

#### Objectives

Students set up a simulation to help evaluate the reasonableness of pending theoretical calculations and solutions. Students draw from a mixture of mathematical concepts and procedures from previous units to help explore the problem. Students use a mixture of data, statistics, graphs, algebra and logic to support their findings. The nature of the task means that all student work will be unique!

#### Vocabulary

• Quadratic Equation
• Binomial
• Coefficient
• Probability
• Experiment

#### 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.