# Frogs, Fleas, and Painted Cubes

## Topics

Quadratic functions, equivalent quadratic expressions

## Overview of Changes

*Minor Changes* Some of the problems have been rearranged.

## Description of Changes

### Investigation 1: Introduction to Quadratic Functions

Investigation 1 is the same as CMP 2 with minor tweaking.

### Investigation 2

Problem 2.2 is a combination of the old Investigation 2.2 and 2.3. The distributive property has received more attention in grades 6 and 7 so we felt the development could move more quickly to multiplication of binomials. The distributive property is used to write equivalent quadratic expressions using the context of area of rectangles. Both cases, ax(x + b) and (ax + b)(cx + d), are addressed. The focus of 2.2 is on multiplying binomials or writing an expression in expanded form.

Problem 2.3 is the old 2.4 and focuses on factoring quadratic expressions.

Problem 2.4: The old 2.4 was replaced with a more hands on introduction to graphing quadratic functions. Students first graph quadratic functions when the quadratic expression representing the dependent variable is written in the form ax2 + bx + c and next when it is written in form (x+a)(x + d). They identify and predict special features of a quadratic function from its graph and equation. Intercepts and maximum/minimum are the main features. The line of symmetry is introduced.

### Investigation 3

The first three problems are the same with minor edits. Problem 3.2 is the old 4.3 At the suggestion of teachers Problem 4.3, *Functions and Patterns of Change*, was moved to this investigation.

### Invesitgation 4

This investigation is essentially the same except for 4.3, *Pulling It All Together* which was moved to Investigation 3.

Problem 4.4: This problem contains a set of cards each with clues such as a graph, table, equation, or information on intercepts or maximum/min. Students sort the cards into families and describe commonalities. They also write another equation that could fit the family and then identify one or more application that would fit with the family. This looks at quadratic, linear, exponential functions as well as inverse and simple cubic functions.

### Overall Changes

Less focus on distributive property, more focus on multiplying binomials; card sort activity with different functions.

New Investigation | Changes in CMP2 Investigations |
---|---|

Investigation 1 Introduction to Quadratic Equations |
Investigation 1 is the same with minor tweaking |

Investigation 2 Quadratic Expressions |
Investigation 2 is similar to CMP2 Investigation 2. Since the distributive property is developed in 6^{th} and 7^{th} grade, the focus in this investigation is more of a review. There is more focus on generalizing features of the graphs of quadratic functions. |

Investigation 3 Quadratic Patterns of Change |
Investigation 3 is similar, except for the focus on patterns of change have been moved from Investigation 4 to this investigation. |

Investigation 4 Frogs Meet Fleas on a Cube: More applications of Quadratic Functions |
Investigation 4 is the same except for the format of Problem 4.4 |