# Vincent Accardi Unit Plan

## Welcome to Math 701

In our first unit of study we will be looking at the ratios we looked at in 6th grade and turning them into Rates and more specific, Unit Rates. In addition we will discuss what a "constant of proportionality" is and its context in real life examples.

## Lesson One: An Experience in Relationships as Measuring Rate

In this introductory lesson, we will be discussing the very important idea of a Unit Rate. Unit rate is often a useful means for comparing ratios and their associated rates when measured in different units. Upon completing this lesson, the students will be able to identify that the unit rate allows us to compare varying sizes of quantities by examining the number of units of one quantity per one unit of the second quantity, this value of the ratio is the unit rate. In this lesson, the students will be completing several tables based on contextual clues and information. Upon completing these tables, the students will be asked which is a better buy? which is the faster rate? All of which are premised on the idea that the students will be able to reduce the ratios in order to compare values.

## Lesson 2: Proportional Relationships

This lesson is really one of keystone parts of the entire year. This lesson introduces the idea of proportional and goes about explaining how to identify proportionality or lack thereof. Vocabulary is going to be a focal point of the lessons as well as their 2 and 3 specific words as can be seen in the following summary of lesson 2: "Measures of one type of quantity are proportional to measures of a second type of quantity if there is a number so that for every measure of a quantity of the first type, the corresponding measure of a quantity of the second type is given by ; that is, . The number is called the constant of proportionality."

Within this lesson, the students are again asked to complete tables to identify ratios and more simplified rates. Once we approach this step, the scholars will then need to identify proportionality based on contextual evidence, tabular evidence, or simple arithmetic. One of the most important aspects of this lesson is that proportional relationships and ratio relationships describe the same set of ordered pairs but in two different ways. Ratio relationships are used in the context of working with equivalent ratios, while proportional relationships are used in the context of rates.

## Lesson 3: Walking Rates

In this lesson, we will focus in one walking rates in specific. The scholars are expected to arrive at a clear understanding of how a change in one variable affects change in the other variable (independent and dependent variables) as seen in a tables, graphs and/or equations. This lesson, which is also has an attached preview on Smore, is all about the Walkathon. The scholars will be recording their walking rates using stopwatches while walking down a measured and taped walking distance in the hallway. The scholars will attempt to predict their walking rates as fun, then actually record the rate. After, they will attempt to convert these rates into unit rates and subsequently use this information to answer several other applied questions. Specifically, they will use this unit rate to write personalized equations, write tables. and draw a graph based on their rate. After this activity, the students will also complete an exit ticket solving the same type of problems but with new numbers.