Using their knowledge on exponential growth, students will forecast the population of their assigned community by the year 2013 and identify the possible problems encountered by the community because of population growth. The students are divided into groups composed of five members, with each taking on different roles as demographer, mathematician, statistician and multimedia designer. They have to visit www.forecastingproject.blogspot.com * the blog site of the teacher for the details of the roles. Students will have to create a blog site also to be used as a collaborative tool and a communication tool as they go through the process of making the project. The product is a multimedia presentation on the result of the research they have to conduct and upload it in the blog site or the wiki site that they will create. (Refer to Teacher’s Guide (doc). An assessment timeline is use to monitor and to evaluate the continuous progression of their work.

Curriculum Framing Questions

**Essential Question**

How can we know what lies ahead of us?**Unit Questions**

How can population be computed?

How can the increase in population affect the health condition of people?

How can population growth affect the life’s condition of people?

How to determine the rate of increase or decrease of exponential growth or decay?**Content Questions**

What is exponential growth/function?

What are the properties of exponential functions?

How to determine the trend of a given exponential function?

How to determine the zero of an exponential function using the laws of exponents?

How can the graph of exponential functions be illustrated?

**Prerequisite Skills**

- Knowledge on exponents
- Research background such as formulating hypothesis and technical writing
- Creation of multimedia presentation
- Interviewing skill
- Data gathering procedure, survey skill

**Instructional Procedures **

**First session
**Motivational activity regarding social issues, problems and concerns. Ask the class a question whether there is a possibility of predicting our future? Introduce the essential question “How do we know what lies ahead of us?” Draw students in understanding the relevance of population and how population makes sense in the overall perspective of humanity. A graphic organizer (doc) is used in the brainstorming session on their knowledge of population, question and answer activity and KWL activity. The following unit questions will be given to the students in this session:

1. How can the increase in population affect the health condition of people?

2. How can population growth affect the life’s condition of people?

**Second Session (2 hours)
**Presentation and discussion of exponential function. After the presentation, discussion and checking of the interactive site, students need to answer the following questions:

1. How can population be computed?

2. How is the rate of increase or decrease of exponential growth or decay determined?

3. What is exponential growth/function?

4. What are the properties of exponential functions?

Students will Refer to powering and exponential growth (doc) reading for in depth understanding of the topic. Visit an interactive site (http://www.analyzemath.com/expfunction/expfunction.html *) that will help the students understand exponential function and let them answer the problems posted in the site by group.

The students will answer the following questions:

1. How is the trend of a given exponential function determined?

2. How is the zero of an exponential function using the laws of exponents determined?

3. How can the graph of exponential functions be illustrated?

In this web quest you will investigate population growth on a particular area. Working in groups you will study the population growth of the different barangays in Davao City. Identify the trend in the population increase every year until 2013. Relate the population growth data with the data on different diseases encountered by barangay every year from 2003 to 2013.

Students will come up with a projective profile of the population of the different barangays by 2013. Come up with hypothetical statement relative to population growth and the health problems encountered by barangay assigned to each group. Each group will come up with a tabular presentation of data, computation of the increase of population integrating the concept of exponential function, formulate hypotheses based on the information gathered and design a power point presentation to show the result of the investigation. The whole class will then process the outputs of the different groups by comparing and contrasting the result of each group.

You will be assigned to a team of five students. Decide on what role you are going to take.

**ROLES/WORK**

**Data/Research Analyst
**Gather data about the population of a specified barangay assigned to your group. You will have to contact the local government unit which is the barangay and find out where you can get pertinent data regarding the population for five years. The data should be from 2003 – 2008. Make a tabular representation of the data gathered. In your presentation see to it that you will have a data showing the age bracket such as children, adolescence, adult. Prepare population forecast. Works closely with mathematician.

(two students)

Responsible for gathering data in relation to size, movement of people in an area that relates to human population such as health. Record the health problems encountered by the people in barangay assigned to your group following the age bracket such as children, adolescence and adult. Make a tabular presentation of the data gathered also from 2003 – 2008.

Will do the basic statistical analysis of the data gathered. Make a graphical representation of the data and formulate hypotheses based on the information provided by the data.

Will Study the trend of the population and presents a mathematical computation that will relate exponential function to population growth. Show the solution of the computation. Work closely with research analyst and demographers.

There will be an orientation about the activity inside the classroom where you will be group as a team of five with each member has a specific role to play as outline above.

(Data/Research Analyst)

1. Identify person in the local government unit who is responsible in keeping the population record of a particular barangay. Be sure to get data from 2003-2008 and record it properly. Come up with a matrix form so that you will have an organize data, where you will include the break down of the population from children, adolescence and adult bracket. (2 days) http://projects.edtech.sandi.net/staffdev/tpss99/processguides/interviewing.html * Please refer to this website to guide you on how to interview a person in-charge of the information you want to gather.

(Mathematician)

2. From the data gathered prepare a population forecast up to year 2013 applying your knowledge in exponential function.

(Demographers)

3. Identify person in the Barangay health center responsible for keeping the record on health problems focusing only on five major diseases per year affecting the specified age group.

4. Prepare a matrix table (doc) to organize your data gathered capturing pertinent data for your final output.

Analyzing the information gathered

(Statistician)

The gathered data will then be forwarded to the statistician for the analysis of it, make a graphical presentation, and formulate hypotheses regarding the data. Analysis will focus on the rate of increase or decrease of barangay population taking into account the age group, the different health problems encountered in relation to increase of population.

Transforming Information into a product

(Mathematician)

Referring to the data gathered by research analyst and demographers, mathematicians will then compute and forecast the possible number of population in different age group, what part of the population will likely be affected by a particular health problem applying the knowledge on exponential function.

(Multimedia Designer)

After the data/research analyst, demographers, statistician and mathematician have done their work its time for the multimedia designer to plan for a power point presentation. He will be responsible for capturing in the presentation the overall concept, design and layout give appropriate explanation on the result submitted by the other members through brainstorming. Tips (ppt) and guide (doc) about the presentation is provided for you.

Upon completion of Webquest activity students will have a realization on the importance of connecting the topic in the classroom to real life issue and how it could be of help in coming up with ways in preparing for whatever happens in the future. It will help them realize that we can make a difference if we do plan ahead of time and if we develop an ability to forecast. Forecasting as defined by Dunn (1994) is a procedure for producing factual information about future states of society on the basis of prior information about policy problems. The result of their project can be presented to barangay and can be very useful for planning alternative solutions to issues being covered in the project. Results should be given to the local government in order to address issues pertaining to growth rate of population and the possible problems or factors that may be affected because of the population growth.

Accommodations for Differentiated Instruction

Students with special needs have to be grouped with somebody who can help and assist him/her. Give the student a role that he/she can perform according to his/her ability. Don’t give complex task.

**Nonnative Speakers**

Should be grouped with the native speakers to assist him/her, or identify somebody who is a good translator in order to help the student. Direct the student to a site with a language translator or he/she can use a specialty search engines such as Language Tools at http://www.itools.com/lang/ *

**Gifted/Talented Students**

Give complex task such as additional problems on exponential function for solving as part of exercises or assignment. A research report can be a challenging task for the gifted students. The research report should be evaluated using the rubric.

Forecasting the Future

**Year: **Fourth Year High School

**Subject: **Mathematics

**Time needed: **Three weeks, number of hours is specified per session.