Properties of Water

Properties of Soil and sand

Nutrients for plant growth

Technology

R

Analyzing data

LocalGround

A program that collects geological data

**Consequential Task**

**Design a schoolyard garden using mathematics, physics, chemistry, environmental science, and economics.**

Economic

Domestic policy

Profit maximization/minimization

Equilibrium point

Cost-Production

**Mathematics**

**Food**

Engage

Logistics

Explore

Explain

Elaborate

--- Calculus I

Logistics

Lesson Sources

Constructive teaching pedagogy through collective knowledge

Foster Communities of Learning, from Brown and Campione

Sharing information

Performing a consequential task.

Ms. Chase

Lesson Sources

Focus/Essential Question

Student Learning Objective

California State Standard

Student Prior Knowledge

Lesson Outline for Your Student

Lesson Rationale

Materials and Technology List

Preparation Tasks

Safety Concerns

Evaluate

Focus/Essential Question

This lesson focus on how to interpret the relationships between population growth and food production from a mathematical perspective, so that students can use this knowledge to design a both prolific and sustainable garden.

Student Learning Objective

Synergistic momentum with group work.

Meta-cognitive learning process.

Students should master the use and reasoning for the relationships among functions, first derivative of the functions and second derivative of the functions.

Students also will be able to explain the mathematical meaning of an integration and the practical meaning of their calculations.

Preparing students to perform the consequential task.

Student Prior Knowledge

Students should have know how to:

Compute definite integrations

Perform basic mathematical computations including, addition, subtraction, multiplication, and division.

Use TI-83/84 graphing calculator

Tracing functions to find their intersections and zeros with graphs and tables

Calculating derivatives

Integrating a function with given range.

However, it is very likely that there are academic gaps among students, which means teachers need to assess and utilize students’ prior knowledge by either giving warm-up questions or providing group activities to clear any misconceptions.

Preparation Tasks

Research about the statistics of Berkeley, in terms of population and land.

Preparing students’ worksheets of food consumption and population growth

Research about the statistics of Norway, US, India, China, Mexico, and French, in terms of population and food production.

Provide scaffolding questions for students to graph the first derivatives and second derivatives of the functions.

Given specific period of time to integrate the area under each curves, and interpret the meanings for what they calculated.

PowerPoint and Overhead are used for any instructions and examples that need to be shown to class.

Buying candies is to personalize the experience of food consumption at Berkeley.

Teachers may need to rearrange tables into group of four or more if needed.

California State Standard

This lesson relates to the following Standards for Mathematical Content in the Common Core State Standards for Mathematics:

Describe qualitatively the functional relationship between two quantities by analyzing a graph. (8.F)

This lesson relates to the following Standards for Mathematical Practice in the Common Core State Standards for Mathematics:

Reason abstractly and quantitatively. (2)

Construct viable arguments and critique the reasoning of others. (3)

This lesson relates to the following Higher Mathematics Standards in the Common Core State Standards for Mathematics:

Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function. (4.1, Calculus)

Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems. (27.0, Calculus)

Materials and Technology list

Information sheet about statistic of Berkeley

Worksheets of calculating food consumption and population growth

PowerPoint and Overhead

TI 83/83 Calculators

Candies

Lesson Outline for Your Students

Day 1: Engage-- thinking about the trade-offs between food production and land use for Berkeley.

Day 2: Explore-- using data to graph population growth and food consumptions for given a period of time for different countries.

Day 3: Explain-- reflecting on what they observed from the graphs that they made, the meanings for the result that they calculated.

Day 4: Elaborate-- thinking about how to improve food production for Berkeley

Lesson Rationale

Hypothetical model in the topics of land use and food production at Berkeley

Lead to the notion of how to produce enough food to feed everyone.

From a mathematical approach

Find the population growth and food production rates across the world

Interpret the meanings for the trend.

Redirecting students to think about the reality in Berkeley

Introduce the idea of designing gardens.

To complete the ultimate goal, students also need to incorporate the knowledge from other fields.

Explain

Discussion for observation and plain thinking

Prompts for foster sharing and critical listening and thinking

Major observations and conclusions

Encourage for critical thinking

Encourage Critical thinking

Students will be simulated with questions similar to the following:

Explain whether the scenario, “population increases, food production decreases, average personal food consumption increase” is feasible or not. This will also encourage to think about other influencing factors.

More Prompts

Students will follow a number of questions:

What did you noticed about each of the result in year 1960, 1980, 2000 and 2010 ?

Can you find a trend, and what do you think this trend is meant?

What are some similarities and differences among each countries in terms of food production?

In addition to the population growth, what else might cause this phenomena?

What evidence would support your claims?

**E-LAB-OR-ATE?!?!**

BIG IDEA!

* Project

* Guidelines

* Project Breakdown Steps

- Research

- Research Question

- Technologique

- Interviews

- Beginning of Project Building

- Mock Presentation

- Vote?

- Take it to the...Dean!

Build your very own community garden!!!!

Project

Guidelines

Groups of 4 (Make sure even # of groups)

Each Group responsible for an equal sized portion of the garden

One crop per section/ group

Each pair within the groups will interview two food producing establishments and each student individually will interview a friend or family member

Each group responsible for proposal

The final project will be to convince the rest of the class why they should agree to their proposal and end goal being to convince the principle

Project Breakdown

1. Research

2. Research Question

3.Technologique

Continued...

4. Interview Questions/ Mock Interviews

5. Interviews

6. Beginning of Project Building

Cont...

7. Mock Presentation

8. Vote?

9. Take it to the...Dean!

**Engage**

1. Choose: You either have a house, or a farm.

-Farm: you get two candies, but you can't sit down

-House: you can sit down, but you don't get candy

2. Choose any seat you want.

3. If you have extra candy, you can choose to share it with someone who has no candy. If you do share, you can sit down.

What's the point?

Prompt thinking about agriculture and population

Students must work together

Use of logic and algorithm

Introduction to consequential task

Physics

Making Measurements

Mass

Volumn

Density

Environment Science

Air quality

Waste recycling

Land restoration

Biology

Photosynthesis

Ecosystem

Yeast process

**Explore**

**Using data to graph population growth and food consumption around the world**

=

Population Growth in America vs. India

Now students are given a variety of questions in which they analyze the graph and apply

Get two graphs for their country (population growth and agricultural index).

Be assigned a country.

Use tracing paper to overlay the two graphs and answer questions about the composite graph.

Each Group Will:

Graph the derivatives of the two original graphs, overlay them, and answer questions about the composite graph.

Let's do an example!

+

Food Production in America vs. India

=

+

After this, groups will change: One person from the India group and one person from the America group will join up and share their experiences.

Which increases faster? How do you know?

National-wise, India has a relatively faster increase in population because the rate of India population growth is about 18.2 Million people per year and the rate of US population growth is about 7 Million people per year based on the increase from 1990 to 2000.

Population growth for India and US

Which increases faster? How do you know?

National-wise, India has a faster increase in food production because the rate of food production for US is about 1.8 per year and the rate of food production for India is about 2.2 per year based on the increase from 1990 to 2000.

Can you find a trend? What does this mean in terms of food production and population growth?

In general, food production and population are increasing for both US and India, but India population and food production grow faster than US ones.

Food Production for India and US

Do you think Indian per capita food production more than US have, and why?

No, because the initial average food production in US is about 0.3088 per million people in the year of 1990, but the initial average food production in India is about 0.0806 per million people. Looking at the year of 2000, the average food production in US is about 0.3416 per million people, but average food production in India is about 0.0882 per million people.

This means that the US per capita food production increase more than 10.6 percent from 1990 to 2000, but India only increase about less than 9.5 percent.

**Example**

Make a graph

What does the area under the graph represent?

The area under the curve represents the total per capita food production from 1990 to 2000.

Algorithm