LandscapersChallenge.doc

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Mathematics Senior Level Capstone Course Unit Overview

Title of Unit: Landscaper’s Challenge Unit Designers:

(Name and School Division) Rebecca Bienvenue – Stafford Chris DuBois – Stafford

Denise Glassford – Spotsylvania Kim Riddle – Spotsylvania Pam Bailey - Spotsylvania Context of the problem: Given a landscape, students are to design an efficient system that will water

the green areas at the optimal cost. Number of Class

Hours:

12.5 Unit

Design: Problem Based Unit Other Subject

Areas/Disciplines Addressed:

Environmental Science, Business Education (Accounting and Finance)

Driving Question:

How would you water a landscape at optimal cost?

Mathematics Content Addressed:

Area, perimeter, volume, circles (radius and diameter), budgeting, Pythagorean theorem, proportions, measurement conversions, estimation

MPE Addressed:

(Organizing Themes)

Problem Solving, Decision Making, and Integration

Verification and Proof

Assumption of Prior Knowledge:

Students will:

 calculate the length of the hypotenuse of a right triangle using the Pythagorean Theorem  find the area, perimeter, and volume of a given space

 use Excel to prepare a budget for the installation and maintenance of a watering system  use proportions to convert units of measurements

College and Career

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Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37

Communication (Oral and/or Written) E & A Technology E &A

Critical Thinking/Decision Making E &A Other: (Describe)

Major Products and/or Performances:

Group – Blueprint, budget, and 2-page paper Presentation Audience:

x Class

School

Individual contributions to group product Expert

Community Other:

Launch: Event or experience used to engage the students interest and inquiry:

Volume Estimation Activity

Materials: 5 different containers (examples: character cake pans as they all hold the same volume but have different surface area)

Have students rank the pans based on volume using a scale of 1 to 5 with 1 being the smallest volume and 5 being the largest volume. Have the students report out and record in a matrix. Discuss similarities and differences of the pans including surface area and calculation of surface area. Teacher makes decision whether or not to reveal that the cake pans all have the same volume.

OR Compare the distribution of water from different nozzle settings on a spray bottle. How many sprays does it take to cover a piece of paper? As an opening launch to the activity and the unit, the opening credit to the movie

Caddyshack could be used (1 minute in length). Evaluation: Formative Assessments

(During the Unit)

Interview Practice Presentations

Mathematicians Journal x Notes

Preliminary

Plans/Outlines/Prototypes (HO #2 and HO #3)

x Checklists

Rough Drafts Concept maps

Field Tests Other:

Summative Assessment Written Products, with a rubric x Peer Evaluation, with a x

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(End of Project) rubric

Oral Presentation with a rubric x Self Evaluation, with a rubric

x

Other Product(s) or

Performance(s), with a rubric

Other:

Resources Needed: On-site people, facilities:

Equipment/Technology: Computers with Microsoft Excel(or similar program), word processing software, and internet access

Materials:

Community Resources:

Landscaping/irrigation expert

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal x Small/Focus Groups

Whole Class Discussions Fishbowl Discussions

Survey Other:

Material Adapted From: (Provide credit for any materials or activities adapted from other sources.)

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U N I T C A L E N D A R

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TITLE: Landscaper’s Challenge Time Frame: 12.5 Hours

P R O J E C T W E E K S O N E A N D T W O

Notes – Developed for a block schedule.

Day 1 – Engage and Explain (HO #1 & Rubric)

Day 2 – Explain (HO #2 & HO #3)

Day 3 – Explore (guest speaker, research)

Day 4 – Revisit explain (HO #1, 2, 3, & Rubric)

Day 5 – Elaborate (students begin work)

P R O J E C T W E E K S T H R E E A N D F O U R

Day 6 – Elaborate (students working in groups)

Day 10– Evaluate (student presentations)

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Virginia’s Senior Level Capstone Course Instructional Plan

Unit Title: Landscaper’s Challenge

Driving Question: How would you efficiently water a landscape at minimal cost? Problem: Given a landscape, students are to design a system that will water the landscape at the optimal cost.

ENGAGE

 Introduce the Problem

Number of hours __0.5 hr__

Volume Estimation Activity

Materials: 5 different containers (examples: character cake pans as they all hold the same volume but have different surface area)

Have students rank the pans based on volume using a scale of 1 to 5 with 1 being the smallest volume and 5 being the largest volume. Have the students report out and record in a matrix. Discuss similarities and differences of the pans including surface area and calculation of surface area. Teacher makes decision whether or not to reveal that the cake pans all have the same volume.

OR – alternate introduction might be

Compare the distribution of water from different nozzle settings on a spray bottle. How many sprays does it take to cover a piece of paper? As an opening launch to the activity and the unit, the opening credit to the movie Caddyshack could be used (1 minute in length).

Students are presented the Landscaper’s Challenge problem:

A family is investigating ways to water the given landscape. How should the green areas be watered with concerns of time, cost, and efficiency?

Students are given a copy of the teacher’s evaluation rubric (HO#6), and the teacher describes expectations and final work products. Provide students with a copy of the Landscapers Challenge problem (HO#1a) and a plat of the family’s landscape (HO #1b). The teacher reviews the specific products required.

 Blueprint of the layout of the watering system  Cost analysis and budget for the installation and

maintenance of the watering system

 Minimum of 2 page paper providing a description of all materials and supplies needed for installation

Mathematician Journal Prompts

What is a blueprint and how will it be helpful for this scenario?

Brainstorm some ideas for ways to water a lawn.

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and maintenance of the watering system as well as mathematical justification of the team’s choices for materials and layout

 Oral presentation (5 to 7 minutes) to the family. Presentation needs to be flexible in the event the family has questions or desires changes.

EXPLORE Group Discussions

Number of hours _1 hr__

Tutorials and Resources

Pythagorean Theorem

 http://www.khanacademy.org/math/geometry/ triangles/v/the-pythagorean-theorem

 http://www.khanacademy.org/math/geometry/ triangles/v/pythagorean-theorem-ii

 http://regentsprep.org/Regents/math/geometry/ GP13/indexGP13.htm

 http://www.shodor.org/interactivate/activities/ PythagoreanExplorer/

Area, Perimeter (including composite figures)  http://www.khanacademy.org/math/geometry/

basic-geometry/v/perimeter-and-area-of-a-non-standard-polygon

 http://www.khanacademy.org/math/geometry/ basic-geometry/v/area-and-perimeter

 http://www.regentsprep.org/Regents/math/ ALGEBRA/AS1/indexAS1.htm

 http://www.shodor.org/interactivate/activities/ AreaExplorer/

Volume

 http://www.khanacademy.org/math/geometry/ basic-geometry/v/solid-geometry-volume  http://regentsprep.org/Regents/math/geometry/

GG2/indexGG2.htm

 http://www.regentsprep.org/Regents/math/ ALGEBRA/AS2/indexAS2.htm

 http://www.shodor.org/interactivate/activities/ SurfaceAreaAndVolume/

Proportions & Conversions

 http://www.khanacademy.org/math/algebra/ solving-linear-equations/v/writing-proportions 

http://www.khanacademy.org/math/algebra/ratios-proportions/v/u-s--customary-and-metric-units 

http://www.khanacademy.org/math/algebra/ratios-proportions/v/unit-conversion

 http://www.regentsprep.org/Regents/math/ ALGEBRA/AO3/indexAO3.htm

 http://www.regentsprep.org/Regents/math/ ALGEBRA/AM2/indexAM2.htm

 http://www.shodor.org/unchem/math/r_p/index.html

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Resources

www.irrigationtutorials.com www.toro.com/en-us/homeowner/do-it-yourself-irrigation/Pages/defaults.aspx www.rainbird.com http://www.ehow.com/how_4695906_install-sprinkler-systems.html

Teacher contacts and invites a professional in the field of irrigation and/or landscaping to the classroom to offer advice to students and is available for questions from students. If there is an agricultural program in the school, the teacher may also seek assistance or offer invitations to instructors in the agricultural program.

EXPLAIN Expectations for students work and working together

Number of Hours_2__

Each group of 3 students should discuss and complete HO#2 with the following information:

 What do you know?

Students should give answers such as: - Size of lawn

- Obstacles to avoid when watering

 What do we need to know? What questions does the problem raise?

Students should come up with questions such as:

- How much water does the lawn need?

- What types of watering systems are available? - What is the water volume output for various

watering systems?

- What time of day should you water the landscape?

- How much piping/tubing/garden hose do you need?

- How do you avoid watering obstacles such as trees, driveway, house, etc?

- If you use sprinkler heads, what is the ideal placement?

- Should you create watering zones?

- What is the cost difference for the various types of watering system (garden hose vs. sprinklers, etc)?

- What type of family lives in the home? What are the family’s needs?

Compare/contrast three different watering systems for a lawn.

How much water does a lawn need each week? Support your answer well.

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 Beginning Steps – Teams need to determine what steps they need to take first. Each group also completes the Problem Goal Sheets (HO #3) to map out a plan for their work as well as a list of which tasks each student in the group will work on.

 Resources needed- Groups develop a list of resources they need to complete the problem. This includes research that needs to be completed and data that needs to be gathered.

 Group members will reach consensus by listing expectations of each other and for the problem (refer to HO #2).

 Presentation to family needs to be flexible in order to make adjustments according to the family’s needs. It is suggested that students use Excel or a similar software product. All questions must be answered during the team’s presentation to the family. The presenters will be unable to return on the following day.

ELABORATE Students working in groups

Number of Hours__7.5___

Students working in groups using research to develop a workable solution to the following problem:

A family is investigating ways to water a given landscape. How should the green areas be watered with concerns of time, cost, and efficiency?

Each team’s solution should include the following:  Blueprint of the layout for the watering system  Cost analysis and budget for the installation and

maintenance of the watering system

 Minimum of 2 page paper providing a description of all materials and supplies needed for installation and maintenance of the watering system as well as mathematical justification of your team’s choices for materials and layout.

 The team must also make a 5 to 7 minute presentation to the family so that the family may wisely choose the watering system that best fits the family’s needs.

The teacher will assist as needed.

What is/are the biggest obstacle(s) in

completing this problem?

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EVALUATE Working groups submit products and make presentations

Number of Hours_1.5__

Students present their solution to an audience.

 Provide audience (class members acting as family members) with observation criteria/rubrics. (HO#4)  Each team will complete self and peer evaluations.

(HO#5)

 Teacher will complete observation rubric.(HO #6)

Map the Unit

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What do students need to know and be able to do to complete the problem successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.

Task:

Given a landscape, students are to design an efficient system that will water the green areas at the optimal cost

KNOWLEDGE AND SKILLS NEEDED Assumed

already learned

Students will self-assess

Will be learned during the unit 1.

Area, Perimeter, and Volume X X

2.

Pythagorean Theorem X X

3.

Proportions X X

4.

Excel or similar software X X

5.

Conversions of measurement units X X

6.

7.

8.

9.

10.

11.

What project tools will student’s use? X Know/need to know lists

X Daily goal sheet (HO #2 and HO #3) X Mathematician’s Journals

 Briefs/Memos  Task lists

X Planning Calendar

□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________

HO #1a

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