Mathematical Standards and Benchmarks are defined as the relationship of ... equivalent ratios can...

Mathematical Standards and Benchmarks CCSS.MA.7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.• CCSS.MA.7.RP.1: Compute unit rates associated

with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour.

• CCSS.MA.7.RP.3: Use the proportional relationships to solve multistep ratio and percent problems.

Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

CCSS.MA.7.G.6: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.CCSS.MA.7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects.

Supporting Standards and ValuesNa Honua Mauli Ola:

Photo by Jeff Kubinahttp://commons.wikimedia.org/wiki/File:Sandbar_shark_newport.jpg

• NHMO Value 14: Plan for meaningful learner outcomes that foster the relationship and interaction among people, time, space, places, and natural elements around them to enhance one’s ability to maintain a ‘local’ disposition with global understandings.

• NHMO Value 15: Engage in experiences which malama the entire learning community and the

environment to support learning and good practices of stewardship, resource sustainability, and spirituality.

• Learners will be able to . . . • . . . develop a sustainable food production system• . . . participate in conservation and recycling

practices and activities.

Ethnomathematics 2

WATER, WATER

Linda Higashi

7th Grade7-8 (60 minute) class periods

EVERYWHERE?

How might ratios and proportional reasoning be used to explain real world relationships? • Students will apply proportional reasoning to solve real-world mathematical problems

in a culturally relevant context.

Next Generation Science Standards

Hawaii Content and Performance Standards III (HCPS III)

MS-LS2 Ecosystems: Interactions, Energy, and Dynamics• MS-LS2-5: Evaluate competing design solutions for maintaining biodiversity and ecosystem services.

Science - Standard 1 -The Scientific Process: Scientific Investigation: Discover, invent, and investigate using skills necessary to the scientific process.• HCPS.SC.7.1.1: Design and safely conduct a scientific investigation to answer a question or test a hypothesis• HSCP.SC.7.1.3: Explain the need to revise conclusions and explanations based on new scientific evidence.

Career and Technical Education – Standard 1 – Technological Design: Design, modify, and apply technology to effectively and efficiently solve problems.• HCPS.CTE.7.1.1: Apply the design process through a set of methodical steps for turning ideas into useful and

ethical products and systems.• HCPS.CTE.7.1.2: Assess a product or solution for possible modifications.

Water, Water Everywhere?3

TASK

Authentic Performance TaskEngineers create designs by understanding the restrictions imposed by the nature of a product and by its purpose. Building must meet the needs of those using it, for example, in the northern United States buildings must be able to shelter people from cold weather conditions. The building must be able to maintain a comfortable indoor temperature even when outdoor temperatures fall below 0 degrees. Design constraints include the specifications and restrictions that will make the building useful.

You will be given a cardboard box that represents a house. Design a roof that will protect it from the rain and allow you to collect as much rainwater as possible.

Flow-rate calculations

The State Department of Parks and Recreation has an isolated sub-station on Oahu. The station is not connected to the grid. Recently added photo-voltaic panels provide the necessary electricity; however, crew members must carry in water supplies. The Department is researching strategies to limit impact on the environment by into installing a rain catchment system to provide crew members 30 gallons of non-potable water per day. The station’s square rooftop has a footprint of 625 square feet. Use the attached average rain data chart to design a water catchment system that will meet the needs of the station. Prepare a report detailing the design proposal, the necessary tank size, and the time it will take to initially fill the tank with rainwater.

Critical Skills and Concepts

Part 1 - Engineering Design problem

Part 2 – Performance Task

Other Evidence

• Using concepts of ratio and rate to solve problems.• Reason about multiplication and division to solve real-world ratio and

rate problems.• Reason about quantities – understand the relationship between two

quantities (how the change in one attribute impacts the second attribute).• Effective use of the Engineering Design Process (EDP) to design, test, revise

a system.

Ethnomathematics 4

BACKGROUNDTeacher Background Information

The ability to attend to two quantities simultaneously is critical to reasoning with ratios. Ratios are formed generally formed in two different ways. The first is to use the multiplicative comparison of two quantities where students need to be able to differentiate between additive and multiplicative comparisons. Students should build ratios by composing two quantities to create a ‘composed’ unit. Composed units can be either iterated (repeated) or partitioned (broken into equal-sized parts) and are important part of reasoning when used to support students understanding proportions. Proportions are defined as the relationship of equality between two ratios. This idea is a central hallmark of proportional reasoning. Students must understand that the ratio of two quantities remains constant even with changes to corresponding values of the quantities. Thus, students must understand that (a) equivalent ratios can be created by iterating and/or partitioning a composed unit, and (b) maintaining proportional relationships mean that changes to one quantity in the ratio (through multiplication or division) must be linked to multiplying / dividing the other quantity by the same factor.

Rainwater harvesting, a practice that has been used throughout the world for many centuries, diverts and stores rainwater for later use. Capturing rain as it falls can be done through a variety of ways for multiple purposes. Students explore water catchment systems in relationship to malama ‘aina. Calculation of rainwater collection is generally determined by the following relationship: Calculations of rainwater collection amounts generally include a factor of loss due direct loss and/or evaporation. Students accessing online resources may include this factor in their calculations. Students should explain all components used in their determination of the amount of potential rainwater collection amounts in the performance task.

Fostering a mindset of sustainability in keeping with Native Hawaiian’s cultural respect for the environment is the goal of exploring water conservation and recycling practices. Rainwater harvesting, one conservation system, is designed to capture and store rainwater for use in various purposes such as household needs, landscaping, and/or agriculture. This practice saves money and reduces demand on municipal water supplies, while making efficient use on a valuable resource that would otherwise be lost to waste. Sufficient and safe drinking water is essential to life, however, throughout the world, millions of people do not have consistent access to this basic necessity. Rainwater harvesting is one potential system to provide clean, reliable water sources that has been adopted in areas of the world where conventional water supply systems are not available. Students will be asked to malama ‘aina the land through understanding the natural rhythm of the environments seasonal changes of rainfall as students participate in water conservation.

Mathematical Understanding

Rainwater Harvesting Understanding

Cultural Connections

Water, Water, Everywhere?5

LESS

ONLearning PlanDay One

Students will know: Students will be able to:• Ratios are multiplicative

comparison of two quantities.• Proportional reasoning involves

relationships among ratios.

• Determine, represent, and calculate proportional relationships between quantities in tables, equations, diagrams and/or verbal descriptions.

• Compute unit rates.• Use proportional relationships to solve

multi-step problems.

Learning Goals

Teachers Action• Building Meaningful Student

Connections**: Provide a visual cue for the target mathematical concepts (Reproduce & display Diagram 1)

• Announce: Today we are going to activate your prior knowledge for the following standards: 7.RP.1 [Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units] AND 7.RP.3 [Use proportional relationships to solve multistep ratio and percent problems]. These concepts and skills will help you as you work on your next performance task.

• Say: ‘You will need to use these same types of skills for today’s Do Now**.’ Direct students to work together with your elbow partner to complete work on the problem. Remember to be ready to share your thinking with the class. Note: Teacher will post Do Now and circulate to address student needs during the problem solving process.

Learning Target: Explicitly review mathematical concepts to identify the concepts and skills students will apply (CCSS.MA.7.RP.1; CSS.MA.7.RP.3)Instructional Strategy : **Building Meaningful Student Connections (See: http://fcit.usf.edu/mathvids/strategies/bmsc.html

Student Actions:Students review poster – allow for discussion with elbow partner as neededmathvids/strategies/bmsc.htmlTime Frame: 1 - 2 min

Ethnomathematics 6

LESSONTeachers Action• Do Now: “Micah earned $43.50 for five

hours of gardening. At this rate, how much will he earn if he works for 7.5 hours?” [$65.25 – unit rate is $8.70/hr.]

• Possible Questions to support student learning (consider pre-selecting groups to be prepared to answer these questions in the whole group discussion)

• Explain in detail how you figured out your solution.

• How did you make your mathematical reasoning clear to others?

• Think of a method that can be used with any situation / quantity.

• What is the relationship between total earnings and hours worked?

• How many hours would Micah have to work to earn $113.10 [13 hours]?

• How much would Micah make for five hours of work if the hourly rate increased by $0.50 [$46.00]?

• Teacher asks pre-selected groups to share their solution process and mathematical thinking with the whole class. Lead the discussion to ensure that students understand the conceptual basis for finding unit rate. Discuss possible strategies to organize and use data. Note: student should recognize phrases associated with unit rate (cost per hour; for example: if it takes 1.5 hours to wash and wax a car the unit rate is 1.5 hrs. per car, 1.5 hr./1 car or 1.5 hr./car)

• After completing the discussion, ask: Are there any additional questions about the mathematics needed to complete the next performance task?

• Answer questions as needed.

Lesson Plan:** “Do Now” a classroom management routine designed to engage students in learning at the beginning of a class/lesson. (See: https://www.teachingchannel.org/videos/class-starting-teaching-strategy)

Student Actions:• Students work with elbow

partner to solve the problem. • Students practice active

listening skills as peers present their process

• Students turn and talk with their elbow partner to paraphrase and clarify mathematical thinking of presentations.

• Students ask clarifying questions as needed

Time Frame: 7-9 min

Student Actions:• Collaborative teams present

their mathematical thinking / solution pathway

• Students practice active listening as peer teams present their solution / mathematical thinking.

Time Frame: 5-7 min

Student Actions:• Students ask teams clarifying

questionsTime Frame: 2-3 min

Water, Water, Everywhere.7

LESS

ONTeachers Action• Explore: Show Act 1 “the faucet leaking”

video (~20 seconds)• Ask students – “What questions might you

have after watching the video?” • Record ALL questions (if a student offers a

‘repeated’ question – ask if you can combine the questions – and add a tick mark to the repeated question)

Leaky Faucet Task[video resources: http://threeacts.mrmeyer.com/leakyfaucet/] Download video from Liveinder Equipment: Computer with LCD projector; Internet access

Students brainstorm Possible questions include:• How long will it take to fill the sink

from start to finish?• How much water does it take to fill

the sink?

• How many drips are in a gallon?

Time Frame: 3-4 min

Students Actions: Students discuss the pros/cons of possible questions – students can advocate for any question.Time Frame: 2-3 min

Students Actions: Students individually use whatever process / logic they want to ‘guess’ an answer – how long will it take to fill the sink?Students individually determine an answer that is too high / too low.

Time Frame: 1 min

Students Actions: Students share their guess with their elbow partner. •Students participate in the process of sharing responses that are higher / lower to determine the highest and lowest guess from the class.

Time Frame: 1 - 2 min

• Lead students in a discussion to develop the target question: “How long will it take the sink to fill up?” Note: save other student-developed questions for individual exploration and/or another class session.

• Ask students to write down a guess (How long will it take to fill the sink?).

• Materials: Small post-its or scratch paper• Ask students to write down an answer they

know is too high . . . write down an answer you know is too low.

• Ask for volunteers to share their guess. After 1-2 student responses; ask students to turn to their elbow partner to share their response.

• Ask students to report if their partner shared a response that was higher. Poll the class to find the highest estimate). Post the highest estimate on the board.

• Replicate the process to find the lowest estimate. Post the lowest estimate on the board.

Ethnomathematics 8

LESSONTeachers ActionStudents Actions:

Students discuss resources needed to determine an accurate answer Time Frame: 2 min

Students Actions: Students work collaboratively in partner groups to solve the problem. Time Frame: 5 min

Students Actions: Students participate to brainstorm – possible information needed.Possible student questions:

• How many drops per second? [rate of leak]

• How many ml per second? [rate in ml]

• What is the capacity of the sink?

• How many ml are in one gallon?

Time Frame: 3 -4 min

• Concept Development – Act 2: Discuss the class data – note the different answers (range high to low) – ask students to consider what resources are needed to determine an accurate answer that will resolve the conflicting information.

• Brainstorm to determine • What information would be helpful

to have?• What tools are needed?• What tools do you already have?

• Teacher lists all student responses – no comments –Teacher provides answers to support student solution process. (See video clips on-line)

• Note information to provide:• 5 drops / second• 85 ml / 10 minute• Sink capacity = 3 gallons• 1 gallon – 3785.41 ml• Possible tools include: calculator, graph

paper, computers with excel software, graphing calculators

• Teacher assigns students to two-person groups. Students will solve the problem – remind them to be ready to prove that their answer is correct.


• Explain in detail how you figured out your solution.• How will you make your mathematical reasoning clear to others?• What method can be used with any situation / quantity?• What is the relationship between total time and amount of water (ml or gallon) in

the sink?• How much water is in the sink after 1 second? 1 minute?• How long does it take to fill the sink to the 1 gallon mark?


LESS

ONTeachers Action• Application: • Teacher – leads a discussion to compare the

estimates (high/low) to the final answer: ask pre-selected groups to share their solution process and mathematical thinking with the whole class. Ensure that students understand the conceptual basis for finding unit rate. Remind students of strategies to organize and use data used in the “Do Now.”

• Reinforce mathematical concepts as needed. • Teacher shows the Act 3 video reveal

[22 hours 4 minutes 41 seconds]

Students Actions: • Collaborative teams present

their mathematical thinking / solution pathway.

• Students practice active listening as peer teams present their solution / mathematical thinking.

• Students ask teams clarifying questions.


Students Actions: • Two or three groups

present their scenario and solution process.

• Non-presenting students practice active listening skills.

• Non-presenting students work in their teams to solve the presenting teams’ scenarios.


Students Actions: • Students work with their elbow

partners to develop a scenario• Students write their scenario

along with the solution process in a team journal.

Time Frame: 5 min

• The Sequel (Part 1): Ask students to describe a scenario that the leaking faucet would take a week to fill up something.

• Teacher circulates to answer questions and monitor understanding. See sample questions above.

• After groups have finalized their work, teacher allows two or three pre-selected teams to present their scenarios.

Ethnomathematics 10

LESSON

Teachers Action• Lesson Introduction: • Collaborative team process**: divide

students into triads. Ask each group to select one member for the following roles:

• Facilitator / Reporter: The facilitator keeps the group on task. The facilitator will be responsible to stay with the group poster and answer questions as needed (The reporter is permitted to request collaborative support from teammates as needed).

• Recorder: the recorder documents the group decisions and/or answers [Teacher will have poster paper and markers available]

• Reflector: The reflector / reporter leads the group in critical thinking. This person makes sure that the team reflects on how the team is working together and on what they have learned through the problem solving process.

• Ask the recorder to come to the resource center to get poster paper and markers.

• Ask students to identify the group facilitator/reporter; recorder; reflector [use this to ensure that each student has a role within the group structure – suggest adjustments as needed]

Students Actions: • Students assign task to each

participant.• Reporter comes to get poster

paper / markers for group work

Time Frame: 2 min

Day Two

Students would be able to: Students will know:

Students would be able to:

• Effectively use of the Engineering Design Process (EDP) to design, test, revise a system.

• Effectively use of the Engineering Design Process (EDP) to design, test, revise a system.

• Strategies to conserve and/or purposefully use water.

• The interrelationship between personal actions and global conditions.

• Understand conservation strategies that incorporate the natural rhythm of the water cycle.

• List multiple ways to conserve water.• Recognize wasteful uses of water in

their environment.

Learning GoalsEngineering Design Targets Cultural Learning Targets

Learning Target: “Waste Not, Want Not”-developing responsible water use habits through conservationLesson adapted from Environmental Protection Agency Education Resources [http://www.epa.gov/region07/education_resources/teachers/activities/wateractivity2.htm]Handouts and Teacher resources are available in the live binder – “Waste Not . . . “ tabInstructional Strategy: **Collaborative learning groups strategies and structures. [See: http://www.pgcps.pg.k12.md.us/~elc/learning1.html](See: http://fcit.usf.edu/mathvids/strategies/bmsc.html


LESS

ONTeachers ActionLearning Target:

Prepare ahead of time: bring two 2-gallon buckets. Label one with “Water Supply” and the second with “Water Used”. Fill the “Water Supply” bucket with two gallons of water. Duplicate and cut out water use number and letter cards (teacher sheets).

• Direct students to work in triads to discuss the ways they use water in a single day.

• Circulate to ensure students are on-task. Answer questions as needed.

• Encourage students to consider indirect use of water.

Students Actions: • Students participate in small

group discussion.

Time Frame: 2 min

Students Actions: • After 2 minutes – ask students

to categorize the list by type of usage (home, work, play).

• Students post their group work

Time Frame: 2 min

Students Actions: • Group facilitator stays with

the group poster to answer clarifying questions as needed

• Other group members circulate to posters and take notes (to be shared with group facilitator).

• Students share their notes with team mates. Team revises / refines the chart as needed.


• Announce: Groups now that you have brainstormed several water uses – please take 2.5 minutes to classify your entries by type of usage (home, work, play). The group will develop a visual display to share with the whole group.

• Have students post their display.

• Distribute 1 post-it notes to each student. Announce, you have 3 minutes to gallery walk and review each groups’ list. Take notes of unique water usage entries. Group members will be responsible to share their notes with the facilitator. Note: The group facilitator is responsible to stay with the group chart to answer questions from other groups.

Ethnomathematics 12

LESSONTeachers ActionLearning Target:

Whole Class Demo - Materials List:

• Two 2-gallon buckets• 2 gallons water• 2 measuring cups• Water Use cards (see attached)• Student sheets (attached)• Teacher sheet (attached)• Ruler• Scissors• Glue• Markers• Poster Paper (11X17 or larger)• 3 inch post it notes

ORCollaborative Learning Teams- Materials List: Prepare one set per student team

• Two 2-cup containers (for example: peanut butter jars)

• 2 measuring spoons (tablespoon size)

• Modified Water Use cards (see attached)

• Student sheets (attached)• Teacher sheet (attached)• Ruler• Scissors• Glue• Markers• Poster Paper (11X17 or larger)• 3 inch post it notes

Students Actions: • Students participate in small group discussion.

Time Frame: 2 min

Whole Class Demo:• Water Use Number Cards group – students read their

water use card aloud and confirm that the “Quantity Control Officer” removes the appropriate amount of water.

• All other students – monitor the process.• After all of the number cards have been read – the

“Quantity Control Officer” will read the remaining depth of water and record the total on the board.

• Repeat process with Water Use Letter Cards (note: consider allowing another student to serve as “Quantity Control Officer”)

Time Frame: 6 min

• After 3 minutes – have students return to their collaborative group

• Ask students to share their findings with the other group members – groups may revise / refine their chart as desired

• Whole Class Demo: • Randomly distribute “Water Use Number

Cards” to half of the students / teams and the “Water Use Letter Cards” to the other half of the students / teams.

• Begin with Group 1:• Assign one student to serve as “Quantity

Control Officer” – this person will remove the appropriate amount of water from the water supply bucket and place it in the bucket labeled “Water Used.”

• Begin with card 1 / A: Ask the student to read his / her demand and the amount of water is moved as needed. Continue process until all cards are used.

• Measure the depth of the water left in the “Water Supply” bucket. The “Quantity Control Officer” is responsible to record the results on the board.

• Repeat the process for Group 2 cards.


LESS

ONWhole Class Demo: After both water levels are recorded: students work in triad groups to discuss data and formulate explanations.


Whole Class Demo: Students individually write 3-5 ways to conserve water in their math journal.

Time Frame: 3 min

Collaborative Learning Teams: See above – modify as indicated for small group investigation.

Time Frame: <1 min

• Compare the difference in water levels between group 1 & group 2.

• Ask students to formulate explanations• Discuss strategies to conserve water.• Each student writes 3-5 ways to

conserve water.

Teachers Action

• Collaborative Learning Teams: • Assign one team member to serve as

“Quantity Control Officer” – this person will remove the appropriate amount of water from the water supply bucket and place it in the bucket labeled “Water Used.”

• Begin with card 1 / A: Ask the team members to alternate reading water use cards; the amount of water is moved as needed. Continue process until all cards are used.

• Measure the depth of the water left in the “Water Supply” bucket. The “Quantity Control Officer” is responsible to record the results on the board.

• Ask teams to post their final water level on the board.

• Ask students to discuss the class data... compare the difference in water levels between group 1 and group 2.

• Ask students to formulate explanationsNote: Discuss strategies to conserve water.

• After discussion – ask each student writes 3-5 ways to conserve water.

Ethnomathematics 14

LESSON

Student Actions: Students share their experience / knowledge about rainwater collection.

Time Frame: 2 min

Student Actions: Students brainstorm sources of water, responses documented in journal.

Time Frame: 2 min

Student Actions: Selected students share their responses. The rest of the class adds to their journal.

Time Frame: 3 min

Student Actions: Students participate in discussion of possible water sources. Encourage students to take notes in their math journals

Time Frame: 2 min

Teachers Action• Transition to Rainwater Collection

System engineering design project. • Introduce rainwater collection as one

method used to conserve water and protect natural resources. (Background information available in Live binder)

• Ask: Where do we get our water? While students discuss – circulate to monitor behavior, to answer questions as needed, to ask questions (to redirect student conversations), and to select possible students for sharing to the whole class

• Have 3-4 groups share their responses. • Possible discussion includes:

• Salt water (address the need to remove salt – desalination. The process is expensive and only used in situations where freshwater supplies are not available).

• Artesian wells• Lakes / rivers• Catchment systems

• Share: In some areas consistent freshwater sources are limited. Some of those areas use water catchment systems to collect water for drinking or other uses. Today, we are going to design a water catchment system.

• Assign students to continue working with their triad group.

• Distribute Engineering Project Journal (remind students to put their name on the packet – it helps!) (see Live binder – Engineering Project Journal tab)

• Post the supply list on the board. Each group will have:

• 1 corrugated cardboard box• scrap cardboard (2 square feet)• 2.5 linear feet of 12” aluminum foil• 10 drinking straws• 1 – sixteen ounce cup with lid (possible

substitution – use plastic wrap stretched over the top of the cup)

• 12 inches tape• Scissors• Ruler

Learning Target: Engineering Design Project: Rainwater Collection SystemHandouts and Teacher resources: See live binder – Engineering Project tabAdapted from: TechXcite – Discover Engineering! – “Green Building: Rainwater Harvesting” curriculum http://techxcite.pratt.duke.edu/curriculum/rainwaterharvesting.phpAdditional supplies:

• 2 gallon watering can• Scissors• rulers

Student Action:Students participate in discussion of possible water sources. Encourage students to take notes in their math journals

Time Frame: 2 min


LESS

ONStudent Action:Students discuss with members of their triad group.

Time Frame: 2 min

Student Action:Students discuss with members of their triad group.

Time Frame: Last 5 min of class

Student Action:Students copy supply list into their math journal.Students take notes as needed – begin completing Engineering Project Journal (Steps 1-3)

Time Frame: 4 min

Student Action:Students move to demo site – bring math journal and pencilStudents watch demo – encourage them to discuss with their triad group

Time Frame: 4 min

Student Action:Students share their observations (note: encourage students to note that the cardboard gets soaked without the use of a waterproofing materials.

Time Frame: 2 min

Student Action:Students begin planning in triad groups. If the group wants additional resource materials, they will be responsible to assign one member to bring it to the next class period.


Teachers Action• Review the design challenge and

specifications.• Describe materials available for the

challenge.• Move outside the classroom to a grassy

area and/or courtyard to demonstrate the testing parameters. Note: You will need to select a test site close to a water sourceNote: Before class the teacher will need to prepare the demonstration cardboard ‘house’ without a roof.

• Announce: I will demonstrate how the ‘rain’ will fall on your house. Carefully observe how the water falls so that you can design your catchment system to collect the most rainfall. Also note how the construction materials react to the rain. Use your data to design your system.

• Begin by pouring (approximately 1 gallon) water on the roofless house using a 1-2 gallon sprinkling water can. Pour so that most of the water lands on the top of the house. Announce that this is their design will be tested.

• Ask students to comment on the demonstration (they should note that the cardboard is not protected/ waterproofed. Ask students to consider this concern in their design.

• Announce that teams will have the remaining time in this period to plan. Construction and testing is scheduled for the next class period. Students will have 40 minutes to prepare their house.

• Announce – students should consider additional materials that they might want to bring from home – refer to the posted supply list

• Announce – groups will have 10-15 minutes to plan for their design

• Just prior to the end of the class session:• Ask – what questions might you have?• Answer questions – and have students plan

with their triad groups.

Ethnomathematics 16

LESSON

Student Action:Students work in their triad group to design / build / test / redesign their catchment system. Students develop a design plan – documenting the specifications, measurements, plan, and revisions in their design journal.


Student Action:Students bring their design, design journal, handouts, and pencilStudents take data on their design’s performance


Student Action:Triad group members discuss results, suggestions for improvement / modificationsStudents can ask other triad teams clarifying questions and/or offer feedback Each member of the design team receiving feedback/questions should note the comments in their engineering journalStudents work in triad teams to redesign prototype. Each student documents design modifications in the Engineering Project Journal.


Teachers Action• Group students in their triads (from

previous class session).• Students need to get the Engineering

Journal (distributed previous class period)• Announce – students will have 35

minutes to complete the design and building process.

• Circulate to ensure groups are on-task. Ask questions to help groups that are stuck.

• At the end of the 35 minute time – determine whether or not groups need additional time (limit the extra time to an additional 10 minutes – for a total of 45).

Day Three & Four

Students will be able to:• Effectively use of the Engineering Design Process (EDP) to design, test, revise a system• Develop a hypothesis, procedure, materials list• Design an investigation related to the topic

Engineering Design Targets

Learning Target: Engineering Design Project: Rainwater Collection System

• Move students to the test site. • At the test site, remind students to collect

data as to how much water their catchment system was able to capture. The teacher should pour the water at a constant rate.

• After each design is tested – ask the other teams to ask any clarifying questions and/or provide feedback to the design team. The design team should take notes

• Announce – work with your triad team to analyze the data. Take 10 minutes to redesign your prototype. Be sure to document the redesign in your engineering journal.


LESS

ONTeachers ActionStudent Action:

Students work in triad teams to rebuild prototype.

Time Frame: 7 min

Student Action:Students move to test site

Time Frame: 12 min

Student Action:Students bring their design, design journal, handouts, and pencil.Students take data on their design’s performance.

Time Frame: 15 min

Student Action:Triad group members discuss results, suggestions for additional improvement / modificationsStudents journal as Homework assignment – due next class period

Time Frame: 5 min

• Announce – use your redesign plan to build your second prototype. You have 7 minutes to complete the rebuild.

• Move students to the test site. • At the test site, remind students to

collect data as to how much water their catchment system was able to capture. The teacher should pour the water at a constant rate (Note students can ‘pour’ if you have adequate supplies)

• After testing all designs – teacher assigns students the following journal prompt as an individualized homework assignment

• Analyze your design – discuss the performance (i.e., how much water did your catchment system capture?)

• What are some things you noticed about your design and catchment systems?

• Which ideas worked? Why? Which ideas didn’t work as well? Why?

• Name one or two ways you might improve your design?

• Briefly discuss any examples of capillary action noted during the activity

Ethnomathematics 18

LESSON

Teachers Action• Collect Engineering Design Journal• Assign students to work in partner teams.

Day Five

Students will know: Students will know:• Ratios are multiplicative comparison

of two quantities.• Proportional reasoning involves

relationships among ratios.




How much rain can we collect?

Learning Target: Collect HomeworkRainwater Runoff – How much rain can we collect?Download from livebinder:“Rainwater Runoff” Powerpoint slides (Slide show of rainwater runoff and flooding - feel free to add ‘local’ slides)Equipment: Computer with LCD projector

Student Action:Students submit homework per standard class collection procedure.Students move to partner grouping.

Time Frame: 1 min

Student Action:Students discuss possible questions in partner teams.Students brainstorm Possible questions include:

• How much rain water can be collected from a typical rooftop for each 1 inch of rainfall?

• How much rain falls for each 1 inch of rainfall?

• How many square feet are in 1 acre?

• How do we determine the size of the typical rooftop?

Time Frame: 1 min

• Explore: Show Act 1 “Rainwater runoff” slideshow (~20 seconds)

• Ask – “In light of yesterday’s engineering design of a water catchment system, what questions might you have after watching the slideshow?”

• Record ALL questions (if a student offers a ‘repeated’ question – ask if you can combine the questions – and add a tick mark to the question)


LESS

ONStudent Action:Students discuss the pros/cons of possible questions – students can advocate for any question.Students individually use whatever process / logic they want to ‘guess’ an answer.Time Frame: 4 min

Student Action:Students participate to brainstorm– possible information needed.Possible questions:How many gallons of rainfall for each inch of rain per acre of land?How many square feet per acre?Time Frame: 2 min

Student Action:Students individually determine an answer that is too high / too low.Time Frame: 1 min

Student Action:Students share their guess with their elbow partner. Students participate in the process of sharing responses that are higher / lower to determine the highest and lowest guess from the class.Time Frame: 1 min

• Lead students in a discussion to develop the target question: “How much water can we collect from a typical house rooftop with 1 inch of rainfall?”

• Note 1: students will need to define the size of a ‘typical’ house / building rooftop. Students can use different size houses/buildings as long as they define the footprint of the roof.

• Note 2: Save alternate student-developed questions for individual exploration and/or another class session.

• Ask students to write down a guess (to how much water falls on a roof for each 1 inch of rainfall).

• Materials: Small post-its or scratch paper• Ask students to write down an answer you

know is too high . . . write down an answer you know is too low.

• Ask for volunteers to share their guess. After 1-2 student responses.

• Ask students to turn to their elbow partner to share their response.

• Ask students to report if their partner shared a response that was higher. Poll the class to find the highest estimate). Post the highest estimate on the board.

• Replicate the process to find the lowest estimate. Post the lowest estimate on the board.

• Concept Development – Act 2: Discuss the class data – note the different answers (range high to low) – ask students to consider what resources are needed to determine an accurate answer that will resolve the conflicting information.

• Brainstorm to determine • What information would be helpful to have?• What tools are needed?• What tools do you already have?

Teachers Action

Ethnomathematics 20

LESSONTeachers Action• Teacher lists all student responses

– no comments –Teacher provides resource information to support student solution process.

• Note information to provide:• 1 inch of rainfall results in 27,150 gallons of water

per acre• 1 acre = 43,560 square feet• 1 gallon – 3785.41 ml• 7.48 gallons per cubic foot• To calculate the (average) rooftop area → use area

of the rooftop ‘foot print’ • Possible tools include: calculator, graph paper,

computers with excel software, graphing calculators.

• Teacher assigns students to two-person groups. Students work to solve the problem, remind them to be ready to prove that their answer is correct.


• Explain in detail how you figured out your solution.

• How will you make your mathematical reasoning clear to others?

• Can you think of a method that can be used with any situation / quantity?

• What is the relationship between size of the rooftop and amount of rainfall (ml or gallon)?

• Teacher circulates to manage class behavior and use facilitative questions to ensure student group progresses toward a possible solution pathway.

• Application: • Teacher – leads a discussion to compare the

estimates (high/low) to the final answer: ask pre-selected groups to share their solution process and mathematical thinking with the whole class. Ensure that students understand the conceptual basis for finding unit rate. Remind students of strategies to organize and use data used in previous sessions – refer students to strategy poster.

Learning Target: How Long to fill a circular Water Catchment Tank???Download picture from the following site: Live Binder – Day 5 “Water Catchment Tank picture”

Student Action:Students work collaboratively in partner groups to solve the problem. Students practice active listening skills as peers present their process.Students will turn and talk with their elbow partner to paraphrase and clarify mathematical thinking of presentations.Time Frame: 9 min


LESS

ONTeachers ActionStudent Action:

Students participate in the discussion / respond to teacher questions.Two or three groups present their scenario and solution process.Non-presenting students practice active listening skills. Non-presenting students work in their teams to solve the presenting teams’ scenarios.Time Frame: 5 min

Student Action:Students work individually to compute Extension Task – task is to be completed for homework if not finished by the end of the period.Students submit completed task (to be completed as homework if needed).Time Frame: 15 min

Student Action:Students work with their elbow partners to develop a scenarioStudents write their scenario along with the solution process in a team journal.Time Frame: 8 min

• Reinforce mathematical concepts as needed.

• The Sequel (Part 1): Show picture of water catchment tank Ask students to determine how much rainfall is needed to completely fill the water catchment tank (start at completely empty tank).

Learning Target: How Long to fill a circular Water Catchment Tank???Download picture from the following site: Live Binder – Day 5 “Water Catchment Tank picture”

• Provide the tank dimensions – 20 foot diameter by 10 foot height. Note: students will have to calculate the capacity of the tank [23,600 gallons]

• Teacher circulates to answer questions and monitor understanding. See sample questions above.

• After groups have finalized their work, teacher allows two or three pre-selected teams to present their scenarios.

• Extension: Distribute “Kaneohe Monthly Rainfall Chart”

• Ask student to individually complete this next task: “If the water catchment tank is completely empty on March 1st – how long will it take the tank to completely fill up given the average rainfall temperature chart?” (Note: assign this task for homework if students cannot complete it during the class period.)

Ethnomathematics 22

LESSON

Learning Target: Water Drip Performance Task: Part 1: Note students work in partner teams to collect class data for the first part of the task. Part 2: Students work individually to complete the assessment task using class data.

Materials Preparation: Prior to class gather / prepare the following resource materials (See Livebinder powerpoint):

• 10 student computers with Excel software OR TI-nspire calculators

• Graph paper• 21 graduated cylinders (50 – 100 ml)• 20 pre-drilled water bottle caps

• Pre-drills bottle caps (drill in the center of the bottle cap)

• Drill 4 caps of each of the following sizes: • 1/16 inch• 5/64 inch• 3/32 inch• 7/64 inch• 1/8 inch• Randomly number caps (1 through 20) – use

permanent marker.• Prepare (but do not distribute) a “Bottle Cap

Key” to document each cap number and its hole size.

• 20 bottomless twenty-ounce water bottles• Prepare bottles by cutting off the bottom part of

each water bottle (see attached picture)• 20 topless twenty ounce water bottle

• Prepare by cutting the ‘neck’ off of each water bottle (see attached picture)

• 20 – 12 ounce cup• 20 stopwatches (alternative resource – have

students use their cell phone stopwatch)• 10 + rolls of masking tape• 8-10 shared water buckets with approximately

2 gallons of water (can be used for 2-3 partner teams)

Day Six and SevenStudents will know:

Students will know:

Students will be able to:

• Ratios are multiplicative comparison of two quantities.

• Proportional reasoning involves relationships among ratios.

• Understand conservation strategies that incorporate the natural rhythm of the water cycle.




Cultural Learning Targets


LESS

ON

Teachers ActionStudent Action:Students submit homework using routine classroom proceduresTime Frame: 1 min

• Teacher collects homework.• Teacher prepares materials prior to

class session.

Collaborative activity: You discovered a leak in the water catchment system. Your first task is to determine the rate of the leak.Development of learning team solutions: Planning session – teams

develop hypothesis and draft of an investigational design.Product: Learning Teams submit a draft plan (including a materials list) for teacher review / feedback.

• Announce – we have been exploring the relationship between mathematics and conservation of our natural resources – specifically water. Today we are going to explore proportional relationships with water drips. Initially, you will work in two-person teams to collect data. After the data is collected, you will be given an individual performance task to complete using the class data.

• Distribute “Water Drip Lab/Journal” from Live Binder. Announce: Today’s scenario – “You discovered a leak in the water catchment system. Your task is to determine how quickly water leaks out of your system.”

• Say: “Your task is to develop an efficient plan for solving the problem. Work together on the task. Take turns to explain your method to your partner. Listen carefully to each other. Ask questions (if you don’t understand or agree. If you discuss more than one method, together decide which method is best. Then, on the EDP plan document, write a complete design plan explaining your reasoning. Be sure that you both understand and can explain your team’s method.” You will submit your design to the teacher to receive feedback.

• Ask: What questions might you have about the today’s task?

Learning Target:

Student Action:Students move to assigned partner teams.Students listen attentively and take notes as necessary.Time Frame: 4 min

Ethnomathematics 24

LESSONTeachers ActionStudent Action:

Students ask clarifying questions as needed.Time Frame: 2 min

Student Action:Students work collaboratively in their learning team to brainstorm possible design. solution(s) to water drip problem. Students document design process / set-up in journal.Time Frame: 4 - 5 min

Student Action:Learning Teams individually present design proposal to the teacher for approval. Time Frame: 2 - 3 min

Student Action:Upon receiving approval, learning team builds and tests prototype #1Students work collaboratively in their learning team to review the data collected from prototype #1. Students use data to redesign the process / system for prototype #2.Time Frame: 10 min

• Answer any student questions as needed.• Announce: After the plan is approved, come

to the resource center to get your materials.

From that point, you will construct your prototype and test to collect at least three sets of data for analysis.

• Teacher - Review group design and provide feedback. Ask students to revise the design

as needed. Once the design is approved, distribute investigation materials (see below).

• Each team needs one set of the following materials [post list on board]:

• 2 Water Drip Lab handouts (i.e., one per student)• Graph paper• Optional: computers with Excel software• 1 graduated cylinder• 1 pre-drilled water bottle cap• 1 bottomless twenty ounce water bottle• 1 topless twenty ounce water bottle• 1 – 12 ounce cup• 1 stopwatch• Access to shared water bucket

• Monitor learning team progress with implementation. Possible formative assessment questions:

• Explain how you are collecting your data (probe for details)?

• Explain how your method works?• What is the relationship between the data

points collected?• Explain what happens to the time it takes for the

water to flow as the size of the holes change? • How are those components (size of hole and time

to empty container) related? • What predictions can you make based on

that information?

• Product: Students will submit their procedure, data tables, and calculations of


LESS

ONStudent Action:Upon receiving approval, learning team builds and tests prototype #1Students work collaboratively in their learning team to review the data collected from prototype #1. Students use data to redesign the process / system for prototype #2.Time Frame: 10 min

Student Action:Student groups will notice that different learning teams calculated different flow rates. Students offer possible reasons for different flow rates:

• Students may attribute the different flow rates to process – have the students briefly share their process to determine the similar processes.

• Students may discuss data collection errors .

• Students will note the different sized holes relate to different flow rates.

Student Action:Students post data online.Students review posted data from other learning teams.Time Frame: 5 min

Student Action:Students discuss what they notice with their learning team partners.Time Frame: 3 min

water flow rates for their system.• Reminder Announcement: After collecting

and reviewing data for your first prototype, continue working in the Water Drip Journal. Move to the redesign process. Review your prototype #1 data, make adjustments and redesign the product / process for prototype #2.

• Announce: Post your data online (provide posting information).

Teachers Action

• Teacher – combine / overlay all graphs.• Announce: Analyze the data collected by

other teams. Ask: What do you notice?• Teacher leads whole class discussion:• Ask – what might be a possible reason for

these differences?• Use facilitative questioning to guide

discussion for possible reasons for differing flow rates.

• As students suggest possible reasons for different data – have them consider/review

• Design Process: compare the data collection / design process

• Data collection error – compare data collected in each trial vs average data

• Materials – teams discover the different sized holes in the bottle caps result in different flow rates

• Ask – What additional data might you need to verify your hunches?

• Teacher documents student responses – when students propose a hunch that is already listed – teacher asks if it matches the existing response – and adds a tick mark to document the repeated response.

• After discussion – provide students with the “Bottle Cap Key”

Ethnomathematics 26

LESSONStudent Action:Students review class data.Student teams discuss what they notice (document on post-it notes.)Student teams discuss what they noticed – possible student responses:

• Different flow rates• Fastest / Slowest rate

Students discuss possible additional data needed to verify their hunchesTime Frame: 4 min

Student Action:Students / teams ask questions as neededStudents brainstorm additional needed data. Students use the “Bottle Cap Key” data to complete analysis of their learning team data. Students work in learning teams to identify the corresponding hole size given each teams flow rate data.Students work with their team to individually complete Water Drip Journal – this will be submitted at the end of the periodTime Frame: 20 - 30 min

Student Action:Students work individually to complete Flow Rate Performance Task.

Student Action:Students submit Water Drip Journal and Water Drip Performance Task.

Teachers Action• Announce – work as a team to use the

information from the “Bottle Cap Key” to identify the corresponding hole size for each teams’ flow rate data. Each partner is responsible to submit the completed tabl

• Remind students that you will collect Water Drip Journal at the end of the session (along with their individual Flow Rate Performance Task

• End of Collaborative Work• Announce – Use the information collected

in part 1 to individually complete the assessment task.

• Distribute Flow Rate Performance Task (note: there are three possible tasks – distribute randomly to students) to students.

• Teacher circulates to answer questions as needed. Refer students to available data. Note: This is a summative assessment task – therefore, be sure that student work demonstrates their understanding (vs. your input).

• Collect Water Drip Journal and Water Drip Performance Task

• Use Water Drip Assessment Rubric to assess student work.


DIAG

RAM

Visual cue of the target CCSS-Mathematics target standards.For more information – review CCSS-Mathematics Progressions document (http://commoncoretools.files.wordpress.com/2012/02/ccss_progression_rp_67_2011_11_12_corrected.pdf)

Diagram #1

Ethnomathematics 28

APPENDIXContents: Ethnomathematics Livebinder http://www.livebinders.com/edit/index/1362168

Appendix A

Tab Name Tab Content SubTab Content TimelineWater, Water Every-

where??Lesson Design

(word document)N/A N/A

Leaky Faucet Task (Dan Meyer)

Leaky Faucet Resource

Internet Link:http://threeacts.mrmeyer.

com/leakyfaucet/

N/A Day 1

Waste Not, Want Not – Malama ‘Aina

Green Education Foundation Lesson

Internet Link:http://www.

greeneducationfoundation.org/institute/lesson-

clearinghouse/219-Waste-Not-Want-Not.html

1. Water Use Cards Handout Day 2

Engineering Project – Rainwater Collection

TechXcite Resources

Internet Link:http://techxcite.pratt.duke.

edu/curriculum/rainwaterhar-vesting.php

1. Rainwater Collection System (teacher resource powerpoint)2. Rainwater Collection System – Engineering Project Journal (Handout)3. Rainwater Collection system - Student Handout (pg. 1)4. Background: Guidelines on Rainwater Catchment5. Background: Designing a Rainwater Collection System

Day 2 - 4

Rainwater Runoff – How Much Water Do

We Collect?

Handouts to support Rainwater Runoff Investigation

1. Rainwater Runoff (powerpoint)2. Background: Rainwater Calculator (online resource)3. Resource: Conversion Information (FYI online resource)4. Average Rainfall in Kaneohe, Hawaii - NOAA data (Handout -Days 5 & 7)5. Drip Calculator (online resource)6. How much water is in an inch of rain? (online resource)7. How many gallons of water in 1 cubic foot? (online resource)8. Water Catchment Tank (online picture file)9. How much water can you collect in rain barrels during a rainfall (online resource)

Days 5-7

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