Common Core Math · High School

HSG-MG.A.3 Apply geometric methods to design problems

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost).

Why water teaches this standard well

Students design a rainwater cistern shape that meets a required storage volume while minimizing the material needed to build it, balancing a physical constraint against a cost goal. This design-under-constraint problem mirrors real decisions engineers make when specifying tank geometry.

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39 materials aligned to HSG-MG.A.3

Lesson plans

Grade 10 Lesson plan

Sizing Sattersley's Constructed Treatment Wetland

A 60-minute grade 10 lesson where students size a constructed wetland that strips nitrogen from treated wastewater, using loading rate and detention time.

Science 60 min Answer key

Grade 11 Lesson plan

Millbrook Boil-Water Notice: Typographic Hierarchy

Grade 11 students set a boil-water notice for a fictional water district, sizing headline and body type and testing the column measure against the page.

Art & Music 60 min Answer key

Grade 11 Lesson plan

Stonecross Rainfall Bands: A Woven Data Lesson

Grade 11 students encode a year of fictional rainfall as stripe widths on a woven band, choosing a scale that fits a fixed warp length.

Art & Music 2 sessions, ~90 min total Answer key

Grade 12 Lesson plan

Water Age in the Quintrell Ridge Tank: A Turnover Lesson

A grade 12 lesson where students compute water age in a fictional storage tank from volume and daily throughput, then weigh storage size against disinfectant residual.

Engineering & Design 55 min Answer key

Worksheets

Grade 9 Worksheet

Culverstone Main Replacement: Sizing a Thrust Block

A grade 9 worksheet on a fictional water main replacement where students find the thrust at a bend under test pressure and size the concrete block that resists it.

Engineering & Design 40 min Answer key

Math problem sets

Grade 10 Math problem set

Vireo Landing Filtration Plant: Sizing Basins and Filters

A grade 10 engineering math set that sizes a fictional plant's sedimentation basin and filters, checking detention time and filter loading against standard design ranges.

Engineering & Design 45 min Answer key

Classroom activities

Grade 10 Classroom activity

Hobbleton Ridge Percolation Stations: Sizing a Drainfield

A grade 10 station rotation sizing a soil absorption field for a fictional rural school, from a percolation test through trench layout, reserve area, and tank volume.

Engineering & Design 50 min Answer key

Grade 12 Classroom activity

Pinderloe GAC Contactor Sizing Relay for PFAS Removal

Grade 12 teams pass one spec sheet through four desks, size carbon vessels for a fictional plant, find the contact time falls short, and redesign the bed depth.

Engineering & Design 60 min Answer key

Grade 11 Classroom activity

Brackenhill Filter Section: A Scale Drawing Relay

Teams of four build a large cross-section of a fictional plant's sand filter on butcher paper, adding one layer per round at a single stated scale.

Art & Music 60 min Answer key

Grade 11 Classroom activity

Ravensford Reclamation Tour: Wayfinding Sign Stations

Four rotating stations in which grade 11 students size signs, draw pictograms, and scale a route map for a fictional reclaimed water plant's public tour.

Art & Music 65 min Answer key

Projects

Grade 11 Project

Thistlecomb Road Culvert: A Fish Passage and Flood Design

A six-session grade 11 project in which teams size a stream crossing that passes the design storm, restores trout passage, and fits a fixed budget and closure window.

Engineering & Design 6 sessions, ~360 min total Answer key

Grade 11 Project

Ashgrove Water Museum: A Three-Panel Exhibit Design

Over four sessions, grade 11 teams design three exhibit panels for a fictional town water museum, working to fixed panel sizes, type minimums, and a print allowance.

Art & Music 4 sessions, ~240 min total Answer key

Grade 10 Project

Hollowdale Farm Irrigation Water Budget Design Project

A grade 10 project where teams design a season's irrigation plan for a fictional 40-acre field, comparing flood and drip efficiency to fit a water and equipment budget.

Math 4 sessions, ~200 min total Answer key

Quizzes & test questions

Grade 10 Quiz & test questions

Kilnbury Water Main Thrust Blocks: A Grade 10 Design Test

A grade 10 engineering unit test on thrust restraint: students find the force at a capped end and at a bend, then size the concrete block that holds the fitting.

Engineering & Design 50 min Answer key

Grade 11 Quiz & test questions

Harkin Row Campus Stormwater Retrofit: Design Assessment

A grade 11 engineering assessment on a campus stormwater retrofit, covering impervious area, runoff volume, bioretention storage, drawdown time, and cost per gallon.

Engineering & Design 45 min Answer key

Grade 12 Quiz & test questions

Grebe Point Lift Station: Wet Well and Force Main Test

A grade 12 quiz on a fictional lift station mixing multiple-choice and computation: wet well volume, fill and pump-down times, cycle time, and force main velocity.

Engineering & Design 35 min Answer key