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7th, 8th Grades  Project 8 weeks

Quadrant Quest: Build-a-City Math Challenge

Jessica C
Updated
CCSS.Math.Content.7.G.B.6
CCSS.Math.Content.7.G.A.2
CCSS.Math.Practice.MP5
CCSS.Math.Practice.MP2
CCSS.Math.Practice.MP7
+ 11 more
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Purpose

Students act as city designers to solve a real planning challenge by creating a scaled city map and 3D model that use area, perimeter, proportional reasoning, and coordinates in all four quadrants. They apply geometry and measurement to place buildings, streets, services, and landmarks in ways that are efficient, welcoming, and easy to navigate. Through feedback from peers, community partners, and design professionals, students revise their plans to better respond to real community needs and defend their decisions with precise mathematical evidence.

Learning goals

Students will plot and interpret ordered pairs in all four quadrants and use scale drawings, area, perimeter, and geometric construction to design accurate city maps and building layouts. They will apply proportional reasoning and mathematical modeling to organize streets, zones, landmarks, and access routes that are efficient, safe, and easy to navigate. Students will use tools strategically, explain and defend design decisions with precise mathematical evidence, and revise their work using peer, teacher, and community partner feedback. They will also strengthen collaboration, communication, and self-direction by co-planning a city design that responds to real community needs and presenting it through a detailed map, 3D model, and design board.

Standards
  • [Common Core] CCSS.Math.Content.7.G.B.6 - Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
  • [Common Core] CCSS.Math.Content.7.G.A.2 - Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
  • [Common Core] CCSS.Math.Practice.MP5 - Use appropriate tools strategically.
  • [Common Core] CCSS.Math.Practice.MP2 - Reason abstractly and quantitatively.
  • [Common Core] CCSS.Math.Practice.MP7 - Look for and make use of structure.
  • [Common Core] CCSS.Math.Practice.MP1 - Make sense of problems and persevere in solving them.
  • [Common Core] CCSS.Math.Practice.MP3 - Construct viable arguments and critique the reasoning of others.
  • [Common Core] CCSS.Math.Practice.MP6 - Attend to precision.
  • [Common Core] CCSS.Math.Content.7.G.A.1 - Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
  • [Common Core] CCSS.Math.Practice.MP4 - Model with mathematics.
Competencies
  • Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.
  • Collaboration - Students co-design projects with peers, exercise shared-decision making, strengthen relational agency, resolve conflict, and assume leadership roles.
  • Effective Communication - Students practice listening to understand, communicating with empathy, and share their learning through exhibiting, presenting and reflecting on their work.
  • Content Expertise - Students develop key competencies, skills, and dispositions with ample opportunities to apply knowledge and engage in work that matters to them.
  • Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
  • Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.

Products

Students will create draft coordinate-grid city plans, lot-size sketches, and scale drawing revisions as they test area, perimeter, and proportional layout decisions for streets, zones, services, and landmarks across all four quadrants. Midway through, they will produce a gallery-walk draft with labeled ordered pairs, measurement calculations, and brief annotations explaining design choices for accessibility, safety, and efficient navigation. By the end, each team will present an urban design board with quadrant-based coordinates, proportional street layouts, and annotated decisions, along with a detailed city map and 3D model showing buildings, streets, zones, and landmarks. Teams will also prepare a short portfolio of before-and-after maps and reflection notes to defend how their design responds to community feedback and real neighborhood needs.

Launch

Open with a “City in the Quadrants” design challenge: in teams, students use a giant taped coordinate plane on the floor to place building and landmark cards at ordered pairs across all four quadrants while trying to meet quick community needs like housing, parks, safety, and access. Then introduce a surprise client brief from a neighborhood association leader or community nonprofit describing what makes a public space feel welcoming and easy to navigate, and have students revise one placement using area, perimeter, and proportional reasoning. Close with a fast gallery share where teams explain one math-based design choice and one question they have about how real cities use space.

Exhibition

Host a Neighborhood Night Market where students stand beside presentation-ready design boards, detailed city maps, and 3D city models and guide families, peers, a neighborhood association leader, and a community nonprofit through their quadrant-based layouts and measurement choices. Invite a city planning or zoning representative and a local architect or urban designer to circulate, ask questions, and offer feedback on safe public spaces, efficient navigation, lot sizes, and welcoming design. Set up a walking exhibition with sticky-note feedback stations so guests can respond to each city’s use of area, perimeter, proportional street layouts, and coordinate placement. End with brief student portfolio talks that show before-and-after drafts and explain how each design responded to real community needs.