Designing+Mathematicians

Original NTTI lesson was designed for 4th grade geometry. It is designed to use Google Sketch-up. I have left it up for now, but have revised it for a 5th grade advanced math class, using FabLab software. That is the link for the Revised NTTI lesson, following NTTI lesson development criteria. The lesson plan below is a simplified version of the original, using the Fabrication Lesson Design Template. I am leaving the original lessons attached here in case anyone wants to look at them. NTTI of course requires using as much technology as one can fit in, so that lesson is entirely built around technology, including use of Math Forum (web usage), Discovery Education (will we have a subscription any more??), the FabLab technology, and using flip cameras to record student presentations.

Fabrication Lesson Design Template


 * Lesson Designer: Anne Geraty**


 * Title: Designing Mathematicians**

This lesson will introduce students to the authentic applications of geometric concepts of area, perimeter, volume, ratio and scale, and shape by architects and designers. Students will compute the area and perimeter of the floor spaces in a shopping mall by using known dimensions. Students will compute the number of floor tiles needed to outline the perimeter of the space and will then design an addition to the mall, including a courtyard with a sculpture using geometric shapes. Finally, students, acting as architects for their designs, will make scale models of their design proposals to present to hypothetical prospective clients.
 * Description:**


 * Grade Level/Content Area:** 5th grade, with some extension into middle school curriculum in the application of scale and proportion**;** Geometry and measurement

SOLs Addressed**:**
 * Concepts:**
 * SOL: 5.8a The student will: a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation; c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S. Customary and metric units; and e) choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units.
 * SOL 5.9 The student will identify and describe the diameter, radius, chord, and circumference of a circle.
 * SOL 5.11 The student will measure right, acute, obtuse, and straight angles
 * SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will a) develop definitions of these plane figures; and b) investigate and describe the results of combining and subdividing plane figures**.** The student will measure and draw right, acute, and obtuse angles and triangles, using appropriate tools
 * SOL 5.14 The student will classify angles and triangles as right, acute, or obtuse.
 * SOL: 5.15 The student, using two-dimensional (plane) figures (square, rectangle, triangle, parallelogram, rhombus, kite, and trapezoid) will b) identify and explore congruent, non-congruent, and similar figures;
 * SOL 6.12 The student will determine congruence of segments, angles, and polygons.

At the conclusion of this unit, the student will understand that**:**
 * Understandings:**
 * Attributes of objects can be measured using processes and quantified units, and the use of appropriate techniques, tools, and formulas **.**
 * That simple plane figures can be combined to make more complicated figures; and, complicated figures can be subdivided into simple plane figures.
 * Know that 2-dimensional and solid figures are unique in their defining properties.
 * Understand that similar geometric figures have the same shape but may have different sizes.
 * Understand that similar shapes have congruent angles and corresponding sides or edges with equivalent ratios to each other
 * Understand the use of scale or ratios to determine the measurements of the sides or edges of similar larger or smaller 2-dimensional and solid shapes


 * Learning Targets:**


 * I can:**
 * Identify, describe, and distinguish between area, perimeter, and volume, and explain and use the computation of area, perimeter and volume as a planning tool for architectural design;
 * Identify the uses of geometric shapes in architecture and sculpture and describe the component shapes (solids) in a given piece of architecture or sculpture, using number of faces, edges, corners (vertices), and the shape of the faces;
 * Measure in both metric and customary units to the nearest appropriate unit using a variety of measuring instruments, can choose an appropriate unit for the task, and can convert between smaller and larger units in the same system as is appropriate;
 * Construct models of 2- and 3-dimensional figures using a variety of resources, to include drawing paper, measurement tools, and Fab Lab design technology;
 * Use ratios and proportions to determine the length of something that cannot be measured directly, i.e. convert the units of measurement for the model to the units of measurement for the corresponding dimensions of the full-sized object.

Your creation should include a document upon which you calculate: Name your sculpture. Math Forum problem on area and perimeter; document camera for sharing student work; graph and drawing paper; rulers**;** cardstock; FabLab Design Maker software; computers--1 per student; Diecut machine for FabLab software--at least 1; Sticky feed sheet for the diecut machine; tape and glue
 * Process and Procedures:**
 * 1) Provide the students with the math puzzle--Math Forum problem. Present it as a puzzle activity. Allow the students to use calculators and to work in pairs or groups to come up with solutions to the puzzle.
 * 2) Students will use the overhead projector (the document camera) to share some of their work. Ask: “From your work, what are some ideas you have about how this would be used in the real world? Why does this matter?” Have students brainstorm ways that concepts of area and perimeter might be used in the real world and list on the board.
 * 3) Play Introduction to Properties of Geometric Shapes. This is a video available through Discovery Education. If not available, substitute another resources for introducing the use of geometric shapes in architecture and sculpture.
 * 4) Ask students to summarize how architects and builders use geometry to help in their professions. Add to the original list generated at the beginning of the activity.
 * 5) Students are assigned the following project:
 * **Step 1**: Design and draw an addition to the shopping mall that doubles the square footage of the mall. The design should not merely be a mirror image of the mall nor should it be merely the addition of a second story to the existing mall.
 * Show the locations of the additional space and how it will be sub-divided into stores.
 * Include math computations that proves that the additional space doubles the square footage. Calculator usage is acceptable for all computations, but the results should be recorded completely.
 * Calculate the new total square footage.
 * **Step 2**: Design an outdoor space for the mall that is __approximately__ 1/3 of the total square footage of the store space. This does not have to be exact.
 * Show the computations for the courtyard.
 * Make a bird’s eye drawing of the courtyard that shows paths, seating, plants, and the placement of a geometrically inspired sculpture and which includes the labeled dimensions of the courtyard and of the base of the sculpture.
 * **Step 3:**Use grid paper or drawing paper to plan your sculpture.
 * **Step 4**: Use Fab Lab Design Maker to create a scale model of your sculpture. Your design should include the following:
 * 1) At least 3 different geometric solids;
 * 2) A base which may be either a 2-dimensional delineated space or a 3-dimensional platform of an identifiable geometric solid;
 * 3) Precise measurements of the length, height, and depth of the solids in the sculpture and of the base, as well as of the angles. In the case of a sphere, provide a statement of the radius or diameter of the circular plane that divides the sphere into 2 hemispheres and of the circumference of the sphere at its widest point.
 * 1) Precise measurements of the length, height, and depth of the solids in the sculpture and of the base, as well as of the angles. In the case of a sphere, provide a statement of the radius or diameter of the circular plane that divides the sphere into 2 hemispheres and of the circumference of the sphere at its widest point.
 * 1) The surface area of each face of each geometric solid, assuming that the shapes are separate shapes and that no part of the surface is covered by the surface of another shape. Identical faces need only be calculated once;
 * 2) The area required for the footprint of the actual sculpture if it were built;
 * 3) The approximate volume of space required for the actual sculpture (you can do this by calculating its total height and width and depth at the widest and deepest points);
 * 4) Extra credit for computing the volume of each separate solid in the sculpture, especially if not rectangular prisms—we can find formulas to calculate these where they exist;
 * 5) The scale of your model to the actual sculpture. Any reasonable unit of measurement is acceptable, but keep in mind that your measurements should be either metric or customary, not a mixture of both.
 * 6) All measurements should be in appropriate units.
 * Step 5**: Optional: Use flip cameras to record a role play presentation by the students as though they were presenting their proposal to a client who commissioned them to make a design.
 * Materials:**

The products created in the culminating activity (and presentations, if used) will be used to assess student understanding, with attention paid to the following criteria:
 * Assessment:**
 * Accuracy and completeness in computing area, perimeter, volume, and scale for all parts of the project;
 * Completeness and organization of written communication about calculations used;
 * Product meets all required criteria;
 * Drawings are neatly done and appropriately labeled.