Michigan Curriculum Framework Standards and Benchmarks
II. Geometry and Measurement
Content Standard 2: Students identify locations of objects, identify location relative to other objects, and describe the effects of transformations (e.g., sliding, flipping, turning, enlarging, reducing) on an object. (Position)
Benchmark 2:   Locate and describe objects in terms of their orientation, direction and relative position, including up, down, front, back, N- S- E- W, flipped, turned, translated; recognize symmetrical objects and identify their lines of symmetry.
Benchmark 3:  Explore what happens to the size, shape and position of an object after sliding, flipping, turning, enlarging or reducing it.
Content Standard 3: Students compare attributes of two objects, or of one object with a standard (unit), and analyze situations to determine what measurement(s) should be made and to what level of precision. (Measurement)
Benchmark 4: Explain the meaning of measurements and recognize that the number of units it takes to measure an object is related to the size of the unit.
Benchmark 5: Explore scale drawings, models and maps and relate them to measurements of real objects.
Benchmark 6: Apply measurement to describe the real world and to solve problems.

National Education Standards
NM-GEO.3-5.3: Apply transformations and use symmetry to analyze mathematical situations
NM-MEA.3-5.1: Understand measurable attributes of objects and the units, systems, and processes of measurement
NM-MEA.3-5.2: Apply appropriate techniques, tools, and formulas to determine measurements

Objectives
Students will be able to:
     Create a scale drawing of their own invention.
     Explore drawings to measure scale factor they used.
     Use tools like calculators and rulers to create a drawing that is to scale.

Materials
Blueprints of school or home
8 ½ X 11 copy paper
8 ½ X 11 1/4 inch graph paper
Pencils
Calculators
Rulers

Engage
BEFORE THE LESSON
This lesson is expanding on our Inventor/Invention unit. Introduce the idea of inventing a piece of playground equipment.  Give students a chance to draw their inventions on a piece of regular 8 ½ X 11 paper.  Use the smaller paper since students will be enlarging their original drawing in another lesson.

This lesson is expanding on our Inventor/Invention.  Show students a copy of blueprints from my house.  Discuss how this drawing/picture helped the builder build the house the correct size.  Ask students how they think the builder knew what the artist/designer was trying to tell them to do.  Ask how they could use some of the things we discussed (the space is labeled bedroom, the lines they draw, and the scale factor being measured is labeled) to draw a picture of their own invention 8 ½ X 11 graph paper (1/4 inch).  (Their invention is a piece of playground equipment.)  Tell students that this is what they are exploring today.

Explore
Release students to work in pairs to create their drawing.  Remind students that they have many tools to use such as rulers and calculators.  Students should use these tools to draw picture with a specific scale factor that is measurable.  Tell students that in their drawing they need to specify what the scale factor is.  All drawings created will be on the 1/4 inch graph paper that is 8 ½ X 11.

Explain
Tell students that what they have been exploring today is called scale. When a scale picture is drawn, all measurements have a scale factor that is used.  This scale factor is what will be used to determine the actual size of the object.

Extend/Apply
Use the blueprints to point out the scale factor used on the plans.  Show that every so many centimeters is equal to so many feet.  This is how architects and builders can work together to build things like homes, schools, offices and other buildings..

Assess
Give students short “assessment quiz” that tries to see if students can draw two pictures correctly using a given scale factor.  Students will be required to draw a
4cm x 4cm cube first then draw a cube that is 2 times larger and one that is 3 times larger.