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Getting Life in Proportion:  Scale and Mapping

Grade Level: 6-8

Time Frame: 2 class periods

Subject:  Math

Introduction to Lesson: 

In this lesson students will explore the use of pictures and maps to represent physical spaces.  We will explore the concepts of scale and conversions between pictures, maps and real-world units.  Conversions between kilometers and miles, meters and feet and meters to centimeters and kilometers will also be practiced within the context of the learning experience.

New Jersey Core Curriculum Content Standards

STANDARD 4.1 (Number and numerical operations) All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

A. Number Sense

·          Use real-life experiences, physical materials, and technology to construct meanings for numbers 

·          Explore the use of ratios and proportions in a variety of situations.

C.  Estimation

·          Use a variety of strategies for estimating both quantities and the results of computations.

·          Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

·          Determine the reasonableness of an answer by estimating the result of operations.

·          Determine whether a given estimate is an overestimate or an underestimate.

STANDARD 4.2 (Geometry and measurement) All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

D. Units of Measurement

·          Use a scale to find a distance on a map or a length on a scale drawing.

·          Convert measurement units within a system (e.g., 3 feet = ___ inches).

·          Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).

·          Use measurements and estimates to describe and compare phenomena

E. Measuring Geometric Objects

·          Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).

STANDARD 4.3 (Patterns and algebra) All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes

A. Patterns

·          Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.

o        Descriptions using tables, verbal rules, simple equations, and graphs

C. Modeling

·          Use patterns, relations, and linear functions to model situations.

o        Using variables to represent unknown quantities

o        Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

STANDARD 3.1 (Reading) All students will understand and apply the knowledge of sounds, letters, and words in written English to become independent and fluent readers, and will read a variety of materials and texts with fluency and comprehension.

A. Concepts About Print/Text

·          Use a … glossary independently and appropriately.

C. Decoding and Word Recognition

·          Apply knowledge of new words correctly

STANDARD 3.5 (Viewing and media literacy) All students will access, view, evaluate, and respond to print, nonprint, and electronic texts and resources.

A. Constructing Meaning

·          Respond to and evaluate the use of illustrations to support text.

·          Use graphs, charts, and diagrams to report data.

STANDARD 6.6 (Geography) All students will apply knowledge of spatial relationships and other geographic skills to understand human behavior in relation to the physical and cultural environment.

The World in Spatial Terms

·          Distinguish among the distinct characteristics of maps, globes, graphs, charts, diagrams, and other geographical representations, and the utility of each in solving problems.

·          Translate maps into appropriate spatial graphics to display geographical information.

·          Explain the spatial concepts of relative and absolute location and distance.

·          Estimate distances between two places on a map using a scale of miles, and use cardinal and intermediate directions when referring to a relative location.

·          Use geographic tools and technologies to pose and answer questions about spatial distributions and patterns on Earth.

STANDARD 1.2 (Creation and Performance) All students will utilize those skills, media, methods, and technologies appropriate to each art form in the creation, performance, and presentation of dance, music, theater, and visual art.

D. Visual Arts

Individually or collaboratively create two and three-dimensional works of art employing the elements and principles of art.


  1. Students will demonstrate understanding of the concept of maps and scale and why maps are important in their lives
  2. Students will interpret information in a picture and use it to solve conceptual problems relating to the information in that picture
  3. Students will practice conversions between and within units (feet to meters, meters to centimeters etc.)
  4. Students will master the ability to convert distances on a chart to the distances they represent in the world and visa versa
  5. Students will work together to build an accurate map of their classroom, including scale bars etc.

Materials and Resources:






Measuring tapes


Student Worksheets


Getting Life in Proportion (.doc format;  .pdf format)


Classroom Mapping (.doc format;  .pdf format)


Map: A drawing showing the locations of different places as if you were looking at it from above

Symbol: A picture or icon that stands for something else

Cardinal directions:  The directions of north, east, south, west

Map Legend:  The part of the map that tells what the shapes and symbols mean

Compass: the symbol on the map that shows the cardinal directions

Anticipatory Set: 

The teacher will elicit the students prior knowledge:  What is a map?  What does it look like?  What do we use one for?  Why are they important?   The teachers will then show some example maps e.g. maps of area of school that students are attending or of local areas of interest (Google maps or mapquest are great sources of images that would work well for this.  Maps from a social science text books would also work well).  In so doing, teacher should highlight examples of map symbols and engage students in a discussion of how to find out what symbols on a map mean.

Sequence Instruction:

 Scale Assignment

  1. The picture above is of a scientist named Kristen Saltonstall who has carried out a great deal of research on Phragmites.  Dr. Saltonstall is 5’6” tall.   Using a ruler measure the image of Dr. Saltonstall in the marsh.  How many inches high is she in the picture?
  2. Given her real height (above), how many inches on the ruler represent 1 foot in the real world?
  3. Write a formula for how to convert between inches on the picture and real world units
  4. Place a scale bar on the picture that represents this formula.  E.g. O------O = 1 foot
  5. How many inches high is the Phragmites in the picture?
  6. Use that formula to determine how tall the Phragmites is in the real world.
  7. Given that 1 foot = 0.305 meters, how tall is Dr. Saltonstall in meters?
  8. 1 meter = 100 cm.  How tall is Dr. Saltonstall in centimeters?
  9. How tall is she in inches?
  10. How tall is the Phragmites in this picture in meters?
  11. What are three adjectives that you might use to describe the Phragmites in this picture?


















  1. This picture is of another scientist, Dr. Robert Meadows, who works for the Delaware Division of Fish and Wildlife and who also studies Phragmites.  Use a ruler to measure the image of Dr. Meadows in the marsh.  How many inches high is he in the picture?
  2. Dr. Meadows is 6’ tall.  How many inches on in the picture correspond to 1 foot in the real world?
  3. Write a formula for how to convert between inches on the picture and real world units.
  4. Place a scale bar on the picture that represents this formula.  E.g. O------O = 1 foot
  5. How many inches high is the invasive Phragmites in the picture?
  6. Use that formula to determine how tall the invasive Phragmites in the picture is in the real world
  7. Given that 1 foot = 0.305 meters, how tall is Dr. Meadows in meters?
  8. 1 meter = 100 cm.  How tall is Dr. Meadows in centimeters?
  9. How tall is he in inches?
  10. How tall is the invasive Phragmites in meters?
  11. What are three adjectives that you might use to describe the Phragmites in this picture?

Mapping Activity

  1. Using a tape measure, measure the width and length of your classroom in feet.
  2. Brainstorm within groups.  To make a map of your classroom that will fit on a regular sheet of paper what scale will you need to use (1 inch = how many feet?)
  3. Draw the shape of the room using the scale you have decided upon.
  4. With the teacher’s help measure the distances between the main items in the room (doors, windows, desks, benches, tables etc.) and the sizes of each.
  5. Add these to your map, remembering to show them on the same scale.
  6. Be sure to put a scale bar onto your map

Accommodations and Modification:                                                                        

bullet Group students into groups such that each has a mix of students with different learning styles and strengths.
bullet If needed, pair students so that one student can read directions aloud to another
bullet Provide handouts and worksheets with larger font sizes, raised or embossed writing, or Braille for visually impaired students
bullet As a time modification, or for classrooms with students with mobility challenges have pre-existing measurements for items in the classroom so that students can work with the pre-existing numbers to build their maps

Assessment / Anchor Activity / Homework (if lesson goes shorter than planned)

Provide students with maps or pictures with scale bars.  Have them measure distances between two places, or the size of an item on the map  / picture and convert it back to scale units.  Alternately, give students a scenario where a building of a given size must be located at a specific location on a map and ask them to sketch what it would look like, to scale on the original map. 


In the few minutes of class provide each student with an index card and have them write on it

bullet 3 things they found interesting about today's class,
bullet 2 things they learned and
bullet 1 thing they still have a question about.

Collect the cards as the students leave and use the results to see if there are any ideas clearly in need of review at the start of the next class before starting in on the next lesson plan.


TEACHER FEEDBACK REQUEST:  We are always to working to improve these lesson plans. If you use this lesson plan, we'd love to hear from you with your thoughts, comments and suggestions for future improvements.  Please take the time to fill in our survey at .  Thanks!

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© 2009.  Louise Wootton   Edited by Claire Gallagher  

 Although the information in this document has been funded wholly or in part by the United States Environmental Protection Agency under assistance agreement NE97262206  to Georgian Court   University, it has not gone through the Agency's publications review process and, therefore, may not necessarily reflect the views of the Agency and no official endorsement should be inferred.


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