Posted by: degarcia | April 13, 2009

Area and Perimeter

NCTM Standards

http://standards.nctm.org/document/appendix/meas.htm NCTM standards and expectations for k-12

UEN Core Curriculum

http://www.uen.org/core/core.do?courseNum=5040– Utah Core curriculum for 4th grade. Area is Standard 4 Objective 2. There are lesson plans and links included for the standard.

http://www.uen.org/core/core.do?courseNum=5050-Utah Core curriculum for 5th grade. Area is Standard 4. There are lesson plans and links included for the standard.

http://www.uen.org/core/core.do?courseNum=5060– Utah Core curriculum for 6th grade. Area is Standard 4. There are lesson plans and links included for the standard.

 

Definitions/Formulas

-Area describes how much surface a shape take sup in square units.

-Perimeter is the measurement in units of length of the outer edge of an area.

-The terms width and length can be compared and connected to the words rows and columns.

            -Width: Width is the short dimension of any object.

            -Length: Length is the long dimension of any object.

-Square- A polygon with four equal side and all angles = 90 degrees.   A = S^2

402px-kvadrato_svg

-Triangle: A polygon with three corners or vertices and three sides or edges, which are line segments.  A = 1/2bh

452px-triangle_illustration_svg 

-Parallelograms: A parallelogram is a quadrilateral with two sets of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal size.  A = L x W

 255px-parallelogram_svg

-Circle: A circle is a simple shape consisting of those points in a plane which are the same distance from a given point called the center.594px-circle_1_svg

Misconceptions

-Perimeter and Area are always the same

-Perimeter and Area are interchangeable

-Square units means the object is a square

 

Student examples of misconceptions

  • – Brynne says that the area inside a fixed-length loop of string is always the same because the length is always the same.
  • – Darill says that if the area of a rectangle is 50 square cm, then the perimeter is always 30 cm.

 

How to best teach

-Inquiry: Studies have proven that inquiry is one of the best ways to teach mathematics. Inquiry implies that students explore and solve mathematical problems through trial, error, and personal experience rather than simply being handed equations or given answers. If concepts are derived for self, this information is much more likely to become solidified in the students mind and aid in concrete understanding. The three parts of inquiry include launch, explore, and summarize.

            -Building figures with square tiles

picture-2

            -Drawing models with 1-1 corresponding pictures using graph paper

            -Using open arrays or sketches and labeling them with numbers

-Real life connection: Students learn area and perimeter best when they can make connections to real life examples. Ideas include tiling a room, surface area for pool covers, fencing, and room layouts.

 

Lesson Plans

Using Inquiry to Teach Measurement

Deriving the area of a quadrilateral

Launch Cycle 1

Teacher shows picture of a quadrilateral made from graph paper on board or overhead.  She asks students to discuss with their partner how many square units is inside the quadrilateral. 

Explore Cycle 1

Students discuss with a partner.

Summarize cycle 1

As a class students share answers and strategies of how they figured it out.  Some will have counted, some using repeated addition, and some using multiplication.  Teacher makes sure to introduce the vocabulary of length and width.

 

 

Launch Cycle 2

Teacher states that the students are going to figure out a strategy that they can use with any rectangle, even if they don’t know what the measurement of the sides are.  She hands the small groups with several quadrilaterals they can explore.

Explore Cycle 2

Students work in small groups to find the areas of their quadrilaterals and try to generalize a way to find the area of any quadrilateral. 

Summarize Cycle 2

As a class, students discuss that they notice that are multiplying one side times the other side, or length times width, in each figure.  When asked to write an equation to show this, they write:  length x width = area.  The teacher further asks them to write the equation using letters to stand for the words, so students derive l x w = a.

 

Supplements

http://college.cengage.com/education/bahr/elementary_math/1e/resources.html This site includes information for purchase as well as a few free useful links for teachers.

http://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inc. Generate shapes to explore perimeter in an interactive and fun way!

http://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.weml Use this site for free information or sign up for cool videos. Free 5 day trial.

 

Resources

Bahr L. Damon & de Garcia A. Lisa, Elementary Mathematics Is Anything but Elementary 2010

Wikipedia. Retrieved April 15, 2009, from http://en.wikipedia.org/wiki/Main_Page

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