Strategies for Teaching Elementary Mathematics

7/31/2019 Strategies for Teaching Elementary Mathematics

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Strategies for Teaching Elementary MathematicsA resource to improve the teaching and understanding of elementary mathematics.

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Technology ActivitiesPosted by: ldegarci | April 27, 2009

Exceptional LearnersStudents with Special Needs / Struggling LearnersGifted Students

Comments OffPosted inUncategorizedPosted by: degarcia | April 20, 2009

Big Idea: Relations and FunctionsBIG IDEA #12RELATIONS & FUNCTIONS: Mathematical rules (relations) can be used to assign members ofone set to members of another set. A special rule (function) assigns each member of one setto a unique member of the other set.Examples of Mathematical Understandings: Mathematical relationships can be represented and analyzed using words, tables, graphs, and equations. In mathematical relationships, the value for one quantity depends on the value of the other quantity. The nature of the quantities in a relationship determines what values of the input and output quantities are reasonable. The graph of a relationship can be analyzed with regard to the change in one quantity relative to the change in the

other quantity. The graph of a relation can be analyzed to determine if the relation is a function.

In a linear function of the form y = ax, a is the constant of variation and it represents the rate of change of y withrespect to x.

The solutions to a linear function form a straight line when graphed. A horizontal line has a slope of 0, and a vertical line does not have a slope. The parameters in an equation representing a function affect the graph of the function in predictable ways.Web Links:

http://www.purplemath.com/modules/fcns.htmhttp://www.mathwarehouse.com/algebra/relation/math-function.phphttp://en.wikipedia.org/wiki/Function_(mathematics)http://www.nointrigue.com/docs/notes/maths/maths_relfn.pdfStandard 2Students will use patterns, relations, and algebraic expressions to represent and analyze mathematical problems and numberrelationships.Objective 1Analyze algebraic expressions, tables, and graphs to determine patterns, relations, and rules.

Describe simple relationships by creating and analyzing tables, equations, and expressions.

Draw a graph and write an equation from a table of values.Draw a graph and create a table of values from an equation.

Activity:http://illuminations.nctm.org/LessonDetail.aspx?ID=L293


Equations and Inequalities- Caitlin HauserWhy This is a Big Idea:

3rd Grade Standards:

Represent numerical relationships as expressions, equations, and inequalities.

Order and compare whole numbers on a number line and use the inequality symbols , , and = when comparing wholenumbers.

Represent numerical relationships as expressions, equations, and inequalities.

4th Grade Standards:Objective 2Use algebraic expressions, symbols, and properties of the operations to represent, simplify, and solve mathematicalequations and inequalities.
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5th Grade:

Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.

6th Grade:

Describe simple relationships by creating and analyzing tables, equations, and expressions.

Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems thatcorrespond to given situations.

Properties of Equality

Properties of Equality If the same real number is added or subtracted to both sides of an equation, equality is maintained.

If both sides of an equation are multiplied or divided by the same real number (not dividing by 0), equality is maintained.

Two quantities equal to the same third quantity are equal to each other.

EQUATIONS & INEQUALITIES: Rules of arithmetic and algebra can be used together with notions of equivalence to transformequations and inequalities so solutions can be found.

Examples of Mathematical Understandings:

A solution to an equation is a value of the unknown or unknowns that makes the equation true.

Properties of equality and reversible operations can be used to generate equivalent equations and find solutions.

Techniques for solving equations start by transforming the equation into an equivalent one.

A solution or solutions to a linear or quadratic equation can be found in the table of ordered pairs or from the graph oftherelated function.

Techniques for solving equations can be applied to solving inequalities, but the direction of the inequality sign needs to beconsidered when negative numbers are involved.

More Information:

Anequationis simply an assertion that twoexpressionsare related by equality.Inmathematics, an inequality is a statement about the relative size or order of two objects, orabout whether they are thesame or not.An understanding of equalities and inequalities is so important. Students at a young age should be exposed to theimportance of equality and the true meaning of an equal sign. Children can also be exposed to inequalities at a young age.Its important for students to develop their own understanding of equalities and inequalities so they can apply future

mathematics principles to these big ideas. A lot of mathematics rely on using equations and that is why it is such a big ideathat needs to be used inside the classroom.

An equation is a sentence involving numbers, or symbols representing numbers where the verb is equals (=). There arevarious types of equations:

3+4=7 True Equation

3+4=9 False Equation

2x+5x=7x Identity Equation
http://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Equationhttp://en.wikipedia.org/wiki/Expression_(mathematics)http://en.wikipedia.org/wiki/Expression_(mathematics)http://en.wikipedia.org/wiki/Expression_(mathematics)http://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Expression_(mathematics)http://en.wikipedia.org/wiki/Equation


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x+4= 9 Conditional Equation

Equations are used to state the equality of two expressions.

Inequalities are demonstrated through the following signs:

The notation a < b means that a is less thanb.

The notation a > b means that a is greater thanb. The notation ab means that a is not equal tob, but does not say that one is bigger than the other or even

that they can be compared in size.In all these cases, a is not equal to b,hence, inequality.These relations are known as strict inequality

The notation ab means that a is less than or equal tob (or, equivalently, not greater thanb);

The notation ab means that a is greater than or equal tob (or, equivalently, not smaller thanb);

Lesson Plans:

http://www.uen.org/Lessonplan/preview?LPid=11051 Commutative Cookie activity for 3rd graders where students create acommutative equation.

http://www.instructorweb.com/lesson/numbersequal.asp Lesson plan for kindergartners or 1st graders on understandingwhat the equal sign means.

http://www.uen.org/Lessonplan/preview?LPid=16330 Lesson Plan for 4th graders on understanding what is an equation andwhat is not an equation.

http://www.uen.org/Lessonplan/preview?LPid=16326 Lesson plan addressing different strategies to solve equations for 4thgraders.

http://www.uen.org/Lessonplan/preview?LPid=6103 Lesson plan for 4th graders on symbols in inequalities.

http://www.uen.org/Lessonplan/preview?LPid=11207 Lesson plan for 4th graders on relationships between equations. Helpsstudents understand equal values.

http://www.uen.org/core/lessonList.do?courseNum=5050&itemId=3022

A list of 5th grade lesson plans on equations.

Games:

http://www.math-play.com/Equation/Equation-Game-Online.htmlMatching equations with answers. For upper Levelelementary grades.

http://www.math-play.com/One-Step-Equation-Game.html Another equation game finding answers to equations for upperlevel grades.

http://education.jlab.org/sminequality/question.php?7466566 Speed math inequality game for 5-6 graders.Comments Off

Posted inUncategorizedPosted by: degarcia | April 17, 2009

Integrating Math and LiteratureLiterature can be a great resource when teaching mathematics. Integrating literature and math can both teach students literacy and motivate them to stayengaged during math time.

Some suggest that the literature connection motivates students (Usnick & McCarthy, 1998), provokes interest (Welchman-Tischler, 1992), helps studentsconnect mathematical ideas to their personal experiences (Murphy, 2000), accommodates children with different learning styles (Murphy, 2000), promotes

critical thinking (Murphy, 2000), or provides a context for using mathematics to solve problems (Jacobs & Rak, 1997; Melser & Leitze, 1999).

http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65
http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/17/integrating-math-and-literature/http://mathteachingstrategies.wordpress.com/2009/04/17/integrating-math-and-literature/http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://mathteachingstrategies.wordpress.com/2009/04/17/integrating-math-and-literature/http://mathteachingstrategies.wordpress.com/category/uncategorized/


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Ways to use Childrens Literature in Teaching Mathematics1. To provide a context or model for an activity with mathematical content.2. To introduce manipulatives that will be used in varied ways (not necessarily as in the story).

3. To inspire a creative mathematics experience for children.4. To pose an interesting problem.5. To prepare for a mathematics concept or skill.

6. To develop or explain a mathematics concept or skill.7. To review a mathematics concept or skill.

List by Welchman-Tischler (1992)

http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65

Integration IdeasMany types of literature can be used to integrate with math such as picture books, short stories, novels, folktales, poetry, songs, news articles, and more! Somebooks explicitly present problems in the context of the reading but others are implicit and will require some creativity. Here are some compiled lists:

Picture Books

Annos Counting Book by Mitsumasa Anno

Annos Counting House by Mitsumasa Anno

Annos Mysterious Multiplying Jar by Mitsumasa Anno

The Napping House by Audrey and Don Wood

One Monkey Too Many by Jackie French Koller and Lynn Munsinger

How Much is A Million? by David M. Schwartz

A Million Dots by Andrew ClementsThe Hersheys Milk Chocolate Bar Fractions Book by Jerry Pallotta

The Greedy Triangle by Marilyn Burns

Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander

Sir Cumference and the Sword in the Crone by Cindy Neuschwander

Sir Cumference and the Dragon of Pi by Cindy Neuschwander

The Grapes of Math by Gregory Tang and other books by Greg Tang

Round Trip by Ann Jonas

Eight Hands Round by Ann Whitford PaulCompilations:

http://www.edselect.com/mathbooksbowen.htm

http://childrenspicturebooks.info/articles/picture_books_for_math.htm

http://teacher.scholastic.com/reading/bestpractices/pdfs/mbmath_TitleList.pdf

FolktalesGoldilocks and the Three BearsThe Three Little Pigs

Three Billy Goats Gruff

Rapunzel (hair length, time for hair growth)

Poetry

Marvelous Math: A Book of Poems by Lee Bennett Hopkins

Math Poetry Book: Linking Language and Math in a Fresh Way by Betsy Francohttp://literacyconnections.com/Tang.html

Songs

A list of songs that can be integrated with math can be found at the following website :http://www.songsforteaching.com/

More Information:

Education WorldWiZiQScholastic

References:http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65

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

Integrating Reading and MathematicsUploaded bylee-LutheronWiZiQ Tutorials


Surface Area
http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.edselect.com/mathbooksbowen.htmhttp://www.edselect.com/mathbooksbowen.htmhttp://childrenspicturebooks.info/articles/picture_books_for_math.htmhttp://childrenspicturebooks.info/articles/picture_books_for_math.htmhttp://teacher.scholastic.com/reading/bestpractices/pdfs/mbmath_TitleList.pdfhttp://teacher.scholastic.com/reading/bestpractices/pdfs/mbmath_TitleList.pdfhttp://literacyconnections.com/Tang.htmlhttp://literacyconnections.com/Tang.htmlhttp://www.songsforteaching.com/http://www.songsforteaching.com/http://www.songsforteaching.com/http://www.education-world.com/a_curr/curr249.shtmlhttp://www.education-world.com/a_curr/curr249.shtmlhttp://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://teacher.scholastic.com/reading/bestpractices/math.htmhttp://teacher.scholastic.com/reading/bestpractices/math.htmhttp://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://www.wiziq.com/tutor-profile/4217-lee-luther-filemaker-teacherhttp://www.wiziq.com/tutor-profile/4217-lee-luther-filemaker-teacherhttp://www.wiziq.com/tutor-profile/4217-lee-luther-filemaker-teacherhttp://www.wiziq.com/content/http://www.wiziq.com/content/http://www.wiziq.com/content/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://www.wiziq.com/content/http://www.wiziq.com/tutor-profile/4217-lee-luther-filemaker-teacherhttp://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65http://teacher.scholastic.com/reading/bestpractices/math.htmhttp://www.wiziq.com/tutorial/231-Integrating-Reading-and-Mathematicshttp://www.education-world.com/a_curr/curr249.shtmlhttp://www.songsforteaching.com/http://literacyconnections.com/Tang.htmlhttp://teacher.scholastic.com/reading/bestpractices/pdfs/mbmath_TitleList.pdfhttp://childrenspicturebooks.info/articles/picture_books_for_math.htmhttp://www.edselect.com/mathbooksbowen.htmhttp://www.apples4theteacher.com/resources/modules.php?op=modload&name=News&file=article&sid=65


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Surface Area: In general, the surface area is the sum of all the areas of all the shapes that cover the surface of

the object.

In order for students to understand surface area, they first need to understand concepts such as base, height,

diameter, radius, pi, etc.

Surface area can be a challenging concept for students because of the different formulas that are used when

dealing with different geometric shapes.

http://www.math.com/tables/geometry/surfareas.htm-This is a link to a website that lists the formulas to

find the surface area of specific shapes.

Standards

Here are the links to the Utah State Core Curriculum for teaching surface area.

http://www.uen.org/core/core.do?courseNum=5060-5th

grade core for surface area. It is found in Standard 4.

http://www.uen.org/core/core.do?courseNum=5050-6th

grade core for surface area. It is also found in

Standard 4.

The standard from the NCTM for 5th

grade is listed like this:

Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their

properties, including volume and surface area.

Students relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids,describing them by the number of edges, faces, or vertices as well as the types of faces. Students recognize

volume as an attribute of three-dimensional space. They understand that they can quantify volume by findingthe total number of same-sized units of volume that they need to fill the space without gaps or overlaps. Theyunderstand that a cube that is 1 unit on an edge is the standard unit for measuring volume. They select

appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume. They

decompose three-dimensional shapes and find surface areas and volumes of prisms. As they work with surfacearea, they find and justify relationships among the formulas for the areas of different polygons. They measure

necessary attributes of shapes to use area formulas to solve problems.

(http://www.nctm.org/standards/focalpoints.aspx?id=334 )

Lesson Plans-Here are some links to some websites that have great ideas for surface area lesson plans:

http://www.uen.org/Lessonplan/preview.cgi?LPid=21572

http://io.uwinnipeg.ca/~jameis/PAGES/MYR64.html

http://www.shodor.org/interactivate/lessons/SurfaceAreaAndVolume/http://www.iit.edu/~smile/ma8808.html

Activities-Here are some links to some websites that have great activities that can be used to teach surface

area. The first two links are especially good ideas for teaching surface area of cylinders.

http://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-

Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfThis link is a printable net of a cylinder that students can

cut out and then fold in order to see how the different shapes make up a cylinder.

http://mathteachermambo.blogspot.com/2007/08/surface-area-activity.html-This is an idea of finding the

surface area of spheres by using oranges.

http://www.teachingideas.co.uk/maths/files/areapractical.doc-This link is a worksheet that students can

complete in the classroom. It has to do with finding the surface area of certain things in the classroom.Comments Off

Posted inUncategorizedPosted by: degarcia | April 13, 2009

VolumeVolume is the amount of space taken up by a three dimensional object. Elementary students learn volume in relation torectangular prisms, triangular prisms, and cylinders. Student should be familiar with length, width, and height, as well as thecircumference of a circle. Students should also be able to find the area of two dimensional shapes.

Standards UEN is a great resource for finding out the grade level standards in Utah.5th gradeand6th gradeboth havestandards which cover volume.Lesson Plans for Teaching Volume

Fill Em Up
http://www.math.com/tables/geometry/surfareas.htmhttp://www.math.com/tables/geometry/surfareas.htmhttp://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5050http://www.nctm.org/standards/focalpoints.aspx?id=334http://www.nctm.org/standards/focalpoints.aspx?id=334http://www.nctm.org/standards/focalpoints.aspx?id=334http://www.uen.org/Lessonplan/preview.cgi?LPid=21572http://www.uen.org/Lessonplan/preview.cgi?LPid=21572http://io.uwinnipeg.ca/~jameis/PAGES/MYR64.htmlhttp://io.uwinnipeg.ca/~jameis/PAGES/MYR64.htmlhttp://www.shodor.org/interactivate/lessons/SurfaceAreaAndVolume/http://www.shodor.org/interactivate/lessons/SurfaceAreaAndVolume/http://www.iit.edu/~smile/ma8808.htmlhttp://www.iit.edu/~smile/ma8808.htmlhttp://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfhttp://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfhttp://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfhttp://mathteachermambo.blogspot.com/2007/08/surface-area-activity.htmlhttp://mathteachermambo.blogspot.com/2007/08/surface-area-activity.htmlhttp://www.teachingideas.co.uk/maths/files/areapractical.dochttp://www.teachingideas.co.uk/maths/files/areapractical.dochttp://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/Lessonplan/preview?LPid=18993http://www.uen.org/Lessonplan/preview?LPid=18993http://www.uen.org/Lessonplan/preview?LPid=18993http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5050http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://www.teachingideas.co.uk/maths/files/areapractical.dochttp://mathteachermambo.blogspot.com/2007/08/surface-area-activity.htmlhttp://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfhttp://www.uen.org/Lessonplan/downloadFile.cgi?file=21572-2-27998-Net_of_Cylinder.pdf&filename=Net_of_Cylinder.pdfhttp://www.iit.edu/~smile/ma8808.htmlhttp://www.shodor.org/interactivate/lessons/SurfaceAreaAndVolume/http://io.uwinnipeg.ca/~jameis/PAGES/MYR64.htmlhttp://www.uen.org/Lessonplan/preview.cgi?LPid=21572http://www.nctm.org/standards/focalpoints.aspx?id=334http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5060http://www.math.com/tables/geometry/surfareas.htm


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Candies R Us

Getting Serious About Cylinders-Surface Area and VolumeCube ModelsInteractive Websites for Teaching Volume

3D Model Maker Demonstrates Rectangular and Triangular PrismsInteractive Overview of 3D Shapes Reviews the volume of various 3D shapesInteractive Cube Volume Simulation demonstrates how to find the capacity of a rectangular prism

Comments OffPosted inUncategorizedPosted by: ldegarci | April 13, 2009

Measurement US Customary and Metric Systems Area and Perimeter

Surface Area Volume


Area and PerimeterNCTM Standardshttp://standards.nctm.org/document/appendix/meas.htm NCTM standards and expectations for k-12UEN Core Curriculumhttp://www.uen.org/core/core.do?courseNum=5040- Utah Core curriculum for 4thgrade. 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 5thgrade. Area is Standard 4. There are lessonplans and links included for the standard.

http://www.uen.org/core/core.do?courseNum=5060- Utah Core curriculum for 6thgrade. Area is Standard 4. There are lessonplans 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

-Triangle: A polygon with three corners or vertices and three sides or edges, which are line segments. A = 1/2bh
http://www.uen.org/Lessonplan/preview?LPid=21546http://www.uen.org/Lessonplan/preview?LPid=21546http://www.uen.org/Lessonplan/preview?LPid=21572http://www.uen.org/Lessonplan/preview?LPid=21572http://www.uen.org/Lessonplan/preview?LPid=6399http://www.uen.org/Lessonplan/preview?LPid=6399http://www.shodor.org/interactivate/activities/surfaceareaandvolume/?version=1.6.0_11&browser=Mozilla&vendor=Sun_Microsystems_Inc.http://www.shodor.org/interactivate/activities/surfaceareaandvolume/?version=1.6.0_11&browser=Mozilla&vendor=Sun_Microsystems_Inc.http://www.learner.org/interactives/geometry/index.htmlhttp://www.learner.org/interactives/geometry/index.htmlhttp://illuminations.nctm.org/Activities.aspx?grade=all&srchstr=volumehttp://illuminations.nctm.org/Activities.aspx?grade=all&srchstr=volumehttp://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/measurement-3/http://mathteachingstrategies.wordpress.com/2009/04/13/measurement-3/http://mathteachingstrategies.wordpress.com/2008/12/11/measurement-2/http://mathteachingstrategies.wordpress.com/2008/12/11/measurement-2/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://standards.nctm.org/document/appendix/meas.htmhttp://www.uen.org/core/core.do?courseNum=5040http://www.uen.org/core/core.do?courseNum=5040http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5060http://www.uen.org/core/core.do?courseNum=5050http://www.uen.org/core/core.do?courseNum=5040http://standards.nctm.org/document/appendix/meas.htmhttp://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/volume/http://mathteachingstrategies.wordpress.com/2009/04/13/surface-area/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/http://mathteachingstrategies.wordpress.com/2008/12/11/measurement-2/http://mathteachingstrategies.wordpress.com/2009/04/13/measurement-3/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://illuminations.nctm.org/Activities.aspx?grade=all&srchstr=volumehttp://www.learner.org/interactives/geometry/index.htmlhttp://www.shodor.org/interactivate/activities/surfaceareaandvolume/?version=1.6.0_11&browser=Mozilla&vendor=Sun_Microsystems_Inc.http://www.uen.org/Lessonplan/preview?LPid=6399http://www.uen.org/Lessonplan/preview?LPid=21572http://www.uen.org/Lessonplan/preview?LPid=21546


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

-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.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 alwaysthe same.
http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/452px-triangle_illustration_svg/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/452px-triangle_illustration_svg/http://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/452px-triangle_illustration_svg/


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- 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 studentsexplore and solve mathematical problems through trial, error, and personal experience rather than simply being handedequations or given answers. If concepts are derived for self, this information is much more likely to become solidified in thestudents mind and aid in concrete understanding. The three parts of inquiry include launch, explore, and summarize.

-Building figures with square tiles

-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. Ideasinclude 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 oroverhead. 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 dont know what the measurement of thesides 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 towrite 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 purchaseas well as a few free useful links for teachers.
http://college.cengage.com/education/bahr/elementary_math/1e/resources.htmlhttp://mathteachingstrategies.wordpress.com/2009/04/13/area-and-perimeter-2/picture-2/http://college.cengage.com/education/bahr/elementary_math/1e/resources.html


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http://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Compu

ter,_Inc. Generate shapes to explore perimeter in an interactive and fun way!http://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.wemlUse this site for free information orsign up for cool videos. Free 5 day trial.

ResourcesBahr L. Damon & de Garcia A. Lisa, Elementary Mathematics Is Anything but Elementary2010Wikipedia. Retrieved April 15, 2009, from http://en.wikipedia.org/wiki/Main_Page


Children with Special Needs / Struggling Learners

Exceptional Learners

Struggling Learners and Students with Disabilities

Everything about our educational system is changing, including the students who are in our classrooms. Between dramatic increases in the numbersof minority students and legislation such as the Individuals with Disabilities Education Act and the No Child Left Behind Act, classroom teachers are

experiencing a different population of children than in decades past. Today, it is not uncommon to have children with language, poverty, and learning issues

all within the confines of the general education class (Bahr & De Garcia, 2010).

What kinds of behaviors indicate struggling learners?

Can students with disabilities learn how to do every kind of math? In what areas do these students struggle most?

What can you do to accommodate students with specified disabilities such as ADHD, Dyscalculia, or Autism?
http://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inchttp://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inchttp://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inchttp://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.wemlhttp://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://mathteachingstrategies.wordpress.com/2009/04/13/children-with-special-needs-struggling-learners/http://mathteachingstrategies.wordpress.com/2009/04/13/children-with-special-needs-struggling-learners/http://mathteachingstrategies.wordpress.com/2009/04/13/children-with-special-needs-struggling-learners/http://mathteachingstrategies.wordpress.com/category/uncategorized/http://www.brainpop.com/math/geometryandmeasurement/areaofpolygons/preview.wemlhttp://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inchttp://www.shodor.org/interactivate/activities/PerimeterExplorer/?version=1.5.0_16&browser=safari&vendor=Apple_Computer,_Inc


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Documents

Strategies for Teaching Elementary Mathematics