Laying the Foundations of Geometry for the Math English Language Learners

5th Annual MELL ConferenceJune 30 – July 1, 2009

San Marcos, TX

Lolita GerardoPSJA Memorial High School

logerard23@yahoo.com

Why are we here?

• Share classroom tested activities that works well with the Math English Language Learner

• Share ideas used in the classroom that enhanced learning for the ELL

Geometry Curriculum TEKS

• (G.7) Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

• The student is expected to• (A) use one- and two-dimensional

coordinate systems to represent points, lines, rays, line segments, and figures

• (B) use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons

• (C) derive and use formulas involving length, slope, and midpoint.

MELL CLASSROOM PRACTICES FRAMEWORK (TODOS research monograph, April 2008)

• Multiple representations incorporate mathematics learning levels: concrete, semi-concrete and abstract

• Language support is offered without supplanting English instruction

• Glossary of mathematics terms is always available for reference

• Curriculum is well paced

Stages of Learningaccording to Blooms Taxonomy

1. Acquisition of Knowledge

2. Understanding of Knowledge

3. Application of Knowledge

4. Analytic Thinking5. Critical Thinking6. Creative Thinking

How can the ELL acquire knowledge?

Classroom Observations1. Individual Reading

- pay attention to math vocabulary

2. Through the use of hands- on manipulatives

- Explore - Experiment - Discover

3. Group Discussions- Collaborative Learning

4. Direct Instruction from the facilitator

READING

• Read the following statement

• Comment, ideas . . .

If yuo cna raed this tehn you aer aslo a gneius

ta fsrit I toghhut I nede ot pya aetnttoin ot teh maeinng fo eervy wrod wittren ni teh sneencte.

lttear I funod uot taht sa lnog sa yuo acn raed het frsit nad lsat ltteer oyu liwl udresntnad eht mnenaig fo eth minusactrp.

atefr lal I cuodl fgirue out the cerorct sllepnig fo ecah word eevn the ltteers aer srbaclebd.

• Name_______________________________ Date_____________

• Rewrite the paragraph with the correct word, correct spelling and punctuations.

• If yuo cna raed this tehn you aer aslo a gneius

• ta fsrit I toghhut I nede ot pya aetnttoin ot teh maeinng fo eervy wrod wittren ni teh sneencte. lttear I funod uot taht sa lnog sa yuo acn raed het frsit nad lsat ltteer oyu liwl udresntnad eht mnenaig fo eth minusactrp. atefr lal I cuodl fgirue out the cerorct sllepnig fo ecah word eevn the ltteers aer srbaclebd.

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Rewrite the definition with correct spelling

• A piont si a scipfeic lcaootin ni a lnie, in a palin or in scape.

• A lnie is na ifinntie tes fo pintos liyng sied by sied.

• A sgnemet is a sbuest fo a lien wtih tow ednnopits.

• A panle is na itfinne ste fo pinots ni a falt srfucae.

• Name ______________________ Date __________• Vocabulary Building• Rewrite the definition with correct spelling

1. A piont si a scipfeic lcaootin ni a lnie, in a palin or in scape.

2. A lnie is na ifinntie tes fo pintos liyng sied by sied.

3. A sgnemet is a sbuest fo a lien wtih tow ednnopits.

4. A panle is na itfinne ste fo pinots ni a falt srfucae leoctad in all deritcoins.

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Developing conceptual understanding

Use manipulativesColored chips – represent points,

collinear points, coplanar points

String – represents linesStrips – represent segments, raysWires – represent polyhedrons,

skew linesColored papers – represents

planesGeoboard, Geo Grids, Pattern

blocks Megamagz, Nets, Pentominoes

Summarizing conceptual understanding

• Using the art of origami• Using foldables• Using thinking maps • Graphic organizers• Cue Cards

Vocabulary Review Using origami

• Do origami bird• Write at least ten math

vocabulary used while you were doing origami

• Name____________________ Date______________________

• Title: Modeling Geometric terms and concepts

• Geometric Terms: see attach list

• Materials: Tag boards strips, Fastener, Hole puncher, Colored papers, rulers, markers, wires

• Procedure:• Using your chosen materials, create a

model for each geometric term.• Using colored papers, create a foldable • (mini book note) that contains the following:• - the term (cover page)• - the definition/description • - a drawing or illustration• - an application in the real world or in your • imaginary world• - a problem and its solution• - Information about you, the author, on the • last page

• Reflection:• Write a reflection about your project and

its relevance to your study of mathematics

• Evaluation Criteria:• Originality 25 %• Organization 20 %• Use of correct math term 20 %• Appeal (color, neatness, etc) 15 %• Accuracy or preciseness 20%• Total 100 %

• LAYING FOUNDATIONAL KNOWLEDGE OF GEOMETRY BY MODELING• *** Create a model and record each model in the grid paper. Be sure your line segments are

straight. •

FOUR BASIC UNDEFINE TERMS OF GEOMETRY• POINT LINE PLANE SPACE

• FUNCTIONAL DEFINITIONS• POINT• POINT-RELATIONSHIPS• collinear points noncollinear points• coplanar points noncoplanar points• LINE • SUBSETS OF THE LINE• segments rays• points• LINE RELATIONSHIPS• parallel lines intersecting lines• perpendicular lines Transversals Skew

lines•• PLANE• SUBSETS OF THE PLANE• points• segments rays angles• polygons circles ellipse

parabola hyperbola V-lines

• SPACE• SUBSETS OF THE SPACE• points polyhedrons segments prisms• rays cubes angles triangular prisms• polygons rectangular prisms circles pentagonal prisms• ellipse pyramids parabola square pyramids• hyperbola triangular pyramid V-lines pentagonal pyramid

spheres•• TYPES OF ANGLES BASED ON THE MEASUREMENT• ZERO ANGLE STRAIGHT ANGLE ACUTE ANGLE REFLEX

ANGLES• RIGHT ANGLE PERIGON OBTUSE ANGLE

• ANGLE RELATIONSHIPS WITH RESPECT TO INTERSECTING LINES• VERTICAL ANGLES ADJACENT ANGLES LINEAR PAIRS• SUPPLEMENTARY ANGLES

• ANGLE RELATIONSHIP WITH RESPECT TO SUM OF TWO ANGLES• COMPLEMENTARY ANGLES SUPPLEMENTARY ANGLES

• POLYGONSTRIANGLES OCTAGON QUADRILATERALS NONAGON PENTAGON

DECAGON HEXAGON UNDECAGON HEPTAGON DODECAGON

• TYPES OF TRIANGLES ACCORDING TO ANGLE MEASURE• RIGHT TRIANGLES ACUTE TRIANGLES OBTUSE TRIANGLES• EQUIANGULAR TRIANGLE

• TYPES OF TRIANGLES ACCORDING MEASURE OF SIDES• EQUILATERAL TRIANGLE ISOSCELES TRIANGLE SCALENE TRIANGLE

• QUADRILATERALS

• PARALLELOGRAM FAMILY NON PARALLELOGRAM• SQUARE (regular quadrilateral) KITE• RECTANGLE TRAPEZIUM• RHOMBUS• PARALLELOGRAM• TRAPEZOID

USING THINKING MAPS

• Flow map• Bridge map• Bubble map• Tree map• Flow Chart map• Radiating map• Twirl map• Etc . . .

SAMPLE WORKS

1. What are the different types of

angles? Summarize them using thinking maps.

• Name _____________________________ Date _______________• Using the given Map below, summarize the types of angles

classified according to their size or measurement

TYPES OF ANGLES

ANGLES

TYPES OF

ANGLES

ACUTE ANGLES

RIGHT ANGLES

OBTUSE ANGLES

ZERO ANGLE

STRAIGHT ANGLES REFLEX

ANGLES

PERIGON

Summarize the types of angles

• Use the coordinate map with four quadrants

• Indicate the axes with imaginary lines

TYPES OF ANGLES WITH REFERENCED TO THE LOCATION OF ITS TERMINAL SIDE IN THE

COORDINATE PLANE

ACUTE ANGLES

OBTUSE ANGLES

REFLEX ANGLES

STRAIGHT ANGLE

ZERO ANGLEPERIGON

RIGHT ANGLE

Use foldables to summarize the types of angles

• It must have pages in a book like manner

• It must contain the following information• Title page• Term • Illustration, drawing• Definition, description• Application in real life

problems• Author information

Using foldables to summarize Geometric concepts

ZERO ANGLE ( terminal side has not started rotation)

• ACUTE ANGLE

• RIGHT ANGLE ( terminal side and initial sides are perpendicular)

• OBTUSE ANGLE

• STRAIGHT ANGLE ( initial side and terminal side are opposite each other)

• REFLEX ANGLE

• PERIGON (Has completed one rotation)

Use foldables to summarize each of the angles

• Create a book for each type of angle

• Describe each angle with reference to the coordinate plane

• Draw examples with specific measures

• Name some real scenarios that represents these angles or cut and paste pictures

Modeling angle relationships

• Vertical angles• Adjacent angles• Linear pairs• Complementary angles• Supplementary angles

Modeling polygons

• Triangles • quadrilaterals• pentagons• hexagons• heptagons• octagons• nonagons• decagons• undecagons• dodecagons

MODELING TRIANGLESTYPES OF TRIANGLES

ACCORDING TO ANGLE MEASURE

• RIGHT TRIANGLES• ACUTE TRIANGLES• OBTUSE TRIANGLES• EQUIANGULAR TRIANGLE

TYPES OF TRIANGLES ACCORDING MEASURE OF SIDES

• EQUILATERAL TRIANGLE• ISOSCELES TRIANGLE• SCALENE TRIANGLE

Modeling the quadrilateral family

PARALLELOGRAM FAMILY1. SQUARE (regular

quadrilateral)2. RECTANGLE3. RHOMBUS4. PARALLELOGRAM5. TRAPEZOID

NON PARALLELOGRAM1. KITE2. TRAPEZIUM

REFERENCES

• http://www.tsusmell.org• Center for applied linguistic

(CAL)• SIOP Model• NCTM Standards• Thinking Maps (David Hyerle,

Ed.D Thinking Maps Inc)• Research monograph of

TODOS: Mathematics for all. Vol 1. April 2008

1. In this session I learned . . .

2. I am excited to try . . . In my own classroom.

3. A good topic for next MELL conference would be . . .

THANK YOUHOPE YOU WILL HAVE A

REWARDING NEW SCHOOL YEAR