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• Laying the Foundations of Geometry for the Math English Language Learners

5th Annual MELL Conference June 30 – July 1, 2009

San Marcos, TX

Lolita Gerardo PSJA Memorial High School

logerard23@yahoo.com

mailto: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 Learning according to Blooms Taxonomy

1. Acquisition of Knowledge

2. Understanding of Knowledge

3. Application of Knowledge

4. Analytic Thinking 5. Critical Thinking 6. Creative Thinking

• How can the ELL acquire knowledge?

- 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

• 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 manipulatives Colored chips – represent points,

collinear points, coplanar points

String – represents lines Strips – represent segments, rays Wires – represent polyhedrons,

skew lines Colored papers – represents

planes Geoboard, 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

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

• POLYGONS TRIANGLES 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