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 [email protected]

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? Classroom Observations 1. Individual Reading - pay attention to math vocabulary 2. Through the use of handson 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.

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Name_______________________________ Date_____________

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

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If yuo cna raed this tehn you aer aslo a gneius

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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.

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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

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Name____________________ Date______________________

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Title:

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Geometric Terms:

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Materials:

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Procedure:

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Modeling Geometric terms and concepts see attach list

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

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Reflection:

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Evaluation Criteria: Originality Organization Use of correct math term Appeal (color, neatness, etc) Accuracy or preciseness Total

Write a reflection about your project and its relevance to your study of mathematics 25 % 20 % 20 % 15 % 20% 100 %

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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

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POINT

LINE

FUNCTIONAL DEFINITIONS POINT POINT-RELATIONSHIPS collinear points coplanar points LINE SUBSETS OF THE LINE segments points LINE RELATIONSHIPS parallel lines perpendicular lines lines PLANE

SUBSETS OF THE PLANE points segments polygons

parabola

hyperbola

PLANE

SPACE

noncollinear points noncoplanar points rays intersecting lines Transversals

rays circles

V-lines

SPACE SUBSETS OF THE SPACE points polyhedrons segments rays cubes angles polygons rectangular prisms ellipse pyramids parabola hyperbola triangular pyramid spheres

angles ellipse

prisms triangular prisms circles pentagonal prisms square pyramids V-lines pentagonal pyramid

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TYPES OF ANGLES BASED ON THE MEASUREMENT ZERO ANGLE STRAIGHT ANGLE ANGLES RIGHT ANGLE PERIGON OBTUSE ANGLE

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

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

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POLYGONS TRIANGLES OCTAGON DECAGON DODECAGON

HEXAGON

ACUTE ANGLE

QUADRILATERALS UNDECAGON

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

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TYPES OF TRIANGLES ACCORDING MEASURE OF SIDES EQUILATERAL TRIANGLE ISOSCELES TRIANGLE

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QUADRILATERALS

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PARALLELOGRAM FAMILY SQUARE (regular quadrilateral) RECTANGLE RHOMBUS PARALLELOGRAM TRAPEZOID

Skew

NONAGON HEPTAGON

OBTUSE TRIANGLES

SCALENE TRIANGLE

NON PARALLELOGRAM KITE TRAPEZIUM

REFLEX

PENTAGON

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.

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Name _____________________________ Date _______________ Using the given Map below, summarize the types of angles classified according to their size or measurement

TYPES OF ANGLES

ANGLES ACUTE ANGLES RIGHT ANGLES

OBTUSE ANGLES

STRAIGHT ANGLES

ZERO ANGLE

TYPES OF ANGLES

PERIGON

REFLEX ANGLES

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

OBTUSE ANGLES

STRAIGHT ANGLE

RIGHT ANGLE

ACUTE ANGLES

ZERO ANGLE PERIGON

REFLEX ANGLES

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 TRIANGLES 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

Modeling the quadrilateral family PARALLELOGRAM FAMILY 1. SQUARE (regular quadrilateral) 2. RECTANGLE 3. RHOMBUS 4. PARALLELOGRAM 5. TRAPEZOID NON PARALLELOGRAM 1. KITE 2. 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 YOU HOPE YOU WILL HAVE A REWARDING NEW SCHOOL YEAR