Transcript Preparing for Success in Algebra KICK

Preparing for Success in Algebra
English Language Learners in Mathematics
A Collaboration between:
 Los Angeles Unified School District
 University of California, San Diego
 San Diego State University
 University of California, Irvine
 San Diego Mathematics Project
Welcome
California Mathematics and Science
Partnership (CaMSP)
Year 2, Day 6
October 23rd, 2010
Slide 2
ESSENTIAL QUESTIONS
How can we assist students in conceptually
understanding the Pythagorean Theorem?
 How can we introduce the Pythagorean
Theorem in a tangible, fun, and conceptual?
 How can the relationship between the legs
and hypotenuse of a right triangle become
more visual and concrete?
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Slide 3
ESSENTIAL STANDARDS
Seventh Grade & Algebra Readiness
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Seventh Grade and Algebra Readiness Standard
Measurement and Geometry
3.3 Know and understand the Pythagorean theorem
and its converse and use it to find the length of the
missing side of a right triangle and the lengths of
other line segments and, in some situations,
empirically verify the Pythagorean theorem by direct
measurement.
Slide 4
Frontloading Everyday Vocabulary
Leg
Hypotenuse
Square
Square Root
Right Triangle
Squaring
Area
Units
Conjecture
Slide 5
Preparing the Learner: Connecting
to Prior Knowledge- Frayer Model
Frayer Model for Square and square root.
Slide 6
Preparing the Learner: Finding the
Side of a Square
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Look at the table provided.
Draw the square given the area and identify
the side length.
Make sure to put the information into the
table.
Slide 7
Interacting with the Text: Squaring
the Sided of the Triangle
Using the lengths of your group’s
assigned triangle make a Collaborative
Poster that includes the following:
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Draw the triangles with the given leg lengths.
Draw out the squares on the side of each side of
the triangle.
Find the areas of the squares and record the
results in the table.
Slide 8
Interacting with the Text: Squaring
the Sided of the Triangle
Complete the table based on group reports.
 For each triangle, look for a relationship among
the areas of the three squares.
 What conjectures or predictions can be made
bout the areas of the squares drawn on the sides
of the right triangles?
My conjecture on __________ is…
If I use … then I predict … will happen.
Based on the past results, I predict….
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Slide 9
Interacting with the Text:
Pythagorean Theorem Proof
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There are several arithmetic, geometric and
graphical proofs for the Pythagorean
Theorem.
The following is one:
A Pythagorean Proof
Using the triangles and squares provided
physically generate this proof.
Slide 10
Extending the Learning: My Little
Pythagorean Theorem Book
Having students synthesize their learning is
an essential component of learning. Any
tools we can provide that scaffold this
process will aid students develop their
understanding.
 Fold and create your little book.
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Slide 11
Where does this task fit?
Slide 12
Modeling The Pythagorean
Theorem
Proof 1
 Proof 2
 Proof 3
 Proof 4
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Slide 13
Task Analysis/ Debrief
How did the activities develop
conceptual understanding of the
Pythagorean Theorem?
 How did it foster problem solving skills?
 What are the benefits to tasks of this
type and what are some drawbacks or
precautions to consider?
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Slide 14
Break
15 Minutes
Slide 15