I. Curricular Framework

Concept:

Patterns-wheel 3 of 7

Essential Question:

How has the study of patterns in your world led directly to the study of patterns in math?

Bridge:

Representations of 3

Content:

Pythagorean Theorem and Triangles

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To create an awareness of the importance of the number 3.

Activity: Students view transparencies of haiku poetry. Do not introduce them as haiku. The students will hopefully recognize them as such. (You might inform the English teacher in advance that you will be working with haiku). Examples of haiku that can be used:

A tree frog trilling
softly, the first drop of rain
slips down the new leaves.
Rogetsu

Butterfly, these words
from my brush are not flowers
only their shadows.
Soseki

Well! Hello down there,
friend snail! When did you arrive
in such a hurry?
Issa

High on a mountain
we heard a skylark singing
faintly, far below.
Basho

A hungry owl hoots
and hides in a wayside shrine...
so bright is the moon.
Joso

Hop out of my way,
Mr. Toad, and allow me
please to plant bamboo!
Chora

Broken and broken
again on the sea, the moon
so easily mends.
Chosu


Assessment: Quality of reactions and participation of students.

2. Attend: Attending to the Connection

Objective: To analyze the commonality of the poetry.

Activity: In class discussion, students determine what all of the poems have in common. (3 lines with syllable pattern 5-7-5.)

(A haiku is a poem in three lines of five, then seven, then five syllables. It is made by speaking of something natural and simple suggesting spring, summer, autumn, or winter. There is no rhyme. Everything mentioned is just what it is, wonderful, here, but still beyond.)

Ask students what qualifies a poem as haiku? What stays consistent in haiku?

Assessment: Participation in discussion and quality of ideas.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To deepen the students connection with the number 3.

Activity: Since the haiku had 3 lines consistently, students in groups of four will create a nonverbal/non-numerical symbol or logo that represents the number 3. Students will share their creations and explain.

Assessment: Quality of group work, level of interest.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To provide instruction on triangles.

Activity: Present lessons on:

Identifying similar triangles and using their properties.
Using the Pythagorean theorem.
Using relationships in special right triangles (30-60-90 and 45-45-90).
Using the tangent ratio.

Assessment: Participation in class, notetaking.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To practice skills with triangles.

Activity: Students practice skills using textbook exercises, worksheets and quizzes.

Assessment: Quizzes and tests.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Activity: Go to patterns wheel 7

7. Refine: Refining the Extension

Activity: Go to patterns wheel 7

8. Perform: Creative Manifestation of Material Learned

Activity: Go to patterns wheel 7

Assessment, Phase Five,Performance, Creative Use of Material Learned: