Overview and Background: Unit: Exploring Triangles

Jim Gillett : Cheney USD 268

Mathematics : Mathematics : Mathematics

Cheney Middle School : Grades 0 - 5 : Red Days : Nov. - Nov.

Title:	Exploring Triangles
Topics:	Recognition of triangles in the world around us; Investigation of triangle names, side length & angle requirements; properties of parallelograms; transformations of triangles
Time Frame:	approximately 16, 45 minute class periods
Start Date:	Nov. 1 - Nov. 31

Other Designers:

Summary:
This unit (Triangles and Beyond) is a part of the Mathematics in Context curriculum, developed in collaboration with the Wisconsin Center for Education Research, School of Education, University of Wisconsin-Madison, and the Freudenthal Institute at the University of Utrecht, The Netherlands, with the support of the National Science Foundation. Math in Context is published by the Encyclopaedia Britannica Educational Corporation.

In this unit students recognize triangles around them, learn to name triangles, investigate the contruction of triangles with different side lengths and form a rule about the relationships of the sides of a triangle as well as a rule about the sum of the interior angles, identify the relationship between side lengths and the opposite angles, construct triangles & parallel lines and identify properties of parallelograms, and carry out transformations on triangles.

Print Materials Needed:
Students:
student activity sheets, triangular objects, toothpicks, clay, overhead transparencies, scissors, tape, colored pencils or markers, straightedges or rulers, dry spaghetti, string, compasses, cardboard, protractors or compass cards, tracing paper, drinking straws or stir sticks, construction paper, congruent triangles.

Teacher:
overhead projector & marking pens, examples of different types of triangles, overhead transpariencies

Resources:
Copies of student texts for Triangles and Beyond, (Mathematics in Context)
Teacher's Guide for Triangles and Beyond(Mathematics in Context)

Resource Attachments:

Internet Resource Links:

Notes:

Stage 1: Identify Desired Results

State:	KS
Title:	Kansas Curricular Standards for Mathematics (March 1999)
Standard(s):	Standard 3 - Geometry Benchmark 1 - Geometric Figures and their Properties (7th Grade) Knowledge Base Indicators #2 Classifies triangles ... #6 Determines if a triangle can be constructed from three different lengths. Application Indicators #1a apply angle and side properties of ..., triangles,... Benchmark 3 - Transformational Geometry Knowledge Base Indicators #1 recognizes, describes, and performs single and multiple transformations on two-dimensional figures.

Understandings:
user	Shapes appear in objects in the world around us.

Essential Questions:
user	Does geometry describe our physical world?
user	Can triangles be formed in many ways?
user	Do triangles in real life have sides or angles that would be difficult to measure?
user	Can distances always be measured physically?
user	Does the parallelism of lines depend upon perspective?

Knowledge and Skills:

*Recognize triangles in the world.
*Construct a triangle with given side lengths.
*Use triangle properties (sum of angles, side relationships, and the Hinge theorem).

*Describe geometric figures using words, and/or diagrams.
*Draw parallel lines using a triangle and a straightedge.
*Name quadrilaterals according to their characteristics.
*Identify line symmetry.

*Describe and draw transformations (translate,rotate,reflect).

Stage 2: Determine Acceptable Evidence

Assessment Summary:
Informal assessment opportunities during team investigations.

Try This Activities (as individual quizzes)
Section A - Triangles Everywhere
Section B - The Sides
Section C - The Angles
Section D - Sides and Angles
Section E - Parallel
Section F - Copies

Notes/Journal - homework

Unit Test

Task/Prompt: The Dragline

Type:Performance Task

Topics: Side and angle relationships of triangles.

Summary:
This performance assessment is part of the Triangles and Beyond Unit in the Mathematics in Context curriculum.

A dragline is a machine that works like a crane and is used to dig in ponds or lakes. The most important part of the dragline is the long arm with a hinge at the top like an elbow. The student will be asked a series of questions about the triangle relationships and eventually determine the maximum and minimum distances the arms can reach.

Print Materials Needed:
Students: copies of The Dragline assessment in Triangles and Beyond (Math in Context - Britannnica)

Resources:
rulers

Resource Attachments:

Internet Resource Links:
Link 1:
Link 2:
Link 3:
Link 4:
Link 5:

State:	KS
Title:	Kansas Curricular Standards for Mathematics (March 1999)
Standard(s):	Standard 3 - Geometry Benchmark 1 - Geometric Figures and their Properties (7th Grade) Knowledge Base Indicator #6 Determines if a triangle can be constructed from three different lengths. Application Indicators #1a apply angle and side properties of ..., triangles,...

Notes:

Student Directions:
Is there a maximum and minimum distance that the arm of the dragline machine can reach? Use the drawing on the student pages of the assessment and do the following:

1. Estimate the length of the AB.
2. Draw a scale drawing of when the arm sections of the machine reach out to a certain number of meters.
3. If point B continues moving to the right, the angle at A and the angle at B will become smaller. Will the angle at A always be smaller than the angle at B?
4. Can the machine ever dig a hole 15 meters from A?
Can the machine ever dig a hole 1 meter from A?
Show in the drawing the maximum and minimum distances the arms can reach.

Other assessment evidence to be collected:
Selected Response/Short-answer test/quiz
	Informal assessment opportunities during team investigations. Try This Activities (as individual quizzes) Section A - Triangles Everywhere Section B - The Sides Section C - The Angles Section D - Sides and Angles Section E - Parallel Section F - Copies Notes/Journal - homework Unit Test

Stage 3: Plan Learning Experiences and Instruction

Learning Activities: