GBK GEOMETRYJordan Johnson

TODAY’S PLAN

Greetings / Objectives Warm-up Lesson: Basic Geometric Terms Assignment / Questions Clean-up

WARM-UP

With your compass and straightedge, construct an equilateral triangle with sides 3cm long.

If you remember how, continue and construct a regular hexagon with sides 3cm long.

THE NAZCA LINES

THE NAZCA LINES

THE NAZCA LINES

THE NAZCA LINES

OBJECTS (BY DIMENSIONS)

Zero-dimensional

One-dimensional

Two-dimensional

Three-dimensional

point line,line segment

plane space

“no part” “breadthless length”

length and width

length, width, and depth

DEFINITIONS

Zero-dimensional: Point: a location in space.

(Represented on paper by a dot, usually, but has no dimensions.)

One-dimensional: Line: a straight length that has no breadth

(Or, a one-dimensional object extending infinitely in both directions.)

Note that lines are defined by two points. Line segment: part of a line, bounded by two

endpoints. Two-dimensional:

Plane: a flat surface with no boundaries.

SKETCHES

Sketch examples of lines, points, and planes (to go with your definitions).

Note: use arrowheads to indicate infinite extension of lines:

Name points with uppercase letters.

CLOSED FIGURES

Polygons – 2-dimensional, bounded by line segments Examples:

triangle rectangle pentagon

Polyhedra – 3-dimensional, bounded by polygons Examples:

cube pyramid

QUALITIES OF LINES, PLANES, & POINTS

Lines intersect in points; planes intersect in lines.

Collinear points lie on a single line. Non-collinear points do not.

Coplanar points lie within a single plane. Non-coplanar points do not.

Concurrent lines all contain the same point.

REMARKS ON WORK;ADVICE FROM PAST STUDENTS

 Neatness & Organization of Work;Clarity of Mathematical Writing

Level Description4.0 I list all given information and identify the goal or the facts I want to

prove. I include diagrams for all problems that use diagrams. When I can't find a solution, I instead explain what the obstacles are.

3.5  3.0 My work is easily legible, shows all problems in a clear order, and

has all answers clearly labeled. I define all my variables and say what they represent.

2.5  2.0 I label homework with name, date, period, and a title that includes

chapter/section and page numbers, and turn in my work on neat, undamaged paper.

1.5 Partial success at 2.0 level, but major errors or omissions regarding 3.0 level.

1.0 Partial success at 2.0 and 3.0 with help (such as frequent reminders of the 2.0/3.0 expectations).

0.5 Partial success at 2.0 but not 3.0 with help.

0.0 No success, even with help.

ASSIGNMENT

Now: Textbook, p. 10, Chapter 1 Lesson 1, Set I.

Work alone or in pairs.

Homework due Tuesday:the Set I problems andp. 11, Chapter 1 Lesson 1, Set II. Remember:

Neat writing. Show enough to tell what the original problem was.

CLEAN-UP / REMINDERS

Pick up all trash / items.

Push in chairs (at front and back tables).

See you tomorrow!

REMAINING SLIDES: PERIOD 1

The following slides were used in Period 1’s class.

TODAY’S PLAN (PERIOD 1)

Greetings / GBK Today (period 1) Warm-up Objectives Lesson: Basic Geometric Terms Assignment / Questions Clean-up

WARM-UP

With your compass and straightedge, construct an equilateral triangle with sides 3cm long.

If you remember how, continue and construct a regular hexagon with sides 3cm long.

OBJECTIVES

Objective tables: The slips of paper you got yesterday. Describe what you have to do to pass.

Student progress chart: Page with grids where you will track your

progress.

4.0 I have mastered everything in the 3.0 level and can make neat, accurate sketches of all the shapes and intersections involved, including the 3-D shapes.

3.0 I know all the terms listed in the 2.0 level, and I can give their exact definitions, as well as those of collinear, coplanar, and concurrent. I can tell you how many dimensions each of those shapes requires, and I can write point/line/ray/segment names correctly. I can say what happens when lines and planes intersect.

2.0 I have a basic idea of what points, lines, line segments, planes, rays, angles, polygons, and polyhedra are; I could sketch any of those if you ask me to, and I can tell which ones are 3-dimensional and which are 2-dimensional.

QUALITIES OF LINES, PLANES, & POINTS

Lines intersect in points; planes intersect in lines.

Collinear points lie on a single line. Non-collinear points do not.

Coplanar points lie within a single plane. Non-coplanar points do not.

Concurrent lines all contain the same point.

CLOSED FIGURES

Polygons – 2-dimensional, bounded by line segments Examples:

triangle rectangle pentagon

Polyhedra – 3-dimensional, bounded by polygons Examples:

cube pyramid

REMARKS ON WORK;ADVICE FROM PAST STUDENTS

 Neatness & Organization of Work;Clarity of Mathematical Writing

Level Description4.0 I list all given information and identify the goal or the facts I want to

prove. I include diagrams for all problems that use diagrams. When I can't find a solution, I instead explain what the obstacles are.

3.5  3.0 My work is easily legible, shows all problems in a clear order, and

has all answers clearly labeled. I define all my variables and say what they represent.

2.5  2.0 I label homework with name, date, period, and a title that includes

chapter/section and page numbers, and turn in my work on neat, undamaged paper.

1.5 Partial success at 2.0 level, but major errors or omissions regarding 3.0 level.

1.0 Partial success at 2.0 and 3.0 with help (such as frequent reminders of the 2.0/3.0 expectations).

0.5 Partial success at 2.0 but not 3.0 with help.

0.0 No success, even with help.

ASSIGNMENT

Now: Textbook, p. 10, Chapter 1 Lesson 1, Set I.

Work alone or in pairs.

Homework due Tuesday:the Set I problems andp. 11, Chapter 1 Lesson 1, Set II. Remember:

Neat writing. Show enough to tell what the original problem was.

CLEAN-UP / REMINDERS

Pick up all trash / items.

Push in chairs (at front and back tables).

See you tomorrow!