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Geometry Advanced Trasformations - 10 day full lessons includes lesson plans, worksheets, activities, smart notebook files, ppt, assessments, and answer key

I use Geometer's Sketchpad for this lesson

The student will be able to:

For a pair of points, both on a number line (1D) and the coordinate plane (2D), find a point that is a fractional distance between two points (, , etc.).

Given with A at the origin, then the point P which is of the way from A to B(x, y) is .

Given with A(c,d) not at the origin, then the point P which is of the way from A to B(x, y) is .

Use a similar triangle model to verify the transformation rule.

Point P is a dilation of B with center A.

Draw the reflection, translation, or rotation of a figure using a variety of methods (coordinate plane, patty paper, Geometer’s Sketchpad).

Translations

Concept of Rule: (x, y)®(x+h, y+k)

Verbal description: vertical/horizontal shifts

Reflections

Draw reflection over any line (NEW)

Recognize/draw the line of reflection between a figure and its image given the graph.

Concept of Rules

Across the x-axis: (x,y)®(x,-y)

Across the y-axis: (x,y)®(-x,y)

Across y = x: (x,y)®(y,x)

Dilations

Enlargement: (3x, 3y)

Reduction:

Dilation with center of dilation at the origin

Rotations (NEW)

Clockwise and counterclockwise

90°, 180°, 270°

Concept of Rules ( for multiples of 90)

Ex. 90°: (x,y) ®(-y,x)

Compare non-rigid, proportional transformations to non-rigid, non-proportional transformations

(x,y)®(2x,2y)

(x,y)®(2x,3y)

(x,y)®(2+x,2-y)

Determine and describe the relationship that exists between an image, its pre-image and the:

Line of reflection

Center of dilation

Center of rotation

Determine and describe the line of reflection of an image and a pre-image (on and off the coordinate grid).

Determine and describe the angle of rotation of an image and pre-image (on and off the coordinate grid)

Determine and describe the center of rotation of an image and pre-image (on and off the coordinate grid) when given 2 or more image points and their corresponding pre-image.

Determine and describe the center of dilation by finding the intersections of the lines passing through a point and its image (on and off the coordinate grid) when given at least two points in the image and pre-image

Determine the Image or Pre-image for a composition of transformations on a given two-dimensional figure.

Two or more rigid transformations

Two or more non-rigid transformations

A composition of both rigid and non-rigid

Include dilations where the center can be any point in the plane.

Include reflections over any line.

Include rotations about the origin and not about the origin.

Include rotations of 90°, 180°, 270°, 360° and other degrees or rotation.

Identify lines and/or points of symmetry in figures.

Describe the difference between reflectional and rotational symmetry

Determine whether a figure keeps its original symmetry after one or more geometric transformations are performed on that figure.

Discuss under what transformations a figure will hold its original symmetry and under what transformations it will not hold its original symmetry.

Write the inverse/converse/contrapositive of a conditional statement about geometric transformations and determine its validity.

Identify the inverse/converse/contrapositive of a conditional statement about transformations from a given set of statements.

Write a biconditional statement about geometric transformations and determine its validity.

I use Geometer's Sketchpad for this lesson

The student will be able to:

For a pair of points, both on a number line (1D) and the coordinate plane (2D), find a point that is a fractional distance between two points (, , etc.).

Given with A at the origin, then the point P which is of the way from A to B(x, y) is .

Given with A(c,d) not at the origin, then the point P which is of the way from A to B(x, y) is .

Use a similar triangle model to verify the transformation rule.

Point P is a dilation of B with center A.

Draw the reflection, translation, or rotation of a figure using a variety of methods (coordinate plane, patty paper, Geometer’s Sketchpad).

Translations

Concept of Rule: (x, y)®(x+h, y+k)

Verbal description: vertical/horizontal shifts

Reflections

Draw reflection over any line (NEW)

Recognize/draw the line of reflection between a figure and its image given the graph.

Concept of Rules

Across the x-axis: (x,y)®(x,-y)

Across the y-axis: (x,y)®(-x,y)

Across y = x: (x,y)®(y,x)

Dilations

Enlargement: (3x, 3y)

Reduction:

Dilation with center of dilation at the origin

Rotations (NEW)

Clockwise and counterclockwise

90°, 180°, 270°

Concept of Rules ( for multiples of 90)

Ex. 90°: (x,y) ®(-y,x)

Compare non-rigid, proportional transformations to non-rigid, non-proportional transformations

(x,y)®(2x,2y)

(x,y)®(2x,3y)

(x,y)®(2+x,2-y)

Determine and describe the relationship that exists between an image, its pre-image and the:

Line of reflection

Center of dilation

Center of rotation

Determine and describe the line of reflection of an image and a pre-image (on and off the coordinate grid).

Determine and describe the angle of rotation of an image and pre-image (on and off the coordinate grid)

Determine and describe the center of rotation of an image and pre-image (on and off the coordinate grid) when given 2 or more image points and their corresponding pre-image.

Determine and describe the center of dilation by finding the intersections of the lines passing through a point and its image (on and off the coordinate grid) when given at least two points in the image and pre-image

Determine the Image or Pre-image for a composition of transformations on a given two-dimensional figure.

Two or more rigid transformations

Two or more non-rigid transformations

A composition of both rigid and non-rigid

Include dilations where the center can be any point in the plane.

Include reflections over any line.

Include rotations about the origin and not about the origin.

Include rotations of 90°, 180°, 270°, 360° and other degrees or rotation.

Identify lines and/or points of symmetry in figures.

Describe the difference between reflectional and rotational symmetry

Determine whether a figure keeps its original symmetry after one or more geometric transformations are performed on that figure.

Discuss under what transformations a figure will hold its original symmetry and under what transformations it will not hold its original symmetry.

Write the inverse/converse/contrapositive of a conditional statement about geometric transformations and determine its validity.

Identify the inverse/converse/contrapositive of a conditional statement about transformations from a given set of statements.

Write a biconditional statement about geometric transformations and determine its validity.

Total Pages

50 pages

Answer Key

Included

Teaching Duration

2 Weeks

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