Linear Algebra MONDAY, AUGUST 11

Learning Goal Focus 1  I will understand transformations and use informal arguments to prove congruency between images using physical models, transparencies or geometry software.

Learning Scale In addition to level 3.0 and above and beyond what was taught in class, I may:  Make connection with real-world situations  Make connection with other concepts in math  Make connection with other content areas. I will understand transformations and use informal arguments to prove congruency between images using physical models, transparencies or geometry software.  explain the relationship of the angles formed when parallel lines are cut by a transversal  justify the transformation sequence between two congruent figures I will understand transformations and identify congruency between images using physical models, transparencies or geometry software.  use vocabulary & find missing angles associated with parallel lines cut by a transversal  verify the properties of rotations, reflections, & translations  identify the rigid transformation sequence between two congruent figures  write statements of congruency With help from the teacher, I have partial success with transformations. Even with help, I have no success with transformations.

Today’s Learning Target Target 1: Students will understand what is meant by a l earning goal, l earning target and a l earning scale.

What is a learning goal, learning scale and learning target?  Discuss with your partner.  Share what you came up  Difference between learning goal and learning target  Learning scale

Why do we have learning goals and scales?  Discuss with your partner  Important to reflect on our learning  How does reflecting on our learning help us?

Rate your learning using the scale provided Level 4 In addition to level 3.0 and above and beyond what was taught in class, I may:  Make connection with real-world situations  Make connection with other concepts in math  Make connection with other content areas. Level 3 I will understand transformations and use informal arguments to prove congruency between images using physical models, transparencies or geometry software.  explain the relationship of the angles formed when parallel lines are cut by a transversal  justify the transformation sequence between two congruent figures

Rate your learning using the scale provided Level 2 I will understand transformations and identify congruency between images using physical models, transparencies or geometry software.  use vocabulary & find missing angles associated with parallel lines cut by a transversal  verify the properties of rotations, reflections, & translations  identify the rigid transformation sequence between two congruent figures  write statements of congruency Level 1 With help from the teacher, I have partial success with transformations. Level 0 Even with help, I have no success with transformations

Summarize  Who can define a learning goal, learning scale and learning target?  Why is it important to reflect on our learning?

Today’s Learning Target Target 2 I will define symmetry, a basic design element, reflectional symmetry, a line of symmetry, a transformation and a line of reflection.

Symmetry and Transformations  Symmetry is when one shape becomes exactly like another if you flip, slide or turn it.  Transformation – A geometric operation that relates each point of a figure to an image point. The transformations we will study in this investigation – reflections, rotations and translations – are “symmetry” translations.  Symmetry translation – produces an image that is identical in size and shape to the original figure

Basic Design Element  Basic design element - A part of a pattern or design that, when transformed using at least one type of symmetry transformation will produce the entire design. What is the basic design element of the butterfly design? Where is the line of symmetry? What is the basic design element of the pinwheel design? How many copies do you need to complete the symmetric design? Where is the center of rotation? What is the basic design element for the wallpaper design? What is the direction and distance of the translation?

1.1 Butterfly Symmetry  Reflectional symmetry – A figure or design has reflectional symmetry if you can draw a line that divides the figure into halves that are mirror images.  Line of symmetry – The line that divides the figure into halves.  Reflectional symmetry is sometimes referred to as mirror symmetry or line symmetry.  The design below has reflectional symmetry about a vertical line through its center.

Line reflection  Line reflection - The geometric operation or transformation that “flips” a figure and matches each point to an image point.  To identify the image of a point P, you can use prime notation (P’). You read P’ as “ P prime”.

Summarize Did we define…..  Symmetry  Basic design element  Reflectional symmetry  Line of symmetry  Transformation  Line of reflection Rate your understanding

Learning Target I will define symmetry, a basic design element, reflectional symmetry, a line of symmetry, a transformation and a line of reflection.

Learning target I will understand that a figure has “flip” or reflectional symmetry and how each point is related to its image under transformation by reflection.

Problem 1.1 A We need to a ruler and protractor

Problem 1.1 A

Problem 1.1 B

Problem 1.1 C

Problem 1.1 C – Summarize our Learning The line segments we create J to J’, K to K’, L to L’ and M to M’ are all perpendicular to the line of reflection The line segments we create are all parallel to each other The points (vertices) J and J’ are of equal distance from the line of reflection.

Rate your understanding I will understand that a figure has “flip” or reflectional symmetry and how each point is related to its image under transformation by reflection.

Homework tonight  NONE!