Monday, 2/29/16: Rotation Art Project

We are now in Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

I explained tonight's homework in class tonight.  Students are to take the set of pre-image coordinates that they created from their first art project (the reflection across the x-axis) and create a new image set of coordinates, that will represent a 90-degree clockwise notation.  Each new ordered pair in the image set of coordinates will be of the form (y,-x), where x represents the original x-coordinate for the corresponding pre-image pair, and y represents the original y-coordinate.  That is to say, looking at all of the ordered pairs in the pre-image column, all the student has to do is write new ordered pairs, with the original y-coordinates (y-numbers) written first, and the original x-coordinates (x-numbers) written second, but with the opposite sign.

For example, say that the original pre-image ordered pairs had these:

(-3, 5)
(-5, 7)
(8, -3)
(8, 9)
(2, -4)

The corresponding ordered pairs would look like this:

pre-image:                   image:

(x,y)                            (y,-x)

(-3,5)                           (5, 3)
(-5,7)                           (7,5)
(8,-3)                           (-3,-8)
(8,9)                            (9,-8)
(2,-4)                           (-4,-2)

If you look at all of the y's in the first column, you'll see that they're written as is, but first, in the new second column.  If you look at all of the x's in the first column, you'll see that they are written second in the new second column, but with opposite signs for each.

Then students would graph the new ordered pairs (in the image column) that they just created.  This is how computers manipulate the pixels to render a 90-degree rotation clockwise.  Tonight's homework is to create new ordered pairs off of the original ordered pair (pre-image) data set, and then create the new graph which should be a 90-degree rotation to the right.

Friday, 2/26/16: Laying Foundation for Coordinate Relationships in Transformations

We are now in Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

Today we set up a model A+ paper for an upcoming memorization quiz on the relationships of the coordinates of images pre-image to image.

Some students misunderstood my substitute's instructions yesterday, hearing that the work I had left yesterday was classwork.  Actually, all 28 problems on that Equations Practice #1 were intended as classwork / homework.  I gave those students who did have all 28 problems completed 5 points extra-credit, and for those who do not have all 28 problems done, that is the homework for the weekend.  This will be a 20-point assignment, four times the normal weight for an assignment, and I will be verifying completion of it Monday.

Thursday, 2/25/16: Reviewing Solving Multi-Step Equations

I was at the district office today for a meeting.  Tonight's homework is for students to complete a photocopy, "Equations Practice #1," all problems front & back, due tomorrow.

We'll resume our work on reflections tomorrow.

Wednesday, 2/24/16: Evaluating the Reflection Art Project

We are now in Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

We are between topics presently; no formal homework is assigned for tonight.  However, students can be studying Lessons 9-2 and 9-3 from their textbook pages or online at my.hrw.com .

Tuesday, 2/23/16: Reflection Art Project

We are now in Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

Tonight's homework is for students to finish their reflection art project that we have been working on in class.  Students must have recorded the coordinates pre-image and image, in order to get credit for this assignment when I check it first thing tomorrow.

Monday, 2/22/16: Coordinate Relationships / Reflection Art

We are beginning Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

We have been reviewing the Lesson 9-1 homework (three simple translations), analyzing the coordinates pre-image to image.  We are also in the midst of a reflection art project.  Last Thursday when I was out at a meeting, I had students create artwork on a coordinate grid, which we are going to reflect across the x-axis.  (Later we are also going to do a rotation with the same art.).  Students are recording coordinates pre-image to image in this reflection of their art, and thus are discovering the important pattern associated with the reflection.  I would rather have my students do art work presently (as opposed to working solely out of the textbook), because this is how transformational geometry is used in the real world, by computer animators.  Tomorrow night for homework (Tuesday) students will be completing this project, but for tonight, no formal homework is assigned.  However, students can be studying Lessons 9-1 and 9-2, either from the textbook pages they have or online at my.hrw.com .

Friday, 2/19/16: Exploring Translations

We are beginning Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

Today in class we reviewed the Lesson 9-1 homework which would have been due yesterday while I was out.  There are important patterns in the coordinates of the vertices (corner points) pre-image to image, and we explored those today.  This is critical material which cannot be rushed, if students are going to be powerful with it.  No formal homework is assigned for the weekend, but students can be studying Lessons 9-1 and 9-2, either from the textbook pages they have or online at my.hrw.com .

Thursday, 2/19/16: Reflections Activity

Apologies for the missed post yesterday.

We are beginning Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

I was out for an articulation meeting with La Serna High School today.  Today the students did an art assignment, for which they are soon going to create a reflection.  Assuming that they are done with that, no further homework is assigned for this evening.  However, I did have the guest teacher distribute an extra-credit assignment (10 points), for students to practice equations.

Wednesday, 2/17/16: Continuing Lesson 9-1, Translations

Homework:  p.284 (4) & p.285 (9,10).

Tuesday, 2/16/16: Beginning Lesson 9-1, on Translations

We are beginning Unit 4, which is on using transformations to establish congruence, using transformations to establish similarity, the Pythagorean theorem, angle relationships in parallel lines and triangles, and the volume of cylinders, cones, and spheres.

We're starting with transformations, of which there are four types:

• translations (slides)
• reflections (flips)
• rotations
• dilations (zooming in or out)

Students, parents / guardians, and tutors, as we move forward, there are going to be two key tools that will help students with transformations (in addition to the normal internet and textbook resources):
First, I've given each student a section of tracing paper (to be kept in the plastic sleeve with the class assignment sheet and used for the entire unit).  For many students this will be of significant help, using the tracing paper to mimic the motion.  Second, look for patterns in the ordered pairs (x and y combinations) pre-image (the before) to image (the after).  From the very beginning, I am going to be making my students record all of the ordered pairs, before-and-after.  The patterns they will discover there will really help them.

We've set up Lesson 9-1 today, but need to continue it into Wednesday.  Formal homework tonight would be counter-productive, but students should be previewing Lesson 9-1 tonight for their "homework."  Many of my students have already done so.  You can expect formal homework beginning tomorrow night.

Tuesday, 2/9/16 through Friday, 2/12/16: Unit 3 Performance Task

The "Performance Task" portion of the Smarter Balanced Assessment Consortium (SBAC) standardized testing (coming up in several months) gives students the opportunity to demonstrate proficiency primarily in three of the four "claims" involved with reporting standardized test scores.  These three are Claim 2: Problem Solving; Claim 3: Communicating Reasoning; and Claim 4: Modeling and Data Analysis.  (Claim 1 is "Concepts and Procedures.")

The format for the performance task is that students are given a scenario (such as running a business), followed by about 6 or so questions related to the task at hand.  The goal of this part of the assessment is not necessarily to test the students' knowledge of their math skills, but more to assess their ability to apply them in context, as they are expected to do so in high school, college or university, and in the real world.

As we did with the end of Unit 1, this week we are having our students on individual computers taking our district's own Unit 3 math performance task.  Today we did the "classroom activity," designed to make sure that students understand the context of the problem.  Wednesday and Thursday students will be on the computers taking the performance task.  Friday we will debrief, which is the most critical part of this exercise.

As we are between units and performing this important task this week, no formal homework is assigned during the week.

However, looking ahead to Unit 4, it is on transformational geometry.  Starting next week we will be working through lessons 9-1 through 9-5.  Although students haven't been given the pages for these lessons yet, they can access the online student textbook through my.hrw.com .

Friday, 2/5/16: High School and Completing the Unit 3 Test on Equations and Systems

We started the first of a series of mini-discussions related to the high school transition, and students completed their Unit 3 Test on Equations and Systems.

We are between units.  No formal homework was assigned for the weekend.

Thursday, 2/4/16: Day 2 of Unit 3 Test on Equations and Systems

Tonight's homework is p.231 (3,4) & p.234 (1,2).

Wednesday, 2/3/16: Unit 3 Test on Equations and Systems

Tonight's homework is p.258 (4-7).

Tuesday, 2/2/16: Final Day of Review for Unit 3 Test on Equations and Systems

Our next test is on solving equations in one variable and systems, and it is tomorrow, 2/3.  The material on it:

• equations (Lessons 7-1, 7-2, 7-3, and 7-4)
• solving systems by substitution (Lesson 8-2)
• solving systems by elimination (Lessons 8-3 through 8-5)

Additionally, Lesson 8-1 should be reviewed, because that involved graphing and set the stage for solving by substitution and elimination.  (We used an excellent worksheet instead of the text for graphing, but the lesson details that aspect.)

I told the students that they do have homework tonight, and that homework is to study for this test (please see the sections and topics above).

Monday, 2/1/16: Day 1 of Reviewing for Unit 3 Test on Equations and Systems

Our next test is on solving equations in one variable and systems, and it is Wednesday, 2/3.  The material on it:

• equations (Lessons 7-1, 7-2, 7-3, and 7-4)
• solving systems by substitution (Lesson 8-2)
• solving systems by elimination (Lessons 8-3 through 8-5)

Additionally, Lesson 8-1 should be reviewed, because that involved graphing and set the stage for solving by substitution and elimination.  (We used an excellent worksheet instead of the text for graphing, but the lesson details that aspect.)

I was available after school today, Monday, 2/1, from 3:00 - 3:30.  I was also available at lunch today, and will be Tuesday. (I'm also available Wednesday, 2/3 from 3:00 - 3:30.)  Normally I'm available from when the school day ends until 3:30 every Monday and Wednesday, but I do have fifteen-minutes of after-school duty this week..

Last Friday students were given a practice version of this test.  For tonight's homework, students need to do problems 9-13 of this practice.