Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Tuesday, 5/22: SBA Testing

Learning Target: Take the Smarter Balanced Math Test.
Handouts: None!

Today was the second day of Smarter Balanced Testing. We will continue for the next several days. There is no homework!

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Monday, 5/21: Math SBA Testing

Learning Target: Take the Smarter Balanced Math Test.
Handouts: None!

Today was the first day of Smarter Balanced Testing. We will continue for the next several days. There is no homework!

Friday, 5/18: Angles & Parallel Lines (Day 3 of 15)

Learning Target: Explore parallel lines in order to discover more angle relationships.
Handouts: Angles & Parallel Lines #1-5 (Turn in: Mon, 5/21)

Today we learned some more angle relationships. When two lines intersect, the angles across from each are equal. Those angles are called vertical angles.

We also looked at the angles that are formed when parallel lines are intersected by another line (a transversal). This forms eight angles with a pattern. The first group of four angles is exactly the same as the second group of four angles! We also learned that the pairs of equal angles have names.

We wrote the following down in our notes:

If you want to see those patterns visually, check out the video…

Your homework is to finish #1-5. Have a great weekend!

Thursday, 5/17: Triangle Similarity (Day 2 of 15)

Learning Target: Work with triangles in order to explore their angle relationships.
Handouts: Triangle Similarity (Turn in: Fri, 5/18)

Today we worked with similar triangles. Remember, similar polygons have the same shape but are different sizes – like when we drew dilations in our last unit! We have learned that the angles of similar triangles are the same. This is also how you check to see if two triangles are similar – if the angles of one triangle match the angles of another triangle, then the triangles are similar!

To find the side lengths of two similar triangles, you multiple each side by the scale factor. Here is the example that we did in class:

As you worked through the classwork, you found a shortcut with the angles on #2. You found that if a pair of triangles have two angle measures in common, then the third angles must be equal too! Therefore, when you have a pair of triangles with two sets of equal angles, then the two triangles are similar! We wrote that in our notes:

Your homework is to finish #1-6.

Wednesday, 5/16: Angle Measures in Geometry (Day 1 of 15)

Learning Target: Use angle relationships to find angle measures.
Handouts: Angle Measures (Turn in: Thurs, 5/17)

Today we started working with angle measures in geometry. There were some definitions and examples that we wrote in our notes:

Geometry is a subject that is very vocabulary heavy and also contains a lot of symbols, so pay attention to these things! It is also very logical, so work through the problems step-by-step and use the angle relationships that we discussed in our notes!

Your homework is to finish #1-8.

Tuesday, 5/15: Transformations Quiz (Day 12 of 12)

Learning Target: Take a quiz on transformations.
Handouts: None.

We had our quiz today! There was no homework!

Monday, 5/14: Transformations Quiz Review (Day 11 of 12)

Learning Target: Review transformations in order to get ready for the quiz.
Handouts: Transformations Quiz Review (Turn in: Tues, 5/15)

We have a quiz tomorrow! For tomorrow’s quiz, you should be able to:
• Perform a reflection, rotation, translation, dilation without tracing paper
• Describe transformations accurately and completely
• Perform multiple transformations on a figure
• Perform transformations and write equations for lines

Your homework is to finish the rest of the Quiz Review!

Friday, 5/11: SBA Practice

Learning Target: Take the Smarter Balanced Practice online test.
Handouts: None

Today, we took the online SBA practice test. This gave you a chance to see the types of questions that are on the test, see the content that is covered, practice working with the online tools, and experience with the online calculator. The practice test is located here

You have no homework! Have a great weekend!

Thursday, 5/10: Mapping Transformations (Day 10 of 12)

Learning Target: Describe a sequence of transformations that moves one figure onto another.
Handouts: Mapping Transformations (Turn in: Fri, 5/11)

We started today by talking again about congruent and similar shapes. Congruent shapes have the exact same shape and size. Similar shapes have the same shape, but different sizes. A few days ago, we found that reflections, rotations, and translations produce congruent shapes, while dilations produce similar shapes.

In today’s assignment, we had to describe how to get one figure to move directly onto another figure. This is what we mean by “mapping”. It is often made up of a sequence of transformations. If it involves dilations at all, then it is a dilation. If it is not a dilation, then it is a congruent shape. Make sure that your descriptions are specific and complete!

Your homework is to finish #1-6. Also, I moved the quiz to Tuesday of next week.

Wednesday, 5/9: Extra Practice (Day 9 of 12)

Learning Target: Master the basic transformations.
Handouts: Extra Transformations Practice Level 1 OR Level 2 (Turn in: Thurs, 5/10)

We did more practice with transformations today, but there were two levels to choose from. If you have been really struggling with the basic transformations, you could choose to do Level 1. It has a lot of basic practice. If you just need practice with the harder transformations (like from yesterday), then you could choose to do Level 2.

Your homework is to finish #1-6.

Tuesday, 5/8: Harder Transformations (Day 8 of 12)

Learning Target: Draw harder transformations.
Handouts: Harder Transformations (Turn in: Wed, 5/9)

Today we had some harder transformations! We had to reflect some figures across lines that were not an axis. We also had to reflect some figures across diagonal lines.

The new problems involved performing two transformations on a figure. You had to show both transformations, and label the second figure with “double primes” which are two prime marks!

In class, you should have finished at least #1-9. Don’t forget that we have a quiz on Friday!

Monday, 5/7: Transformations & Linear Equations (Day 6 of 12)

Learning Target: Review our transformation work.
Handouts: Transformations and Linear Equations (Turn in: Tues, 5/8)

We started today by reviewing what congruent and similar shapes are. Remember that congruent figures have the exact same size and shape. Similar figures have the same shape, but are a different size. Here are the notes we wrote down:

Today’s assignment had a good mix of work on it. There were linear relationships review – so you had to graph lines, transform them, and then write an equation for the new line. You also had some Pythagorean Theorem problems.

Your homework is to finish #1-8. Don’t forget that we have a quiz this Friday!

Friday, 5/4: Other Kinds of Rotations (Day 5 of 12)

Learning Target: Rotate a shape about a point that is not the origin.
Handouts: Other Rotations #1-6 (Turn in: Mon, 5/7)

Today we learned to do other kinds of rotations. The first example we wrote in our notes is a clockwise rotation. This is just like what we have already been doing, but rotating in the other direction. There is a different coordinate rule for it too!

We also learned to rotate shapes when the center of rotation is not the origin. This is a little trickier, because we are used to having the origin and each axis around to help guide the rotation.

To make things easier, I gave you a big tip… draw in a fake set of axes! Make your fake axes cross at the point you are rotating around, then ignore the old axes. Now you can rotate around your new origin just like you did last week! Here are the notes that we took in class…

One important note to make is that if you use the coordinate rules to rotate, you have to use the coordinates of the points based on the fake axes (not the real coordinates). Then you base your rotated coordinates on the fake axes too.

You should have finished #1-6 in class. We will have a quiz on all of this on Friday of next week. Have a great weekend!

Wednesday, 5/2: Rotations (Day 4 of 12)

Learning Target: Draw the rotation of an image on a grid.
Handouts: More with Rotations (Turn in: Fri, 5/4)

Today we had more time to practice rotating on a coordinate grid. Rotating points that are on an axis are pretty easy to locate, but the points that are not on an axis can be hard! I showed you a method in class today that involved turning your paper. To see that method in action, watch this video…

During class, you discovered the coordinate rule for rotating 90° counterclockwise. All you have to do is switch the coordinates around and make the new first coordinate the opposite sign! This is very helpful for those people who have a hard time rotating visually! You could find the coordinates of each point, use the coordinate rules, and then plot the new coordinates to make the rotated shape!
Here are the notes that we wrote down:

Your homework is to finish #1-5 by Friday!

Tuesday, 5/1: Rotations (Day 3 of 12)

Learning Target: Draw the rotation of an image on a grid.
Handouts: Rotations (Turn in: Wed, 5/2)

We started today by writing down the coordinate rules for dilations that we learned yesterday:

Today we learned how to rotate shapes on a coordinate grid! This can be hard to visualize, so for today, I allowed you to use tracing paper to rotate the shapes. Just trace each axis and the shape on the tracing paper, put your pencil point on the origin (center of rotation), and turn the tracing paper. You will know when you have turned 90 degrees when the x-axis matches up to the y-axis! Here is a video to show how to do it:

Here are the notes that we took in class:

Even though you were allowed to use tracing paper today, your goal is to be able to rotate figures without tracing paper! There are some important properties about rotations that will help you. Any point on an axis will end up on the next axis when rotated 90 degrees. Also, the distance from the point to the origin will not change when you rotate it.

For points that are not on an axis, I showed you a method in class today that involved turning your paper. To see that method in action, watch this video…

Your homework is to finish #1-3.