I started today by giving out awards to the top achievers in math class for the semester! I gave you the rest of the period to sign yearbooks! Yay!

]]>Today you got a chance to graph on the graphing calculators! I showed you how to do it and also showed you how you can get the graphing calculator to solve algebra equations! It was due at the end of the period. There is no homework!

]]>You got to work with graphing calculators today! We learned how to do some basic computation with them and use some of the other fancy functions that they have. It was due at the end of the period. There is no homework!

]]>We had a quiz today! There is no homework! Don’t forget that the last day to turn in late/missing work is Monday of next week! Have a great weekend!

]]>We have our last quiz of the year tomorrow! For the quiz, you should be able to:

- Identify and name angle relationships using geometry vocabulary.
- Use angle relationships to find the measures of unknown angles.
- Use the interior angle sum formula.
- Find the measure of one interior angle of a regular polygon.
- Set up and solve algebra equations to find unknown angle measures.

Your homework is to finish up the Quiz Review. Also, the last day to turn in late/missing work is Monday of next week!

Today we had a mixed review of all the geometry work that we have been doing! I even did #1 and #2 with you on the overhead!

Third & fifth periods should finish #1-12. Fourth period should finish #1-13. Don’t forget that we have a quiz on Friday!

]]>Today we learned a few new symbols. The symbols drawn on the angles below show that the angles are equal in measure. Notice that in the parallelogram, one pair of angles is equal, but not equal to the other pair of angles.

If you have a regular polygon, all side lengths are equal and all angles are equal (like the pentagon below). We can actually find the measure of each of the interior angles using the interior angle sum formula. Since all of the angles are equal, divide the interior angle sum by the number of angles!

Third period should finish #1-8. Fourth & fifth period should finish #1-6. Don’t forget that we have a quiz on Friday!

]]>Today we used the interior angle sum formula that we came up with last week. For example, if we know how many sides a polygon has, we can determine the interior angle sum (see the first example below). But today we also had to apply the formula to solve problems. In the second example below, we know the interior angle sum of a polygon, but we want to know how many sides it must have. We can set up and solve an algebra equation using the formula.

Almost every single problem on today’s assignment needed the interior angle sum formula in some way! Your homework is to finish #1-13. Also, we have a quiz on Friday!

]]>All year, you have been seeing the class expectations posters that last year’s students made. Today, you got a chance to make one with your table group. Remember, the best of the best will be put up on the wall for next year’s students to look at every day!

There is no homework. Have a great weekend!

]]>Today we explored the interior angles of polygons. We know that the interior angles of any triangle always add up to 180 degrees. This is called an interior angle sum… because it is all of the interior angles added together (the sum!). Using our knowledge of triangles, we can then find the interior angle sum of any polygon by cutting the polygon up into triangles! To find the interior angle sums, pick a vertex (corner) and draw lines to other corners to form triangles. Since each triangle has 180 degrees in it, the interior angle sum of the polygon will be the number of triangles times 180 degrees.

We did the first part of the assignment together and found that there is a formula for finding this information without cutting up the shapes! If we take the number of sides of subtract 2, we know how many triangles are in the polygon. Then we can multiply that number of 180 to find the interior angle sum! We wrote that formula in our notes:

Your homework is to finish #1-5.

]]>We had more work with the types of geometry problems that we have been doing – completing tables to justify angle measures, setting up algebra equations to solve for unknown angle measures, and determining if triangles are similar.

Your homework is to finish #1-7. We will add some new geometry properties tomorrow!

]]>Today we continued our work finding angle measures using angle relationships, but today you also had to justify your answers! This is what showing your work looks like in geometry. To do this, you complete a two column chart. The first column is titled “Statements” and is where you write the angle measures that you find. The second column is titled “Reasons” and is where you write how you know the angle measure using geometry vocabulary. Here is an example…

I would like you to fill in each line of the table as you find each angle. Do NOT fill in the diagram first and then complete the table because you won’t remember how you found each angle! Find the angle in the diagram, then fill in the line in the table, so that you will be able to correctly state how you know! Also, make sure you write each angle measure into the diagram so that it is easier to find the next angle measure!

Notice a couple of things up above… When we give the angle measures, we include the m before the angle. When we are referring to angles (on the Reasons side), we do not need the m. Also, we list the angles that we find in the order that we find them. This allows a person reading the table to clearly see how the problem was solved. Be sure to include the angles that you are referring to in the reasons column. Don’t just write down “supplementary angles”, state which two angles are supplementary! And finally, notice how I filled in the diagram with the angles.

I would like you to finish #1-6 for the classwork. This is no additional homework!

]]>Today’s focus was on using algebra to solve geometry problems. For each diagram, you had to set up an algebra equation based on the angle relationships. Once you solve it, you then need to go back and calculate the measure of the unknown angles.

Your homework is to finish #1-6.

]]>We started today by writing down the rule for triangle similarity. We know that if two angles of one triangle match two angles of another triangle, then the third angles must also match and the two triangles must be similar!

Yesterday, we looked at the pattern of angles formed when parallel lines are intersected by another line. There are names for each of these angle relationships! Today, we completed the back page of our notes that have all of the angle relationships in pictures!

If you’d like to see a video describing these relationships, check it out here:

We also had some problems where a triangle was intersected by a line that was parallel to one of its sides. We found that this always creates a similar smaller triangle!

In class, you had to complete #1-6. There is no additional homework, so have a great weekend!

]]>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 wrote the following down in our notes:

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

In class, you should have finished at least #1-7. There is no additional homework!

]]>Today we worked with similar polygons. Remember, similar polygons have the same shape but are different sizes – like when we drew dilations in our last unit! You already know that if you have two similar triangles, you can use the scale factor to find the unknown side lengths. Today though, we worked with similar triangles and our focus was on their interior angles.

My demonstration in class showed you that when you enlarge or shrink a triangle, even though the side lengths changes, the angles all stay the same! So if each of the angles in one triangle have the same measure as each of the angles in another triangle, then the two triangles are similar. We don’t even need to look at the lengths of the sides!

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!

Your homework is to make sure you have #1-7 complete.

]]>Today we looked at angles in triangles. We started by taking down some notes:

We know that the interior angles of a triangle always add up to 180 degrees. So if we know the measures of two of the angles, we can always find the measure of the third!

Finding the measures of exterior angles requires just a little more thought. The exterior angle and the angle next to it will always form a straight line, so the two angle measures must add up to 180 degrees. Then if we know the measure of one of the two angles, we can find the measure of the other.

Your homework is to finish #1-6.

]]>Today we started our geometry unit! You got a new packet of notes, and we filled in the front page with some definitions and examples:

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!

In class, you should have completed at least #1-5. There is no additional homework, so have a great three-day weekend!

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We had a quiz today! There is no homework! We will start a new unit tomorrow!]]>

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

• Use the coordinate rules

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

]]>Today we had to describe how to get one figure to move directly onto another figure. This is what we mean by “mapping”. Make sure that your descriptions are specific and complete!

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In class, you should have finished #1-8. Also, we will have a quiz on Thursday!

Today we had some harder transformations! We had some problems that had you perform two transformations. We also had some problems where you had to graph a line and then reflect a shape across that line.

In class, you should have finished #1-7. Also, we will have a quiz on Thursday!

]]>It was back to our regular routine today! Today’s assignment was a good review of the transformation work that we were doing before testing, and it also mixed in graphing linear relationships.

The assignment also referred to congruent and similar shapes. Remember that congruent figures have the exact same size and shape. Similar figures have the same shape, but are a different size.

In class, you should have finished #1-7 (if you were SBA testing during the period, you do not have to do the assignment!). Have a great weekend!

]]>Today was the last day of in-class SBA Math testing! We will be back to the normal class routine tomorrow! If you still need time to finish, don’t worry… you will be pulled out to finish tomorrow.

]]>Day 3 of SBA Math testing! Don’t forget to bring a book tomorrow, so that you can read when you are finished!

]]>Today was our second day of SBA Math testing! Make sure that you bring a book tomorrow, so that you can read when you finish!

]]>Today we took the Math SBA Test in class. We will continue with the testing tomorrow. There is no homework!

]]>Today was a review of grade level math concepts. There is no homework. We start SBA Math testing on Monday!

If you would like to do the online practice test, you can do it at home! Here is the link to the practice test!

]]>Today we learned how 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.

Your homework is to finish #1-8, and there is no extra homework worksheet!

]]>It was a short day today! In periods 4 and 5, we took notes on rotating clockwise (3rd period will do it tomorrow). Here are the notes:

If you are still having trouble visualizing the rotations, just use the coordinate rules! Remember though, there are different rules depending on which way you are rotating!

Third period should finish the packet. 4th and 5th periods should complete #1-6.

]]>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 a shape, 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. There is no additional homework!

]]>Today, you got a chance to take the online practice test for the SBA Math test! I really wanted you to get a chance to understand how tools in the online test work, especially the calculator and the graphing tool.

If you would like more time on the practice test, you can do it at home! Here is the link to the practice test!

You have no homework!

]]>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 know it will 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…

In class, you should have easily completed at least #1-4b. Have a great weekend!

]]>We started today by writing down the coordinate rules for translations (slides). We found yesterday that there are simple rules when sliding a point:

Today, we learned a new transformation called a dilation. When we perform a dilation, the image has the same shape but is a different size than the original! When drawing dilations, you have to know two things… the scale factor and the center of dilation. The center of dilation is where everything is based out of. The scale factor is how many times bigger (or smaller) you are making the shape. To draw the dilation, count the distance from the center of dilation to a point on the shape. Multiply that distance by the scale factor, and then plot it!

Watch the video below, because it is much easier to understand when you can see it being done!

Here are the notes and examples we wrote down:

While working on the classwork, you should have discovered the coordinate rule for dilations centered at the origin. Just multiply the original coordinates by the scale factor!

For homework, you should finished #1-6.

]]>We started a new unit today on transformations. A transformation is basically when you take a figure and make a copy of it somewhere. Sometimes the figure will be the exact same shape and size, and sometimes it won’t be. This is a very visual unit and most kids find it to be the easiest unit.

There are four types of transformations, but two that we learned about today are reflections and translations. Most of you know all about reflections, because you look into a mirror and see your reflection everyday! The key to drawing an object’s reflection is to pay attention to where your line of reflection is (think of it as the mirror). The reflection of each point is the same distance from the line of reflection, but on the opposite side!

A translation is when you slide a shape over! It is the easiest transformation of the four, because all you have to do is slide each point the stated distance and directions, and then connect the points.

Here are the notes that we took:

When drawing transformations, make sure that you label the points and include prime marks on your new points. The prime marks signify that the point is a copy, and not the original point!

During classwork, we discovered two rules for finding the location of reflected points. This allows us to find the location of a reflected point without even having to plot it! We wrote them above in the “coordinate rules” section. We will talk about the coordinate rules for translations tomorrow.

For homework, finished #1-6. There is no additional homework!

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