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

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

]]>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!

]]>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.

]]>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.

]]>We had our quiz today! There was no homework!

]]>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!

]]>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!

]]>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.

]]>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.

]]>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!

]]>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!

]]>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!

]]>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!

]]>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.

]]>We started today by writing down the coordinate rules for reflections and translations (slides). We found that you can easily find where a point will be when it is either reflected or translated:

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!

Here is a video explaining the steps:

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!

Your homework is to finish #1-4.

]]>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!

You should have finished #1-2 in class. Have a great weekend!

]]>We had one more day of grade-level review, since many kids needed more time to finish their SBA testing.

You got a packet today and will turn it in the next time I see you. You do not have to finish the entire packet, but you can if you’d like! There is no homework tonight!

]]>We are spending Monday, Tuesday, and Wednesday doing some grade-level review. This will give you a chance to review the concepts that you will need to know on the Math SBA in three weeks!

You got a packet today and will turn it in the next time I see you. You do not have to finish the entire packet, but you can if you’d like! There is no homework tonight!

]]>We are spending Monday, Tuesday, and Wednesday doing some grade-level review. This will give you a chance to review the concepts that you will need to know on the Math SBA in three weeks!

You got a packet today and will turn it in the next time I see you. You do not have to finish the entire packet, but you can if you’d like! There is no homework tonight!

]]>We are going to spend Monday, Tuesday, and Wednesday doing some grade-level review. This will give you a chance to review the concepts that you will need to know on the Math SBA in three weeks!

You got packet #1 today and will turn it in the next time I see you. You do not have to finish the entire packet, but you can if you’d like! There is no homework tonight!

]]>We had a quiz today! Your homework was the After the Quiz worksheet. Have a great weekend!

]]>We have a quiz tomorrow, so today was a quiz review day!

For the quiz, you should be able to:

• Make, read, and interpret a scatter plot

• Make, read, and interpret a two-way table

Your homework is to finish the rest of the Quiz Review. Remember, you have to have the Quiz Review completed to take the Quiz!

]]>Today, we collected data from our own class and analyzed it. We had four questions that we were trying to answer:

- Do boys play more video games than girls?
- Do kids who use their planner get better grades?
- Does doing your homework lead to better test scores?
- Do kids who eat breakfast perform better during first period?

Each class period had a different set of data. You can access your class’s data here:

3rd Period Data

4th Period Data

5th Period Data

Your homework is to finish #1-3. Don’t forget that we have a quiz on Friday!

]]>The whole point of making these two-way tables and relative frequency two-way tables is to analyze data and make conclusions about the information. That was our focus today.

Remember, the focus of your conclusion will depend on which relative frequency table that you are writing about. Look at the examples from our notes:

The percents in the first table are based on gender, so first pick a gender column. Then, look at the data in the column to see what it tells you. For example, if I chose boys, then I could say **“Boys like scary movies. I know this because 75.7% of boys like scary movies.”** If I chose girls, then I could say **“Girls are split pretty evenly about scary movies. I know this because 52.2% of girls like scary movies and 47.8% of girls don’t.”**

The percents in the second table are based on opinions of scary movies, so first pick a row about scary movies. If I chose liking scary movies, then I could say **“Kids who like scary movies are mostly boys. I know this because 70% of the kids who like scary movies are boys.”** If I chose not liking scary movies, then I could say **“Kids who do not like scary movies are split pretty evenly among boys and girls. I know this because 55% of kids who don’t like scary movies are girls and 45% are boys.”**

To justify your statement, use data from the relative frequency table. In other words, use the percentages!

Your homework is to finish #1-4. Don’t forget that we have a quiz on Friday!

]]>We continued our work with two-way tables again today, but it got a little bit harder. We have found that it is difficult to compare data in two-way tables because different columns and rows have different total amounts. So that we can have comparable amounts, we can change them into percents (relative frequencies)! The examples that we did in our notes are based on the two-way table we did a few days ago.

Just like we can read the table in different ways to find percents, we can make a two-way relative frequency table in different ways to show the percents. There were three kinds of relative frequency tables in today’s assignment. One where you used the total number of people surveyed to find the percents (then all of the percents should add up to 100%). Another was where you used the total in each column to calculate the percents (then each column should add up to 100%). And the last was where you used the total in each row to calculate the percents (then each row should add up to 100%).

If you would like to watch a video explaining it, watch this:

Your homework is to finish #1-3. We have a quiz on Friday to wrap up this unit!

On Wednesday, we are going to gather data from our class! Make sure that you know about how long per day that you play video games, your 3rd quarter Language Arts grade, and your 3rd quarter grade in your first period class.

]]>We did more work with two-way tables today! We did #1 together in class and learned how to turn a table of data into a two-way table.

You should have finished #1-6 in class – if not, then you have homework! Have a great Spring Break!

]]>So far for this unit, we have been comparing two sets of numerical data (data that is made up of numbers) in scatter plots. Today, we learned how to compare two sets of categorical data (data this is made up of words). We can accumulated and organized the categorical data into a two-way table. Here are the notes that we took:

We can fill in the table by using the information in the story and logic. Two-way tables are called “two-way” tables because you can read them in two different ways. Reading the table vertically, you see we are looking at girls and boys. Reading the table horizontally, you can see that we are looking at kids who like scary movies and kids that don’t. We can use the table to answer questions:

**What percent of girls like scary movies?**

Since there were a total of 23 girls and 12 of them like scary movies, 12 ÷ 23 ≈ 52.1%.

**What percent of kids who like scary movies are girls?**

Since there are a total of 40 kids who like scary movies and 12 of them are girls, then 12 ÷ 40 = 30%.

Notice that the two above questions are slightly different! The first one reads the table vertically and the second one reads the table horizontally. They also give two totally different percentages!

Your homework is to finish #1-6.

]]>Our focus today was on understanding what scatter plots tell us about the relationship between the variables. When a scatter plot shows a positive association, it means that as one variable increases so does the other one! When it shows a negative association, it means that as one variable increases the other decreases!

We also focused on what the equation for the line of best fit tells us. The y-intercept gives us information about the starting value of one the variables, and the slope tells us the rate of change.

For 3rd period, your homework is to finish #1-6. For 4th and 5th periods, your homework is to finish #1-3.

]]>Today we continued with scatter plots, but this time we added something… you had to find and use the equation for the line of best fit! Here is the example that I showed you in class:

When finding the equation for your line of best fit, keep the following things in mind:

- The scale may or may not be going up by 1’s, so pay attention to it!
- When picking two places on your line for the slope, pick two places
**far away from each other**! This will help make your slope more accurate and make the margin of error from estimating a lot smaller. - List the slope as a decimal instead of a fraction. This makes it easier for us to compare slopes and it will make it easier for you to compute with it!

In class, you should have finished at least #1-5. For #3, make sure that you write the equation into your notes so that you can refer to it later! Your homework is to finish #1-5.

]]>We started a new unit today! This unit is on data, but more specifically, bivariate data. Bivariate data is when you have two sets of data that you are analyzing. Here are some new definitions:

The first type of data display we are making in this unit is a scatter plot. It allows us to compare two sets of numerical data and see if there is an association (relationship) between the two.

After making the scatter plots, we look at the points to see if they form some kind of pattern. If there is a pattern, then there is an association (relationship) between the data sets. I suggest that you outline the data to help you see the pattern. If it is linear, you can draw a line of best fit through the data to show the overall pattern of the points.

When we describe the association between the variables, we are describing their relationship. We do this by stating if it is strong/weak, positive/negative, and linear/nonlinear.

Your homework is to finish #1-6. We have a district interim assessment in class tomorrow on the laptops!

]]>We had a quiz today! Your only homework is the Unit Reflection. Have a great weekend!

]]>We have a quiz tomorrow! For the quiz, you should be able to…

• Use the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle.

• Find the volume of prisms, cylinders, cones, and spheres.

• Use algebra to solve problems involving volume

• Use the Pythagorean Theorem to find unknown dimensions of solids.

• Solve problems involving cube roots.

• Solve algebra equations involving cube roots.

Your homework is to finish up the rest of the quiz review!

]]>Today, our focus was on story problems. You had to sketch a labeled diagram for each situation, write an algebra equation, and then solve it. I also mixed some volume problems in there for the practice!

Your homework is to finish #1-10. Don’t forget that we have quiz on Friday!

]]>We started today by solving an example problem in our notes:

Notice that in this example, we have an approximate volume and not an exact volume in terms of pi. This doesn’t change how we solve the problem, but it does make things a little messy! We had to eventually divide by pi and get numbers in decimals. Make sure you use the “previous answer” button on your calculator so that you save yourself from having to retype those numbers! The final answers come out very very close to whole numbers!

We also had a pop quiz today!

Your homework is to finish #1-8.

]]>Today we learned how to solve a new kind of algebra equation. These equations have x^{3} in them. To undo x^{3}, you have to cube root it! Here is the example that we did in our notes:

Just like when solving equations with x^{2}, we undo the exponent last. Also notice that we do not have a plus/minus answer. With cube roots, there is only one solution!

We learned earlier in this unit that there is a relationship between squares and square roots. If you square root the area of a square, then you get the side length. There is also a relationship between cubes and cube roots. If you cube root the volume of a cube, then you get the side length!

Your homework is to finish #1-6. Don’t forget that we have quiz on Friday!

]]>Today we learned something new to almost everyone, cube roots! We already know that the square root of a number is a number that when raised to the second power gets you the given number. The cube root of a number is a number that when raised to the third power gets you the given number! There are a lot of similarities between square roots and cube roots, but cube roots are a little trickier because they are not as intuitive. Here are the notes that we took:

We learned earlier in this unit that there is a relationship between squares and square roots. If you square root the area of a square, then you get the side length. There is also a relationship between cubes and cube roots. If you cube root the volume of a cube, then you get the side length!

Calculating cube roots on a calculator can be a little tricky. Let me know if you need help doing it on your own calculator! Your homework is to finish #1-10. Have a great weekend!

]]>Today we combined all of the volume work that we have been doing with algebra! For some of the problems, you had to use the Pythagorean Theorem to find an unknown side length. Remember, you can only use the Pythagorean Theorem on right triangles, so look carefully to find them!

There were also some problems where I gave you the volume and you had to use it to find an unknown side length of the object. I want you to set up an algebra equation for it, simplify it, and then solve it to find the unknown dimension. Use the volume formulas that we have learned that past two days! Here is the example we wrote in our notes:

Your homework is to finish #1-5.

]]>Today we learned how to find the volume of round solids – cylinders, cones, and spheres. Cylinders are not prisms (because they are round), but the volume formula is similar to a prism. Multiply the area of the base times the height. Since the base is a circle, multiply **πr ^{2}** times

Yesterday we found that a pyramid is one third the volume of a prism. Today, we saw that a cone has a similar relationship to a cylinder. It takes three cones to fill a cylinder, so the volume formula for a cone is the same as the cylinder, but then divide by 3.

The sphere volume is the hard one to remember, but the more that you use it, the easier it will be to remember! It is **(4/3)πr ^{3}**.

For each volume today, I want you to give your answer in two forms… in exact form and rounded to the nearest hundredth. Pi is irrational, so giving the answer in exact form means that you leave pi in your answer and simplify the rest of the equation. To get the approximate answer, use the pi button on your calculator and then round it to the nearest hundredth. Here is an example from class:

Your homework is to finish #1-3.

]]>Today we found the volume of prisms and pyramids. You can think of a prism as a loaf of bread or a block of cheese… if you can slice it up so that every slice is the exact same size and shape, then it is basically a prism!

The shape of the slice is the base (remember, it is not always on the bottom!). The direction that the slices are stacked is the height of the prism.

Prisms are named for the shape of their base. If the base is a triangle, then it is a triangular prism. If the base is a trapezoid, then it is a trapezoidal prism. The volume of a prism is simply the area of the base times the height.

Here are the notes that we took in class. Notice that I showed how I would slice up the prism and I shaded in the base.

Pyramids are not prisms, since you cannot slice them into the same sized slices. But, as we saw in class, they are related to rectangular prisms (boxes)! Multiply the area of the base by the height, but then do one extra step and divide by 3. This is because a pyramid’s volume is 1/3 the volume of a prism with the same dimensions!

I would like you to show your work by writing out what you typed into your calculator. For example:

Also, don’t forget that the units for volume are cubed (to the third power)!

For homework, finish #1-6.

]]>Today, we learned how to check if a triangle is a right triangle. If we perform the Pythagorean Theorem on a triangle’s side lengths and it works, then the triangle must be a right triangle. This is called the Converse of the Pythagorean Theorem, and it is our way of identifying right triangles.

Here are the notes that we wrote and two examples:

The key to checking the side lengths is determining which side would be the hypotenuse. Remember, the hypotenuse is always the longest side! Once you identify the hypotenuse, do a^{2}+b^{2}=c^{2} and see if the equation works. If it works, then the triangle is a right triangle. If it does not work, then it is not a right triangle.

Your homework is to finish #1-10. I showed you how to start #8, 9, and 10 in class!

]]>We took a quiz today. There was no homework! Have a great weekend!

]]>We have a quiz tomorrow, so today was our review day. For the quiz, you should be able to:

• Use the Pythagorean Theorem to find the side lengths of right triangles.

• Use the Pythagorean Theorem to solve story problems.

• Find the distance between two points (on a coordinate grid and using the distance formula).

• Give answers in simplified exact form and rounded to the nearest hundredth.

Your homework is to finish the rest of the Quiz Review. Don’t forget, you have to complete the Quiz Review in order to take the quiz!

]]>Yesterday, we learned that we can find the distance between two points on a coordinate grid by drawing a right triangle and using the Pythagorean Theorem. But what if the two points are very far apart on a grid? It turns out, you don’t have to plot the points and draw the triangle every time!

We found that there is a quicker way to find the lengths of the legs of the triangles. If you subtract the x-coordinates, it gives you one of the leg lengths. If you subtract the y-coordinates, it gives you the other leg length. This will allow you to use the Pythagorean Theorem without even looking at the right triangle on the grid!

It doesn’t matter what order you subtract the x’s and y’s, because when you square them in the formula, you will still get the same answer!

Your homework is to finish #1-4. Don’t forget that we have a quiz on Friday!

]]>Today we learned how to find the distance between two points on a coordinate grid. When the points line up with one another along a grid line, it is easy because you can just count over. But when the points are diagonally away from one another, you have to use the Pythagorean Theorem! Here is the example we wrote in our notes:

Connect the points and then form a right triangle. The distance between the points is the hypotenuse, and the legs are easily countable along the grid lines. Use the Pythagorean Theorem to find the distance between the points, giving your answer exact (simplified) and approximate (rounded to the nearest hundredth).

While we worked, we found that we could find the side lengths of the triangle without even plotting the points! We will go more into this tomorrow, because it leads us to a formula that we can use for finding the distance between any two points, even if they are too far apart to graph!

Your homework is to finish #1-4 (5th period needs to do #1-7). Don’t forget that we have a quiz on Friday!

]]>Today, all of the problems were story problems! For each problem, you had to sketch a labeled diagram for the situation. Here is the example that I showed during class:

Be sure to label the lengths that you know and the right angle! Once you have done that, you should be able to find the missing side length using the Pythagorean Theorem. Don’t forget to label the units on your answers!

You should have finished #1-8 in class. I also passed back your quizzes from last week. We have another quiz scheduled for this Friday!

]]>Today we built on our Pythagorean Theorem work. We used the Pythagorean Theorem and algebra to find the unknown side length of a right triangle, but this time you had to simplify all of the square root answers! Be sure to show each of your algebra steps and include the units on both answers (exact and approximate)!

In class, you should have finished #1-4. Have a great weekend!

]]>Today, we reviewed the goals that you wrote for yourself at the beginning of the school year and then looked for work samples to include in your Student-Led Conference binder.

Your homework is to finish the Extra Practice worksheet. Remember, you are going to turn two things in tomorrow – the Extra Practice assignment from today and the Pythagorean Theorem assignment from yesterday!

]]>Today was a very important lesson in math class! We learned how to use the Pythagorean Theorem and algebra to find the unknown side length of a right triangle! You are going to use this a lot in your math career. Here are the notes we wrote down:

Remember that the legs are always labeled **a** and **b**, and the hypotenuse is always labeled **c** – labeling the three sides should be the first thing that you do! Be sure to show each of your algebra steps and give your answer in two forms – exact and approximate. Also remember to include the units on both answers!

Your homework is to finish #1-3, then turn it in on Friday (tomorrow is a goal setting day)!

]]>We started today with some notes about right triangles. Each of the sides of a right triangle has a name. Which side is which depends on its relative position to the right angle:

Today’s assignment had several right triangles on a dot grid. Squares were attached to each side of the right triangles. Your job was to find the area of each of the squares. Some of the square were easier than others, because some of them had sides that lined up with the dot grid (just do length times width!). However, the tilted squares required you to cut them up, find the area of each of the pieces, and then add up the areas.

As you found the areas of each set of three squares, you should have found a relationship among the areas. For each triangle, the areas of the squares on the legs always added up to the area of the square on the hypotenuse! This is a big deal… and it is known as the Pythagorean Theorem! We will spend the rest of this unit working with this! We summarized this in our notes and wrote down the formula:

Your homework is to finish #1-8.

]]>