Monday, October 31st

Sixth Grade

Today the class practice a little more on reducing fractions and writing mixed numbers as improper fractions. For homework, finish the two handouts.

Seventh Grade

Math - Percent of Change. Remember, you are only doing #2-9 on the worksheet tonight. Follow the steps for Method #1, but if that is confusing, here is another example:

So, in the example, I first found the amount of increase by subtracting the starting amount from the new amount. The amount increased $16. That goes on the top of the fraction. The bottom is always the original amount, which would be the starting price - $22. So I then divided 22 into 16. I added a decimal point and moved it into the answer. Then I added three zeros, just in case I needed to round to the nearest percent. Once I divided, I saw that I did need to round to the nearest percent. Even though I could keep dividing once I'd gone to the third place, I stopped so I could round it. Looking at the 7 in the third place, I saw that it was 5 or bigger which made the 2 round up to a 3. So, my new decimal was 0.73, which is 73%. That's it! Email me if you have any questions.

Geography - We read Chapter 7, Section 3 today - about the Midwest of the US. Answer the questions on the assessment - #1-4 and #7.

Eighth Grade

Both classes played an equations game today to help clarify and solidify slope and y-intercept. Everyone did a great job! No homework.

See you tomorrow!

Mrs. Swickey

Thursday, October 27th

Sixth Grade

Do your best to answer the rest of the questions on the Cartoon Corner! We won't have math class tomorrow, so you have until Monday.

Seventh Grade

Math - Finding a discount. Remember, to find a discount, take the percent and first move the decimal two places to the left. (So, 15% becomes 0.15 ; 25% becomes 0.25 ; 40% becomes 0.4) Then, multiply that decimal by the dollar amount. Remember to move the decimal number over enough places. This amount is your discount. If you get an amount that doesn't look like money because it has too many decimal places, round to the second decimal place. For example, if you have multiplied the dollar amount and the decimal and you get something like 5.275, you would need to round to the second place. The 7 is in the second place, so you look at the 5. 5 makes the 7 go up 1 to 8. Now you have 5.28 and that can be written as money, $5.28. Once you have your discount, you can find the amount you pay by subtracting the discount from the original amount.

Geography - Finish reading Chapter 7, Section 2 and answer the assessment questions #1-4.

Eighth Grade

Pre-Algebra: Graph the 15 equations. Remember, an equation that only contains one variable will be either vertical or horizontal. If it a y equals equation, then it is a horizontal line and crosses the y-axis at the the number. So, y = -3 would be a horizontal line on -3 on the y-axis. For x = -2, that would be a vertical line, crossing the x-axis at -2.

Algebra I: Parallel and Perpendicular lines: Parallel lines have the same slope, so if you need to write an equation of a line that is parallel to another line, all you need from the other line is the slope. It will be the same. Sometimes, you can make up the y-intercept, but on others, you will have to find the y-intercept because it will tell you that your new line goes through a given point. Here is an example:

Write the equation of a line that is parallel to the given line and passes through the given point:

y = -2x + 4 ; (-2, 3)

Since it is parallel to the line, y = -2x + 4, you know it will have the same slope. The slope is -2. You don't know the y-intercept of the new line, but you do know a point the new line will go through. Use the slope and the coordinates of the point to solve for the y - intercept:

y = -2x + b

3 = -2 times -2 + b

3 = 4 + b

-1 = b

Now that you've solved for the y-intercept, you can plug that into the equation:

y = -2x -1

To write equations for perpendicular lines, you will do the same process. Just remember that the slope has to be the opposite reciprocal of the given line's slope.

EMAIL ME IF YOU HAVE QUESTIONS! You WILL have class tomorrow!

See you then,

Mrs. Swickey

Monday, October 24th

Sixth Grade

Today, the class worked on more fraction of a number problems. They were given a list of 12 problems and each student had to write a word problem for the math problem and draw a picture representing the answer. For example, if the problem was, "1/3 of 24", then the word problem could be something like:

1/3 of the frogs jumped into the pond. If there were 24 frogs, how many jumped into the pond? Then they would solve that to find that 8 frogs jumped into the pond and then draw a picture of 8 frogs in a pond.

You only have to do 10 of the problems. There are 12, but pick any ten to do.

Seventh Grade

Math - Today, we practiced more sales tax. Many students struggled with this assignment last week so there are 5 extra problems from the board to solve. Then, they are supposed to finish the decimal division worksheet.

Geography - Chapter 6 Test is tomorrow! Be sure you are studying your notes and the terms from each section.

Eighth Grade

Pre-Algebra:

Graphing from slope-intercept form.

Remember that the slope-intercept form of any line is: y=mx + b

m is the slope. So whatever is in front of the x, is your slope.

b is the y-intercept, which means that the line crosses the y-axis at this number.

To graph the line, you first put a dot at the y-intercept, so if your equation is y = -3x +4, then you would put a dot at + 4 on the y -axis. So, go up 4 and put a dot.

Next, you would do the slope. Since the slope is -3, that means it is -3 over 1. You would go DOWN 3 and to the right 1 and put a dot there. Do the slope again so you have three points (unless you are going down or to the right 6 places or more) and draw a straight line through them. Remember, if the slope is negative, that goes with the top number and you would go down from the y-intercept. If the slope is positive, you would go up from the y-intercept.



Algebra I - Writing the equation of a line with given information. First, you are writing equations of lines from graphs. This is the easy step. Remember, every equation of a line needs a:

1. Slope
2. y-intercept

So, if you are given a graph, you can find the y-intercept first. Then, find the slope with the points that are given on the graph. Remember that you must reduce fractions, but you can leave them improper. Here is an example:



In the above graph, the line crosses the y-axis at positive 3. So +3 is your y-intercept. Counting from the points you are given, you see that the "rise" is 1 and the run is 3. Since Slopeman would be skiing downhill, your slope is negative. So, you write your equation in slope-intercept form, plugging the y-intercept in for b and the slope in for m. y = -1/3x + 3

To write the equation of a line when all you are given is the slope and a point it crosses through, you have to find your y-intercept. This is an example of how you do it:

The third way you will be writing the equation of a line is when you are given only two points that the line crosses through. First, you need to find the slope by using the slope formula. Once you have the slope, then you can do the exact same thing as the example above, choosing one of the two coordinate points to plug in. Here is an example:

See you tomorrow!

Mrs. Swickey

Today, October 20th

First, I want to apologize for not blogging this week. As you know, we've had parent teacher conferences each night and it's just been really busy! However, I definitely wanted to blog tonight to give examples on math in 7th and 8th grade. Unfortunately, my Mimio Pad is not working because it needs to be charged. The cord is at school! I have typed out the examples as best I can...I think it's still pretty clear, but please email me if you have questions!

Sixth Grade

The class was on a field trip today so I didn't have class with them. Your worksheets over fraction problems is due tomorrow.

Seventh Grade

Math - Sales Tax worksheet - Remember, you only have to do the front - #2-12. Find the tax AND the total. You will have two answers on each.

To find the tax, first you take the percent and change it to a decimal by moving the decimal point 2 places to the left. So if you have 7%, you would change that to .07 to make it a decimal. Once you have the decimal, multiply that by the dollar amount. Your answer is the tax. Be sure to round to the nearest cent (the second place after the decimal) if it doesn't look like money. So, if you have the following question:

Find the tax and the total on a new sweater that costs $49.75 with a tax rate of 6%. You would first change the 6% to a decimal by moving the decimal point two places to the left. (Remember, decimals are at the end of whole numbers.)

So 6% would become 0.06 and you would multiply that by $49.75. Once you multiply, you would have 2.9850 - the decimal goes between the two and the nine because there are 4 decimal places in the problem. But 2.9850 doesn't look like money.

You have to round to the 2nd decimal place. The 8 is the second place, so you look at the 5. Since it is a 5, it will make the 8 go up 1. So now you have 2.99 - you can drop off the 50. That now looks like money, so the tax is $2.99.

Remember, always think about if the answer makes sense. If you got the tax as 29.95 that wouldn't make sense because the item only cost $49.75! So to find the total, you would add $2.99 to $49.75 and get $52.74.

To solve one that has a fraction in it, you first need to change the fraction to a decimal and THEN change the % to a decimal. So, if you had 4 1/2%, you would first change that to 4.5%. Now you can move the decimal two places to the left to get 0.045 - that would be the decimal you would multiply by. Notice that there are three decimal places in this number now. PLEASE email me if you have questions!

Geography - For review over Chapter 6, complete the worksheets from each section. Many students finished in class or are almost done. Also, don't forget that if you haven't taken your country quizzes yet, you will have to do that tomorrow!

Eighth Grade

Pre-Algebra:

To tell if a line is positive or negative that's on a graph, you would look at the line from left to right. If it is going up, it's a positive line. If it is going down, it is a negative line. To tell from an equation (which is what you will do for the top half), you look at the number that is in front of the x.

For example, if you are given these equations:

y = -2x +4 ; negative slope because there is a -2 in front of x.

y = 5x -3 ; positive slope because there is a +5 in front of x. (remember, a number is positive if there is no negative sign)

y = -1/2x -7 ; negative slope because there is a -1/2 in front of the x.

So that's pretty easy!

To graph the ones that are circled, you have to use the table of values like you did yesterday. So, make a table and put in the numbers -2, 0, 2 for the x values. This part is exactly like yesterday's assignment. Then, once you have the values for y, graph the line on a coordinate plane.

To do the bottom half of the assignment, you are checking to see if the ordered pair is a solution to the equation. If it isn't a solution, then that point wouldn't be on your line on the graph. You don't have to graph to find out though.

Here is an example:

y = -5x+9 (2, -1)

To tell, you would plug in the values for x and y from the ordered pair. An ordered pair is always (x, y) - so the first number is your x value and the second number is your y value. Put them in the equation and see if you get a true statement.

So: -1 = -5 times 2 + 9

-1 = -10 + 9

-1 = -1

Since this is true, (2, -1) IS a solution and you would write YES. You must show the work though. Don't just write yes or no.

Here is another example:

3x + 4y = -20 (3, -5)

You would plug in 3 for the x and -5 for the y like this:

3 times 3 + 4 times -5 = -20

9 + -20 = -20

-11 = -20

Since this isn't true, (3, -5) is NOT a solution and you would write NO.

Please email me if you are still confused! I'll be happy to help through email.

Algebra I

For each equation today, you will find the slope and the y-intercept and then graph the line.

Remember, the slope is ALWAYS what is in front of the x. The y-intercept is ALWAYS the constant term after the x term. The line has to be written in slope intercept form, but you already know that the ones you are working with tonight are already written that way.

Here is an example of how to find slope and y-intercept:

y = -2/3x +5

Since -2/3 is in front of the x, -2/3 is your slope. You would write: m = -2/3

Since the constant term is 5, then your y-intercept is 5. You would write: b = 5

Now, to graph this, you would first put a point on the y-intercept and that means to put a point on the y-axis at that number. You would go up and put a dot at the 5.

Now, to do the slope, you look at it and see it is -2/3. That means the "rise" is -2. (If the slope is negative, the negative sign ALWAYS goes with the "rise".)

The run is 3 because it is on the bottom of the fraction. (If the slope is a whole number or NOT a fraction, the run will always be 1 because a 1 is always under a whole number.)

To graph the slope, you would put your pencil at the y-intercept, which is at the 5 on the y-axis in this problem, go DOWN 2 because your "rise" is -2, then go to the RIGHT 3 because your run is 3. Remember, you always RUN TO THE RIGHT. Now, put a dot at this point. You can do the slope again by going down 2 and going to the right 3 and putting another dot. Draw the line by connecting the dots.

Now, if your equation looked liked this:

y = x - 3, your slope would be 1, so you would write: m = 1

You know it is 1 because there isn't a number in front of the x, so it is understood to be 1!

If you had a problem like this:

y = -3x

your slope is -3, so you would write: m = -3

Since there is no number after the -3x, you have a y-intercept of 0! When you graph that, you would put a dot on the zero on the y-intercept, which is the origin and then go down 3 for the rise and to the right 1 for the run.

As always, email me if you have questions!

See you tomorrow,

Mrs. Swickey

Thursday, October 13th

Sixth Grade

Today, we practiced adding and subtracting fractions on the white boards. I am very impressed with how well everyone is doing! You all had a terrific teacher last year. There is no homework!

Seventh Grade

Math - During math class today, we had to work on one of the ITBS tests. There is just one test left, so we will be all finished tomorrow! Be sure to have your dividing fractions worksheet done for tomorrow.

Geography - There was a test today over Chapter 5. No homework!

Eighth Grade

Pre-Algebra: There is a test over graphing data that shows positive, negative, or no correlation. Be sure you go over your notes from class today so you are ready for tomorrow!

Algebra I: More word problems - some with consecutive integer problems. Please email me if you are stuck! I will be more than happy to help you work through the problems.

See you tomorrow!

Mrs. Swickey

Wednesday, October 12th

Sixth Grade

Today we practiced subtracting fractions. Everyone was doing really well! Here are some tips:

First, if you are subtracting a mixed number from a whole number (whole number on top without a fraction), then you have to borrow from the top whole number. Cross it off and write the number that is one less. Then make a fraction equal to one that has the same denominator as the bottom fraction. So, if the bottom fraction is 1/3, then you would make the new top fraction 3/3 so the denominators match.
When you have a mixed number minus another mixed number, you first check to make sure the denominators are the same (the ones I gave you today had all the same denominators). Then, if the top numerator is smaller than the bottom numerator, you have to borrow from the whole number. Remember, when you borrow in fractions, it's different. You get the new top numerator by adding the denominator to it. So if you had 1/3 as the top numerator and you had to borrow, then it would become 4/3 after borrowing. You get that because you are adding "1" to it infractions and 1 = 3/3, so you are adding 1/3 + 3/3 to get 4/3.

Here are a few examples:

Seventh Grade

Math - We tested today during math class. Don't forget that the dividing fractions worksheet is due tomorrow!

Geography - We reviewed for a test over Chapter 5. Study your notes and the Lewis and Clark video questions.

Eighth Grade

Pre-Algebra: We did an activity today in class using slinkys! Everyone finished and turned in their work.

Algebra I: No class today due to testing. You have the equations from words due tomorrow!

See you then...

Mrs. Swickey

Tuesday, October 11

Sixth Grade

Adding Mixed Numbers with Different Denominators - Remember that the first step is to find a common denominator. To do this, you are looking for the first number they both go INTO...just like least common multiple. It will always be one of the numbers OR something bigger. It will NEVER be a number that is smaller than either of the numbers. So, if you have denominators of 4 and 8...your least common denominator cannot be 4 because 4 is SMALLER than 8. However, since 4 and 8 both go into 8, you can use 8 as your common denominator. Once you've found the common denominator, make equivalent fractions by seeing how you changed the denominator. If you didn't change the denominator, you don't change the numerator for that fraction. If you changed the denominator by multiplying by 2, then multiply the numerator by 2 to get the new numerator. Then add the numerators and simplify if it is an improper fraction. Here are a few examples - follow the colors for the steps:

Seventh Grade

Math - Dividing Mixed Numbers:

Remember that first you make the mixed numbers improper by doing the u-turn. Write whole numbers over 1. Then, you change the division to multiplication and flip the second fraction. Then you cross cancel where you can. Multiply across and change back into a mixed number if it is improper. Here are a few examples:




You can do all 30, but mark 5 as extra credit before class tomorrow. Or, you can skip 5 of your choosing...also mark which ones you are skipping before class.

Geography - Do the timeline activities on page 101. Remember, for your timeline, add 5 more events other than your birth. For the timeline of Canada, be sure you are including ALL the events listed in the paragraph.

Eighth Grade

Pre-Algebra: We didn't have class today due to testing, but your graphs of your experiments are due tomorrow.

Algebra I: Putting word problems into equations and solving. I will not see you tomorrow due to testing, so have these finished by Thursday.

See you tomorrow!

Mrs. Swickey

Monday, October 10th

Sixth Grade

Math - Least Common Multiple. Remember, when you are finding the LCM, you are finding the first number your numbers go INTO. There is an endless number of multiples, so you want the smallest one that they go into. For example, if you want to find the LCM of 12 and 20, you would start with 20...your biggest number and do the multiples of it:

20, 40, 60, 80

Now, look at that list. Is there are number that 12 goes into? You might see that 12 goes into 60, but if you don't know that, you would need to do a list with the multiples of 12:

12, 24, 36, 48, 60

And then you'd see it.

So the LCM of 12 and 20 is 60.

Just so you know, I think I figured out what was wrong with my "cake" example today! I'll explain tomorrow.

The assignment is #1-22 on the homework page.

Seventh Grade

Multiplying Fractions - Remember, in order to multiply two fractions or mixed numbers, you first have to change any mixed numbers into improper fractions by using the u-turn. Then, cancel where you can by dividing a top number and a bottom number by the same thing. Then multiply across and then if your answer is improper, change into a mixed number by dividing bottom into top. Here are a few examples:

Geography - Read the rest of Chapter 5, Section 4 and complete the worksheet over the section. You do NOT have to do the section assessment in the book...just the worksheet.

Eighth Grade

Pre-Algebra: We did not have class today because of testing. We will resume class on Wednesday.

Algebra I: Solving equations for y. Everyone really seemed to get the hang of it today. Do the 10 problems I wrote on the board.

See you tomorrow!

Mrs. Swickey

Thursday, October 6th

Sixth Grade

There is no homework. We played a math game today.

Seventh Grade

Math - We reviewed fractions today. The homework is to do the 10 problems from the board - adding and subtracting fractions.

Geography - We read Chapter 5, Section 2. Do questions #1-5 on the section assessment.

Eighth Grade

Pre-Algebra: Today the class developed experiments to show positive or negative correlations and began testing. We will finish testing tomorrow and graph the data.

Algebra I: Today we continued working with literal equations. If you don't remember how to solve for y, scroll down to yesterday's blog post and click on the Purple Math link. Then click on the second link on that page. There are several examples for solving for y there. For the tables, just plug in the values for x in the equation and solve for y. Let me know if you need help!

See you tomorrow,

Mrs. Swickey

Wednesday, October 5th

Sixth Grade

Today, we reviewed how to turn improper fractions into mixed numbers and then how to add fractions with like denominators with both reducing and changing into mixed numbers. Here are some examples:



My Mimio Pad needs to be charged so I can't do anymore pictures! I'm sorry!

Remember that when you add two fractions, you are only adding the tops. The bottom stays the same. So after adding, if the top is bigger than the bottom, then you need to change it into a mixed number. Do that by "dividing bottom into top". How many times it goes in becomes your new whole number. The left OVER, is your new numerator. (It's left OVER so you put it OVER in the fraction.) The denominator stays the same. In the above example, I started with 12 over 5. Then I divided 5 into 12. It went in 2 whole times...that's my new whole number. I had 2 left over so put a 2 over the 5. Remember, the denominator will always stay the same!

So, after you do that, if your fraction can be reduced....be sure to reduce it!

Seventh Grade

Math - Today's assignment is to do the top part of the sheet I sent home. It's mental math multiplying or dividing with powers and multiples of 10. I shouldn't see ANY work since you are doing it all mentally! You do not have to do the bottom half yet.

Geography - We finished watching the Lewis and Clark video today and the class turned in the questions over the video.

Eighth Grade

Pre-Algebra: Finish graphing the Bike Weights and Jump Heights.

Algebra I: Literal Equations. My Mimio Pad needs to be charged and the cord is at school! I can't give you examples, but I found this website with examples on how to solve in formulas as well as how to solve for "y". The examples for solving for "y" can be found on the second page. Scroll to the bottom and hit "next". I hope it's a useful site! The pages you want are the first two links: Purple Math

See you tomorrow!
Mrs. Swickey

Tuesday, October 4th

Sixth Grade

Today we worked on reducing fractions. The class already had a pretty good grasp of it so we spent some time going over what "relatively prime" means. Remember, two numbers are relatively prime if the only common factor they have is 1. So, even though the numbers 4 and 15 are both composite, they are relatively prime because their only common factor is 1. the factors of 4 are 1, 2, and 4. The factors of 15 are 1, 3, 5, and 15. So we say they are relatively prime - relatively is like "related to each other". The assignment is to complete the Relatively Prime worksheet for extra credit and then to do the back side with reducing fractions as well as the reducing fractions page where you make stars.

Seventh Grade

Math - Today the class worked on division estimates and quotients. Remember to estimate, you first need to round the numbers to compatible numbers. So, if you are supposed to divide 4782 by 83, you could round the first number to 4800 and the second to 80. Then you could divide 4800 by 80 easily - it's 60. If you rounded 4782 to the nearest thousand, you would have 5000 divided by 80. That isn't easy to do. The estimates are handy because you can then see if your actual answer is correct. In this case, it would be: 57 r 51. That's close to 60. You know the first number will be 6 or something close because your estimate was 60 - you can use that to narrow your guesses when dividing.

The assignment is to do #1-12 only - estimate each answer first in the left column of your paper. Then do the division on the right column.

Geography - We watched part of a National Geographic Video on Lewis and Clark today. While watching, the class answered questions relating to the video. Everyone did a terrific job listening and not disturbing others. We will finish the video tomorrow!

Eighth Grade

Pre-Algebra: Today we did another graph activity on Whale Weight. Everyone finished the first part in class. The second part is to graph the actual data.

Algebra I: Today we worked on an activity where the students would discover the weight of my car by measuring the footprint of each tire as well as the tire pressure. Using that information, the students could see how much weight each tire supported and adding those together, how much my car weighed. Each person needs to finish the calculations and you must show your work on your paper! No calculators allowed.

See you tomorrow,
Mrs. Swickey

Monday, October 3rd

Sixth Grade

Last week, there were several students having trouble with factor trees. Today, I showed them a more visual way to do the trees - with squares of different colored construction paper. One color is for composite numbers and another color is for prime numbers. The starting number is another color too, although it is also composite. Everyone liked the color square factor trees.

The homework is to do the 10 numbers I wrote on the board using the squares. Once you have the tree done with the squares for each number, write down the factor tree on paper and write out the prime factorization.

Seventh Grade

Math - Today, the class worked on "Item Analysis". I passed out a paper where I had worked out 10 addition, subtraction, multiplication, and division problems. I intentionally made a mistake on 8 of them. The purpose is for the students to find the errors, explain in a sentence what the error is for each problem, and rework the problem correctly.

Geography - I finally told everyone the purpose of the pictures today! The class made passports that they will get stamped after passing a Country Quiz for the countries in each unit. I will update the blog with deadlines for the quizzes, because the students will do them when they are ready. Since our current unit is on the United States and Canada, there will only be 3 country quizzes this unit. The deadline to have them both done is the end of the nine weeks. Each quiz will consist of the same 10 questions. The students wrote them down today, so they know what facts to look up.

We then read Chapter 5, Section 1. The homework for today is the handout over the section.

Eighth Grade

Pre-Algebra: Today we worked through a lesson about Skin Weight. It sounded a bit gross, but was still interesting. A person's skin weighs about 1/16th the total body weight. I gave them a table with various weights and skin weights and the class used the info to finish the table and complete a graph using the information. Most everyone finished the table in class, but will need more time to graph the information. Tomorrow, we will talk about whale weight!

Algebra I: Today, the class worked on Item Analysis. I gave them 10 equations worked out. They had to analyze my work to see where I made mistakes and write in a sentence what the mistake was. Then, they had to rework the equation correctly. There are 2 correct equations!

See you tomorrow,
Mrs. Swickey