Today we covered and verified that in fact all bases to the power of zero are always equal to 1.
Any base that has a negative exponent, you must take the reciprocal of that number. For example; x^-2 = 1/x^2
Overall, any x^-n = 1/x^n
Sorry about the notation, the blogger isn't as useful as a word processing document to do equations.
Out of textbook pg. 211-213 #1a-c, 2e-k, 4, 6ab, 7, 8, 10, 20, 28, 29.
Good luck and I will be checking your homework tomorrow afternoon.
Mrs. Gascho
Thursday, February 26, 2009
Grade 10 - take up Test
Today we took up the Unit Test - Linear Relations. Overall this test seemed challenging for many students.
We went through and made corrections to the questions. The test was then allowed to be resubmitted for 2 additional marks. For some students this made the difference between not passing and being successful on the test.
I am in the process of touching bases with all parents of the students that were not successful in passing at 2 or more categories.
Hopefully the next unit will be more successful for those of you that did not feel success on this one.
Many of you have questions from yesterday's homework to complete by tomorrow.
Friday we will work on two-step algebra questions. If you work well in class you will have no homework for the weekend. :)
From the handout: #1-17, 19, 20abc, 23, 24
We went through and made corrections to the questions. The test was then allowed to be resubmitted for 2 additional marks. For some students this made the difference between not passing and being successful on the test.
I am in the process of touching bases with all parents of the students that were not successful in passing at 2 or more categories.
Hopefully the next unit will be more successful for those of you that did not feel success on this one.
Many of you have questions from yesterday's homework to complete by tomorrow.
Friday we will work on two-step algebra questions. If you work well in class you will have no homework for the weekend. :)
From the handout: #1-17, 19, 20abc, 23, 24
Wednesday, February 25, 2009
Grade 9 - Powers
Good class today.
Today we reviewed the power rules and touched on negative exponents.
Questions assigned were pg. 203-205 #1-4ac, 5ef, 6, 7, 8, 9, 13, 14, 17, 18
Tomorrow we are going to do negative exponents in alot more detail.
Today we reviewed the power rules and touched on negative exponents.
Questions assigned were pg. 203-205 #1-4ac, 5ef, 6, 7, 8, 9, 13, 14, 17, 18
Tomorrow we are going to do negative exponents in alot more detail.
Grade 10 - Algebra
One-step equations:
Note: Notice that addition and subtraction are the opposite operations of each other. x + 9
= x + 9 - 9
= x
When we add and subtract the same number, they cancel out.
In equations, we want to solve for unknowns.
Ex.1: x + 4 = 7 We want x all by itself, so how do we get rid of the +4?
Subtract 4 from both sides
x + 4 - 4 = 7 - 4
x = 3
Ex. 2 y - 8 = 12
y -8 + 8 = 12 + 8
y = 20
Once you do enough of the questions, you'll notice we are just putting the opposite operation on the other side of the equal sign.
Also notice multiplication and division are also opposite operations.
3x = 12
Divide both sides: 3x/3 = 12/3
x = 4
Complete Handout. #1-6,9,11,14,15,17,19
Note: Notice that addition and subtraction are the opposite operations of each other. x + 9
= x + 9 - 9
= x
When we add and subtract the same number, they cancel out.
In equations, we want to solve for unknowns.
Ex.1: x + 4 = 7 We want x all by itself, so how do we get rid of the +4?
Subtract 4 from both sides
x + 4 - 4 = 7 - 4
x = 3
Ex. 2 y - 8 = 12
y -8 + 8 = 12 + 8
y = 20
Once you do enough of the questions, you'll notice we are just putting the opposite operation on the other side of the equal sign.
Also notice multiplication and division are also opposite operations.
3x = 12
Divide both sides: 3x/3 = 12/3
x = 4
Complete Handout. #1-6,9,11,14,15,17,19
Tuesday, February 24, 2009
Grade 9 - Started Powers
Sorry to be blogging after the class and not before. Today we had a SUPER class.
We started by doing a paper folding activity (similar to Mythbusters). Trevor managed to get something really close to 8 folds in class (with a little help from glue). Way to go!
There were many students that could get a pretty good looking 7 folds. I couldn't get past 6....geez.
Anyways, we then went into a note on Power rules.
Brief overview: when multiplying with the same base, add the exponents
when dividing with the same base, subtract the exponents.
when a power is to a power, multiply the exponents.
We then played a few intense games of MATHO! Similar to BINGO but the little bit nerdier version. Danny did get the first MATHO! Kayla then came out of nowhere with the first to get 2 lines and then she also was first to get the FULL CARD!
Congratulations! We will have to play MATHO more often.
Tomorrow we will continue with power rules.
Mrs. Gascho
We started by doing a paper folding activity (similar to Mythbusters). Trevor managed to get something really close to 8 folds in class (with a little help from glue). Way to go!
There were many students that could get a pretty good looking 7 folds. I couldn't get past 6....geez.
Anyways, we then went into a note on Power rules.
Brief overview: when multiplying with the same base, add the exponents
when dividing with the same base, subtract the exponents.
when a power is to a power, multiply the exponents.
We then played a few intense games of MATHO! Similar to BINGO but the little bit nerdier version. Danny did get the first MATHO! Kayla then came out of nowhere with the first to get 2 lines and then she also was first to get the FULL CARD!
Congratulations! We will have to play MATHO more often.
Tomorrow we will continue with power rules.
Mrs. Gascho
Grade 10 - Test Day
Hopefully you completed the practice test and feel confident for today's Unit Test.
The test is 3 pages long and covers graphing lines, equations of a line ( y=mx + b, Ax + By + C = 0, and y = m(x-p) + q)
I will be in the my classroom at 8:30am if you have some last minute questions.
Good luck.
New Unit starting tomorrow.
Mrs. Gascho
The test is 3 pages long and covers graphing lines, equations of a line ( y=mx + b, Ax + By + C = 0, and y = m(x-p) + q)
I will be in the my classroom at 8:30am if you have some last minute questions.
Good luck.
New Unit starting tomorrow.
Mrs. Gascho
Wednesday, February 18, 2009
Grade 10 - Finally finishing Standard Form
Thursday Feb. 19th.
Small note on Standard Form; Ax + By + C = 0. We will follow the note with a couple examples on how to change y = mx + b into Standard form.
For example: y = 3/4 x + 2
in order to get rid of the 4 on the denominator we must multiply the entire equation by 4. Doing this we get: 4y = 3x + 8. The last step is to order the letters x then y then any numeric value = zero (in this case we will move everything to the left side of the equation).
-3x + 4y - 8 = 0
This is standard form with A = -3, B = +4, and C = -8.
You will complete pg. 105-106 #1ac, 2bc, 3acde, 4ace, 5ae, 6cef, 8
Lastly, you will be given a practice test to complete for homework to prepare for the test.
It is advisable to come in before class in the morning to check your answers to the practice test.
Good luck!
Mrs. Gascho
Small note on Standard Form; Ax + By + C = 0. We will follow the note with a couple examples on how to change y = mx + b into Standard form.
For example: y = 3/4 x + 2
in order to get rid of the 4 on the denominator we must multiply the entire equation by 4. Doing this we get: 4y = 3x + 8. The last step is to order the letters x then y then any numeric value = zero (in this case we will move everything to the left side of the equation).
-3x + 4y - 8 = 0
This is standard form with A = -3, B = +4, and C = -8.
You will complete pg. 105-106 #1ac, 2bc, 3acde, 4ace, 5ae, 6cef, 8
Lastly, you will be given a practice test to complete for homework to prepare for the test.
It is advisable to come in before class in the morning to check your answers to the practice test.
Good luck!
Mrs. Gascho
Grade 9 - Unit Test (Numeracy) Feb. 19th
Test, test, test.
You were given a practice test today and the solutions were posted in class. Many of you worked so well and I am hoping for complete success on the test tomorrow. The unit test is a very similar style as the practice test.
Study and review a few tough concepts and the test will go well.
Good luck
Mrs. Gascho
You were given a practice test today and the solutions were posted in class. Many of you worked so well and I am hoping for complete success on the test tomorrow. The unit test is a very similar style as the practice test.
Study and review a few tough concepts and the test will go well.
Good luck
Mrs. Gascho
Tuesday, February 17, 2009
Grade 9 - Practice Test
Wednesday I will be distributing a practice test with the same format as the test. You will be able to find solutions to the test on the blog following tomorrow's class.
Test on Thursday.
Mrs. Gascho
Extra review questions: Go through previous 2 weeks of questions and pick extra parts that were not assigned. I have additional worksheets in class if necessary.
Test on Thursday.
Mrs. Gascho
Extra review questions: Go through previous 2 weeks of questions and pick extra parts that were not assigned. I have additional worksheets in class if necessary.
Grade 9 - Multiplying and Dividing Rational Numbers
Today we are going to finish the last new material before the test on Thursday. When multiplying/dividing rational numbers you must consider two signs the same make a positive and different signs make a negative.
These questions should be similar to the questions the other day. When estimating make sure you use numbers that you can do in your head. It is important to always practice mental math.
pg. 49-53 #1,2,4,5,10,11,13,14,15,17
These questions should be similar to the questions the other day. When estimating make sure you use numbers that you can do in your head. It is important to always practice mental math.
pg. 49-53 #1,2,4,5,10,11,13,14,15,17
Grade 10 - Mrs. Wright
Good morning Grade 10s
I will be away at another math workshop this morning. I am confident you will have a great morning. Mrs. Wright is going to teach you an even easier form of the Equation of a line.
There is an assembly this morning so you will not have as much math as normal, I know this worries you.
I will see you this afternoon.
pg. 65-66 # 2ace, 3ab, 4, 5defg, 6 (these are the same questions you were assigned on Thursday but you are going to solve them an entirely different way). These answers will now mesh with the answers in the back of the textbook.
Good luck!
Test on Thursday.
Mrs. Gascho
I will be away at another math workshop this morning. I am confident you will have a great morning. Mrs. Wright is going to teach you an even easier form of the Equation of a line.
There is an assembly this morning so you will not have as much math as normal, I know this worries you.
I will see you this afternoon.
pg. 65-66 # 2ace, 3ab, 4, 5defg, 6 (these are the same questions you were assigned on Thursday but you are going to solve them an entirely different way). These answers will now mesh with the answers in the back of the textbook.
Good luck!
Test on Thursday.
Mrs. Gascho
Friday, February 13, 2009
Grade 10 - Equation of a line worksheets
Good morning,
Today you will have a homework check on the questions from yesterday. You will then work through 2 worksheets to complete the equation of a line.
When we all return on Tuesday we will explore y = m(x-p) + q as well as Standard Form Ax + By + C = 0
These will be the last new things before our unit test on Thursday.
Have a great weekend.
Mrs. Gascho
Today you will have a homework check on the questions from yesterday. You will then work through 2 worksheets to complete the equation of a line.
When we all return on Tuesday we will explore y = m(x-p) + q as well as Standard Form Ax + By + C = 0
These will be the last new things before our unit test on Thursday.
Have a great weekend.
Mrs. Gascho
Thursday, February 12, 2009
Grade 9 - Adding and Subtracting Rational Numbers
Today you have a wonderful supply teacher. I am away all day at a math teacher workshop. I know, extremely exciting.
I have left a quick board note that she will go through with you. This topic is similar to the lesson from yesterday. We will now add and subtract the rational numbers. Please leave all answers in fraction form if possible.
Have fun and if you finish all the seat work early, the cards are at the front of the room to play Fraction Action.
Remember, Unit Test on Thursday.
See you on Tuesday.
Mrs. Gascho
pg. 43-45 #1ace, 2ace, 3, 4, 6, 8, 10, 12 (leave as a fraction), 13ace, 14, 17, 19
I have left a quick board note that she will go through with you. This topic is similar to the lesson from yesterday. We will now add and subtract the rational numbers. Please leave all answers in fraction form if possible.
Have fun and if you finish all the seat work early, the cards are at the front of the room to play Fraction Action.
Remember, Unit Test on Thursday.
See you on Tuesday.
Mrs. Gascho
pg. 43-45 #1ace, 2ace, 3, 4, 6, 8, 10, 12 (leave as a fraction), 13ace, 14, 17, 19
Wednesday, February 11, 2009
Grade 10 - Equation of the line
Today we are going to continue with figuring out the equation of a line from a point and a slope, two points, or a slope and y-intercept.
Using the textbook we will complete
Practice your skills; 2 (all)
Exercises. pg. 65-66 # 2, 3, 4, 5abc, 6
This will be one technique to solve an equation. There will be a small note on the board taking up homework from Tuesday.
Friday we will continue on to the "Point Slope Form" y = m(x-p) + q
Using the textbook we will complete
Practice your skills; 2 (all)
Exercises. pg. 65-66 # 2, 3, 4, 5abc, 6
This will be one technique to solve an equation. There will be a small note on the board taking up homework from Tuesday.
Friday we will continue on to the "Point Slope Form" y = m(x-p) + q
Grade 9 and 10 - Fog day
Good morning,
Today the school is open for study purposes only. We will continue tomorrow with the last blog. Grade 9s we will do rational numbers Thursday, Grade 10s we will finish equation of the line.
Enjoy your day at home and get caught up on missed work.
Mrs. Gascho
Today the school is open for study purposes only. We will continue tomorrow with the last blog. Grade 9s we will do rational numbers Thursday, Grade 10s we will finish equation of the line.
Enjoy your day at home and get caught up on missed work.
Mrs. Gascho
Tuesday, February 10, 2009
Grade 9 - Rational Numbers
Rational numbers: any number that can be written in the form m/n, where m and n are integers and n cannot equal zero.
Ex. 0.4, 4/7, -1.23
We will explore number lines and integers to determine which rational expression is larger.
Ex. Which rational number is larger? 1/4 or 3/4
Ex. Which rational number is larger? -2/3 or -3/2
Why?
What is the difference between an integer and a rational number? Integers are whole numbers like -3, -2, -1, +1, +2, +3. Rational numbers can have decimals like 1.4 and -2.3.
Without a calculator, estimate the answer. (5)(-3)/(-7) = -15/-7 = 2.1
Using the textbook, complete pg. 37-40 #3, 4ace, 5acegik, 6all, 7, 9ace, 10(only the ones that can be written as integers), 14, 15, 20, 21, 23acegi, 24(use a calculator and compute the final answer showing the steps).
Happy Calculating!
Test on Numeracy Wednesday, Feb. 18th.
Ex. 0.4, 4/7, -1.23
We will explore number lines and integers to determine which rational expression is larger.
Ex. Which rational number is larger? 1/4 or 3/4
Ex. Which rational number is larger? -2/3 or -3/2
Why?
What is the difference between an integer and a rational number? Integers are whole numbers like -3, -2, -1, +1, +2, +3. Rational numbers can have decimals like 1.4 and -2.3.
Without a calculator, estimate the answer. (5)(-3)/(-7) = -15/-7 = 2.1
Using the textbook, complete pg. 37-40 #3, 4ace, 5acegik, 6all, 7, 9ace, 10(only the ones that can be written as integers), 14, 15, 20, 21, 23acegi, 24(use a calculator and compute the final answer showing the steps).
Happy Calculating!
Test on Numeracy Wednesday, Feb. 18th.
Grade 10 - Linear Models
Today we will take up any problems from the handout from yesterday. Especially focusing on #5, and 8.
We will continue determining the equation of the line, using two points on a line and applying y2-y1/x2-x1.
Ex. 1: A line with slope 2 passes through the point (4,3). Determine the equation of the line.
Solution: m = 2
y = 2x + b (solve b)
plug in the value x = 4 and y = 3
3 = 2(4) + b
3 = 8 + b
3 - 8 = b (subtract 8 from both sides)
-5 = b
Therefore, y = 2x -5
Ex. 2: Given the points (-1,4) and (5,13). Determine the equation of the line.
M=y2-y1/x2-x1
=13-4/5-(-1)
= 9/6
= 3/2
Then to figure out the b value, we must use y=mx + b and substitute what we know.
y = 3/2x + b
pick one of the two points and plug in the values. Picking the 1st point, (-1,4) we get 4 = 3/2(-1) + b and then we can solve for b.
4 = -3/2 + b
4 + 3/2 = b (add 3/2 to both sides)
8/2 + 3/2 = b (make a common denominator, if you use your calculator at this step that is okay)
11/2 = b
Therefore, the equation of the line is y = 3/2x + 11/2
Using the handout supplied in class, complete #1 ac, 2ac, 3ac, 5aceg, 6all, 7ace
I will be doing a homework check tomorrow. I am available at lunchtime if you require some help.
Mrs. Gascho
We will continue determining the equation of the line, using two points on a line and applying y2-y1/x2-x1.
Ex. 1: A line with slope 2 passes through the point (4,3). Determine the equation of the line.
Solution: m = 2
y = 2x + b (solve b)
plug in the value x = 4 and y = 3
3 = 2(4) + b
3 = 8 + b
3 - 8 = b (subtract 8 from both sides)
-5 = b
Therefore, y = 2x -5
Ex. 2: Given the points (-1,4) and (5,13). Determine the equation of the line.
M=y2-y1/x2-x1
=13-4/5-(-1)
= 9/6
= 3/2
Then to figure out the b value, we must use y=mx + b and substitute what we know.
y = 3/2x + b
pick one of the two points and plug in the values. Picking the 1st point, (-1,4) we get 4 = 3/2(-1) + b and then we can solve for b.
4 = -3/2 + b
4 + 3/2 = b (add 3/2 to both sides)
8/2 + 3/2 = b (make a common denominator, if you use your calculator at this step that is okay)
11/2 = b
Therefore, the equation of the line is y = 3/2x + 11/2
Using the handout supplied in class, complete #1 ac, 2ac, 3ac, 5aceg, 6all, 7ace
I will be doing a homework check tomorrow. I am available at lunchtime if you require some help.
Mrs. Gascho
Monday, February 9, 2009
Grade 9 - Percent Contd
After a successful class of percentage, we will continue with this topic to further expand percent into word problems. Continuing on pg. 29-33 #9a,c,e,g,i, 10, 11, 13, 15, 17, 25, 27.
Now you will be able to determine the marks needed to be successful in math :)
Mrs. Gascho
Now you will be able to determine the marks needed to be successful in math :)
Mrs. Gascho
Grade 10 - Slope continued
Today,
We will go through a PowerPoint presentation on Slope to help better understand the equation of a line. I have attached the files to the C. Gascho website under Feb. 6/09 if you need to review it.
We will then complete a handout practicing our graphing techniques.
(distributed in class).
There will be no textbook homework questions but you will be required to have all of the handout complete for tomorrow's class. From the handout you are expected to do #1, 2ab, 3ac, 5, 6ac, 7(AB, CD), 8, 12
Mrs. Gascho
We will go through a PowerPoint presentation on Slope to help better understand the equation of a line. I have attached the files to the C. Gascho website under Feb. 6/09 if you need to review it.
We will then complete a handout practicing our graphing techniques.
(distributed in class).
There will be no textbook homework questions but you will be required to have all of the handout complete for tomorrow's class. From the handout you are expected to do #1, 2ab, 3ac, 5, 6ac, 7(AB, CD), 8, 12
Mrs. Gascho
Grade 9 - Percent, Decimal, and Estimation
Good morning Grade 9s
Today we are going to be calculating percent from fractions and decimals. We will also be able to estimate percentage in word problems.
There will be a board note and then pg. 28-33 #1,2,3,4,6a,c,f,g,h,7,9,10,12
Additional challenge: (For those of you checking the blog)
Currently there are 33,441,277 residents in Canada. Most recent statistic on StatCan.gc.ca is an unemployment rate of 7.2%. How many people are currently unemployed?
Similarly, there are 4,385,800 youth aged 15-24. There are 2,525,600 employed. What percentage of youths are employed in Canada?
(This math is VERY practical)
Today we are going to be calculating percent from fractions and decimals. We will also be able to estimate percentage in word problems.
There will be a board note and then pg. 28-33 #1,2,3,4,6a,c,f,g,h,7,9,10,12
Additional challenge: (For those of you checking the blog)
Currently there are 33,441,277 residents in Canada. Most recent statistic on StatCan.gc.ca is an unemployment rate of 7.2%. How many people are currently unemployed?
Similarly, there are 4,385,800 youth aged 15-24. There are 2,525,600 employed. What percentage of youths are employed in Canada?
(This math is VERY practical)
Friday, February 6, 2009
Grade 9 - Fun Friday!
Grade 9s you are off to an awesome start!!!
Today we are going to play "Fraction Action" which is a card game similar to war. We will practice our fraction skills and have a little fun too ;)
We will also play a fun game of Jeopardy using math questions for practice.
Lets enjoy the weekend homework free.
Mrs. Gascho
Today we are going to play "Fraction Action" which is a card game similar to war. We will practice our fraction skills and have a little fun too ;)
We will also play a fun game of Jeopardy using math questions for practice.
Lets enjoy the weekend homework free.
Mrs. Gascho
Thursday, February 5, 2009
Grade 9 - Feb. 5/09
Well day 4 of classes.
So far so good. It is expected that you have all four of the puzzle sheets on integer practice complete. You can check the answer key at the back of the room.
Today we are going to work on Fractions continuing with yesterday's note on the rules. We will convert decimals to fractions. Ex. 0.6 --> 6/10 --> 3/5 in lowest terms. A few of the more challenging fractions may be left as a mixed number. Ex. 4.85 --> 4 85/100 --> 4 17/20.
Using your textbook, complete pg. 17-21 #1-5, 10, 11, 12, 17 (do not worry about writing down your keystrokes if you are showing your work).
Enjoy!
Mrs. Gascho
So far so good. It is expected that you have all four of the puzzle sheets on integer practice complete. You can check the answer key at the back of the room.
Today we are going to work on Fractions continuing with yesterday's note on the rules. We will convert decimals to fractions. Ex. 0.6 --> 6/10 --> 3/5 in lowest terms. A few of the more challenging fractions may be left as a mixed number. Ex. 4.85 --> 4 85/100 --> 4 17/20.
Using your textbook, complete pg. 17-21 #1-5, 10, 11, 12, 17 (do not worry about writing down your keystrokes if you are showing your work).
Enjoy!
Mrs. Gascho
Wednesday, February 4, 2009
Grade 10 - Continuing with slope
Hello
Today (Thurs. Feb. 5) we will finish the handout "Graphing Equations of the line". I will be checking to see how successful you were at graphing #1 and 2. Feel free to get help at lunch so you can pass the first homework check of many to come.
We will use the textbooks today to complete graphing with table of values and equations. Pg. 21-24 #1, 3, 4, 5a, b, c, d, 6a, b, c, d, 10.
We are also going to work through a graphed sheet and determine what the equation of the line would be.
Good luck.
Remember to study for your quiz on Friday.
Mrs. Gascho
Today (Thurs. Feb. 5) we will finish the handout "Graphing Equations of the line". I will be checking to see how successful you were at graphing #1 and 2. Feel free to get help at lunch so you can pass the first homework check of many to come.
We will use the textbooks today to complete graphing with table of values and equations. Pg. 21-24 #1, 3, 4, 5a, b, c, d, 6a, b, c, d, 10.
We are also going to work through a graphed sheet and determine what the equation of the line would be.
Good luck.
Remember to study for your quiz on Friday.
Mrs. Gascho
Tuesday, February 3, 2009
Welcome to Math class
Hello everyone.
This is my first blog EVER! I'm hoping we will be able to use this blogspot as a place to check homework and class communication.
My goal is to put up the homework/classwork assigned at the end of every day. If you are away for sports games, vacation, or illness please check here for missed work.
I am super excited for the semester.
Mrs. Gascho!
This is my first blog EVER! I'm hoping we will be able to use this blogspot as a place to check homework and class communication.
My goal is to put up the homework/classwork assigned at the end of every day. If you are away for sports games, vacation, or illness please check here for missed work.
I am super excited for the semester.
Mrs. Gascho!
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