Hello everyone. Please watch the following two videos on Khan Academy. This guy goes over solving equations with multiplication and division in-depth. There's an online practice exercise after the second video if you'd like to complete the questions online. It will tell you how well you did. Happy solving!
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-beginner-equations/v/simple-equations
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-beginner-equations/v/solving-one-step-equations-2
Wednesday, November 5, 2014
Thursday, October 30, 2014
Let's Talk Word Problems
In class today we completed questions 10, 11, 21 and 33. I'd like to walk you through the process of finding the answers to these problems. Please come to class tomorrow prepared with any questions you may have.
When solving word problems, remember to distinguish between what you know and what you need to know. Remember to pay attention to clues like "more than" and "less than" that will indicated whether you need to add or subtract.
10. What we know - There are about 778 million km between the sun and Jupiter.
- This is 550 million km greater than the distance between the sun and Mars.
What we need to know - The distance (d) between Mars and the sun.
Let's set up an equation. Ask the question, what's equal to what here? We know that 778 million km is equal to d (the distance between Mars and the sun) plus an extra 550 million km.
778 = d + 550
Now, solve for d by subtracting 550 from both sides:
778 - 550 = d + 550 - 550
228 = d
The average distance from Mars to the sun is 228 million km.
11. What we know - Speed travels through steel @ 5200 m/s
- This is 2520 m/s faster than the speed of sound through silver
What we need to know - The speed of sound through silver (s)
What's equal to what here? We know that 5200 m/s is equal to the speed of sound through silver (s) plus an extra 2520 m/s.
5200 = s + 2520
Now, solve for s by subtracting 2520 from both sides:
5200 - 2520 = s + 2520 - 2520
2680 = s
The speed of sound through silver is 2,680 m/s.
21. What we know - Distance from Venus to the sun is 108 million km.
- This distance is 42 million km less than the distance from Earth to the sun/
What we need to know - Earth's distance (d) from the sun.
This is very similar to #10. We know that 108 million km is equal to d (the distance between the Earth and the sun) minus 42 million km.
108 = d - 42
d = 150
The average distance from the Earth to the sun is 150 million km.
33. What we know - In '96, 487m people spoke English.
- This was 512m people fewer than the # of people who spoke Mandarin.
What we need to know - How many people spoke Mandarin (n)?
We could think of it like this: If 487 million people spoke English, and that was 512 million people less than those who spoke Mandarin, we must subtract 512 from n to get the 487:
n - 512 = 487 (Answer A)
Monday, October 27, 2014
Worksheet Answers 1 - 9
Hola Amigos,
Please check your answers. Click on the pictures to enlarge (answers are boxed). See the comments if your answer was incorrect and you're not sure where you went wrong. Be sure to come prepared to class tomorrow with any questions you have. See you then!
Number 5 was a big more complex. After changing subtraction to adding negatives, we distributed both the 3 and the negative 4 to their respective parentheses. Then we used integer rules to combine like terms. Negative 12 and positive 12 cancel each other out.
Number 6 could have been done two ways. The first way would include all the steps we see above. The second would entail looking at the problem and saying, "If I've got six times g minus h, and I'm taking away six times g minus h, I'll be left with zero."
Please check your answers. Click on the pictures to enlarge (answers are boxed). See the comments if your answer was incorrect and you're not sure where you went wrong. Be sure to come prepared to class tomorrow with any questions you have. See you then!
Questions 1-4 were pretty straight forward. Change addition to adding the opposite, distribute (if necessary), and combine like terms. Sometimes it helps to put negative numbers in parentheses so as not to confuse the signs with adding, subtracting, negatives, etc.
Number 5 was a big more complex. After changing subtraction to adding negatives, we distributed both the 3 and the negative 4 to their respective parentheses. Then we used integer rules to combine like terms. Negative 12 and positive 12 cancel each other out.
Number 6 could have been done two ways. The first way would include all the steps we see above. The second would entail looking at the problem and saying, "If I've got six times g minus h, and I'm taking away six times g minus h, I'll be left with zero."
For 7 - 9, don't forget that there's always an imaginary 1 next to any variable that's by itself. Changing a variable to its negative would mean that invisible 1 turns into a negative 1.
Friday, September 26, 2014
Chapter 1 Study Guide
Hello everyone. Don't forget your Chapter 1 Assessment is Monday. Here's what will be on the test:
Variable Expressions
- You'll need to know how to write variable expressions for word phrases. For example:
Write a variable expression for a number n increased by 5.
Well, if we're starting with an unknown number (n) and we're increasing by 5, we must be adding. So n + 5 would be our variable expression.
Order of Operations
***Please remember that you should be using the correct order of operations for any math problem you complete - not just problems that specify that you need to "use order of operations to..."***
- Use PEMDAS
- Remember that MULTIPLICATION and DIVISION are on the same level and are performed LEFT to RIGHT
- Remember that ADDITION and SUBTRACTION are also on the same level and are performed LEFT to RIGHT
Evaluating Expressions
- To evaluate an expression, substitute a number for each variable. Then solve using order of operations.
Example:
Evaluate 3x + 4 for x = 5.
1. First, we plug the value in for x: 3 x 5 + 4
2. Next, we multiply: 15 + 4
3. Finally, we add: 19
And voila. We've evaluated the expression.
Integers, Integers, Errry'thang Integers
You'll need to know how to:
- Compare and order integers (remember, as we go further left on the number line, the values decrease; as we go further to the right, the values increase)
- Find the absolute value (remember, absolute values are ALWAYS POSITIVE and absolute value lines act as grouping symbols, just like parentheses)
- Add and subtract with integers
Quick review: Adding with the same sign - add like normal and keep the sign.
Adding with different signs - find the difference of the absolute values and keep the
sign of the "larger" number
Subracting: USE KFC (Keep, Flip, Change); then, use your addition rules.
- Multiply and divide with integers
Quick review: When multiplying OR dividing, if both numbers have the same sign, the answer is
ALWAYS POSITIVE
If the numbers have different signs, the answer is ALWAYS NEGATIVE
Patterns & Reasoning
- Use inductive reasoning to find the pattern. Then write the rule. Remember, that's when we use the "Start with .... and then....." model.
The Coordinate Plane
- Coordinates are (x, y) --- Don't forget, you have to walk into the building before you can take the elevator
- Know your quadrants
Study, study, study your notes! See you Monday!
Variable Expressions
- You'll need to know how to write variable expressions for word phrases. For example:
Write a variable expression for a number n increased by 5.
Well, if we're starting with an unknown number (n) and we're increasing by 5, we must be adding. So n + 5 would be our variable expression.
Order of Operations
***Please remember that you should be using the correct order of operations for any math problem you complete - not just problems that specify that you need to "use order of operations to..."***
- Use PEMDAS
- Remember that MULTIPLICATION and DIVISION are on the same level and are performed LEFT to RIGHT
- Remember that ADDITION and SUBTRACTION are also on the same level and are performed LEFT to RIGHT
Evaluating Expressions
- To evaluate an expression, substitute a number for each variable. Then solve using order of operations.
Example:
Evaluate 3x + 4 for x = 5.
1. First, we plug the value in for x: 3 x 5 + 4
2. Next, we multiply: 15 + 4
3. Finally, we add: 19
And voila. We've evaluated the expression.
Integers, Integers, Errry'thang Integers
You'll need to know how to:
- Compare and order integers (remember, as we go further left on the number line, the values decrease; as we go further to the right, the values increase)
- Find the absolute value (remember, absolute values are ALWAYS POSITIVE and absolute value lines act as grouping symbols, just like parentheses)
- Add and subtract with integers
Quick review: Adding with the same sign - add like normal and keep the sign.
Adding with different signs - find the difference of the absolute values and keep the
sign of the "larger" number
Subracting: USE KFC (Keep, Flip, Change); then, use your addition rules.
- Multiply and divide with integers
Quick review: When multiplying OR dividing, if both numbers have the same sign, the answer is
ALWAYS POSITIVE
If the numbers have different signs, the answer is ALWAYS NEGATIVE
Patterns & Reasoning
- Use inductive reasoning to find the pattern. Then write the rule. Remember, that's when we use the "Start with .... and then....." model.
The Coordinate Plane
- Coordinates are (x, y) --- Don't forget, you have to walk into the building before you can take the elevator
- Know your quadrants
Study, study, study your notes! See you Monday!
Wednesday, September 10, 2014
Subtracting Integers
*Please read the post below this one for tonight's KhanAcademy assignment*
Scared of subtraction involving negative integers? Don't be - remember, it's just addition in disguise!
The rule for subtraction is:
Add the OpPoSiTe!
Who likes fried chicken? It's one of my all-time favorites. :)
Img: thebittenword.com
So... what does fried chicken have to do with subtracting integers? Check out this cool chart from passyworldofmathematics.com:
Then, solve your problem as an addition problem. Here are a few examples:
-5 - 3 = ?
-5 + (-3) = -8 ---> Both numbers are the same sign, so we can add like normal and keep the sign.
7 - (-2) = ?
7 + 2 = 9 ---> Again, both numbers are the same sign, so we can add like normal and keep the sign.
4 - 8 = ?
4 + (-8) = ? ---> Now we've got addition with two different signs, so remember to use your absolute values!
The absolute values are 4 and 8. The difference between 4 and 8 is 4. Now, is it negative or positive? Look at the original number that had the greatest absolute value: -8. Since it's negative, we know the answer is -4.
If you are self-checking subtraction of integers tonight, here are the answers to the Quick Checks from 1-6 (pgs. 30 & 31):
1) a. -5
b. -1
c. -3
2) a. -4
b. -6
c. 5
3) a. 35
b. -106
c. -46
HaPpY SuBtRaCtInG!
Scared of subtraction involving negative integers? Don't be - remember, it's just addition in disguise!
The rule for subtraction is:
Add the OpPoSiTe!
Who likes fried chicken? It's one of my all-time favorites. :)
Img: thebittenword.com
So... what does fried chicken have to do with subtracting integers? Check out this cool chart from passyworldofmathematics.com:
Then, solve your problem as an addition problem. Here are a few examples:
-5 - 3 = ?
-5 + (-3) = -8 ---> Both numbers are the same sign, so we can add like normal and keep the sign.
7 - (-2) = ?
7 + 2 = 9 ---> Again, both numbers are the same sign, so we can add like normal and keep the sign.
4 - 8 = ?
4 + (-8) = ? ---> Now we've got addition with two different signs, so remember to use your absolute values!
The absolute values are 4 and 8. The difference between 4 and 8 is 4. Now, is it negative or positive? Look at the original number that had the greatest absolute value: -8. Since it's negative, we know the answer is -4.
If you are self-checking subtraction of integers tonight, here are the answers to the Quick Checks from 1-6 (pgs. 30 & 31):
1) a. -5
b. -1
c. -3
2) a. -4
b. -6
c. 5
3) a. 35
b. -106
c. -46
HaPpY SuBtRaCtInG!
Tuesday, September 2, 2014
Assignment 1, September 2
Assignment 1
Hello all! Welcome to your very first assignment :)
1. Visit KhanAcademy.org.
2. Click the link below to watch your first video. If it does not take you to a video called "Introduction to Order of Operations," go to the search box at the top of the website and type "Introduction to Order of Operations" - then, select the video.
http://www.khanacademy.org/math/arithmetic/order-of-operations/v/introduction-to-order-of-operations
3. After the video, click the gray "Practice" button that appears on the screen. Try to earn as many energy points as you can! Please remember what we talked about in class:PLEASE EXCUSE MY DEAR AUNT SALLY. Remember that the numerator and denominator in a fraction are grouped together (as though they had parentheses).
*If your practice questions give you negative integers and you're not sure how to add/subtract them, just try your best.*
1. Visit KhanAcademy.org.
2. Click the link below to watch your first video. If it does not take you to a video called "Introduction to Order of Operations," go to the search box at the top of the website and type "Introduction to Order of Operations" - then, select the video.
http://www.khanacademy.org/math/arithmetic/order-of-operations/v/introduction-to-order-of-operations
3. After the video, click the gray "Practice" button that appears on the screen. Try to earn as many energy points as you can! Please remember what we talked about in class:PLEASE EXCUSE MY DEAR AUNT SALLY. Remember that the numerator and denominator in a fraction are grouped together (as though they had parentheses).
*If your practice questions give you negative integers and you're not sure how to add/subtract them, just try your best.*
Thursday, May 22, 2014
Final Study Guide
Hello all. Here's a quick rundown of the concepts you'll need to review for your final. Remember, we'll be taking a practice final next week in class as we review, so you'll know exactly what type of problems to expect on the real final.
Stuff you need to know:
- Integer operations (adding, subtracting, multiplying, dividing w/integers) - ***You will not be able to use a calculator for this portion of the test***
- Writing/evaluating expressions
- Simplifying variable expressions
- Solving one-step equations (some of your equations will include decimals or fractions)
- GCF and LCM using Prime Factorization
- Mean, median, mode, range
- Exponent rules/simplifying expressions with exponents
- Scientific notation (everyone's favorite! :)
- Comparing and ordering fractions/decimals
- Proportions, similar figures, probability
Stuff you need to know:
- Integer operations (adding, subtracting, multiplying, dividing w/integers) - ***You will not be able to use a calculator for this portion of the test***
- Writing/evaluating expressions
- Simplifying variable expressions
- Solving one-step equations (some of your equations will include decimals or fractions)
- GCF and LCM using Prime Factorization
- Mean, median, mode, range
- Exponent rules/simplifying expressions with exponents
- Scientific notation (everyone's favorite! :)
- Comparing and ordering fractions/decimals
- Proportions, similar figures, probability
Tuesday, March 25, 2014
3rd Quarter Extra Credit Option
Create a blog post for next year's Pre-Algebra class focusing on one concept from Chapter 5. (For example, multiplying fractions.)
Your blog post must:
1. Teach students how to perform the particular math operation you're focusing on
2. Include both words and graphics
You can send this to me digitally or hand me a hard copy.
Due date: Friday, 3/28
This extra credit assignment will be worth one homework grade (it will take the place of a homework assignment if you've missed one) or three points added to your lowest test/quiz grade.
Your blog post must:
1. Teach students how to perform the particular math operation you're focusing on
2. Include both words and graphics
You can send this to me digitally or hand me a hard copy.
Due date: Friday, 3/28
This extra credit assignment will be worth one homework grade (it will take the place of a homework assignment if you've missed one) or three points added to your lowest test/quiz grade.
Wednesday, March 19, 2014
Thursday, March 20th
Hey guys. Sorry I can't be there today. Let's pick up where we left off in our (so-far) review of Chapter 5:
pgs. 283-285, #s 8-40.
Remember, we take math notes for a reason!!! Look back through if you get stuck. If you still can't figure it out, skip it and hopefully when we go over the answers on Friday, you'll remember. :) This is not homework if you don't finish. Not on a show night. However, if you do finish in class, please ask your sub politely if you may play CoolMathGames.com. Your other option is to read - don't forget about all the new books on my shelf.
Good luck tonight - first show night!!! Squeeee! Can't wait to hear all about it!
pgs. 283-285, #s 8-40.
Remember, we take math notes for a reason!!! Look back through if you get stuck. If you still can't figure it out, skip it and hopefully when we go over the answers on Friday, you'll remember. :) This is not homework if you don't finish. Not on a show night. However, if you do finish in class, please ask your sub politely if you may play CoolMathGames.com. Your other option is to read - don't forget about all the new books on my shelf.
Good luck tonight - first show night!!! Squeeee! Can't wait to hear all about it!
Tuesday, March 11, 2014
Funky Fractions
Greetings, Mathlings!
Just some review for what we've already learned for adding and subtracting fractions:
When the fractions have the same denominator, simply add or subtract the numerators, keep the denominator the same, and then simplify.
When the fractions have unlike denominators:
1. Find the Least Common Denominator (The LCM of the denominators)
2. Convert to equivalent fractions - "rename" the fractions with the LCD
3. Follow the procedure for adding/subtracting with the same denominator
Remember, we must find the LCD and rename all the fractions when comparing fractions as well.
....but here's a little something extra for you:
The following chart illustrates the "Butterfly Method" we're going to talk about in class today. A lot of people find it easy to use when you're adding or subtracting with two fractions. *Don't forget to simplify!*
Just some review for what we've already learned for adding and subtracting fractions:
When the fractions have the same denominator, simply add or subtract the numerators, keep the denominator the same, and then simplify.
When the fractions have unlike denominators:
1. Find the Least Common Denominator (The LCM of the denominators)
2. Convert to equivalent fractions - "rename" the fractions with the LCD
3. Follow the procedure for adding/subtracting with the same denominator
Remember, we must find the LCD and rename all the fractions when comparing fractions as well.
....but here's a little something extra for you:
The following chart illustrates the "Butterfly Method" we're going to talk about in class today. A lot of people find it easy to use when you're adding or subtracting with two fractions. *Don't forget to simplify!*
Wednesday, March 5, 2014
Wed., 3/5
Hey guys! Happy Wednesday!
Here's the link to the fractions game we played today, in case anyone's interested in playing at home:
http://www.math-play.com/adding-and-subtracting-fractions-game.html
Seems like everyone's gotten the hang of fractions so far. Please be sure to finish today's classwork (p.255, 5-17) and then check your answers (listed below). Remember to bring your assignment to class tomorrow ready with any questions you have.
Here's the link to the fractions game we played today, in case anyone's interested in playing at home:
http://www.math-play.com/adding-and-subtracting-fractions-game.html
Seems like everyone's gotten the hang of fractions so far. Please be sure to finish today's classwork (p.255, 5-17) and then check your answers (listed below). Remember to bring your assignment to class tomorrow ready with any questions you have.
Monday, February 24, 2014
Monday, 2/24
First I'd like to thank you all for doing a wonderful job reviewing for our Cumulative Assessment. You guys did great with reviewing and study time and I enjoyed playing Around The World! Onward to Chapter 5!
Many of you know how to compare and order fractions already. Chapter 5 begins with this very topic - but before we review comparing and ordering fractions, we must master finding the Least Common Multiple (or LCM) or two or more numbers.
Please watch the following video and pay special attention to the Prime Factorization method of finding the LCM:
http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/cc-6th-lcm/v/least-common-multiple--lcm
Then complete pg. 239, #s 5-13. Try to use the Prime Factorization method for at least three of these problems. See you tomorrow!
Many of you know how to compare and order fractions already. Chapter 5 begins with this very topic - but before we review comparing and ordering fractions, we must master finding the Least Common Multiple (or LCM) or two or more numbers.
Please watch the following video and pay special attention to the Prime Factorization method of finding the LCM:
http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/cc-6th-lcm/v/least-common-multiple--lcm
Then complete pg. 239, #s 5-13. Try to use the Prime Factorization method for at least three of these problems. See you tomorrow!
Tuesday, January 7, 2014
Answers to p.228
Howdy guys. Please check your answers to our classwork assignment today so we can workshop with fractions first thing tomorrow. Don't forget to bundle up and stay warm!!! (p.s., that last one - #44 - the "b" kinda looks like a 6, but the answer is "4b")
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