Hello mathlings. Be sure to study for our Chapter 3 assessment on Wednesday! :) Calculators will be allowed for most of the test. Bring one to class. The only section on which you will not be able to use a calculator is adding and subtracting decimals.
Please read the following very carefully:
Each answer will be worth TWO points.
1 point will be given for the correct answer.
1 point will be given for showing your work IF your work is labeled with the corresponding number and if I can read your work.
What's going to be on the test?
There will not be any questions from sections 1 or 2; however, please keep the principles of rounding and estimating in mind as you may need to round an answer to the nearest place-value. It's always, always, always a good idea to estimate your answer before doing the actual math - that way you have a benchmark to look back on and compare your answer. If it's way different than your estimate, you may want to redo the problem.
Questions on the test will be based on what we covered in sections 3 through 6:
3-3: Measures of Central Tendency
- Mean: Add 'em up and divide by how many pieces of data you have (also known as the average)
- Median: First, order the data from least to greatest; then, find the middle number (or the mean of the two middle numbers if there are two)
- Mode: The number(s) which appear most often
- Range: Highest value - lowest value
- Outliers: Any number that's much, much lower or higher than the rest of the data
3-4: Solving Forumlas
- You will be given the formula in order to solve; you don't need to memorize any formulas.
- Plug in the values that you have for the corresponding variables
- Solve for the unknown
-Remember to include your units
3-5 and 3-6: Solving Equations with Decimals
The rules for solving equations with decimals are the same for solving equations with whole numbers. The goal is still to get the variable by itself.
1. Figure out "what's happening" to the variable.
2. Do the opposite of that to both sides of the equation.
3. Remember your integer rules, especially if you aren't using a calculator.
Adding and Subtracting Decimals:
If you still have the worksheet on which we practiced adding and subtracting decimals, look over that to study. Otherwise make sure you take notes tomorrow in class while we review. Remember when you add/subtract decimals that you:
1. Line up the decimals
2. Carry the decimal down before you solve
3. Solve the problem as though there are no decimals. Your decimal will already be correctly placed in your answer.
See you tomorrow! Bring your smarticles!
Monday, January 5, 2015
Wednesday, November 5, 2014
Videos to Watch 11/5
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
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
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.*
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