Here are the links for Orbit Integers (adding integers game) and Integer Warp (multiplying integers game).
http://www.arcademics.com/games/orbit-integers/orbit-integers.html
http://www.arcademics.com/games/integer-warp/integer-warp.html
Wednesday, April 29, 2015
Wednesday, April 22, 2015
Subtracting Integers
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.
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.
Monday, April 13, 2015
Chapter 7 Study Guide
Hey guys. Here's a quick rundown of what will be on your Chapter 7 Assessment this Thursday:
Multiplying Fractions & Mixed Numbers:
Remember to first change any mixed numbers to improper fractions. Then, multiply the numerators straight across and the denominators straight across. Finally, simplify, either by "dividing down" or by using the GCF. Here's a graphic from WikiHow to demonstrate:
Dividing Fractions & Mixed Numbers:
Again, remember to first change any mixed numbers into improper fractions before you proceed. Then, multiply by the reciprocal of the second number (do not change the first number into its reciprocal, only the second). You can either simplify before you multiply or you can simplify after. Here's a graphic from WikiHow:
Finally, we covered patterns & sequences today. Remember to look for the pattern and to test it out before coming to a conclusion about finding the next number.
Happy studying!
Multiplying Fractions & Mixed Numbers:
Remember to first change any mixed numbers to improper fractions. Then, multiply the numerators straight across and the denominators straight across. Finally, simplify, either by "dividing down" or by using the GCF. Here's a graphic from WikiHow to demonstrate:
Dividing Fractions & Mixed Numbers:
Again, remember to first change any mixed numbers into improper fractions before you proceed. Then, multiply by the reciprocal of the second number (do not change the first number into its reciprocal, only the second). You can either simplify before you multiply or you can simplify after. Here's a graphic from WikiHow:
Finally, we covered patterns & sequences today. Remember to look for the pattern and to test it out before coming to a conclusion about finding the next number.
Happy studying!
Thursday, February 5, 2015
GCF and LCM... and fractions!!! Mwahahaha!
Hello all. It's been a while.
Let's review how we can find the GCF (greatest common factor) and the LCM (least common multiple) of each set of numbers by using the prime factorization method.
1) 16, 60
First, find the prime factorization of each:
Next, identify the matches on each side. A "match" is when there's a number on one side (at the bottom of the tree) that has an EXACT twin on the other side. The two numbers team up to create a "match."
We have underlined our matches. There's a "2" on one side, and another "2" on the other side. This gives us our first match: 2. Our second match is also 2, since there is a second two on both sides. As shown in the picture below, the remaining numbers have no matches:
Now, list our matches. We have one match of "2" and another match of "2". We multiply our matches together:
The GCF = 4.
***Please note - if you are finding the GCF of more than two numbers, a number must be present for ALL the prime factorizations in order to be considered a match.***
As for the LCM...
First, find the prime factorization of the two numbers:
8 18
2 x 4 2 x 9
2 x 2 x 2 2 x 3 x 3
Our prime factorizations are at the bottom. Now, we need to multiply all of the bottom "tree" numbers together, using the matches ONLY ONCE. Our only match between the two tree bottoms is a pair of twos (in red), so we use it only once, and then bring all the other numbers down to multiply:
2 x 2 x 2 x 3 x 3 = 72
The LCM of 8 and 18 is 72.
Let's try it with three numbers. Find the LCM of 6, 14, and 28 using prime factorization:
First, find the prime factorization of all three numbers (I'm going to skip the whole tree and go straight to the answers we'd have at the bottom):
6 14 28
2 x 3 2 x 7 2 x 2 x 7
We have a matching 2 for all three trees, so we use it once. We also have a match of 7 between 14 and 28, so we use it only once. Then, we multiply those with all of the leftover, non-matching numbers:
2 x 7 x 3 x 2 = 84. The LCM of 6, 14, and 28 is 84.
***Please note - if you are finding the LCM of more than two numbers, a number need only be present in TWO of the prime factorizations in order to be considered a match.***
Now. What on earth does all this LCM stuff have to do with fractions? Remember, in ancient times (a couple of days ago) when we had to compare fractions, that we used the LCM of the denominators (the "LCD" - least common denominator) to turn fractions with different denominators into fractions with the same denominators. (You can't compare two fractions that have different denominators.) Kinda like giving them the same last name, or putting them into the same "family."
In order to compare fractions with unlike denominators, you must:
1) Find the LCD.
2) Convert the original fractions into equivalent fractions using the LCD.
3) Compare the numerators, and voila!
Let's walk through an example using these steps:
Which is greater, 2/3 or 7/8? (Sorry about the sideways fractions!)
1) Find the LCM of the denominators:
3 8
3 2 x 2 x 2
We have no matches, so we multiply everything together: 3 x 2 x 2 x 2 = 24. This is now the Least Common Denominator we're looking for.
2) Convert the original fractions into equivalent fractions with the Least Common Denominator.
That means we need to change 2/3 and 7/8 into fractions that have 24 at the bottom.
2/3 = ?/24 --- First, figure out how we can get from 3 to 24. Once we realize we multiply by 8, we must do the same thing to the numerator. Our new fraction is 16/24.
7/8 = ?/24 --- How do we get from 8 to 24? We multiply by 3. Do the same thing to the top for our new fraction: 21/24.
3) Now we can finally compare the two fractions by simply looking at the numerator. Which is bigger, 16/24 or 21/24?
We know that 21/24 is bigger. Therefore, 7/8 is greater than 2/3.
And finally... some food for thought from my favorite internet friend, Philosoraptor:
Let's review how we can find the GCF (greatest common factor) and the LCM (least common multiple) of each set of numbers by using the prime factorization method.
1) 16, 60
First, find the prime factorization of each:
***Please note - if you are finding the GCF of more than two numbers, a number must be present for ALL the prime factorizations in order to be considered a match.***
As for the LCM...
First, find the prime factorization of the two numbers:
8 18
2 x 4 2 x 9
2 x 2 x 2 2 x 3 x 3
Our prime factorizations are at the bottom. Now, we need to multiply all of the bottom "tree" numbers together, using the matches ONLY ONCE. Our only match between the two tree bottoms is a pair of twos (in red), so we use it only once, and then bring all the other numbers down to multiply:
2 x 2 x 2 x 3 x 3 = 72
The LCM of 8 and 18 is 72.
Let's try it with three numbers. Find the LCM of 6, 14, and 28 using prime factorization:
First, find the prime factorization of all three numbers (I'm going to skip the whole tree and go straight to the answers we'd have at the bottom):
6 14 28
2 x 3 2 x 7 2 x 2 x 7
We have a matching 2 for all three trees, so we use it once. We also have a match of 7 between 14 and 28, so we use it only once. Then, we multiply those with all of the leftover, non-matching numbers:
2 x 7 x 3 x 2 = 84. The LCM of 6, 14, and 28 is 84.
***Please note - if you are finding the LCM of more than two numbers, a number need only be present in TWO of the prime factorizations in order to be considered a match.***
Now. What on earth does all this LCM stuff have to do with fractions? Remember, in ancient times (a couple of days ago) when we had to compare fractions, that we used the LCM of the denominators (the "LCD" - least common denominator) to turn fractions with different denominators into fractions with the same denominators. (You can't compare two fractions that have different denominators.) Kinda like giving them the same last name, or putting them into the same "family."
In order to compare fractions with unlike denominators, you must:
1) Find the LCD.
2) Convert the original fractions into equivalent fractions using the LCD.
3) Compare the numerators, and voila!
Let's walk through an example using these steps:
Which is greater, 2/3 or 7/8? (Sorry about the sideways fractions!)
1) Find the LCM of the denominators:
3 8
3 2 x 2 x 2
We have no matches, so we multiply everything together: 3 x 2 x 2 x 2 = 24. This is now the Least Common Denominator we're looking for.
2) Convert the original fractions into equivalent fractions with the Least Common Denominator.
That means we need to change 2/3 and 7/8 into fractions that have 24 at the bottom.
2/3 = ?/24 --- First, figure out how we can get from 3 to 24. Once we realize we multiply by 8, we must do the same thing to the numerator. Our new fraction is 16/24.
7/8 = ?/24 --- How do we get from 8 to 24? We multiply by 3. Do the same thing to the top for our new fraction: 21/24.
3) Now we can finally compare the two fractions by simply looking at the numerator. Which is bigger, 16/24 or 21/24?
We know that 21/24 is bigger. Therefore, 7/8 is greater than 2/3.
And finally... some food for thought from my favorite internet friend, Philosoraptor:
Friday, January 16, 2015
Cumulative Review
Howdy everyone. Let's see what we remember so far. Look back through your notes for chapters 1 through 4 if you need help completing the following problems. There are only five, so take your time and do your best! This is a rarity, but I will be grading this homework assignment for correctness and not just completion. Enjoy your long weekend!
1) Write 42 as the product of prime numbers.
2) Find the mean, median, mode and range for the following data:
4.3, 5, 6.2, 3.7, 3.6
3) Students at Thompson Middle School collected toys to give to children. They collected 10 stuffed animals, 9 games, 11 dolls and 7 crafts. Make a bar graph to show the data.
4) 0.05 x 1.3
5) Find the circumference of a circle whose radius is 3.2 meters. Round to the nearest tenth if necessary.
1) Write 42 as the product of prime numbers.
2) Find the mean, median, mode and range for the following data:
4.3, 5, 6.2, 3.7, 3.6
3) Students at Thompson Middle School collected toys to give to children. They collected 10 stuffed animals, 9 games, 11 dolls and 7 crafts. Make a bar graph to show the data.
4) 0.05 x 1.3
5) Find the circumference of a circle whose radius is 3.2 meters. Round to the nearest tenth if necessary.
Wednesday, January 7, 2015
Chapter 4 Study Guide
Hey guys. Here's a study guide for your Chapter 4 assessment (scheduled for Monday, January 12th). We've taken shorter assessments along the way so far in this chapter, but this assessment will cover everything we've learned from the chapter, so please be sure to study by looking back over your previous assignments from Chp. 4 and your notes. Also, don't forget that Glencoe has a GREAT website for studying. Click here: http://www.glencoe.com/sec/math/msmath/mac04/course1/self_check_quiz/index.php/
You can use the online quizzes and personal tutor videos to look back at what we've learned and to practice what you know.
Hooookay. Let's talk about what we've learned in Chapter 4.
Section 4-1: Multiplying a decimal by a whole number
*Remember, you should not line up the decimals when you are multiplying - only when you're adding or subtracting.*
1) Set the problem up as though you were dealing with plain ol' whole numbers.
2) Solve (ignore the decimals for now - remember, we're pretending they are both whole numbers).
3) To place the decimal in your answer:
First, count how many numbers after the decimal in the original problem.
Then, going from right to left in your answer, count that many spaces over and put your decimal there.
Example:
4.23 ---> There are two numbers after the decimal here.
x 6
2538 ---> Now, going from right to left, put the decimal two places from the end.
Answer: 25.38
Section 4-2: Multiplying decimals
This method is exactly the same as the method for multiplying a decimal by a whole number.
1) Set the problem up.
2) Solve just like they're whole numbers (ignore the decimal).
3) How many numbers (TOTAL) are there after all the decimals in your problem? Count them up, and then
place the decimal that many places over in your answer.
Example:
3.65 ---> There are two numbers after the decimal here.
x 2.5 ---> There is one number after the decimal here.
9125 ---> Now, going from right to left, put the decimal three places from the end, since we counted
3 numbers total after decimal points in our problem.
Answer: 9.125
Section 4-3: Dividing decimals by whole numbers
First, carry the decimal straight up. Then divide as with regular numbers. *Don't forget, you may need to annex zeros as you divide.*
Your decimal will already be correctly placed in your answer.
Section 4-4: Dividing by decimals
When dividing any number by a decimal:
1. Turn the outside number into a whole number by moving the decimal.
2. Now go to the inside number and move the decimal the SAME number of spaces.
3. Carry the decimal straight up from its new position & divide using the method we learned in 4-3.
Section 4-5: Perimeter
The formula for the perimeter of a rectangle is 2l + 2w. (Two times the length plus two times the width.)
The formula for the perimeter of a square is 4s (four times the length of one of the sides).
*If in doubt, you can simply add all of the sides together for the perimeter. This is how to find the perimeter of any other figure.*
For example, if you have a rectangle with a length of 18 inches and a width of 11 inches, you can simply substitute the numbers into the formula:
2l + 2w ----> 2 x 18 + 2 x 11 (don't forget order of operations - multiply first)
36 + 22 = 58
So the perimeter of this particular rectangle = 58 in.
Section 4-6: Circumference
Remember that circumference packet we completed? That would be a great tool to use when studying for circumference. Here's a post I made a couple years ago for walking through circumference:
Check out this diagram from kidsmathgamesonline.com:
That about sums it up. As always, please email me if you're having trouble. Look over your notes during the commercials as the Ravens crush the Patriots this weekend.... ;)
You can use the online quizzes and personal tutor videos to look back at what we've learned and to practice what you know.
Hooookay. Let's talk about what we've learned in Chapter 4.
Section 4-1: Multiplying a decimal by a whole number
*Remember, you should not line up the decimals when you are multiplying - only when you're adding or subtracting.*
1) Set the problem up as though you were dealing with plain ol' whole numbers.
2) Solve (ignore the decimals for now - remember, we're pretending they are both whole numbers).
3) To place the decimal in your answer:
First, count how many numbers after the decimal in the original problem.
Then, going from right to left in your answer, count that many spaces over and put your decimal there.
Example:
4.23 ---> There are two numbers after the decimal here.
x 6
2538 ---> Now, going from right to left, put the decimal two places from the end.
Answer: 25.38
Section 4-2: Multiplying decimals
This method is exactly the same as the method for multiplying a decimal by a whole number.
1) Set the problem up.
2) Solve just like they're whole numbers (ignore the decimal).
3) How many numbers (TOTAL) are there after all the decimals in your problem? Count them up, and then
place the decimal that many places over in your answer.
Example:
3.65 ---> There are two numbers after the decimal here.
x 2.5 ---> There is one number after the decimal here.
9125 ---> Now, going from right to left, put the decimal three places from the end, since we counted
3 numbers total after decimal points in our problem.
Answer: 9.125
Section 4-3: Dividing decimals by whole numbers
First, carry the decimal straight up. Then divide as with regular numbers. *Don't forget, you may need to annex zeros as you divide.*
Your decimal will already be correctly placed in your answer.
Section 4-4: Dividing by decimals
When dividing any number by a decimal:
1. Turn the outside number into a whole number by moving the decimal.
2. Now go to the inside number and move the decimal the SAME number of spaces.
3. Carry the decimal straight up from its new position & divide using the method we learned in 4-3.
Section 4-5: Perimeter
The formula for the perimeter of a rectangle is 2l + 2w. (Two times the length plus two times the width.)
The formula for the perimeter of a square is 4s (four times the length of one of the sides).
*If in doubt, you can simply add all of the sides together for the perimeter. This is how to find the perimeter of any other figure.*
For example, if you have a rectangle with a length of 18 inches and a width of 11 inches, you can simply substitute the numbers into the formula:
2l + 2w ----> 2 x 18 + 2 x 11 (don't forget order of operations - multiply first)
36 + 22 = 58
So the perimeter of this particular rectangle = 58 in.
Section 4-6: Circumference
Remember that circumference packet we completed? That would be a great tool to use when studying for circumference. Here's a post I made a couple years ago for walking through circumference:
Check out this diagram from kidsmathgamesonline.com:
Diameter (d) is the distance a cross a circle through its center (it goes all the way through).
Radius (r) is the distance from the center to any point on a circle (it's half of the diameter).
And, as we said, Circumference (c) is the distance around a circle.
There's a formula to figure out what the Circumference of a circle is:
C = πd
This says "Circumference = pi times the diameter"
What is that little symbol? That "pi" thing??? Well, it's not a pie, although I could certainly go for a cherry pie right now.
tasteofhome.com
Anyway. Pi is a number that we use to find Circumference. Use a calculator to find the real value of pi by pressing the π button on your calculator. It goes on forever - so we round it to 3.14.
Now that we know what pi is, we can find the circumference of any circle as long as we know its diameter. Let's say we have a circle with a diameter of 4.5 inches. All we need to do is plug the numbers into the formula:
C = 3.14 x 4.5
Then, using your calculator or your multiplying decimal method, solve for C:
C = 14.13
We know that the circumference is 14.13 inches.
There's another way to find Circumference - this time, using radius. Take a look at the circle diagram above. Did you notice that the radius is exactly half the length of a circle's diameter? So to find the Circumference of a circle using the radius, we use the following formula:
C = 2πr
This says "Circumference equals 2 times pi times the radius of a circle."
Again, all we have to do is plug the numbers in. If we have a circle with a radius of 38 ft, we would plug the numbers in like so:
C = 2 x 3.14 x 38
Now solve for C.
C = 238.64 ft.
That about sums it up. As always, please email me if you're having trouble. Look over your notes during the commercials as the Ravens crush the Patriots this weekend.... ;)
Monday, January 5, 2015
2nd Quarter Extra Credit
Hello mathlings!
Here is your extra credit opportunity for 2nd Quarter. First, please note that in order for me to give your answers credit, all work must be shown.
Due: Monday, January 12th
Assignment: pg. 154, 14 - 19
pg. 168, 45 - 52
Total Questions: 14
Extra Credit: You will receive 1/2 pt. of extra credit for each correct answer.
Total Extra Credit points possible: 7
These extra credit points will be added to whichever assignments from the quarter on which you need the most help. For example, if you missed a homework assignment but also did poorly on an assessment grade, I will "crunch" the numbers to see which way your overall quarter grade will benefit the most and will apply the extra credit accordingly.
Here is your extra credit opportunity for 2nd Quarter. First, please note that in order for me to give your answers credit, all work must be shown.
Due: Monday, January 12th
Assignment: pg. 154, 14 - 19
pg. 168, 45 - 52
Total Questions: 14
Extra Credit: You will receive 1/2 pt. of extra credit for each correct answer.
Total Extra Credit points possible: 7
These extra credit points will be added to whichever assignments from the quarter on which you need the most help. For example, if you missed a homework assignment but also did poorly on an assessment grade, I will "crunch" the numbers to see which way your overall quarter grade will benefit the most and will apply the extra credit accordingly.
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