Wednesday, December 9, 2015
Thursday, December 3, 2015
Friday, November 13, 2015
Weekend Homework 11/13
1) A basketball court measures 26 meters by 14 meters. Find the perimeter of the court.
2) Refer to the question above: Suppose 10 meters was added to each side of the basketball court. Find the new perimeter of the court.
3) The sleeping quarters for a bear at the zoo is a square that measures 5 yards on each side. What is the perimeter of the sleeping area?
4) A picture frame measures 5.1 inches in length and 3.5 inches in width. What is the perimeter of the picture frame?
2) Refer to the question above: Suppose 10 meters was added to each side of the basketball court. Find the new perimeter of the court.
3) The sleeping quarters for a bear at the zoo is a square that measures 5 yards on each side. What is the perimeter of the sleeping area?
4) A picture frame measures 5.1 inches in length and 3.5 inches in width. What is the perimeter of the picture frame?
Wednesday, November 11, 2015
Homework 11/11
Please complete 4-12. Remember to first change the OUTSIDE number (the divisor) to a whole number by moving the decimal to the right, and then to move the decimal for the INSIDE number (the dividend) the same number of times to the right. You will be turning this in.
Tuesday, November 10, 2015
Friday, November 6, 2015
Weekend Assignment 11/6
Hi everyone! Just wanted to take a minute to recap what we've learned so far in Chapter 4 before you complete your questions.
We first discussed the method for 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
Today we talked about multiplying one decimal by another. *Remember, don't line up the decimals since we're multiplying!*
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
We first discussed the method for 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
Today we talked about multiplying one decimal by another. *Remember, don't line up the decimals since we're multiplying!*
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
Here are your 9 questions for the weekend (remember, you must show your work for credit!):
1) 2.34 x 9.3
2) 0.45 x 2.9
3) 1.75 x 4.6
4) 2.22 x 9.4
5) 7.97 x 6.6
6) 6.35 1.1
7) 4.67 x 7.8
8) 8.13 x 3.6
9) 3.87 x 2.1
Wednesday, November 4, 2015
Wednesday, October 28, 2015
Monday, October 19, 2015
Quiz Wednesday - Data
Hello, my wonderful mathlings! Please be sure to review the following concepts for Wednesdays's quiz:
I. Graphing
A. Intervals
1. Intervals should be even (count if you need to)
2. Intervals are usually on the y-axis or are the first category in a frequency chart
3. Think of intervals as "categories"
B. Labels
1. Your graphs should always have a title that pertains to the information being represented by
the graph
2. Your x-axis and y-axis should both have labels, even if the information on the graph seems
obvious
C. Accuracy
1. Always re-check your data after you've made your graph
II. Measures of Central Tendency
A. Mean: (average) - add ALL the data, and then divide by how many data points you have
B. Median: FIRST, line up all the data from LEAST to GREATEST; then, find the middle number.
If there are two middle numbers, find the MEAN of the two middle numbers for your median.
C. Mode: number that appears the MOST
D. Range: highest data point minus the lowest data point
III. Drawing conclusions
A. Real-world connections - be sure to think about the data in a real-world setting and be sure that
your conclusions are realistic
B. Comparisons - when asked to compare data, think about how many TIMES greater one statistic
is than another, rather than how "much" more
C. We will focus on this part heavily on the quiz. Please use complete sentences and proofread your
answers
I. Graphing
A. Intervals
1. Intervals should be even (count if you need to)
2. Intervals are usually on the y-axis or are the first category in a frequency chart
3. Think of intervals as "categories"
B. Labels
1. Your graphs should always have a title that pertains to the information being represented by
the graph
2. Your x-axis and y-axis should both have labels, even if the information on the graph seems
obvious
C. Accuracy
1. Always re-check your data after you've made your graph
II. Measures of Central Tendency
A. Mean: (average) - add ALL the data, and then divide by how many data points you have
B. Median: FIRST, line up all the data from LEAST to GREATEST; then, find the middle number.
If there are two middle numbers, find the MEAN of the two middle numbers for your median.
C. Mode: number that appears the MOST
D. Range: highest data point minus the lowest data point
III. Drawing conclusions
A. Real-world connections - be sure to think about the data in a real-world setting and be sure that
your conclusions are realistic
B. Comparisons - when asked to compare data, think about how many TIMES greater one statistic
is than another, rather than how "much" more
C. We will focus on this part heavily on the quiz. Please use complete sentences and proofread your
answers
Monday, October 12, 2015
Survey Project
Hello Mathlings!
Here are the things that need to be included in your project, which is due for presentation this Friday, 10/16.
- Two graphs which represent your data (the graphs you choose will be approved by me after you turn in your project outline Monday) - Both graphs need to be large enough to display to the class. You may present these graphs digitally on the Polyvision Board or with Posterboards. Please remember to label your graphs and to keep your intervals even - you will be graded on the accuracy of your graphs.
- The four measures of central tendency for your data (mean, median, mode and range)
- One written paragraph (6-8 sentences) which explains your survey and draws conclusions based on the data you collected
We will be working on these all week. In addition to your graphs, your measures of central tendency and your paragraph/conclusions, you will be given participation points this week for working with your group and for participating in your group's presentation of information. Please make sure each group member has an opportunity to speak when you present on Friday.
I'm really interested in the questions you've come up with! Have fun with this!!!
Here are the things that need to be included in your project, which is due for presentation this Friday, 10/16.
- Two graphs which represent your data (the graphs you choose will be approved by me after you turn in your project outline Monday) - Both graphs need to be large enough to display to the class. You may present these graphs digitally on the Polyvision Board or with Posterboards. Please remember to label your graphs and to keep your intervals even - you will be graded on the accuracy of your graphs.
- The four measures of central tendency for your data (mean, median, mode and range)
- One written paragraph (6-8 sentences) which explains your survey and draws conclusions based on the data you collected
We will be working on these all week. In addition to your graphs, your measures of central tendency and your paragraph/conclusions, you will be given participation points this week for working with your group and for participating in your group's presentation of information. Please make sure each group member has an opportunity to speak when you present on Friday.
I'm really interested in the questions you've come up with! Have fun with this!!!
Friday, September 25, 2015
Chapter 1 Study Guide
HELLLLOOOOOOOOOO friends.
So... what's going to be on your Chapter 1 assessment? I've included a run-down below, categorized by section. Don't forget to use the Glencoe website for self-check quizzes, tutor videos, extra examples, and lots of great studying resources. If it's not already saved in your favorites, here's the link:
http://www.glencoe.com/sec/math/msmath/mac04/course1/self_check_quiz/index.php/
*Please note that these are the main concepts that will be included on your test, but your test will also include word problems which will require you to make a plan, use the concepts and solve. Just remember, when solving a word problem, to find out what you know - what you NEED to know - and to think about how you can use what you already know to solve your problem.*
1-3: Prime Factors
- Remember, to "find the prime factorization" of a number, make a factor tree. Your prime factors at the bottom are the answer.
- Always check your answer by multiplying the factors at the bottom of your tree to make sure you get the number at the top.
Example: Find the prime factorization of 42:
42
6 x 7
2x3 x 7 ---> Answer. Check: Does 2 x 3 x 7 = 42? Yes. The answer is correct.
1-4: Powers and Exponents
Here are two previous blog posts that review powers and exponents. Be sure to check out the post that includes how to incorporate exponents into prime factorization.
http://tlsmath6.blogspot.com/2012/09/exponents.html
http://tlsmath6.blogspot.com/2012/09/expressing-prime-factorization-with.html
1-5: Everyone's favorite, ORDER OF OPERATIONS!!!!!!! AHHHHHH!!!!!!!!!
Two things I need you to remember about PEMDAS:
1. Multiplication and Division are on the same level and go LEFT to RIGHT
2. Please, please, PLEASE show your work line-by-line. Once you complete an operation, bring EVERYTHING ELSE DOWN exactly as it appears on the next line. This will help you keep track of what you've already done and will keep you from doing things out-of-order.
1-6 and 1-7: Algebra
These were the sections where we had to plug in a value for the variables and then solve the expressions. Then, we used mental math to solve equations.
Examples:
1. If a = 2 and b = 3, evaluate:
2a + 3b.
--- Remember, a number right next to a variable means multiply. Now, plug in the values:
2 x 2 + 3 x 3
---Now, be sure to use order of operations when you solve (multiply first, then add):
4 + 9
= 13
2. Solve the equation mentally: p + 2 = 9.
---Ask yourself, "What plus two would give me nine?"
---We can conclude that p = 7 because 7 + 2 would give us 9.
1-8: Area of Rectangles
Formula is length x width. Don't forget to include units squared!
So... what's going to be on your Chapter 1 assessment? I've included a run-down below, categorized by section. Don't forget to use the Glencoe website for self-check quizzes, tutor videos, extra examples, and lots of great studying resources. If it's not already saved in your favorites, here's the link:
http://www.glencoe.com/sec/math/msmath/mac04/course1/self_check_quiz/index.php/
*Please note that these are the main concepts that will be included on your test, but your test will also include word problems which will require you to make a plan, use the concepts and solve. Just remember, when solving a word problem, to find out what you know - what you NEED to know - and to think about how you can use what you already know to solve your problem.*
1-3: Prime Factors
- Remember, to "find the prime factorization" of a number, make a factor tree. Your prime factors at the bottom are the answer.
- Always check your answer by multiplying the factors at the bottom of your tree to make sure you get the number at the top.
Example: Find the prime factorization of 42:
42
6 x 7
2x3 x 7 ---> Answer. Check: Does 2 x 3 x 7 = 42? Yes. The answer is correct.
1-4: Powers and Exponents
Here are two previous blog posts that review powers and exponents. Be sure to check out the post that includes how to incorporate exponents into prime factorization.
http://tlsmath6.blogspot.com/2012/09/exponents.html
http://tlsmath6.blogspot.com/2012/09/expressing-prime-factorization-with.html
1-5: Everyone's favorite, ORDER OF OPERATIONS!!!!!!! AHHHHHH!!!!!!!!!
Two things I need you to remember about PEMDAS:
1. Multiplication and Division are on the same level and go LEFT to RIGHT
2. Please, please, PLEASE show your work line-by-line. Once you complete an operation, bring EVERYTHING ELSE DOWN exactly as it appears on the next line. This will help you keep track of what you've already done and will keep you from doing things out-of-order.
1-6 and 1-7: Algebra
These were the sections where we had to plug in a value for the variables and then solve the expressions. Then, we used mental math to solve equations.
Examples:
1. If a = 2 and b = 3, evaluate:
2a + 3b.
--- Remember, a number right next to a variable means multiply. Now, plug in the values:
2 x 2 + 3 x 3
---Now, be sure to use order of operations when you solve (multiply first, then add):
4 + 9
= 13
2. Solve the equation mentally: p + 2 = 9.
---Ask yourself, "What plus two would give me nine?"
---We can conclude that p = 7 because 7 + 2 would give us 9.
1-8: Area of Rectangles
Formula is length x width. Don't forget to include units squared!
Thursday, September 17, 2015
Homework 9/17
To find the speed of an airplane, use the expression d/t ("d divided by t"), where d represents distance and t represents time. Find the speed s of a plane that travels 3,636 miles in 9 hours.
Wednesday, September 16, 2015
Homework 9/16
Tuesday, September 15, 2015
Homework 9/15
Hey guys! Happy Tuesday! Please read the following post to prepare for class tomorrow.
We will be talking about the Order of Operations on Wednesday. Many of you are already familiar with this, so it may be a review for some of you, but that's okay! Fun, random fact: My favorite planet is Neptune.
So... what do I mean when I say "order of operations???" I'm talking about the order in which we solve a math problem. "Operations" refers to the math operations we use, such as addition, subtraction, multiplication, etc. There are very specific rules we must follow in order to arrive at the correct answer, and this order of operations should be used whenever you do math - not just when a problem says "Use the order of operations to solve." :) Another fun fact: Christmas lights make me happy.
We use the acronym "PEMDAS" to remind us of the order of operations:
from: coolmath.com
**Notice that MD and AS are grouped together! We'll talk about why tomorrow!**
A great way to remember the order of operations is to remember "Please Excuse My Dear Aunt Sally" - the acronym fits this phrase. We're also going to talk a little bit about Aunt Sally tomorrow ;) Final fun fact: My TWO favorite movies are "It's a Wonderful Life" and "Interstellar."
Okay. Now that you've read a little preview for tomorrow's lesson, prepare for the drill by making sure you've read this post in its entirety and have found the three facts about Ms. J.!
We will be talking about the Order of Operations on Wednesday. Many of you are already familiar with this, so it may be a review for some of you, but that's okay! Fun, random fact: My favorite planet is Neptune.
So... what do I mean when I say "order of operations???" I'm talking about the order in which we solve a math problem. "Operations" refers to the math operations we use, such as addition, subtraction, multiplication, etc. There are very specific rules we must follow in order to arrive at the correct answer, and this order of operations should be used whenever you do math - not just when a problem says "Use the order of operations to solve." :) Another fun fact: Christmas lights make me happy.
We use the acronym "PEMDAS" to remind us of the order of operations:
from: coolmath.com
**Notice that MD and AS are grouped together! We'll talk about why tomorrow!**
A great way to remember the order of operations is to remember "Please Excuse My Dear Aunt Sally" - the acronym fits this phrase. We're also going to talk a little bit about Aunt Sally tomorrow ;) Final fun fact: My TWO favorite movies are "It's a Wonderful Life" and "Interstellar."
Okay. Now that you've read a little preview for tomorrow's lesson, prepare for the drill by making sure you've read this post in its entirety and have found the three facts about Ms. J.!
Friday, September 11, 2015
Thursday, September 10, 2015
Homework for Thursday, 9/10
Hello, Mathlings! Here's tonight's homework. You may have completed some or all of this in class, but all the questions assigned are posted below. Please complete any you were not able to complete in class.
From pg. 16, #s 31 - 41
Find the prime factorization of each:
31) 24
32) 18
33) 40
34) 75
35) 27
36) 32
37) 49
38) 25
39) 42
40) 104
41) 17
41) 97
From pg. 16, #s 31 - 41
Find the prime factorization of each:
31) 24
32) 18
33) 40
34) 75
35) 27
36) 32
37) 49
38) 25
39) 42
40) 104
41) 17
41) 97
Monday, September 7, 2015
Divisibility Rules for 7 and 8
Hello friends! We've talked about divisibility rules for 2, 3, 4, 5, 6, 9, and 10; let's talk about 7 and 8, which may seem a little more complicated, but are easy to deal with once you get used to them. :)
In order to see if a number is divisible by 8, you only must check to see whether the last three digits of the number are divisible by 8. If they are, then the entire number is divisible by 8 too.
Example 1: Is the number 8347475537272 divisible by 8?
Answer 1: Yes, because the last 3 digits, 272, are divisible by 8.
Example 2: Is the number 314159265358979323846divisible by 8?
Answer 2: No, because the last 3 digits, 846, are not divisible by 8.
In order to see if a number is divisible by 7, you must/;
1. Take the last digit of the number you’re testing and double it.
2. Then, subtract this number from the rest of the remaining digits.
*If this new number is either 0 or a number that’s divisible by 7, then then original number is divisible by seven.
Example 1: Is the number 364 divisible by 7?
Answer 1: Yes: Double the 4 to get 8. Subtract 8 from 36 to get 28. Since 28 is divisible by 7, we can now say for certain that 364 is also divisible by 7.
Example 2: Is the number 8256 divisible by 7?
Answer 2: No, Double 6 to get 12. Subtract 12 from 825 to get 813. 813 is slightly too large to tell whether it is divisible by 7 so we must repeat the process. Double 3 to get 6. Subtract 6 from 81 to get 75. Since 75 is not divisible by 7, neither is 813 or 8256. Therefore, 8256 is not divisible by 7.
In order to see if a number is divisible by 8, you only must check to see whether the last three digits of the number are divisible by 8. If they are, then the entire number is divisible by 8 too.
Example 1: Is the number 8347475537272 divisible by 8?
Answer 1: Yes, because the last 3 digits, 272, are divisible by 8.
Example 2: Is the number 314159265358979323846divisible by 8?
Answer 2: No, because the last 3 digits, 846, are not divisible by 8.
In order to see if a number is divisible by 7, you must/;
1. Take the last digit of the number you’re testing and double it.
2. Then, subtract this number from the rest of the remaining digits.
*If this new number is either 0 or a number that’s divisible by 7, then then original number is divisible by seven.
Example 1: Is the number 364 divisible by 7?
Answer 1: Yes: Double the 4 to get 8. Subtract 8 from 36 to get 28. Since 28 is divisible by 7, we can now say for certain that 364 is also divisible by 7.
Example 2: Is the number 8256 divisible by 7?
Answer 2: No, Double 6 to get 12. Subtract 12 from 825 to get 813. 813 is slightly too large to tell whether it is divisible by 7 so we must repeat the process. Double 3 to get 6. Subtract 6 from 81 to get 75. Since 75 is not divisible by 7, neither is 813 or 8256. Therefore, 8256 is not divisible by 7.
Friday, August 28, 2015
Greetings, Mathlings!!! TUES, SEP. 1
Hello everyone and WELCOME BACK!!!!!!! Grumpy cat says:
(memegenerator.net)
Juuuuuust kidding! I'm super excited to have you all for Math this year. We're going to be doing some fun stuff :)
Today we're going to talk about divisibility patterns (section 1-2 of your textbook).
1) Please see the divisibility rules chart below and copy the rules into the "notes" section of your 3-section notebook. You can copy the chart any way you'd like - keep it simple or make it snazzy!
2) After reading through the rules, please read through pages 10 and 11 in your textbook, individually.
3) Then, working with your group, complete page 12, #s 9 - 20 and # 29. Be sure everyone's name is on your group's paper before you hand it in (you only need to hand one paper in per group).
(reallygoodstuff.com)
Thursday, May 28, 2015
Friday's Assignment
Pick 25 questions from the remaining chapter reviews we haven't completed (remember, your final includes chapters 1 through 0).
Answer those questions (be sure to show all work - go step-by-step). Please turn your work in at the end of class.
We will continue to review on Monday.
Answer those questions (be sure to show all work - go step-by-step). Please turn your work in at the end of class.
We will continue to review on Monday.
Wednesday, May 27, 2015
Final Study Guide
Well, my dear Mathlings, it's that time of year. Time to study for your final. Here are the major concepts from Chapters 1 - 9 that will be on your final:
- Prime factorization
- Powers and exponents
- Order of operations
- Variables and expressions
- Area
- Graphing (Bar/Line graphs)
- Frequency tables & Stem and Leaf plots
- Measures of central tendency (Mean, Median, Mode, Range)
- Adding, subtracting, multiplying, and dividing decimals
- Adding, subtracting, multiplying, and dividing fractions
- GCF/LCM
- Turning fractions into decimals
- Turning decimals into fractions
- Comparing/ordering fractions and decimals
- Adding, subtracting, multiplying, and dividing integers
- The Coordinate Plane
- Powers and exponents
- Order of operations
- Variables and expressions
- Area
- Graphing (Bar/Line graphs)
- Frequency tables & Stem and Leaf plots
- Measures of central tendency (Mean, Median, Mode, Range)
- Adding, subtracting, multiplying, and dividing decimals
- Adding, subtracting, multiplying, and dividing fractions
- GCF/LCM
- Turning fractions into decimals
- Turning decimals into fractions
- Comparing/ordering fractions and decimals
- Adding, subtracting, multiplying, and dividing integers
- The Coordinate Plane
- Solving Equations
The series of review questions we are completing this week are your practice questions for the final. Please be sure to speak up in class when we go over the answers if you need me to refresh a concept for you. Be sure to use your Glencoe resources to study - self-check quizzes, video tutoring, etc. Review your notes - they contain condensed information for each chapter section and are a great way to look back through what we've learned.
Happy studying!
Wednesday, April 29, 2015
Integer Games
Hey guys!
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 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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