9.6 Draw a Diagram (p.218-219)

Steps to Solving Word Problems by drawing a diagram:
1. Think about what you know and what you are being asked to find
2. Plan a strategy - draw a diagram to show what is happening in the question
3. Solve the problem and make sure you are answering the question being asked.

9.5 Subtract Mixed Numbers (p.214-217)

I.Subtract mixed numbers that require borrowing from the whole:
-Use the same steps as before but borrow from a whole when subtracting a larger fraction or turn into improper fractions and then simplify.

Ex. 4 1/2 - 2 4/5 :
-- find a common denominator
4 1/2 = 4 5/10
- 2 4/5 = 2 8/10
--The fraction 8/10 is larger than 5/10 so you need to borrow from the 4 whole.
4 5/10 = 3 15/10 (as an improper fraction)
--Use the improper fraction when subtracting
3 15/10
-2 8/10
-----------
0 7/10 = 7/10

9.4 Add and Subtract Mixed Numbers (p.210-213)

I. Steps for Adding or Subtracting Mixed Numbers
1. Find the LCD
2. Find the equivalent fractions.
3. Add or subtract the fractions and add or subtract the whole numbers.
4. Write your answer in simplest form.

9.3 Add and Subtract Decimals

Three steps for adding or subtracting fractions
1. Make sure denominators are the same. (use LCM to find common denominator)
2. Add the numerators – write the sum over the common denominator
3. Simplify if necessary (this could mean writing as a mixed number).


How to Add & Subtract Fractions -- powered by eHow.com
Check out these examples from mathisfun.com

9.1 Estimate Sums and Differences (p.200-203)

I.Use benchmark numbers to estimate:
A. Benchmark numbers are numbers that are easy to work with --> 0, 1/2, 1 whole
B.Compare the numerator (top) to the denominator (bottom)

Find out if the numerator is:

• far away from the denominator (ex. 1/9: between 0 and 1/2, but closer to 0--> 0)


• close to half of the denominator (ex. 3/5: between 1/2 and 1, but closer to 1/2--> 1/2)


• almost the same as the denominator (ex. 7/8: it is between 1/2 and 1, but closer to 1--> 1 whole )

II. Use a range to estimate when you are working with quarters (equivalent to fourths)

A. 1/4 is exactly in the middle between 0 and 1/2 so we can use either 0 or 1/2 as estimates for 1/4.

ex. 3 1/4 + 2 7/8

3 1/4--> could be 3 or 3 1/2 for our estimate - use both to find the range

2 7/8 would become 3 for our estimate

3+3 = 6

3 1/2 + 3 = 6 1/2

The range is between 6 and 6 1/2, our estimate could 6 1/4 which is between 6 and 6 1/2

Chapter 9 Overview

Chapter 9 is a focus on adding and subtracting fractions. Here is a link from themathpage.com that explains most of the concepts we will be covering in Chapter 9.

8.5 Fractions, Decimals, and Percents (p.191-193)

I. Types of Decimals
A. Terminating Decimal: A fraction in decimal form that has zero has a remainder when you divide using long division.
ex: 1/2 = 0.5 = 0.50000000 (if you would try to keep dividing you would only get 00000... because there is nothing left to divide out)
B. Repeating Decimal A decimal that has a pattern of repeating numbers (or one number)- shown as a remainder when dividing--> use a horizontal line above repeating digits (called a vinculum)
ex: 1/9 = 0.1.... = 0.1
4/11 = 0.363636363636 = 0.36
**Try turning some of these fractions into decimal to find repeating patterns:
2/3
7/12
1/7
1/81

II. Turning common fractions into decimals
A. Divide the top number by the bottom number
Ex. 4/5 = 4÷ 5 = 0.8

III. Decimals into fractions
A. Decimals can be turned into percentages by moving the decimal point two places to the right (the the hundredths place)- this shows the value out of 100 equal parts (per cent=>per 100) making up the whole.
Ex: 1/4 = 1 ÷ 4 = 0.25 = 25%
Ex2: 1/3 = 1 ÷ 3 = 0.33...repeating = 33.3% (there should be a line over the 3 in the tenths place.

Try this activity from mathgoodies.com to see what you know
Here is an explanation from mathgoodies that might help too.

8.3 Compare and Order Fractions (<,>,or =)

I. Find a common denominator:
-when all fractions have a common denominator you can equally compare the parts of the whole because they are all the same size.

II. Tips
-The bigger the denominator (bottom number) the smaller the pieces of the whole
-The smaller the denominator (bottom number) the larger the pieces of the whole
-If the numerator and denominator are close together, you are more likely to have a larger value
-if the numerator and denominator are not close in value, you are likely to have a smaller part of the whole

III. Reminder
<> is greater than
= is equal to

Check out this video from mathplayground.com that explains how to compare and order fractions.

8.2 Mixed Numbers and Fractions

I. Improper Fraction: a fraction whose numerator is larger than the denominator
ex: 11/5


II. Mixed Number: A fraction with a value larger than a whole that is represented as a whole number in combination with a fraction


III. Rewrite improper fractions as whole or mixed number
ex:7/4 is equal to 1 wholes and 3/4 = 1 3/4 because it takes 4/4 to make one whole and you have 3 more fractional parts left.

IV. Convert mixed numbers to fractions: multiply the denominator by the whole number and then add the numerator.
3 x 8 = 24+1 = 25 --> the new numerator becomes 25

You are converting the whole parts into fractional parts. In this case, there are 3 fractional parts in every whole. So the 8 wholes make 24 parts, plus the one from the beginning is 25. The denominator will stay the same because the number of parts that make up the whole is not changing.

Print a certificate showing what you know after trying a few problems from visualfractions.com

8.1 Simplest Form (p.182-185)

I. Simplest form: when the numerator and denominator of a fraction only share “1” as a factor
II. Use division to reduce the terms in a fraction
-Divide the the numerator and denominator by a shared factor
-A fraction is reduced (in the smallest terms possible) when there are no shared factors other than one between the numerator and denominator)
Example: in the case of 6/8 , they share 2 as a factor. When you divide both 6 and 8 by 2 the fraction is reduced to 3/4 = simplest form because 3 and 4 do not share any factors other than 1.
6 ...3
- = -
8 ...4

FRACTION REVIEW:
Fraction: a number representing part of a whole: a ratio between two numbers --> 6 out of 8 = 6/8
numerator: the dividend – amount you start with;
denominator: divisor of a fraction – how many pieces the whole is divided into.

8.1 Equivalent Fractions (p.182-185)

I. Equivalent fractions: fraction showing the same amount of the whole that are equal in value and show the same part of the whole. They show the ratio of parts.

II. Common Factors: use common factors to change the numerator and denominator in the same way to find equivalent fractions and put fractions in simplest form.

Check out this helpful info. from themathpage.com for answers to common equivalent fractions questions.
Use this tool from Harcourt for finding factors to make equivalent fractions.
Try this game from LearningPlanet.com. It gets faster and faster every round :).

7.5 Prob. Solving: Make an Organized List (p.174-175)

When solving story problems lists can help you:

• recognize patterns
• find common multiples or factors
• solve multistep problems

7.4 Greatest Common Factor- GCF (P.170-173)

I. There are two methods for finding the greatest common factor:

• List all factors and find the largest
• multiply the common prime factors

A.List and find largest
1.First, list all of the factors of each number
2.Then, list the common factors and choose the largest one.

B.List the prime factors, then multiply the common prime factors.
1. Find the prime factors for the numbers in question
2.Recognize the common prime factors
3. Multiply them together to find the greatest common factor

Example for list all factors:
Find the GCF of 36 and 54.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The common factors of 36 and 54 are 1, 2, 3, 6, 9, 18

Although the numbers in bold are all common factors of both 36 and 54, 18 is the greatest common factor.

Example for multiplying common prime factors:
Let's use the same numbers, 36 and 54 again to find their greatest common multiple.
The prime factorization of 36 is 2 x 2 x 3 x 3
The prime factorization of 54 is 2 x 3 x 3 x 3


Notice that the prime factorizations of 36 and 54 both have one 2 and two 3s in common. So, we simply multiply these common prime factors to find the greatest common factor. Like this...

2 x 3 x 3 = 18

Both methods for finding the greatest common factor work!

-examples from helpwithfractions.com

7.4 Least Common Multiple (p.170-173) USING PRIME FACTORS

When working to find the LEAST COMMON MULTIPLE (LCM) with large or inconvenient numbers use the prime factors.

1.Find the prime factors for all numbers involved.

2.Count the number of times each prime number appears in each of the factorizations.

3.For each prime number, take the largest of these counts.

4.Write down that prime number as many times as you counted for it in step 3.

5.The least common multiple is the product of all the prime numbers written down.

Example: Find the least common multiple of 5, 6 and 15.
•Factor into primes
Prime factorization of 5 is 5
Prime factorization of 6 is 2 x 3
Prime factorization of 15 is 3 x 5
•Notice that the different primes are 2, 3 and 5.
•Now, we do Step #2 - Count the number of times each prime number appears in each of the factorizations...
The count of primes in 5 is one 5
The count of primes in 6 is one 2 and one 3
The count of primes in 15 is one 3 and one 5
•Step #3 - For each prime number, take the largest of these counts. So we have...
The largest count of 2s is one
The largest count of 3s is one
The largest count of 5s is one
•Step #4 - Since we now know the count of each prime number, you simply - write down that prime number as many times as you counted for it in step 2.
Here they are...
2, 3, 5
•Step #5 - The least common multiple is the product of all the prime numbers written down.
2 x 3 x 5 = 30

•Therefore, the least common multiple of 5, 6 and 15 is 30.

7.4 Least Common Multiple (p.170-173)

Least Common Multiple (LCM)
I. A multiple is the product of a whole number when multiplied by another whole number.
A. For example: 9x1=9,9x2=18,9x3=27,9x4=36, etc... so 9, 18, 27, 36, etc... are multiples of 9.

II. How to find the Least Common Multiples (LCM)
A. Make a list of multiples for the numbers in question
B. Continue the list until their is a common multiple between the two
C. Identify the lowest shared multiple between the shared numbers

III. Tips to finding the LCM
A. Start by making a list for the larger of the two values in question and use your math facts to check in you head if the smaller number is a factor of any of the multiples you are listing
B. Don't forget that the original number is a multiple (multiplied by 1)
C. If you continue your list you will find more factors, but not the "least"

Below is a video example from SchoolTube.com

7.3 Prime Factorization (p.168-169)

I. Use a factor tree to find the prime factors
A. Steps for prime factorization

1. Choose any two factors (other than the 1) for the number in question. Draw two lines, like branches, down from the original number and write the factors at the ends of the lines.
2. Check the numbers at the ends of the branches to see if they are prime or comoposite numbers. If they are prime, circle them to include as prime factors.
3. Draw two more branches out of all composite factors until you only have prime factors at the ends of the branches.

B. You will always end up with the same prime factors (not necessarily in the same order), regardless of the composite factors you start with.

-Below are two different examples of how you could find the prime factors for the number 700.

7.2 Prime and Composite Numbers

I Prime Number
- a whole number that only has two factors: 1 and itself

II. Composite Number
- a whole number that has at least three factors
- All even numbers, except for 2, are composite numbers

***0 and 1 are neither prime or composite

Scroll down on this site from AAAmath.com to take a quiz on prime and composite numbers

7.1 Divisibility

Divisibility Rules:

1. All numbers are divisible by 1
2. If the last digit is even (0,2,4,6,or8) it is divisble by 2
3. If the sum of the digits is divisible by 3, then so is the original number
4. If the last two digits form a number divisible by 4
5. If the last digit is 0 or 5
6. If the number is divisible by 2 and 3
7. Double the last digit and subtract it from the rest of the digits. (Repeat the process
   for larger numbers.) If you get a # that is divisible by 7, then so is the number.
8. If the last three digits form a number divisible by 8
9. If the sum of the digits is divisible by 9
10. If the last digit is 0

Test what you know by applying the divisibility rules for 10 practice numbers at vectorkids.com

Chapter 7 Video Tutorial

Here is a rather lengthy video that covers most of the materials in chapter 7.

6.6 Misleading Graphs (p.146-147)

This unit is practice for determining how conclusions about data can be influenced.

I.Pay attention to the question being asked in a survey:
-Does the question give preference to something (bias)?
-Do the words used influence the person being surveyed?

II.Examine graphs:
-Check the scale to see if it's been stretched or cut off?
-Is the scale consistent or does it change?

6.4-5 Box-and-Whisker Graphs (p.144-145)

I. Box-and-whisker graph
-Show how far apart and HOW EVENLY data are distributed

II. Parts of a box-and-whisker graph: 5 marks seperating data into 4 parts
A. Lower Extreme - the least value in the set of data - the point at the bottom whisker
B. Upper Extreme - the greatest value - the point at the top whisker
C. Median - find the median of the data - this is the middle line of the box
D. Lower quartile - the middle number between the median and the lower extreme - one side of the box
E. Upper quartile - the middle number between the median and the upper extreme - the other side of the box


Harcourt math site for a tool to make Box-and-Whisker Graphs

6.3 Stem-and-Leaf Plots & Histograms (p.140-142)

I.Stem-and-leaf plots
A. Stem is the first or more digits
B. Leaves show the ones digits

II.Histograms
A. Histograms show frequency in data bars for a range of intervals.
B. They are similar to bar graphs but there is no space between the bars.

Check out this link from Purplemath for a more in depth explaination of stem-and-leaf plots.

6.2 Make & Analyze Graphs (p.136-139)

I. Graphs are tools for visually comparing.
II. Pay attention to the following items when analyzing graphs
A. Title: It should cleary explain how to look at the data
B. Lables: describe the variables for both axis
C. Key: the tool that explains symbols
D. Scale: this can drastically change how values are represented

6.1 Make a Graph (p.134-135)

I. Use graphs to compare and show differences between values
II.All graphs should have the following
-Detailed title
-Consistent scale that is large enough for the range of data, but show that data uses almost the whole space when graphing.
-Label units of measurement(feet, inches, etc...) if applicable
-Labels for variables (label each axis)
-Labels for every value represented

5.6 Take a Survey

We will be taking surveys in class. Due to limited time we will have limited options for our survey. You can choose from the following topics:
-Favorite ice cream flavor
-Number of pets at home
-Favorite school subject

The population you will be surveying is your homeroom section.
Click here to see the rubric you will be graded on.

Here is an example:

5.5 Data and Conclusions (p.122-123)

This lesson is about analyzing data. It is important for you to know how information is organized in tables, charts and graphs. Here is a review from BBC on how different kinds of graphs are made and used.

Practice putting data into tables and graphs with the tool from BBC below:

The Harcourt math website has a quick test to see how well you know your stuff. Ride the roller coaster after you've mastered the activity.

5.4 Mean, Median and Mode (p. 118-121)

Listen and learn this song from Harcourt called "In a Nutshell"

I.Three measures of central tendency: Mean, Median, and Mode
1. Mean: usually called "the average"
- find the mean by adding up all the values and dividing by the total number of values
2. Median: the middle number
-find the median by putting the numbers in numerical order and then finding the middle value
3. Mode: the most common number
- find the mode by identifying which number is most common in a set of data. This is easiest if the numbers have been ordered.

5.3 Frequency Tables and Line Plots (p.114-117)

I. Frequency refers to how many times something occurs or happens

• Cumulative Frequency: the running total of the frequencies - add each part together as you go down the column to show a "running total" with each item
  
• Relative Frequency: the frequency of the category divided by the sum of the frequencies (often given as a percentage of the total or shown in a graph for comparison)

I. Ways to show data: Frequency Tables and Line Plots

• A Frequency Table lists the items being recorded and tells how many times each item occurs. Sometimes tally marks are used to count the frequency. Below are two seperate examples.


• A line plot shows the frequency of data on a number line by using an "x" or other symbol

Pictures from icoachmath.com

5.2 Bias in Surveys (p.112-113)

Bias: when certain groups from a population are not represented in the sample.
Unbiased: All individuals in the population have equal chances of being selected for the survey

5.1 Samples (p.110-111)

Sampling a few people in a group is a way to find out information about a group of people. It is difficult to accurately and fairly gather information without asking everyone.

Survey: a method of gathering information about a group
Population: everyone that makes up a specific group (for example - all teenagers)
Sample: a part of the group used to represent a population
Random Sample: sample in which every person in a population has an equal chance of being selected

For example: It would be unfair to only survey your friends, and use the data as a representative of all sixth graders. Just asking your friends, means they were NOT randomly selected.

4.7 Algebra: Decimal Expressions and Equations (p.94-95)

This lesson is practice for plagging in values into algebraic expressions and equations. Please review the notes for all of chapter 4 in preparation for our chapter test on Wednesday, October 21. There are lots of practice problems in the hard cover book on page 96 and 97, in addition to the practice test which will be collected on Wednesday.

4.6 Problem Solving: Interpret the Remainder (p.92-93)

When Solving word problems try the following strategies:
I. Try to make a picture of the situation in your head and draw or show important parts on paper in a way that organizes the information.
II. Make a model of the situation by using boxes or circles to represent groups and

Check out this game from Harcourt that helps you learn how to interpret the remainder.

Congratulations Honduras!

Estamos en Sudáfrica por la Copa Mundial! and....

NO SCHOOL THURSDAY, October 15!

Please be sure to complete your PW 19 homework that was going to be do tomorrow. We will review this material on Friday when we return to school.

The information for Friday's classwork will post tomorrow at 7:00AM as usual. If you are up for the challenge of working ahead on the story problems - check the newest post (4.6 Problem Solving: Interpret the Remainder) and test what you know on PW 20.

Enjoy the celebration!

4.5 Divide Decimals by Decimals (p. 88-91)

I. Follow these steps for dividing a decimal by a decimal
1. Make the divisor a whole number by moving the decimal point to the right (this is like multiplying by 10 for each place you need to move the decimal place over).
2. Move the decimal point in the dividend the same number of places to the right that you moved it in the divisor.
3. Divide like you normally divide by a whole number
4. When you find the quotient, move the decimal point directly up into your answer from the dividend.
5. Check by multiplying the answer by the divisor. It should equal the dividend.

Check out these examples from math.com on how to divide decimals by decimals

4.3-4.4 Divide Decimals by Whole Numbers

I. Use the following steps when Dividing a mixed number by a whole number
1. Divide as usual and be sure to KEEP THE PLACE VALUES LINED UP
2. Place a decimal point in the quotient (space for your answer) directly above where it is in the dividend (the value you are dividing)

Here's some info from Harcourt on how to divide decimals.

4.2 Multiply Decimals (p.80-83)

I. Multiply as if you were multiplying whole numbers (pretend there is no decimal while mulitplying)
II. Count the number of decimal places in the factors (the numbers you multiplied together)
III. Starting at the right of your answer, count over that number of spaces. That is where the decimal point will be placed.

Ex.
0.14 two spaces
x 7 zero space
----
0.98

Here's a link from Harcourt that explains how to multiply decimals.

4.1 Add and Subtract Decimals (p.76-79)

I. Steps for additin of subtracting decimals
1. Line up the decimal points - add zeros to make the same number of digits
2. Bring down the decimal point into the space for your answer.
3. Add or subtract the digits one place at a time - from right to left
4. Estimate to check (usually by rounding)

II. Ways to avoid mistakes:
1. Make sure you have the digits neatly written in columns with the place values correctly lined up (grid or graph paper is a good way to keep things organized)
2. Make sure you include the decimal point in your answer by bringing it directly down from the problem.
3. Regroup just like when you add and subtract whole numbers.


Check out these tutorials from Harcourt on adding decimals and subtracting decimals.

3.4 Decimals and Percents (p.68-69)

I. Percent means "per hundred"
A. Percentages are another way to talke about having a fraction of the whole or part of a whole
1. If you have all of something you have 100%
2. A percentage is like dividing a whole into 100 equal parts then showing how many of those parts you have out of the 100.

II. Converting a decimal to a percent.
1. Move the decimal point two places to the right
a. this is the same as multiplying the decimal by 100 -> turning the whole from 1 equal part into 100 equal parts
2. Put a percentage (%) symbol at the end of the number

III. Changing a percent into a decimal
1. Remove the percent symbol (%)
2. Move the decimal point two places to the left
a. this is the same as dividing by 100 - turning the whole from 100 parts into 1 part

Try this matching game from Harcourt math.

3.3 Estimate with Decimals (p.66-67)

I. Decimals are fractions of a whole - they have relatively small values
A. It's often a good strategy to round decimals to whole numbers
B. Larger numbers = focus on larger place values: In larger numbers, you can even ignore the decimals and focus on rounding to the tens, hundreds, or larger place values.

II. Methods for estimating decimals are the same as for whole numbers**
A. Rounding
B. Compatible Numbers:
C. Clustering
**To review how to do these check the notes from lesson 1.2

Listen to another teacher explain a few examples on this glog from Ms. Seymour. Scroll down to the examples and click on the play button on the left side to learn through some examples.

3.2 Problem Solving: Make a Table (p.64-65)

I. Tables help you organize information and find or use patterns to solve problems.
1. Make sure you understand what you are being asked to find
2. Organize (and order) the information in a table
3. Look for a pattern or sequence
4. Solve the problem
5. Check to make sure you are answering the original question

3.1 Represent, Compare, and Order Decimals (p.60-63)

I. Order Decimals by following these 3 steps
1. Line up the decimal points.
2. Add zeros to make the number size the same
3. Compare numbers from LEFT to RIGHT (Watch this tutorial)

II. Examples of different ways to read and write numbers:
Standard form: 0.392
Expanded form: 0.3 + 0.09 + O.oo2
Word form: three hundred ninety-two thousandths

Watch this tutorial from math6.org and then try this quiz to check what you know. When you think you've got it figured out, try out this game.

Find the hidden treasure in "Attack of the Place Value Pirates" (warning this game involves sword fighting with pirates and may not be suitable for all students)

October 1 and 2

We will have AM schedule on Thursday, October 1 and PM schedule for Friday, October 2
Homework:

• Bible Lesson 3 due Thursday
• Bible lesson 4 due Friday

6A will have math and Bible class on Thurday and Friday

6B and 6C will have a double class on Friday. We will be coving mostly Bible material during this time.

Class September 30

6B and 6C will have a double class period on Wednesday, September 30. The first half of the class we will be discussing the chapter 2 review and the homework from PW12. The second half of class we will take the chapter 2 test.

6A did their chapter 2 review today. They will take the test during our classtime tomorrow morning.

All students need to bring their Bible and Bible workbook with them to class on Wednesday.

September 29 - October 2 homework and schedule changes

Due to the 12:30PM release beginning Tuesday, September 29 we will have some changes in our schedule:
Tuesday: Day 4 morning schedule
Regular morning specials and homeroom class with no afternoon rotation classes
Wednesday: Day 4 modified afternoon schedule
Classtime with homeroom teacher and double class with rotation teachers
Thursday: Day 5 morning schedule
Regular morning specials and homeroom class with no afternoon rotation classes
Friday: Day 5 modified afternoon schedule
Classtime with homeroom teacher and double class with rotation teachers

• PLAN TO TAKE YOUR CHAPTER 2 MATH TEST ON WEDNESDAY, Sept. 30. 6B and 6C will have a double class that day and review session before the test to talk about lesson 2.7 and practice ch. 2 concepts. 6A will have their review session on Tuesday.
• PW 11 is due on Tuesday and PW12 is due Wednesday - you may turn them in both tomorrow if you would like
• You do not need to start on Bible lesson 3 unless school is canceled Tuesday or Wednesday
• Make sure you have your Bible workbook at school on Wednesday to work on Lesson 3 after the test
• Please review the lessons on the blog during your extra time at home to help yourself prepare for the upcoming test.
• Complete the chapter 2 review on your own and be prepared to discuss it and turn it in on Wednesday before the test.

If school is canceled the schedule will shift accordingly.

Ch. 2 Test Prep

Complete the Ch. 2 practice test at home. Use the Ch. 2 notes, games, and tutorials from the blog to help you. The test is has been moved to Wednesday, September 30. to accomodate changes in schedule due to the 12:30 release time.

2.7 Problem Solving: Multiple Steps (p.52-53)

I.To solve a multi step problem, break it down into single steps.
1. Organize the important information (don't use unnecessary info).
2. Follow the steps in the appropriate order.
3. Pay attention to the order of operations within each step.
4.Make sure you are answering the question being asked.
5. Use a label when writing your answer.

Try these activities from Math Playground to check your understanding. You can also watch these videos that explain how to do some different kinds of words problems.

• Complete PW12 in your Practice Workbook

2.6 Order of Operations (p.48-51)

I. Follow this order for evaluating expressions with more than one operation.
1. First, perform operations in parentheses.
2. Clear exponents by replacing with the real value.
3. Multiply and divide, working from left to right.
4. Add and subtract, from left to right.

Ways to Remember

• Parentheses - Exponents - Multiply and Divide - Add and Subtract
  P-E-(MD)-(AS) or "PEMDAS "
• Please (parentheses) Excuse (exponents)My Dear (multiply and divide) Aunt Sally (add and subtract)
  
  Example:
  285+93÷(3-2) x 3 x4²
  285+93÷ 1 x 3 x4² parentheses
  285+93÷1x 3 x16 exponents
  285+93÷1 x3x16 multiply and divide from left to right
  93 x3= 279
  279 x 16 = 4464
  285 + 4464 = 4749 add and subtract
  
  285+93÷(3-2) x 3 x4² =4749
  

For a description of how order of operations works try this link that includes an explanation and practice problems from mathgoodies.com

Here is a game from Harcourt to see how well you know your operations.
Play Rags to Riches to test what you know.

Take this Quiz from math6.org

2.5 Exponents (p.46-47)

I. Exponent: a symbol of repeated multiplication
A. An exponent shows how many times a number is multiplied by itself.
B. Exponent can also be called a "power"

II. Base: the number being multiplied (used as a factor) when working with exponents.
Examples:
The exponent "2" is telling us to multiply the base "4" "2" times. 4x4 =16
III. Rules:
A. Using the power of 1, makes the value equal to the base (original) number
B. Using "0" power of any number, expcept zero, is defined to be 1

IV. Reading exponents: aⁿ or a^n

• a raised to the n-th power,
• a raised to the power [of] n or possibly a raised to the exponent [of] n,
• a to the n-th power or a to the power [of] n,
• a to the n.

A. Some exponents have their own pronunciation: for example, a^2 is usually read as a squared and a^3 as a cubed.

Here is a brief description of exponents from About.com.
Check what you know on this short quiz and get immediate feedback from regentsprep.org.

September 8-21 Activities

Please take advantage of this time and work on your math facts using one of the following tools

• Math Magician
• Academic Skill Builder racing games
• Math Facts Cafe: Really good for 2 and 3 digit mental math facts practice
• Kids Games facts practice
• WildMath.com

This skill is very important for your future success with math. Please challenge yourself to improve your facts knowledge regardless of how well you think you already know them. Pros can still improve their 2 and 3 digit mental math flashcards at Math Facts Cafe.

There will be a facts test the week we get back :) Enjoy!

2.4 Mental Math: Use the Properties (p.42-45)

Lesson 2.4 is practice for applying the properties knowledge we learned in lesson 2.3. Today we learned about one new strategy called compensation

I. Compensation
A. Used for addition and subtraction
1. For addition: change one number to a multiple of 10 and then adjust the other number by
doing the opposite to keep the balance.
Example: 44 +57 = (44 +6) +(57 - 6) = 50 + 51 = 101
Because 50 + 51 is easier to add together.

2. For subtraction: change each number in the same way, so that the last number being
subtracted is a multiple of 10 that ends in 0.
Example: 128 - 56 = (128 +4) - (56 +4) = 132 - 60 = 72
II. Divide Mentally
A. Divide a number by breaking it into smaller,more managable parts.
Example: 396 ÷ 4
396 = 360 + 36 (break it into parts that can be divided by 4)
360 ÷ 4 = 90 and 36 ÷ 4 = 9 (mentally divide the parts by 4)
90 + 9 = 99
So, 396 ÷ 4 = 99.

2.3 Algebra Properties (p.40-41)

Click on the the names of each property to see them explained using models at europa.com
I. Commmutative Property: A property of addition and multiplication that states that if the ORDER of addends or factors is CHANGED, THE SUM OR PRODUCT STAYS THE SAME.

• Addition: 3+9 = 12 = 9 + 3
• Multiplication: 8 x 3 = 24 = 3 x 8
• Watch this video from eHow that explains the commutative property.

II. Associative Property: When adding or multiplying three or more numbers, it doesn't matter the order or how you group your addends or factors because it will not change the sum or product (answer) - it's a lot like the commutative property, but involves more numbers.

• Addition: (8 + 5) + 4 = 8 + (5 + 4) = 17
• Multiplication: (6 x 7) x 2 = 6 x (7 x 2) = 84

III. Distributive Property: When multiplying a sum by a number it is the same as multiplying each addend by the number and then adding the products.

• 4 x (7 +3) = (4 x 7) + (4 x 3) = 40

IV. Identity Property of Addition: the sum of any number and zero is that number.

• 3 + 0 = 3
• 0 + 5 = 5

V. Identity Property of Multiplication: the product of any number and 1 is that number.

• 15 x 1 = 15
• 1 x 9 = 9

Test what you know with this Jeopary style game on Quia.com

2.2 Algebra Mental Math and Equations (p.38-39)

I. Equation: is a statement showing that two quantities are equal (all equations have an equal sign). Examples:
6+7=13
k-3=1
a+b=11

II. Solution: find the solution is finding the value of a variable (a letter or symbol representing a number) in an equation. For example in the following equation:
16=c+9
The solution is c=7

Watch this Explanation of Equations from Harcourt math.

2.1 Algebra: Expressions (p.36-37)

Expressions
--Expressions are combinations of mathematical symbols that express a value.
I. Numerical Expression: an expression that includes only numbers and operations
Examples: 47-38 30+12+9
II. Algebraic Expression: an expression that includes a variable.
Examples: k-3 5+n 6x5xb
A. Variable: A variable is a letter or symbol that can stand for one or more numbers.
Examples: the letters "k" "n" and "b" from the algebraic expressions above are varialbes
B. Evaluate: replacing the variable with a number and then finding the value of the express
a + 150, for a = 8
replace a with 8
a + 150
8 + 150 add
158 : the value of the algebraic expression "a + 150, for a = 8" is 158

Here is an external linke with an introduction to algebra

1.5 Predict and Test (p.28-29)

Predict and Test
I. A strategy for finding an answer by using your number sense (knowledge of math facts and relationships between numbers) to predict an answer.

II. Steps for predicting and testing
A. Figure out what you are being asked to find
B. Pay attention to ALL the information in the problem
C. Try to solve the problem by using your predicted answer
D. Test and adjust your prediction if you're incorrect
E. If you are unsuccessful try a different strategy for solving.

Try some practice problems on this page. You can print it out if you want.
Try more practice problems with this game from mathplayground.com. Get five questions right and you can shoot some hoops.

1.4 Multiplication and Division

Here is a link to our text book's website that explains HOW TO MULTIPLY 2 DIGIT NUMBERS - or in Espanol

Here is a link to our text book's website that explains HOW TO DIVIDED 3 DIGIT NUMBERS. or in Espanol.

Additionally, if you are having trouble with dividing, check out this link with an explanation on how to do long division.

Check your understanding on these quizzes to see how you are doing with multiplication and division.

1.3 Addition and Subtraction (p.22-23)

Today's lesson was review of adding and subtracting large numbers and estimating to check our answers. If you are having trouble remember how to add and subtract you can read about it below.
Click here for help with Addition and Subtraction

If you want to practice some addition and subtraction games try these links.
Math Baseball
Mathcar Racing

1.2 Estimate with Whole Numbers (p.18-21)

• An estimate is a value close to the exact amount
• An estimate should be easier to find than an exact number
• An estimate is quick way to get an idea of about "how much"

I. Ways to Estimate

1. Estimate by ROUNDING: Choose a place to round to-- use the digit to right of the chosen place-- if the digit to the right is 5 or more "raise the score"-- if the digit to the right is 4 or less "let it rest"--numbers to the right of the place being rounded become zeros. If you are have trouble rounding watch the video at this from Math Playgroud
   


2. Estimate by CLUSTERING (when adding): When adding values that are close together, use one number to represent the values and then multiply that number by the quantity of values that have been clustered together.


3. Estimate by using CONVENIENT NUMBERS (when dividing): Use a value close to the original number that can more easily be divided to get an estimate.

II. Types of Estimates

1. Underestimating: When the estimate is less than the exact number - happens when you turn the original number(s) into a smaller value.
2. Overestimating: When the estimate is more than the exact number - happens when you turn the original number(s) into a larger value.

Here is Wikianswers

Practice what you learned about estimation at this site

1.1 Place Value ( p.16-17)

I. The Value of a digit is determined by its position in a number
Ex. 379,421: the value of the 7 is 7 x 10,000
**The of power of zero: 0 is a place holder

II. Place Value Chart
A. Organized into “Periods”
1. A Period is three (3) places
2. Periods are separated by commas (,)
a. When you get to a comma you say the name of the period








III. Writing Numbers
A. Standard Form: 4,927
B. Expanded Form: 4,000 + 900 + 20 + 7 = 4,927
C. Word Form: four thousand, nine hundred twenty-seven

Practice what you learned about place value at Funbrain