Number Sense Class Notes

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 A B C D E F G H I J K L M N O Algebra Puzzles Divisibility RulesFOOFrames Greatest Common Factor Interpreting Variable Directions Least Common Multiple Logic Grids The Magnitude of NumbersOne-Step Equations P Q R S T U V W X Y Z Patterns & AlgebraPlace Value ChartPrime FactorizationPrime NumbersProperties Shape EquationsSquare Numbers & Square Roots VariablesVariable ExpressionsVariable Substitution

Algebra Puzzles-
Logic Grids, Shape Equations , & Weight Scales.  Just another way to look at variables in the world of algebra.  Make sure you can make a connection:
• between variable expressions and input output tables.
• between input output tables and the coordinate grid.
• between an expression and an equation.
• and finally, how logic grids, shape equations and weight scales relate to an equation.
And, isn't it so much better to do algebra with shapes than with numbers!?!?!?

Divisibility Rules-Six coaches have 42 girls that signed up to play intramural basketball this year.  Can each team have the same number of girls?  Decide if 42 is divisible by 6, but don't divide!!! What do you mean don't divide?  There are Divisibility Rules you can use to determine if a number can be divided by a number without leaving a remainder.

Fundamental Order of Operations (FOO)-We use FOO so that everyone in the world has the same set of "rules" when doing math--so we all get the same answers on the stock market, at the deli counter at the grocery store, and when we vote on American Idol!  Here are FOO Class Notes.

Greatest Common Factor-Otherwise known as "GCF," find the greatest common factor of two or more numbers using subsequent division, aka "monkey division."  The GCF of two numbers is the largest number that divides evenly into both numbers with no remainder.  Remember, factors can be SMALLER numbers, so don't be fooled by the word GREATEST.  Here are GCF Class Notes

Try some GCF practice problems as well.

Least Common Multiple-The least common multiple (LCM) of two numbers is the smallest number that the two given numbers divide into evenly with no remainder.  Use subsequent division to find the LCM of two or more numbers.  Remember, multiples are LARGER numbers, so don't be fooled by the word LEAST.  Here are Least Common Multiple Class Notes.

Try some LCM (and GCF) practice problems as well.
Logic Grids-Here is more algebraic thinking!  Try to solve these online logic grids.  Remember, find the value of each of the three objects presented in the puzzle. The numbers given represent the sum of the objects in each row or column. Sometimes, only one object will appear in a row or column. That makes the puzzle easier to solve. Other times, you will have to look for relationships among the objects.

The Magnitude of Numbers
• How big are the numbers in our world?  Here are a few examples...
• Email examples you find to lgordon@livingston.org

 FINANCE What is our National Debt?  The United States government debt, commonly called the "public debt" or the "national debt", is the amount of money owed by the Federal government of the United States to holders of U.S. debt instruments. How much is it?   As of 10/2011, it is approximately \$14,800,000,000,000dollars! (more than 14 trillion) Source:  http://www.usdebtclock.org/ SCIENCE:  ASTRONOMY The Milky Way, or simply the Galaxy, is the galaxy in which the Solar Systemis located. It is a barred spiral galaxy that is part of the Local Groupof galaxies. It is one of billions of galaxies in the observable universe. The oldest known star in the Milky Way Galaxy is approximately 13,400,000,000,000 years old.  (13.4 trillion years) Source:  http://www.nasa.gov/ New Cell COMMUNICATIONS Sprint, a global communications company, claims there are over 250,000,000 (250 million) mobile phones in the United States. New Cell  How many years will it take John Parks to call 250,000,000 people? New Cell John Parks, a fictitious Sprint customer, is so happy with the cost of his monthly cell phone plan, he is planning on calling every mobile phone in the country. See for yourself:  Go to youtube.com and look-up a sprint commercial for the NOW NETWORK. Sprint continues to take a statistics-based approach to advertisting. See how many numbers you can follow in these two TV Spots. Source: YouTube.com How many...?1. ...people are on the NOW network?2. ...couples are breaking up?a. ...by email?b. ...by phone?c. ...by text message?3. ...people are streaming pandora on a bus?4. ...friends found their friends on looped?

One-Step Equations-This is where all our work with FOO, PEMDAS, variables, algebra puzzles, frames, shape equations, logic grids and weight scales comes together.  All that work to get us to this point:  your goal is to isolate the variable and use inverse operations to determine the value of the variable.

Have a look at the Solve One-Step Equations Class Notes to get started.

Next, give different values to your x variable--both positive and negative--and put those values in an input/output table.  Finally, plot your points on a coordinate grid

I think you've done a pretty thorough job of representing variables in "various" ways!!!

Patterns & Algebra-

"Math is a science of pattern and order."

John Van de Walle, 2006

Patterns repeat.  That's why they are patterns.  They allow us to make predictions in all aspects of our lives.

Did you know...? that patterns are everywhere!  Just open up your eyes and see differently!
• the timing of traffic lights, the growth structure of tree branches, the facade of buildings in architectue, wallpaper, fabric, floor tile, in medicine, daily routines at home.

...are all examples of numerical and geometric patterns in your life.

Here are some words you can get to know and ways to recognize patterns that may help you:

• If you become a Pattern Detective, you'll be able to recognize similar processes around you.  You'll be able to count without counting by looking for relationships among the items you're analyzing.
• There are steps you can follow to determine a pattern:

Patterns can be represented in a sequence, in a table, on a graph and in an equation--that's how they tie themselves into algebra.  Once you know how the pattern repeats, you can generalize them and determine any term in the sequence.

Here are some examples of patterns that student created in a three-dimensional format of a mobile and presented to our class. Enjoy!

Making Predictions

Pattern Mobiles:

Place Value Chart-What happens when you move to the left on the place value chart?  To the right?  What is 10 to the zero power? To the 4th power...?  Learn more here with this Place Value Chart

Prime Factorization-Prime factorization is a way to represent a number as the product of prime factors ONLY.  It also helps us hunt down the number of factors a composite number has.  We use subsequent division to find the prime factorization because factor trees are "so yesterday...".  Here are Prime Factorization Class Notes.

Prime Numbers-If you can sing "Jingle Bells" you can learn the 25 prime numbers between 1 and 100.  Here are the prime numbers in their own Prime Number Song to the tune of "Jingle Bells,"--one of the few secular songs written about winter.  Songs not your thing?  Try this version of Prime Numbers Between 1 and 100, it might be better for you.  Here are some Prime Number Class Notes for you to learn more.

Properties-We use properties to make computing easier!!!  Here are Properties Class Notes.

Shape Equations-(also called "Algebra Puzzles" or "Frames")  Just another way to replace variables with numbers in systems of equations--this time by using shapes!  You still have to:
• identify the relationships among the variables and
• use substitution as a method for solving systems of equations.
Plus, you'll be making inferences about how shapes (variables) are different...are the same...which equations should you deal with first...and "plug it in" to check your work!!!
Here are:

• Shape Equation/Frames/Algebra Puzzle:

Square Numbers and Square Roots-Represent numbers by using exponents.  The exponent tells us how many times to use the base as a factor.  Memorize your Square Numbers (and square roots) up to 20 today!

Here's a fun fortune teller for the important squares up to 20 that you didn't learn in 5th grade...  Squares Fortune TellerInstructions.

Variables, Variable Expressions, Interpreting Variable Directions, & Variable Substitution-Variables are letters or symbols that represent a quantity that can change or vary.  They are typically lower case.  Learn how to translate between words and math.  You thought Spanish, Italian, French, and Chinese were world languages...?  Wait until you see how you can translate math into words.  Click here for Variables Class Notes.