I'm PRIME!

Prime Numbers!

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Prime numbers are an infinite set of whole numbers that are only divisible by 1 and the number itself. (example: 13/1=13 and 13/13=1 There are no other divisors).

Some reminders about prime numbers are:

*Number 1 is not a prime number but rather a natural number.

*Any even number that is greater than 2 is not prime. 

Sound easy enough to teach? Well, the ability to know what the divisors are can be complicated. A student needs to have the skill of factorization and division well understood in order to find those prime numbers. 

This rap is a great way to get them to remember as well. Music has an amazing way of teaching concepts and being able to recall easily. After watching this video, ask students to prepare their own rap. By using the information they know, they will recall it well into the future and not just for a test. 

Prime Numbers Rap Typography 

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Have students rediscover factors for reinforcement if needed. This is a fun game similar to "Who Wants to Be a Millionaire" that will be an effective way to review instead of just reviewing on the board. 

Factors Millionaire Game

Depending on the grade, have students find prime numbers up to a certain number (for example, 4th graders can get to the 300's easily since they know their factors and division quite well, whereas 3rd grade can perhaps get to the 100's).

Prime Numbers Game

Fruit Shoot-Prime and Composite

Make Fractions Fun!

Make Fractions Fun!

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Fractions can be another very intimidating concept in math. When reinforcing the concept, it is important to make connections with real life. One very simple connection is that of pizza. A lesson on fractions and pizza will be more ingrained in their memory. Below you will find a video on this same topic. A teacher created a very hands-on lesson that integrates both math and language. Take a look...







His video is entitled, My Fraction Pizza: Integrating Mathematics and Literacy
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Once students have the concept of wholes, halves, quarters, equal parts, etc... the possibilities are endless. His idea of constructing a pizza and being able to write about it descriptively and then passing it on after deconstructing the pizza is fabulous. The students have to make sure not only their math is right on but their writing as well. Now the job of each student is to read and recreate their classmate's pizza. Try it out! 

You could even use cookies with different ingredients as a variation on this assignment. Possibilities include chocolate chips, M&M's, white chocolate chips, sprinkles, or anything kids like in cookies that are countable once made. A suggestion would be not to mix them in but to place them on top so they take on the same idea as pizza ingredients. 

Other fraction games are listed below:

Sheppard Software has many fraction games. Just scroll down to the section on fractions. 

Bridge Builders

Order of Operations

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When students see so many symbols on math problems, it can be overwhelming. Getting a grasp on number sense is first but then figuring out how they can be used to add, subtract, multiply and divide is a feat within itself. Now add parentheses and it may be just too much clutter for some. 

So, how can we help students remember the order of operations? One strategy that has been around for a while is to remember PEMDAS. PEMDAS is an acronym for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction (in that respective order). Students need to then be reminded to work left to right. Many people use the acronym Please Excuse My Dear Aunt Sally.

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Here's an example: 7 - 9 x 3 + 4=
If you start from left to right without PEMDAS you will find the answer to be 2.

With PEMDAS, you will find the answer to be -16. 

Start with 9 x 3=27. Then, 7-27= -20 + 4=16.
The order of operations must be in place to find the correct answer.


Another example: 7 x (4+3) =
Start with 4+3 as it is in parentheses. Answer 7. Now, 7 x 7 = 49. 
Without PEMDAS and working from left to right, you would get 31. A big difference!

Here's a fun video!

PEMDAS - Order of Operations RAP

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Try out these interactive games as well:
Order of Operations Millionaire Game
Fun Brain (various levels of difficulty available)

Cinderella Rule of Rounding

Rounding is Magical!

Have you ever wondered how rounding can be made magical? One strategy I like to use with my students (and is used by many) is the Cinderella Rule of Rounding. The Cinderella Rule of Rounding gives characters to numbers and tells a story in the process. Here’s an example:

Say you are rounding to the nearest hundred in 7,865.

*The number you are rounding to will become Cinderella. Therefore the eight represents Cinderella. Underline the 8.

7, 8  6 5 rounds to 7,900

*Look at the digit to the immediate right of Cinderella. That digit represents the fairy godmother. If the digit is 5 or greater, the fairy godmother has power and can change Cinderella into a new gown (POOF!) for the ball. In this case the 6 rounds the 8 to a 9. Therefore Cinderella will round up.  7,900

*If, however, the digit is 4 or less, the fairy godmother does not have power and Cinderella cannot change her dress for the ball. She will remain the same. In this case, 3 is less than 5 so the 8 stays the same.

7, 8  3 5 rounds to 7,800

*The fairy godmother then disappears leaving only zeros after Cinderella.

*If there are digits to the left of Cinderella, they are her loyal friends (the birds, mice, etc…) and they stay the same.

Try this with your students and hopefully this strategy will click with some and they will find success.  

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Mean, Median, Mode, and Range!

Mean, Median, Mode and Range

Many times when studying mean, median, mode and range, students get confused, however if we can help them make connections with the meaning of the word or with a way to remember what it is asking, they are bound to be successful. The more repetition, the better.

Let's start with mean. Mean sounds much like the word mean when referring to the way the students may think of you for making them do this! Remind them that you are not mean, but sometimes the process may seem that way since it takes a while. Add all the numbers in the data set up and divide them by the number of numbers in the data set.
Example:

31, 24, 26, 33, 33, 29, 27

31+24+26+33+33+29+27=203        203/7=29      29 is the mean.

Moving on to median...Have students line the numbers up in order from least to greatest. Then the clue is to find the middle, which is similar to the word medium, which is often a middle size.
Example:

24,26,27,29,31,33,33       29 is the median. 

If however you have an even number of numbers, remind students to add the two middle numbers and divide by 2 to find the median.

Range is the difference between the largest and smallest values in the data set. Looking at the numbers in the data set, find the largest and smallest and subtract to find the difference. In this case it is: 33-24= 9
I like to remind students that a range is a big open area. So, the numbers stretch from smallest to largest.

Finally, finding mode is probably the easiest. Mode is the "moda" (fashion in Spanish) and the number that appears most often (number of highest frequency). Not every data set has a mode. In this case it does. The mode is 33 since it is repeated. If there is a 24, 24, 33, 33, 33. The mode would be 33 since it is repeated most often.

Here are a couple videos related to finding mean, median, and mode. Remember, make it fun!

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Numbers and Origins

Place Value and Making Sense….A few thoughts and ideas

Often times students become robots with the place value system. Many may memorize the theory but really don’t understand the underlying properties of the theory. So, how do we help them make sense of it all? Our fundamental goal is for them to understand why there are two ones written side by side in the number eleven. The fact that one of the 1’s is a completely different value than the other is what they need to truly understand. In order to do so, let’s take a look at the history of numeric systems.

Let’s travel to what is today known as northern Central America. Who lived there? Have students analyze the symbols of the Mayan numeration system and decide why each number means what it does. This is a great opportunity for web quests and research to enrich their geography skills.  Students are very intrigued by puzzles and in essence that is exactly the skill they are practicing. They are becoming detectives as they unravel the number behind the symbols and analyze their meaning, the thought behind them and their equivalent to the numeration system they use every day all while creating a deeper understanding for place value.

Mayan Numeration System

Mayan Explanation

Mayan history

Mayan Math Unit


Continue your travels to Egypt where you can continue to unravel the meaning behind the place value in that system.

Egyptian Numeration System

Egyptian Explanation

Interactive game

Last but not least, stop by Ancient Babylon. Have the students play with this system and continue to reinforce the concept of place value. Make comparisons and contrast ideas.

Babylonian Numerals

Babylonian Numerals Explanation

Babylonian History

Class activity


In case students need a review along the way, have them check out the Hindu-Arabic system we are accustomed to. Challenge them to find the history behind the system we use in the USA today.

Hindu Arabic System

Explanation

Place Value Interactive Game

Artists and Mathematicians 

Throughout this journey, students have discovered new ways interpret numbers, enriched their prior knowledge and gained insight into geography, history and how it plays a role in place value. Challenge them to create their own numeration system. Which symbols would they use? How would they stay consistent in their concept? How user friendly would it be? The possibilities are endless.