Math Notes: Multiplying by 10s

We are working on multiplying by powers of 10 (10, 100, 1000, etc.) and multiplying by multiples of 10 (20, 320, etc.), especially using some "shortcuts" or mental math.

Click HERE to access a PDF of today's math notes.

Math Notes: Circumference

You can view circumference notes HERE (PDF download).

Math Notes: Dividing Fractions

Click HERE for a PDF explaining how to divide fractions. Remember: keep, change, flip!

Math Notes: Multiplying Mixed Numbers

Click HERE for the PDF of math notes.

Math Notes: Mulitplying Fractions

Click HERE for a PDF of how to multiply fractions.

Math Notes: Subtracting Mixed Numbers (with Regrouping)

You may have heard that our classroom has received a Promethean interactive board (AKA a "smart" board). We are still learning how to use it! Rather than take a photo of the notes, I can actually save what the students see on the screen. (Unfortunately my handwriting is even worse on this board, but I will work to get better.) Once I save the screen shot, I can then have to turn it to a PDF file. It means extra steps for all of us, but here they are: Click HERE for a PDF file of these math notes.

Math Notes: Order of Operations (a.k.a. PEMDAS)

When you have a math problem with multiple operations (+,-,x,/) in the same problem, you MUST follow the order of operations. There is a well-known mnemonic device that parents and grandparents might even remember from their school days: Please Excuse My Dear Aunt Sally. Some people remember this as "PEMDAS." It stands for the order you should do your math operations:
Please = parentheses
Excuse = exponents
My = multiply*
Dear = divide*
Aunt = add*
Sally = subtract*

*What most students forget is that when you get to the multiply/divide operations, you must work from LEFT to RIGHT (so you could divide before you multiply). This also applies to the addition/subtraction operations. When you've done everything else, then you add and subtract from LEFT to RIGHT.

For example: Solve (7 x 9) - 5 x 4 + 7.
A. Start with the parentheses: (7 x 9) = 54
The problem is now 54 - 5 x 4 + 7.
B. Check for exponents. There are none so move on.
C. Multiply or divide from left to right. Since 5 x 4 is 20, the problem is now 54 - 20 + 7.
D. Add or subtract from left to right. 54 - 20 = 34. Add 7. The final answer is 41.

Math Notes: Mr. DL

Some students struggle with moving the decimal when multiplying or dividing. Mr. DL can help! Simply multiply right and divide left.

In class, we also practice the "Cupid Shuffle":
To the right, to the right, to the right...
To the left, to the left, to the left...

BUT they sometimes forget which one is multiplication and which one is division. Mr. DL to the rescue!

Math Notes: Mixed Numbers Converted to Improper Fractions

To rewrite a mixed number (a whole number with a fraction) into an improper fraction, begin by multiplying the denominator times the whole number and then adding the numerator. The number you get is the equivalent improper fraction's numerator. You keep the same denominator. (I call this "swooshing" for lack of a better term.)

Math Notes: Simplifying Improper Fractions (AKA Improper Fractions Converted to Mixed Numbers)

Remember that the fraction bar means "divide."

Rewrite the improper fraction as a division problem. (It is "top heavy" so it falls over. Timber!) The numerator goes "in the house," and the denominator is the divisor.

Divide.

The remainder is the new numerator over the same divisor. Simply that fraction if possible.

Math Notes: Reciprocals

To get a reciprocal of a fraction, turn it upside down!

A fraction times its reciprocal equals one.

3/4 x 4/3 = 1

Math Notes: Proper and Improper Fractions

A proper fraction has a numerator that is LESS THAN its denominator.

An improper fraction has a numerator that is EQUAL TO or GREAT THAN its denominator.

NEW FEATURE: Math Notes

Ever get stuck on your 5th grade math homework? If you take your math notes home, that should really help! I am going to start a new feature of posting photos of some of our math notes here on the blog. You will be able to find them easily by finding the label list on the sidebar and clicking on "math notes." Please let me know what you think of them! It would be really nice to get some feedback from time to time. I know you're lurking! Thanks!