Fractions with the Magician

Fractions are SCAREY to left brained kids (or visual learners as I call them).  But...if you can convince them that they are really MAGIC tricks, math and algebra can be FUN. 

For example,  when you want to eliminate a fraction--or magically make it disappear--just invert it.  I tell the kids, "Just stand it on its head and make it multiply."  Use the example of the fraction     4. 
                         8
 If you stand it on its head or invert it, you end up with 8. 
                                                                                4



 Then multiply these two fractions. 4   x   8 
                                                   8        4       

 Tell the kids that the multiplication sign is like the magician's magic wand. They can cross multiply and cancel the fours, then cross mulitply again and cross out the eights, resulting in the single RABBIT named ONE.

Mathematically,  if you multiplied the numerators and denominators, the result would be
 32 
 32   which equals ONE.   


In an algebraic equation this concept comes in really handy.  Remind the students that when solving an equation, make sure the variables remain on the left hand side of the equation.  (See my Tagalong blog,)  Remind the students that whatever the magician does to one side of an equation, he must do the same thing to the other side of the equation.

                 Example:  3x = 15
                       5

Using the new trick,  invert the fraction and multiply on both sides of the equation.

                 Step one:           5 . 3  x = 15 . 5
                                          3    5         1   3

                  The inverted fraction multiplied by 3/5 results in 1x.


                                          
                 Step two:            1x = 15 . 5
                                                           1    3
   
          Always place a whole number over one to make it a fraction.  You can explain cross canelling here, or leave it as it is in step three.


                 Step three:        multiply right side of the equation. 

                                                 x = 75  = 25
                                          3

 

Baby Game

  I researched information on the internet from baby experts.  I came up with the following true false game for a baby shower.  Most of the party goers could not guess the true answer, so this was fun.  You could even have just the mom-to-be take the test and others could bet on whether she'll get them right.

1. You should feed a baby cereal before it is 3 months old.  (False)
2. You can eliminate the night feeding at 8 weeks. (True)
3.  It is okay to let a baby sleep on a couch.  (False)
4. Put the baby in his crib while he's still drowzy, but not asleep. (True)
5. Long naps for a baby in the daytime are okay. (False)
6. It really is okay for babies to sleep on their stomachs. (False)
7. It is better to have a new baby share a room with you. (True)
8.  It is okay to have a plush toy in a crib. (False)
9. All newborns, in the first 5 months, experience unsoothable crying jags. (True)
10. At six months, a baby can work an activity center. (True)
11. When a baby throws things, it is a good thing. (True)
12. Use wipes with alcohol to clean the baby. (False)
13. Reasearch has shown to not use petroleum jelly for cleaning a baby. (False)
14.  Toddlers can drown in toilets. (True)
15. Medical visits are scheduled at the following months: 1,2, 4, 6, 9, 12, 15, and 18. (True)
16.Diaper rash can be caused by too vigorous cleaning. (True)
17.  You can give motrin to children under one. (False)
18.  When a baby has diarrhea, give it plain water to hydrate. (False)
19. It's okay to cuddle and sing to a baby during the middle of the night feeding. (False)
20. You can give an infant under 6 months 4-6 oz of juice. (False)

Algebra No Fruit Salad in Equations

  In my imaginary Land of Quadrants (algebra), I tell the visual students that the aliens sometimes take on the forms of fruits and vegetables.  When they see a term such as:

                               2t + 3b + 5t + 6c + 2b - 3c

they need to be reminded that in the L.O.Q. these people do not mix (add) together.  There is NO FRUIT SALAD in this alien land.  They may, however, combine, like variables.

If they look at the variables in the above term, the bs are bananas.  The t is a tomato.  The c's are carrots.  I tell the students to assign shapes to each of the fruits (variables) in the terms to be simplified.    I would use a circle for the tomatoes, a rectangle for the bananas, and a triangle for the carrots.

  The top line of shapes above is the original term in shapes.  The bottom row is the answer in simplified term.  Remind students that when drawing the shapes, the sign goes with the variable (always) and into the shape itself.

Peanut Sauce

 I started making this sauce when we stopped eating processed foods.  We make our own chicken nuggets and dip them in this sauce.  Yum !

                   

2 Tblsp peanut butter          

2 Tblsp soy sauce

2 cloves minced garlic                                                                              

½ cup water                

2 Tblsp brown sugar

1 lemon

Bring water, lemon juice, soy sauce, and garlic to a low boil.  Add peanut butter and brown sugar.  If you have an emersion blender, use it to blend while boiling.  Keep over low heat until it thickens.

I have used this as both a dipping sauce while thick, and as a coating for pasta to make peanut noodles, just add shredded cooked chicken.

Pumpkin Roll Cake

• 6 eggs separated
• 1/4 tsp salt
• 1/2 cup sugar
• 1 tsp vanilla
• 1/2 cup flour (plain cake roll) or 1/2 cup spice cake mix

Preheat over to 400 degrees.  Spray cookie sheet with sides (jelly roll pans) with flour/grease mixture.  Lay wax paper on top of this and then spray the top with the same mixture.  Lay out clean dishtowel on counter. Dust towel with confectionary sugar.

 

Beat egg whites with salt until they stand in soft peaks.  Add four tablespoons sugar, on at a time, and continue beating until meringue is very stiff.  In a separate bowl, beat egg yolks with remining sugar and vanilla until fluffy.  For pumpkin roll, add 1/2 cup canned pumpkin to egg yolk mixture and continue beating until fluffy.

 

Gently fold about 1/4 of the meringue into the egg yolk mixture.  This makes the yolk mixture lighter.  Pur back into bowl of meringue.  Sprinkle with two tablespoons of flour/or cake mixture and fold by hand into meringue mixture. Continue  folding in until flour/or cake mixture is gone.  Do not over mix. Bake 10-12 minutes in the 400 degree oven until golden.

 

As soon as the cake is baked, remove it from oven and invert it onto the towel, waxed paper on top.  Do NOT remove the waxed paper.  Roll cake tightly in towel starting at the narrow end. Allow to cool.

 

Carefully unroll cake and peel off waxed paper.  Spread thin layer of frosting on the top.  Add whipped cream or Cool Whip (flavored with pumpkin).  Reroll and refrigerate for an hour.  Frost outside of cake as desired.

 

Algebra and The Brady Bunch Teaches You about Exponents

 When trying to explain multiplying variables with exponents, the students could not remember whether to add or multiply the exponents.  I could understand their frustration.  So I used the Brady Bunch as an example. 

 I told them that in the Land of Quadrants (my imaginery algebraic world), the variables with exponents were like match.com.  People didn't use their real names, just user names.  They went searching for a match.  But, in my land, you were required by law to only make a match with someone who had the same initials as yourself. 

 In the example:  

                           c ³  x  d⁵        

^{this couple would not be a match.  A Carol, Cathi,or Cindy with three kids could not marry a David, Doug, or Dilbert with five kids because you can not multiply unlike variables.}

In the Land of Quadrants  a match could be made with 

                                

                                            b ² x b⁴ = b⁶

       ^{A Barbara, Brenda, or Bethany with twi kids can match with a Billy, Bob, or Bud with four kids.  But, the law requires them, in my imaginary land, to take on a new name with the same initials-- such as Brady. In this example, the Brady's combined or added their kids together (exponents) to make a new family of six kids.}

^{It is important to remember, that unlike variables (letters) can not be multiplied together in algebra.  This rule comes in handy when distributing and simplifying complex expressions.} 

Algebra and "Yes, MAM ," I can FOIL to Multiply Polynomials

I volunteered in an algebra class for a year to find out what the kids just weren't getting.  How to multiply monomials and polynomials.  Even those words are SCARY to a visual learner.  A very basic example of this would be (x + 3) (x + 4). 

Most teachers use the FOIL method.  This is VERY CONFUSING to visual learners.  So, let's begin learning a different way.  Let's call the lady sergeant above MAM. I am taking creative license with this spelling. This is not only a polite way to address her, but it is another way to learn how to multiply these scary equations.

What MAM  is going to teach you is how to play tic-tac-toe with these expressions.  This is similar to the "box" method, but easier to understand.  Your sergeant (MAM) is going to ask you to rewrite the two monomials like one of the samples below:

                                 

              

Your sergeant is going to remind you that, like the army, numbers need to be lined up to keep things organized. In the left hand sample above, when you put variables and numbers inside of parentheses, it ALWAYS means to multiply.  We are just lining them up easier to multiply these two expressions.   In the second sample above on the right, the big X in the middle also reminds the recruits to multiply. 
      If you are using the right box to explain the concept, tell the recruits to multiply along the lines.   So, starting on the left side of the box, multiply the x's.  Then go to the right side of the box, multiply the numbers. Next, go to the inside of the box and multiply along the lines.  In this example, you would multiply to get 3x and 4x.  If there are negative numbers, the answers would also be negative.  Tell your recruits that the negative signs are army swords.  The soldier with the sword wins the sign.  Unless they BOTH have swords, then they cancel each other out for a POSITIVE answer.  You ADD the two middle results.  In the acronym MAM,  M=multiply  A=add  M=multiply.
  If your recruits prefer the example on the left above, let them  play tic-tac-toe.  The first player gets to be X.  The second player gets to be numbers. 
                    
Player One:   gets to mark two squares with x in the first column. The first letter in MAM stands for MULTIPLY.  So player one gets to also mark the bottom box in the first column with the answer, which in this case is x squared.  

Player Two:  gets to mark two squares in the last column.  Because player two is the numbers player, they get to put one number (or term) from each of the monomials (parentheses).  The third letter in MAM stands for MULTIPLY.  
Because both of the numbers are positive numbers, the result is a positive number.

The middle letter in MAM is for addition.     
You will see that I lined up these two parentheses on top of each other to make it easier for the students to actually see the cross multiplying that will take place in the middle column.  If you let them make an x with a colored pencil between the top x and  bottom +4 and the bottom x and the top +3 that visually adds to their learning.  The result of the box filling for the middle column is 3x and 4x.  Since we are ADDING in the middle column,  and the terms are both positive, the answer for the middle box is +7x.


I am now going to do another MAM with negative numbers.  I will have previously explained to the students that multiplying in algebra can be compared to marrying.  The object of marriage is to multiply (have kids).  The older kids get this little joke.  This idea comes in handy when you begin to multiply numbers and variables with exponents.  A real marriage needs lots of positive attitudes.  I tell the kids that if one of the partners is negative, the results are always negative.  So a positive multiplied to a negative, results in a negative.  If both partners are negative, they need marriage councelling.  That always results in a positive result.

                  Example two:   (x -6) (x - 5)

                          


In the game below (problem), you can see that player one got to place the two x's and multiply them to get x squared.  Player two got to place the two negative numbers from the parentheses in column three.  Multiplied they made a positive 30 because they each had a negative attitude and had to go to councelling.  If you draw the x lines in colored pencil above, you will multiply to get -6x and -5x.  Remind the kids that the signs ALWAYS stay with the term behind them.  The result of adding these two terms in -11x.  Go see my Darth Vadar blog about adding and subtracting with negative numbers.  The answer is in the bottom row.



    



                                           
                                           



Algebra and The Lifeguard Rescues the Distributive Property in Algebra

 Visual learners, who need stories to help them understand math,  might enjoy the story about the lifeguard saving swimmers to understand the use of the distributive property to remove grouping symbols in algebra.

    In the first example:  2(x+ y),   I tell students that the numbers in the parentheses are the swimmers in the pool.

  The children in the clipart above would represent the x and the y.   The 2 outside the parentheses represents the lifeguard.  I then tell the students that the lifeguard needs to dive into the pool to rescue each of the kids (using the distributive property).  First he dives in and attaches himself (herself) to the x  making 2x.  Then he dives back into the pool and attaches himself to the y making 2y.  Because there was a positive or plus sign in the parentheses, the result is 2x + 2y.  There needs to be a LOT of reinforcement of this idea before any other signs are involved.

       In this next example:  -3(x-5) can be very confusing to a visual learner.  Just tell the students that this time the lifeguard -3 has a lifesaving board with him.  This takes some of the scariness away from the negative number and replaces it with a visual image.

So, the lifeguard and his board dive into the pool.  He attaches himself to the x making

 -3x.  But, when the lifeguard dives into the pool a second time, the second swimmer already has his own board.  Isn't that handy?  He really doesn't need rescuing, and what a POSITIVE thing that is.  But, he rescues away anyway.  So he attaches himself to -5 and the result is +15. 

(Remind the kids that a negative sign ALWAYS goes with the number or variable behind it).

               The result of this lifesaving simplifying experience is -3x + 15.





  

Pre-wrapped gift boxes

For YEARS my family has been making fun of my pre-wrapped gift boxes.  About ten years ago, after buying the expensive wrapping paper the schools sold for fund raisers, I decided that it was so wasteful to throw this beautiful paper away.  So, I still bought it, but I started wrapping the bottoms and tops of gift boxes separately. 

  I started by buying the boxes at first.  Then over many birthdays and holidays, when I received a box with itq own separate top, I saved it.  When I first started, I locked myself into my bedroom to wrap the boxes, and I watched holiday movies all afternoon. 

  I never use the boxes outside of my immediate family.  I can't always count on getting them back.   

  At first, my husband and kids made fun of me and my boxes.  Soon, as the kids got jobs and were busier, they'd come to me and ask, "Mom, can I borrow some of your boxes?"  When the holidays get extra busy, as I shop, I simply bring the newly purchased items into the house and put them in one of these boxes.  I DO use new ribbons every year, but there have been some REALLY CLEVER Pinterest tag ideas I am going to try this year.  You, realize, of course, that you can't tape tags to these precious boxes.

Fall Clipart for Spinner and Graphing

 Copy and paste these to your favorite program.  Or...save each one separately as a jpeg and insert them onto your Smartboard.  If you don't have one, make a big spinner.  See directions on my Halloween spinner blog.                      

                             

                         

Me Me Me Me Me

"I am shouting."  Stop using ME at the beginning of sentences.  Start singing this ditty to remind yourself.

.

                        
      Me, me, me's NOT at the beginning of a sentence.

Even if you bring someone else along.

Me and him aren't going someplace.

Oh, my goodness, that is wrong.

Me and Sally are going to the store. 

          Betty and me are doing a chore.

WRONG

Her and me want to play together.

Me and her are enjoying the weather. 

 WRONG.

Me, me, me's at the end of a sentence.

If you use it right,

I'll stop singing this song.

Best Way to Learn Skip Counting by Threes

get free clip art here for your school projects

I have been using a jar of chocolate coins for years now in the first grade. I use this visual idea to teach them skip counting by 3's.  Once they learn the poem, if they can recite it for me without a mistake (or counting in their heads), they get to go into the jar and take three gold coins.  Since they eagerly line up to do this for me, I know that the poem is working.  One third grader came up to me in the hall and thanked me.  He told me that the poem really helped him when he had to do his multiplication tables.

         So here goes:

Three, six, nine, twelve

Take the jar off the shelf.

(I ask them what's in the jar.  They shout, "Candy."

Fifteen, eighteen, twenty-one

Counting candy's lots of fun.

Twenty-four

Shut the door.

(Someone might be coming and see you eating the whole jar of candy)

Twenty-seven

Tastes like heaven.

Thirty

My hands are dirty.

(And sticky from eating all that candy)

Learning Time with Bus Stops

  

After teaching time for many years, I came up with a new idea to make time "manageable" in the lower grades.  I start the lesson by explaining about bus stops.  I ask the children if the bus stops at EVERY house.  They tell me no. " Well, where does it stop?" I ask.  They tell me it stops at corners and kids walk to that corner.  I ask them if they have ever seen the big bar that swings out from the front of the bus.  They tell me yes and we discuss what the big bar does. (It stops cars so that kids can cross the street).

   Then I explain that the minute hand is like that big bar.  It reaches all the way to the edge of the clock to touch the bus stops AND the kids.  They giggle, and we go on.  Visual learners need comparisons.  They have trouble differentiating between the short hand and the long hand, and how they are used.

                                     


               Do you see in the clipart above how it might be hard for kids to tell the difference between the length of the clock's hands?

   I explain that the four "bus stops" on the clock are like real bus stops.  They make it quicker to get around the clock.  I then label the stops  :00   :15   :30   :45.
  I actually climb up and put the labels on the wall by the clock.  This is all done on day one.

  On day two, the class is allowed to shout (quietly) everytime the bus arm (longer hand) reaches a bus stop.  They LOVE doing this.  They get used to time in quarter segments.

  From then on, I use the clock for time management.  I might say, "Look at the schedule.  We have two bus stops until P.E.  What bus stop would that be?"   or  "You have until the next bus stop to complete this task."   

   I do not introduce the hour hand yet.  I wait months until they have been accustomed to this idea.  I might tell them the correct time, but I do not ask them the time. 

   In first grade,  after much practice, I will give them a time like 3:50.  I will ask them which bus stop is closer?  Can they count on from that bus stop to tell me the time?

   This concept really works well for visual learners, but is still fun for all.
   Will it work?  Only time will tell.