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Domino Math

Dots Fun for Everyone
It is believed dominoes evolved from dice. In fact, the numbers in a standard double-six set of dominoes represent all the rolls of two six-sided die. It is thought they originated in China around the 12th century. They have been used in a large variety of games for hundreds of years, and today, dominoes are played all over the world.

Games allow children to learn a great deal concerning mathematical concepts and number relationships. Often they are required to use critical thinking skills as well as varied math strategies to solve them. Since dominoes make a great manipulative for hands-on learning, I created a 29 page book of domino activities for grades 3-5 that are great for students who finish early or for introducing a new mathematical concept or for use at a math center. Using dominoes for a math practice center is a way to engage students in math center practice while giving them a chance to review math facts.

The activities and games vary in difficulty; so differentiated instruction is easy. The variety of pages allows you to choose the practice page that is just right for each student. This resource correlates well with the math series, Everyday Math, as well as with the CCSS standards.

Some of the domino activities in this resource use games while others will extend, enhance or introduce a new math concept. Since children are curious and inquisitive, plus some may have never seen dominoes, allow time for play and exploration before beginning any instruction. This is constructive as well as a productive use of class time. If they are not given this, most children will fool around and investigate during the teaching time. The activities include four digit place value, using the commutative property, problem solving, reducing proper and improper fractions and practicing multiplication and division facts. The games involve finding sums, using <, >, and = signs and ordering fractions.

To view examples from this resource as well as a complete Table of Contents, download the preview or FREE Version.

A Go Figure Debut for A Homeschool Teacher Who is New

Beverly's TPT Store
Beverly lives in Texas, and this will be her 9th year as a homeschool teacher. She has three children, a daughter who is 17 and two boys, ages 14 and 11. Beverly's favorite thing about homeschooling is getting to spend a lot of time with her children and being able to let them really pursue their interests. Her youngest, for example, is interested in computer programming. Beverly has some experience in that area so she found an online course, and she and her son learned the basics of Python together.  Her classroom is a little media room/playroom upstairs where she has a bulletin board, white board, book cases and a long table. At the moment, she is in the process of reorganizing it which includes painting the walls.

Before homeschooling, Beverly taught preschool. The children in her class were only two years of age; so, there wasn't a lot of formal teaching going on, but she absolutely enjoyed the experience.

Beverly has 99 products in her store which is called Terbet Lane; including six that are free. She has a lot of decor and brag tags as well as creative writing and math sets.

Only $6.00
One of her paid items is a set of  Halloween themed story element cards.  She uses these cards in her homeschool. She wanted to create something that would give her children a jumping off place to write creatively and that could change and be something different each time. Her middle son does not like to write and really needed the structure of using these cards to help him think of something to write and to give his writing direction.

To use the cards, have a child choose one card from each category: character, conflict and setting. They are required to use these elements in their story but can add any new characters, settings, etc. that they choose. Her children have really enjoyed using these cards and actually ask to do them. Yeah!

 
Free Resource
One of her free resources is a Halloween coloring page. With Halloween just a month away, this would be the     perfect freebie to download for those students who finish early or for those who just like to color.  (I still do!)

In addition, Beverly has a blog called Terbet Lane although it is pretty new. Her July post was about family fun. Genealogy is one  of her main hobbies, and this post contains some activities that are a fun way to involve younger kids and spark some interesting conversations about family.  I especially like her list of questions to ask grandparents because interviewing an older relative is a great way for kids to learn about their history while connecting with grandparents, aunts, and uncles. I hope you have time to check it out. Also take time to visit her store and see those 99 resources she has created!

Factorial Fun

Factorial is a word that mathematicians use to describe a special kind of numerical relationship. Factorials are very simple things. They are just products, indicated by the symbol of an exclamation mark. The factorial function (symbol: !) means to multiply a series of descending natural numbers. For instance, "five factorial" is written as "5!" (a shorthand method) and means 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in determining the numbers of combinations and permutations and in finding probability.


Now all of that may seem above your mathematical head, but let me introduce you to the book Anno's Mysterious Multiplying Jar by Masaichir and Mitsumasa Anno.  It is a story about one jar and what is inside it. Anno begins with the jar, which contains one island, that has two countries, each of which has three mountains. The story continues like this until 10 is reached.  The colorful pictures are arranged within borders on the page as many times as the number of objects being discussed. For instance when four walled kingdoms are introduced, four kingdoms are on the page.

The explanation of 10! in the back of the book is also very helpful. Even if children do not understand the concept being taught, they will certainly appreciate the detailed colored drawings and imaginative story! The book is best for kids who have been introduced to at least basic multiplication facts, but younger kids will enjoy counting and looking at the pictures even if the rest of it is over their heads; so, this book helps with multiplying skills as well as the mathematical concept of factorials.

You might give the students a worksheet to keep track of how many islands, rooms, etc. there are. The final question is how many jars are there. Hopefully there will some students who catch on to the factorial concept, find the pattern and discover the answer! 

Here is an example of how you might use factorials in solving a word problem.  How many different arrangements can be made with the letters from the word MOVE?  Because there are four different letters and four different spaces, this is how you would solve the problem.

____   ____   ____   ____ 
Four Possible Spaces

All four letters could be placed in the first space. Once the first space is filled, only three letters remain to fit in the second space. Once the second space is filled with a letter, two letters remain to write in the third space. Finally, only one letter is left to take the fourth and final space. Hence, the answer is a factorial (4!) = 4 × 3 × 2 × 1 = 24 arrangements.

Try some problems in your classroom. Start with an imaginary character, Cal Q. Late, who is working at an Ice Cream Store called Flavors. A hungry customer orders a triple scoop ice cream cone with Berry, Vanilla, and Bubble Gum ice cream. How many different ways could Cal Q. Late stack the ice cream flavors on top of each other?

You could answer the question by listing all of the possible orders of the three ice cream flavors from top to bottom. (Students could have colored circles of construction paper to physically rearrange.)

  1. Bubble Gum - Berry - Vanilla
  2. Bubble Gum - Vanilla - Berry
  3. Berry - Vanilla - Bubble Gum 
  4. Berry - Bubble Gum - Vanilla
  5. Vanilla - Berry - Bubble Gum
  6. Vanilla - Bubble Gum - Strawberry
Or, if we use factorials, we arrive at the answer much faster:  3! = 3 × 2 × 1 = 6

Learning about patterns and the use of factorials will stretch a students' mathematical mind.  Why not try a few problems in your classroom?  And by all means, check out Anno's Mysterious Multiplying Jar.

Using Mnemonic Techniques

In my college class entitled Conquering College, we have been working on ways to remember for tests. Of course, mnemonic devices came up. Mnemonics connect new learning to prior knowledge through the use of visual and/or acoustic cues. Such strategies assist students in remembering and recalling larger pieces of information for tests. Included in mnemonics are acronyms, initialism, acrostics, rhyme, rhythm and song and association in addition to visualization using the loci and peg systems. Let's look at four of these categories.


1) Acronyms - A word formed from the first letters of each one of the words in a phrase.
  • HOMES – The names of the 5 Great Lakes – Huron, Ontario, Michigan, Erie, Superior 
  • ROY G. BIV – The colors in a rainbow – Red, Orange, Yellow, Green, Blue, Indigo, Violet 
  • SCUBA - When you’re scuba diving, you’re using a “self-contained underwater breathing apparatus.” 

2) Acrostics – Sentences created from the first letters of key words.
  • Please Excuse My Dear Aunt Sally – for the order of operations 
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction 

    **I personally prefer the phrase: Pale Elvis Meets Dracula After School. 
  • My Very Earthly Mother Just Sliced Up Neptune.  – the planets in order from largest to smallest: 
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune 

   **I particularly like this one since Earthly gives you a clue that the third planet is earth and Neptune is listed last. This means you only have to know 6.


Free Resource
3) Rhyme, Rhythm, Song – poems, limericks or silly songs – These work well for auditory learners.
  • I before E, except after C and in sounding like A as in neighbor and weigh.
  • In 1492, Columbus sailed the ocean blue.
  • Twinkle, twinkle little star; circumference is 2 π r.       (I actually sing this for my students!)


4) Association – finding a common element. The association is usually coincidental.
  • Litmus Paper: Blue = Base – both begin with “B”. 
  • Arteries: Artery = Away – both begin with “A”. 
  • The principal is my PAL. Helps to distinguish from principle. 
  • Affect = Action (a verb) Helps to separate it from effect which is a noun.
These ideas plus many more are in a free resource called Mnemonic Techniques found on Teachers Pay Teachers. All you have to do is download it!


The ROOT of the Problem

When students skip count, they can easily say the 2's, 5's, and 10's which translates into easy memorization of those particular multiplication facts.  Think what would happen if every primary teacher had their students practice skip counting by 3's, 4's, 6's, 7's, 8's and 9's!  We would eradicate the drill and kill of memorizing multiplication and division facts.

Since many of my college students do not know their facts, I gravitate to the Divisibility Rules.  Sadly, most have never seen or heard of them.  I always begin with dividing by 2 since even numbers are understood by almost everyone.  (Never assume a student knows what an even number is as I once had a college student who thought that every digit of a number must be even for the entire number to be even.) We then proceed to the rules for 5 and 10 as most students can skip count by those two numbers.

Finally, we learn about the digital root for 3, 6, and 9. This is a new concept but quickly learned and understood by the majority of my students. (See the definition below).


Here are several examples of finding Digital Root:

1) 123 = 1 + 2 + 3 = 6. Six is the digital root for the number 123. Since 123 is an odd number, it is not divisible by 6. However, it is still divisible by 3.

2) 132 = 1 + 3 + 2 = 6. Six is the digital root for the number 132. Since 132 is an even number, it is divisible by 6 and by 3.

3) 198 = 1+ 9 + 8 = 18 = 1 + 8 = 9. Nine is the digital root for the number 198; so, 198 is divisible by 9 as well as by 3.

4) 201 = 2 + 0 + 1 = 3. Three is the digital root for the number 201; so, 201 is divisible by 3.

The first time I learned about Digital Root was about eight years ago at a workshop presented by Kim Sutton. (If you have never been to one of her workshops - GO! It is well worth your time.) Anyway, I was beside myself to think I had never learned Digital Root. Oh, the math classes I sat through, and the numbers I tried to divide by are too munerous to mention! It actually gives me a mathematical headache. And to think, not knowing Digital Root was the ROOT of my problem!

Divisibility Rules



A teacher resource on Using the Divisibility Rules and Digital Root is available at Teachers Pay Teachers. If you are interested, just click under the resource cover on your right.

A Go Figure Debut for an Iowan Who Is New!

 Today’s Go Figure Debut teacher has been in the classroom for just over a decade; however, she is currently taking a few years off to raise her little ones. (Adelaide is three and Joseph is one.) She loves to see students grow and discover who they are and what they think. This is one of the reasons she enjoys middle schoolers so much. She finds that students at this age are starting to develop into their own persons, and they are questioning and forming their own thoughts. She loves being front and center to this change and helping her students successfully navigate this transition.

Rebecca describes her classroom as a place where it is okay to question and to just be yourself. It is a place where learning and independent thought are encouraged and where students are pushed to try new things and do their best. She believes that one of the most important things she can teach her students is how to form an educated opinion and defend it in a civilized manner as well as to listen and respond to others who may or may not hold the same opinion.

Rebecca married her high school sweetheart, Kyle. They currently live in the heart of Iowa Amish country where it is just as common to see a horse and buggy go by their front window as it is to see a car go by. (I use to live in Plain City, Ohio so I identify with this.) Besides teaching, she has also sung in several Gilbert and Sullivan operettas, including a lead in The Gondoliers. In addition, she possesses several random skills including the ability to ride and drive horses, bake bread, make jam and pie crusts from scratch and design and sew costumes for the stage.

Rebecca has over 100 products in her store, and eight
of them are free. One of those free items is
Free Resource
Romeo and Juliet Character Quizzes and Keys: Descriptions and Quotes. These two print and go quizzes on Romeo and Juliet by William Shakespeare are designed to be used after reading the play. They make great comprehension checks or review activities. Quiz One has the students match the description of the character to the character's name. Quiz Two requires the students to match the famous quote to the character who said it and then explain one quote. Answer keys are included.
                                                 
Another of her resources is a 115 page bundle entitled: Six
$13.50, save $2.50
Story O. Henry Product Bundle Plus Author Study Activity.
This bundle includes everything you need for a unit on O. Henry - full texts, lessons and activities on six O. Henry stories plus an author study activity. By buying the bundle, you save $2.50!

Rebecca does have a blog called Rebecca's Classroom and Kitchen. (I guess she gets pleasure from both!) Her blog's motto is, "Feed Your Mind and Your Tummy!" (Sounds like a plan to me!) Before mentioning any blog, I always check it out just to see what is contains and if I think it is valuable. Recently, she wrote a four part-series entitled Freedom in the Classroom which I really appreciated reading. You should check it out as well. It will cause you to reflect as well as to evaluate just how much freedom any teacher truly has.


Using Number Tiles to Problem Solve in Math

Math Activities for Grades 5-8
I prefer using hands-on activities when teaching math. One of the most successful items I have used is number tiles. Because number tiles can be moved around without the need to erase or cross out an answer, I have discovered that students are more at ease and more willing to try challenging activities. There is something about not having a permanent answer on the page that allows the student to explore, investigate, problem solve, and yes, even guess.

I have created several number tile booklets, but the one I will feature today is for grades 5-8. It is a 23 page booklet containing 15 different math problem solving activities that range from addition and multiplication, to primes and composites, to exponent problems, to using the divisibility rules. Since the students do not write in the book, the pages can be copied and laminated so that they can be used from year to year. These activities may be placed at a table for math practice or as a center activity. They are also a perfect resource for those students who finish an assignment or test early. Use these activities to reteach a concept to a small group as well as to introduce a new mathematical concept to the whole class.

Free Resource
Students solve the Number Tile Math Activities by arranging ten number tiles, numbered 0-9. Most of the number tile activities require that the students use each tile only once. The number tiles can be made from construction paper, cardboard, or square colored tiles that are purchased.  (How to make the number tiles as well as storage ideas is included in the handout.) Each problem is given on a single page, and each activity varies in difficulty which is suitable for any diverse classroom. Since the students have the freedom to move the tiles around, they are more engaged and more willing to try multiple methods to find the solution. Some of the problems will have just one solution while others have several solutions. These activities are very suitable for the visual and/or kinesthetic learner.

A free version for each of my number tile resources is listed below. Just click on the link to download the freebie.

A Go Figure Debut for a Texan Who Is New!

Jill's TPT Store
Today my Go Figure Debut introduces “The Teacher Down the Hall”. Joy is from Waco, Texas and has been teaching for 24 years. She is a former high school coach, so she has many opportunities to use those coaching strategies in her classroom. For example, she shows students how to conquer an objective, and then pushes them to do their very best. She encourages them when they are down, drives them when they are lazy, and celebrates with them when they are successful!

What she likes most about teaching is the opportunity to develop new friendships with her new students every year, as well as the life-long friendships she has with co-workers! Her teaching style is always evolving as she has changed grade levels and teaching assignments many times. From coaching high school athletics, to teaching Kindergarten, or 4th grade writing, what she has noticed is that kids will perform their best when they are having the most fun. Therefore, she does everything she can to turn each lesson, or repetitive exercise, into a fun activity.

Joy has three children and a daughter-in-law who is expecting her first child in December which will make Jill a first time Grandma! Joy’s favorite hobby is cycling. She rides long distances on her road bike and rides trails on her mountain bike. She even has the awesome opportunity to ride regularly with former president George W. Bush when he is at home on his ranch in Crawford. She says that he and his wife, Laura, are incredibly friendly people! Jill even has a cat from the Crawford Ranch, named Walker - after our 43rd president! (I’m not sure if the cat is a Republican or not.)

Only $2.50
Since many classrooms are making use of Google Classroom, I would like to use this opportunity to promote Joy’s Google Interactive Classroom resource on Area and Perimeter. Students draw lines to match answers, write in the correct measurements, and drag buttons to the correct answers! They will also…

Multiply to find area.
 Add to find the perimeter, or the sum of two areas or perimeters.
Subtract to find the difference between two areas or perimeters.
Divide and subtract to find missing sides in a given shape.

This is a great way for students to practice this skill independently, during centers or at home!!

Free Resource
Out of the 235 resources featured in her store, Joy offers 27 that are free. One is also a Google Classroom product entitled, “Google Interactive Classroom – Volume.” One person who downloaded this free item said, “Thank you for sharing this paperless resource. There is such a push to go digital and paperless and this is a great resource to start with. I love how you can pick and choose the pages you want various students to use and how the students submit their finished work. Super resource!!!”

So if you are going paperless, this may be a resource you should check out for yourself! Since it is already completed and free, you can’t go wrong!


Shaving Cream And Summer Fun

Again, I am going to deviate from the subject of math and offer a fun summer activity I do with my grandchildren. It involves a can of shaving cream, cleaning rags and lawn furniture that has set out all winter.

Were you aware that there are many unusual ways to use shaving cream besides using it for shaving? Did you know that you could...

1) Clean jewelry with it? Spray it on your jewelry and use a soft “old” toothbrush to get off the grime. Rinse with water.

2) Give chrome faucets a brilliant shine? Apply the shaving cream to a sponge and rub it on the faucet. Then wipe it off with a damp cloth.

3) Easily remove paint from your hands? Rub the shaving cream onto your hands; then rinse it off with soap and water.

4) Remove carpet stains? Blot the soiled area with a damp sponge and then spray on the shaving cream. Wipe clean with a damp sponge and let the area dry. It will also work on various clothes stains.

5) Clean vinyl lawn furniture? Spray the lawn furniture with the shaving cream and wipe the grubby areas with a damp rag. Rinse when finished.

Item #5 is what I do each summer. Our lawn furniture sets out over the winter on our patio and even though it is covered, it is filthy when summer comes. I always go to the store and purchase the cheapest shaving cream I can find. (Here in Kansas, Barbasol sells for about $.89 a can. Depending on the number of grandchildren coming over, determines how many cans I purchase. This year, it was three.) No matter their age, this is one activity that they all look forward to because it is messy!

I write the child’s name on their can of shaving cream and then assign them a piece of furniture to clean. When everyone is done scrubbing and wiping, we get out the garden hose to spray off the remaining shaving cream, and frequently we end up spraying each other.

But what happens to the leftover shaving cream? I think the picture says it all!



Skip Counting and Learning How to Multiply

Most elementary teachers use a Hundreds Board in their classroom.  It can be used for introducing number patterns, sequencing, place value and more. Students can look for counting-by (multiplication) patterns. Colored disks, pinto beans or just coloring the squares with crayons or colored pencils will work for this. Mark the numbers you land on when you count by two. What pattern do they make? Mark the counting-by-3 pattern, or mark the 7's, etc. You may need to print several charts so your students can color in the patterns and compare them. I usually start with the 2's, 5's and 10's since most children have these memorized.

On the other hand, the Hundreds Board can also be confusing when skip counting because there are so many others numbers listed which easily create a distraction.  I have found that Pattern Sticks work much better because the number pattern the student is skip counting by can be isolated. Pattern Sticks are a visual way of showing students the many patterns that occur on a multiplication table.  Illustrated below is the pattern stick for three. As the student skip counts by three, s/he simply goes from one number to the next (left to right).


Martian Fingers
For fun, I purchase those scary, wearable fingers at Halloween time. (buy them in bulk from The Oriental Trading Company - click under the fingers for the link.) Each of my students wears one for skip counting activities. I call them the Awesome Fingers of Math! For some reason, when wearing the fingers, students tend to actually point and follow along when skip counting.

Most students enjoy skip counting when music is played. I have found several CD's on Amazon that lend themselves nicely to this activity.  I especially like Hap Palmer's Multiplication Mountain.  My grandchildren think his songs are catchy, maybe too catchy as sometimes I can't get the songs out of my mind!

Think about this.  As teachers, if we would take the time to skip count daily, our students would know more than just the 2's, 5's and 10's.  They would know all of their multiplication facts by the end of third grade. And wouldn't the fourth grade teacher love you?!?

IMPORTANT:  If you like this finger idea, be sure that each student uses the same finger every time to avoid the spreading of germs. Keeping it in a zip lock bag with the child’s name on the bag works best. (Believe it or not, when I taught fourth grade, the students would paint and decorate the fingernails!)


Cold Treat for Those Hot Days of Summer


June always brings the first day of summer. I'm not sure where you live, but I live in Kansas, and each day it is getting hotter and hotter! On a hot day, when you have been outside, there is nothing better than an ice cold treat. For years, I have made homemade Popsicles, first for my children and now for my grandchildren. I thought I would share the quick and easy recipe with you. (I know this might be considered the "far side" of math, but recipes do contain measurement and sometimes, even fractions!)

Popsicles Recipe - Will make 18

1 small package of Jello (any flavor)  As you can see, my grandchildren like the Berry Blue.)
1/2 cup sugar
2 cups boiling water
2 cups cold water

Boil water. Add to the sugar and package of Jello. Stir until all the Jello is dissolved. Add the cold water and stir again.

Pour into three sets of Tupperware Popsicle Makers. If you don't have these (I don't think they sell them anymore), use Popsicle molds found in stores. or use ice cube trays.

Place in the freezer until hardened. Eat and enjoy just like my grandchildren do!


A Go Figure Debut for an English Teacher Who Is New!

Lindsay's TPT Store
My newest Go Figure Debut is a high school English teacher from Illinois. Lindsay has been teaching for 13 years. She describes her classroom as student-centered and connection-driven as she wants her students working harder than she does and taking responsibility for their own learning. This happens when students are engaged in what they are doing and feel like they belong.

At the high school level, students have "been there, done that" with just about every type of English assessment and experience; so, it's a matter of finding ways to up the rigor, innovating to find a real-world skill application or asking them to take more ownership of their work than ever before. Besides the students themselves, this is her favorite thing about teaching - designing experiences and activities that will engage and excite.

When Lindsay is not teaching, she is hanging out with her husband and two awesome kids or helping her husband with his wedding photography business. Her children are little; so, they are her "hobby" right now. She is looking forward to spending more time with them this summer.

The name of her Teachers Pay Teacher's store is Lindsay Ann Learning. Currently, she has 121 products featured in her store with five of them being free. Her resources are for middle and high school English Language Arts - writing, reading, and digital interactive resources.

Free
One of those freebies is entitled Close Reading Introduction.  With these time tested resources, students can learn a successful pattern for thesis statement writing and close reading analysis. It is an excellent way to break down the thesis so that students can understand each component, as well as unpack the evidence from the text. In addition, it is a very effective tool that scaffolds textual analysis step-by-step.

$20.00
Her paid product is called Slam Poetry which is a no-prep, engaging, CCSS-aligned slam poetry unit with student-centered activities and assignments designed to promote inquiry and self-expression. Lindsay believes that writing poetry can be a fun, interactive, student-centered experience that engages every learner! With the digital and print resources in this resource, you can build writing, reading, speaking and listening and meta-cognitive skills . A comment left by a recent buyer says; “What a fabulous unit! The resources are well organized and the online links have saved me hours of preparation time. Thank you so much!”

Additionally to teaching and selling on TPT, Lindsay has a blog entitled Lindsay Ann Learning. The theme of her blog is... 


Take a few moments to check out her blog as well as her store. You will find that many of her quality resources are interactive which makes them very desirable.


"Sum" More Quick Tricks

Sometimes, my students think, I am a magician who pulls answers out of a hat. Over the years, I have learned that mathematicians are ingenious people who are always looking for quick and easy ways to do things. Maybe that's why we now have graphing calculators and computer programs to figure taxes.
I have a friend who teaches math on the college level in North Carolina. In fact, we have been friends since 6th grade, but that's another story. When she read one of my posts, she shared a trick for quickly finding a sum. Her trick has to do with a sequence that begins with any number, with any number of terms as long as they are separated by the same amount. For instance, the series below is a six number sequence with a difference of two between each number.
Here is what you do to quickly to find the sum. Add the first and last terms. 5 + 15 = 20. Now multiply by the number of terms which in this case is 6. 20 x 6 = 120 Finally, divide by 2. So, mentally this is what it would look like.


Now, how many of you went back to add up 5 + 7 + 9 + 11 + 13 + 15? Did you get the answer of 60? Isn't it amazing!?! Maybe math teachers are magicians after all!

   

Quick Times

I am always looking for different strategies when working with my remedial college students since many of the ways they were taught to do math aren't working for them.  I came across this "Quick Times" method and thought it would be another approach I could share with my mathphobics for multiplying.  They love anything that is different, quick and makes them look astute when doing mathematics.

Let's assume we have the multiplication problem of 41 x 12.  In the Quick Times method, first start by multiplying the first digit of 41 by the first digit of 12 to get the first digit of our answer.  We then multiply the second digit of 41 by the second digit of 12 as seen below to get the last digit of our answer (the ones place).

Now we need to find the middle digit of the product.  This is done by multiplying the outside digits, then the inside digits, and adding those two products together as shown below.

This quick method will only work when multiplying two digit numbers by two digit numbers, but it does cause the students to do mental math.  My students like the challenge of doing all of the computation in their heads.  Let's try another one that is a little different.  Let's do 63 x 41.  Again we multiply the first digit of each number and then the second digit of each number to get the first digits of the answer and the last digit of the answer.


As before, multiply the outside digits, then the inside digits, and add the two products together.
Now we must put the 18 into the middle spot, but there is only room for one digit in the tens place.  YIKES!!  What do we do now?  Very easy....because we can only have one digit where the question mark is, we must regroup (carry) the one in the tens place of the 18 and then add it to the 24.

Have you figured out the final answer?  It is.....

You are probably thinking the old method works so much better, but that is only because that is the method you are use to using.  Why not try the ones below using the Quick Times method and see if you get the correct answer.  Use the old method or a calculator to check your answers or go the the answer page above.

a)  36 x 21       b)  24 x  12      c)  48 x 29       d)  59 x 18       e)  63 x 13     


Why I Use Tailwind

Maybe you have heard of Tailwind and maybe you haven't. To set the record straight, it is not a wind blowing in the direction of travel of a vehicle or aircraft or a wind blowing from behind. It is a Pinterest and Instagram Marketing, Scheduling and Analytics Tool.

I was first introduced to it on the Teachers Pay Teachers blog. Since I use Pinterest (I have 84 different boards, some that are collaborative boards.), I am always pinning new ideas, teaching strategies, Ohio State stuff (Go Buckeyes!), ideas for my college classes, etc., I decided to try using Tailwind instead of individually pinning each resource from my TPT store or blog. Before deciding if the paid plan was right for me, I was able to schedule up to 100 pins on Pinterest, and 30 posts on Instagram for free . What was nice is that there was no time limit on that free trial! It allowed me to schedule up to 100 pins on Pinterest, and 30 posts on Instagram while I could watch my analytics and the number of repins my items were receiving before deciding if the paid plan was worth the money.

I saw several benefits right away! More traffic was coming to my Pinterest boards as well as to my Teachers Pay Teachers StoreI therefore decided to invest in the annual Plus plan, a pay-as-you-go plan. This plan allows me to schedule 400 pins a month.  I am aware that pinning everything all at once isn’t ideal; consequently, it's important to space pins out a little so I'm not overwhelming my followers. Pinterest has even suggested that too much pinning in a short time period could be viewed as “spammy”, potentially hurting my rankings in search results and feeds. With Tailwind, I have the ability to create my own posting schedule, and I can use interval pinning to space out my pins so "spamming" doesn't happen. I can set a time period between when each image that is pinned anywhere from 10 minutes to 90 days apart. Tailwind even gives me the best times and days to post.

Here are some ways I am currently using Tailwind:
  1. To schedule pins
  2. To know when the best time to pin is using the Smart Calendar
  3. To schedule multiple pins to different boards at the same time
  4. To use interval pinning
  5. To use the Tailwind Analytics - to know which are my best pins and where my repins are going
  6. To find my best pins using Pin Inspector
I know this sounds like a long advertisement for Tailwind, but I am so excited about the many benefits and results of this service, I just had to share it with you, my readers. If you are interested in joining Tailwind, I have a Tailwind tribe called Math Counts where any teacher who teaches 4th grade through high school can post math resources for free. Each person in the tribe adds their own pins in the queue. Once you see the pins in the queue, you can add them to your scheduled pins in Tailwind so your resources keep getting repinned to different boards. Tailwind has said that you do not have to be a paying member of Tailwind to be in a Tribe. Here is the link if you are interested in joining Math Counts. Just copy and paste it into any search engine.

https://www.tailwindapp.com/tribe/join?d=eyJpdiI6IlNKaVwvY1FaN2dCSlVzOTV1dE85TmNBPT0iLCJ2YWx1ZSI6Ilk4NElMK2huTGpXWTQ4eVlOeE5PSjVFVDZDQ2R0WlNjOE9kVWFBVzFBbXo5UzMyazAybnA4MlJVWE5wNGlVa0xDcjFzcDJQSnFLYzdZajA2dnlscituSTZQOVUyUVdWSUVaTXMzK2FIVHBFPSIsIm1hYyI6IjA3OTk3MjZkN2MyNzE3MTExZTdjMjQ3NTlhMTM2MWRhNTFlMzg3OTcyYTQ0YTM0NWJiNzI5NWIwMDU4MDEyYjYifQ%3D%3D

If you decide to join my tribe (which costs you nothing), you will also get a free month ($15 credit) if you ever decide to join the Plus plan. 

Getting started with Tailwind is easy. In the members area are five training videos that walk you through everything step-by-step and in much more detail than this blog post. There’s also an in-depth FAQ section, and if you get stuck with anything, their customer service is responsive and helpful. All I can say is that it makes running my Pinterest account much easier; I can be more strategic in my Pinterest marketing efforts plus it saves me a ton of time!  I hope you will check it out.

A Go Figure Debut for a Home-School Teacher/Mom Who Is New!

Erin taught at the elementary level in a public school in the suburbs of Chicago for about ten years. Currently she is homeschooling her three children (ages 3, 4, and 6). She says it is a wonderful blessing to be doing what she loves most with her own kids! She also teaches a few classes once a week at the homeschool co-op that she is a part of. She claims that teaching is in her blood, and she cannot imagine her life without teaching in some capacity.

Whether at school or homeschooling, Erin’s classroom is student-centered and child-friendly. She always displays student work, has materials easily accessible to the kids, exhibits bulletin boards and posters that are meaningful and helpful, and creates an atmosphere where children are comfortable to take risks and make mistakes.

As you can tell, Erin loves working with children! She enjoys seeing the light bulb go off when children learn, grasp and apply a concept. Struggling learners have always tugged at her heart, and when she was a classroom teacher, she was always thrilled to see their names on her class list. She also likes all things that are teacher related such as planning, creating, organizing and decorating. She has always enjoyed creating educational resources, but since she started selling on Teachers Pay Teachers, this has become her number one hobby!

Her TPT store is called Erin Guge. (What Else?) It currently contains 36 products although she is constantly adding new ones! Her resources focus on PreK–5th grades with the spotlight primarily on PreK-3rd. Three of her resources are free, and one of those is called Poem of the Week Routine.

Free Resource
When she was getting ready to teach her daughter kindergarten, Erin knew she wanted to incorporate a Poem of the Week to practice beginning reading skills; however, she didn’t want the skill focus to be haphazard or hit-or-miss. Since she wanted a comprehensive plan, she created a Poem of the Week Routine

It is an easy-to-use one-page reference. Specific concepts and prompts are listed under each day of the week to ensure the time spent on your Poem of the Week is maximized and efficient.  Each day contains a different focus (print concepts, phonemic awareness and phonics, word focus, comprehension, and fluency). Whether you display your poem on a Smartboard, under the doc camera, on a chart, or in individual poetry notebooks, and whether you do this as a whole group, with a small group, or one-on-one, use this product to guide discussion as well as to direct student interaction with the poem (circle certain words, underline others, point to this, put a start by that). The options are endless! Since it is free, all you have to do is download it! 

One of her paid resources is called Reading Comprehension Strategies and Skills Posters and Cards. The goal for this resource is to present the strategies and skills in a way that is simple and brief; yet clear and meaningful even to young students. These 27 posters are a wonderful reference for introducing and practicing reading comprehension strategies and skills. They contain a brief definition and a helpful picture. Small cards are also included (identical to the posters), which can be used during guided reading, one-on-one and independent reading. The posters are one full page each, and the cards are small (9 per page).
Additionally, Erin has created other reading poster/card sets (genres, nonfiction text features, word attack strategies and figurative language/poetic elements). So if you are looking for quality and reasonably priced reading materials and activities, I suggest you check out Erin's store and her various resources. I know you will be pleased!

Making Gifts - Not Something I Normally Do

At this time of year, we have many friends retiring or celebrating those "up-in-years" birthdays. Many of the invitations read, "No Gifts, Please." I understand at this point in our lives, we have more than we need, but it is always nice to bring something to show your friend that you care. We just attended a 70th birthday party for someone we have known for years. Not only is he our friend, but he is someone both my husband and I have taught with. I looked on Pinterest (where else?) and found several ideas that I combined. Here is what I came up with - a large birthday card that was editable!!


Here is what I purchased to complete the giant card.

  1. A large folding poster (You need heavy poster board to hold all of the candy!)
  2. A Nestle's Symphony Bar
  3. A Snickers Bar
  4. Nestle Crunch
  5. One package of EXTRA chewing gum
  6. 100 Grand Candy Bar
  7. Butterfinger
  8. Skor Candy Bar
  9. Mr. Goodbar
  10. Package of Milk Duds
  11. Package of Whoppers
I hot glued each of the candy bars or packages of candy onto the poster. I then used rubber cement to attach the phrases. I created my own phrases that sort of matched the candy, but if you are making a card, get creative and make up your own. You might even find some better candy bars or items to put on the card.

I have to say this birthday card was a real "hit" and even became a center piece of the party. Also, the party goers thought it was extremely yummy!


Math Vocabulary Practice

I have discovered teaching the language of math is significant to teaching math concepts and procedures. Students need to use correct mathematics terminology as vocabulary knowledge provides students with a mathematics foundation they can apply and build on whether they are in or out of the classroom. It really is all about the word, the right words! Since mathematical language is used and understood around the world, conventional mathematics vocabulary gives our students the means of communicating those concepts universally.

With that said, I have discovered that my college students hate learning, reviewing or even practicing math vocabulary. I always begin the semester with a Mathematical Language Activity (see below) in which the students write two paragraphs about how they feel about the math language. You'd be surprised at how much I learn!


Even though my students have vocabulary assignments, and we play vocabulary games, especially before a test, many times they do it begrudgingly. Knowing that most of them like word puzzles, I created several math vocabulary crosswords to use in my classroom. The purpose of these puzzles is to have my students practice, review, recognize and use correct geometric vocabulary. I've made all of the crosswords free-form puzzles with the clues written in the form of definitions. 

Often, I create two different puzzles for the same math vocabulary. The first puzzle is easier as it contains a word bank while the second puzzle does not. Since both puzzles are laid out differently, I can use one as a review and the second one as a homework assignment or maybe even as a quiz.

Only $1.50
My newest one is on circles. Both puzzles feature 18 terms associated with circles. The words showcased in both puzzles are arc, area, chord, circle, circumference, degrees, diameter, equidistant, perimeter, pi, radii, radius, secant, semicircle, tangent and two. 

Also available are crosswords on polygons (includes 16 geometric shapes with an emphasis on quadrilaterals and triangles), plain geometry (features 25 different geometry terms with an emphasis on points, lines, and angles), and solid geometry (emphasizes polyhedrons, circles, and formulas for area, surface area, and volume).

To keep my old gray matter working, I do the paper crossword every Sunday. To many of our students, math is like a puzzle, but maybe they can learn to love figuring out the puzzle by doing these crosswords. Why not give one a try in your classroom?

The Left Angle Mystery

Geometry is probably my favorite part of math to teach because it is so visual; plus the subject lends itself to doing many hands-on activities, even with my college students.  When our unit on points, lines and angles is finished, it is time for the unit test.  Almost every year I ask the following question:  What is a left angle?   Much to my chagrin, here are some of the responses I have received over the years.

1)   A left angle is the opposite of a right angle.

2)  On a clock, 3:00 o'clock is a right angle, but 9:00 o'clock is a left angle.

3)  A left angle is when the base ray is pointing left instead of right.

    4)      A left angle is 1/2 of a straight angle, like when it is cut into two pieces, only it is the part on the left, not the part on the right.
5)      A left angle is 1/4 of a circle, but just certain parts. Here is what I mean.


Now you know why math teachers, at times, want to pull their hair out!  Just to set the record straight, in case any of my students are reading this, there is no such thing as a left angle!  No matter which way the base ray is pointing, any angle that contains 90is called a right angle.


If you would like some different ways to teach angles, you might look at the resource entitled, Angles: Hands-on Activities.