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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.

A Go Figure Debut for A Texas Teacher Who Is New


Lauren's Store
Lauren is a Texas girl who has been a teacher for 12 years! She has taught a variety of 5th and 6th grade math and science classes, and this is her fourth year as an instructional math coach. She works at an intermediate (5th/6th grade) campus that serves a diverse group of students that includes many English language learners and at-risk students.

Lauren loves working with students in small group instruction for math. This was her favorite part of her day when she was in the classroom and one of the ways she still interacts with students in her job as an instructional coach. She also enjoys designing curriculum with her teachers and creating new lesson ideas to teach difficult topics. Her favorite topics to teach are fractions and proportionality. In science, she likes teaching about plate tectonics.

Lauren has three sons from 18 months of age to 11 years old. Together, they like to watch movies and play outside. Between her boys and her work, she stays really busy, but she still finds time to read science fiction books and create educational resources (Surprising, right?).

Her Teachers Pay Teachers store, Leaf and STEM Learning, focuses on resources for 4th - 7th grade. Teachers can use them for guided math instruction, including centers and stations materials, problem solving, utilizing manipulatives plus concept development. Her materials are aligned with Common Core and the Texas TEKS. Since she has used these materials in her own classroom or in classrooms throughout her school and school district, you can be confident in using them in your classroom, too!
Free Resource

Currently, her store contains just over 100 resources, with eight of those resources being free. One of those freebies is entitled Place Value & Powers of 10. Using an engaging low prep interactive notebook set, this resource introduces and practices using powers of ten for place value notation. All the included parts, an interactive mini book, practice activities and formative assessment, are designed to fit perfectly in your students' composition books or math journals.

I am really partial to her paid resource called Ratios & Proportions. These differentiated task cards have 132 total questions that go with 44 real world and model scenarios. Students write ratios in word form, colon form, fraction form and decimal form and solve proportional relationships and percent problems.

Only $3.00
Three levels of questions can be selected randomly by rolling dice or by the teacher with the differentiated dice cards to make the perfect practice for your students. The task cards can also be used as prompts for small group instruction or tutorials. Also included are a teacher guide to help you set up, student instructions, a student recording sheet, and a full answer key.

Her Blog
Lauren has a blog entitled Leaf and STEM Learning, just like her store. She not only shares interesting posts about teaching, but in addition she gives instructional tips and specific ideas for math teachers. Maybe you have heard the common adage that teachers must learn how to “beg, borrow, and steal” to find the best resources and practices for their classroom. Because this saying resonates true for most of us, you ought to take a moment to read her “Steal It” articles! I believe they will really “hit home” as they did with me!

Happy Earth Day

Happy Earth Day Everyone! 
Earth Day is observed each year on April 22nd. The purpose of the day is to encourage awareness of and appreciation for the earth's environment. It is usually celebrated with outdoor shows, where individuals or groups perform acts of service to the earth. Typical ways of observing Earth Day include planting trees, picking up roadside trash, and conducting various programs for recycling and conservation.


Symbols used by people to describe Earth Day include: an image or drawing of planet earth, a tree, a flower or leaves depicting growth or the recycling symbol. Colors used for Earth Day include natural colors such as green, brown, or blue. The universal recycling symbol as seen on your left is internationally recognized and used to designate recyclable materials. It is composed of three mutually chasing arrows that form a Mobius strip which, in math, is an unending single-sided looped surface. (And you wondered how I would get math in this article!?!) This symbol is found on products like plastics, paper, metals and other materials that can be recycled. It is also seen, in a variety of styles, on recycling containers, at recycling centers, or anywhere there is an emphasis on the smart use of materials and products.

Free 8 Page Resource

Inspired by Earth Day, Trash to Treasure is an eight page FREE handout. Discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom. To download the free version, just click under the cover page on your right.




Recycled Butterflies

Two of my grandchildren are in kindergarten and of course, everything is new and exciting to them.  They came home one day with egg carton caterpillars.  I know most of us have made one of these in our lifetime, but to these two, they were the best craft ever!

They told me that their teachers were raising butterflies in their classroom, and soon they would hatch.  Anticipation and excitement reigned until the day they came out of school telling everyone that one of the butterflies had hatched.  However, much to their chagrin, the teacher was going to let it go.  They just couldn't understand why or how their teacher could do that!


But, here is the good part!  They got to make a cocoon out of a toilet paper cylinder.  They covered it by gluing on white cotton balls.  Then the made a butterfly out of tissue paper and a small plastic bag tie.  They put the butterfly inside the cocoon and then pretended to have the butterfly hatch!  This was done over and over and over until the cocoon was no more.  Luckily, I was able to get pictures before both were literally destroyed!

Now, what does all of this have to do with math?  I contemplated all the ways to use recycled products to make items for the classroom.  Thus Trash to Treasure was created. It is 34 pages of art ideas, fun and engaging mini-lessons as well as cute and easy-to-construct crafts all made from recycled or common, everyday items.
Only $7.00

Find out more than 14 ways to use milk lids for math. Did you know that you can practice math facts using clear plastic containers? Learn how to take two plastic plates and turn them into angle makers. How about using two plastic beverage lids to make card holders for kindergartners or for those whose hands are disabled? Discover ten ways to use carpet squares as well as nine ways to use old calendars. How about playing hop scotch on old carpet squares? Were you aware that butter tubs can become an indoor recess game to practice addition or multiplication facts? These are just a few of the fun and exciting activities that use recycled items found in this 34 page resource entitled Trash to Treasure.

Because these numerous activities vary in difficulty and complexity, they are appropriate for any PreK - 3rd classroom, and the visual and/or kinesthetic learners will love them.

Yes or No? Stay or Go? Solving for "x".


My basic algebra classes have just begun solving equations containing one unknown. As I tell them, we are inquisitive detectives looking for the unknown.

My students' greatest difficulty is deciding what stays and what goes in an equation. In other words, which term should be cleared by using the inverse operation and which term should stay where it is?

Hands-On Equation
 Balance Beam
www.borenson.com
I always start this chapter using Hands-On Equations®. I have used them for years because it provides a visual for those concrete learners. I also refer to the written equation as a teeter-totter or a see-saw which must always stay balanced. In other words, the equal sign is the pivotal point and both sides of that = sign must be the same.  (Notice that Hands-On Equations® uses a balance beam.) We also discuss the importance of the"Whatsoever thou doest to one side of the equation, we must doest to the other". (Out of necessity, I admit that I was with Moses when he received the Ten Commandments, but it "fell upon me" to convey The First Commandment of Solving Equations to future mathematicians.)

One Unknown
After much practice with the Hands-On Equations®, we move to actual written equations such as: x + 9 = 12. Here's the rub; a few of my students know the answer and do not want to show any of their work. Maybe some of you have this type of student as well. Since, after 30+ years, I am still unable to grade what is in their minds, I insist that all steps are written down. I explain that it's like riding a tricycle to ride a bicycle to ride a unicycle.

First, I instruct the students to look at the equation and determine which terms are out of place. (Side note: Because my students are easily confused, at the present, we keep all of the unknowns on the left side and all of the numbers on the right side of the equal sign.) Let's go back to our sample of x + 9 = 12. Because the x is already on the left side of the equation, the students write a "Y" over it for the word, "Yes". The 9 is on the wrong side of the equal sign, so the students write a "N" over it for "No".  Finally, they write a "Y" over the 12 since it is the correct place. They now have exactly what they want, a Y and N on the right side and a Y on the left side. They now must clear anything that has a "N" over it.  The students recognize they if they use the inverse operation of addition, they can clear the 9. They therefore subtract 9 from each side of the equation resulting in an answer of 3.

Many algebra teachers will have the students write the step x + 0 = 9.  You may wish to include this step in the process, but since my college students readily see that +9 and -9 make zero, they put an X over the two opposites to show that they cancel each other out or when added together, they equal zero.

What if the equation is: 3 = y - 4? This always freaks my students out; yet, if they do the yes/no process, they will discover that they have two "no's" and one "yes", not a yes, no = yes.  This means they can rewrite the equation as y - 4 = 3 to get a yes, no = yes. The problem can now easily be solved like the one above.

Unknown on both sides
of the equation
The next step is what to do when an unknown appears on both sides of the equal sign.  Usually, my students are sure they are incapable of solving such a difficult problem, but let's use the yes/no method and see what it looks like. 

Notice in the sample on the left that we have a yes, no = no, yes. We start by clearing the "N" on the left hand side of the equation by using the inverse of -9. We then go to the right side and clear the y by using the inverse operation of addition. (Yes, I am aware both can be cleared at the same time, but again simple and methodical is what is best for my mathphobics.) We then divide each side by 4 resulting in the answer of 3. When the problem is completed, my students are amazed and proud that they could solve such a long equation. (You might notice in the illustration, a dotted line is drawn vertically where the equal sign is. This helps my visual students to separate the two sides of the equation.)

If any of you try this approach with your students or have a different method, I would love to hear from you. Just leave a comment and a short statement of how this process worked for you or what process you use that is even better. That way, we can learn from each other.

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Hands-On Equations® is algebra for the visual and kinesthetic learner. This system, developed by Dr. Henry Borenson, enables students (even those in 4th or 5th grade) to easily learn essential algebraic concepts and skills. Dr. Borenson received a U.S. patent for his teaching invention.

Metrics - Not Going the Whole Nine Yards!

Did you know that there are only three nations which do not use the metric system: Myanmar, Liberia and the United States? The U.S. uses two systems of measurement, the customary and the metric. Yes, since our country does use the metric system, we have given more than an inch, but we haven't gone the whole nine yards.

Today, when we shop for groceries, soda is sold in liters. Medicine is sold in milligrams, food nutrition labels are metric, and what about a 100-meter sprint or a 5K race? Still, we are the only industrialized nation in the world that does not conduct business in metric weights and measures. To be or not to be a metric nation has been a question of great consternation for our country for many years.

Here are some reasons why I think our nation should go to the metric system.
  1. It's the measurement system 96% of the world uses. 
  2. It is much easier to do conversions since it is based on units of ten. Water freezes at zero, not 32°, and it boils at 100, not 212°. 
  3. Teaching two measurement systems to children is time consuming and confusing. 
  4. It is the "official" language of science and medicine. 
  5. Its use is necessary when you travel outside of the United States. 
  6. Conversion from customary to metric is often fraught with errors. Because the metric system is a decimal system of weights and measures, it is easy to convert between units. 
  7. There are fewer measures to learn. Once you learn the meaning of the prefixes, you can easily convert mass, volume and distance measurements. No further conversion factors need to be memorized except the specific power of 10. For the Customary System you have to remember 5280 feet = 1 mile, 4 quarts = 1 gallon, 3 feet = 1 yard, 16 oz. = 1 pound, etc. 
  8. And just think, I would have less clutter in my kitchen since I wouldn’t need liquid and dry measuring cups or teaspoons and tablespoons! All I would need is a scale and liquid measuring cups!
So, while most nations use the metric system, the United States still clings to pounds, inches, and feet. Why do you think Americans refuse to convert? I’d be interested in your perspective and ideas.

A Go Figure Debut for Amy Lynn who is new!

Amy Lynn's Store
Amy Lynn has been teaching for 12 years. For her first three years, she was a K-5 science teacher at a magnet school in Tampa, with a side role of being the drama teacher. From there, she and her husband moved to NYC so she could pursue acting, and he could pursue music. While in New York, she taught second grade for seven years at a Christian school while starting up a drama club on the side. (She studied and performed improv at night with the upright Citizens Brigade Theater).

Amy then discovered she was pregnant! A son was born, and the three of them lived in a tiny (280 sq. ft.) studio apartment. (Talk about tiny house living!) At that point, they were a bit tired, and having accomplished a great deal, they packed up and moved back to Tampa, where she is now an elementary special needs teacher. As you can see, her teaching experience is broad...from inner city science...to a private school...to now. Knowing that no day or year is the same is what she loves about teaching.

Amy claims to be eclectic, as is her classroom. It is colorful, with a side of the arts and a side of Zen. She incorporates skits into many lessons (Her drama background seems to keep rearing its head). She has a corner filled with tactile stress balls/tubes/instruments that students can visit when they just need a mental break. Other teachers stop in and use them too, which is always fun. She LOVES fun. She loves it when her students laugh and feel safe to be themselves.

Only $7.00
Amy married the boy next door whom she met as a seven year old and has loved ever since. (They are those kind of people.) They both work hard during the week; so, on the weekends, when not at church, they can be found on the beach, on a bike trail, or just at home, reading books together in a hammock.

Amy is a HUGE fan of creating materials that any teacher can use with as little prep as possible. One such resource is entitled Word Wall - 100 Printables for Any Word Wall. This product includes 100+ printables/activities/skits to use with any class word wall.  It can be used as centers, seatwork, early-finishers or more! Skit writing and performance pages, creative writing, seatwork for individual and for partner work, dictionary and Thesaurus skills, poetry, games, and much more are included in this activity pack of 106 different printables and games for ANY WORD WALL!

Amy currently has over 134 products in her store. Of these, 24 are free, many of which are science items.

One such freebie is on food chains. It contains four fun and simple activities to help engage students as they learn! Included is:
Free Resource
  • A graphic organizer for students to color and fill in their prior knowledge
  • Two "Create a Food Chain" pages
  • A full color page that can be used as seat-work, and then as a colorful wall display of what your students have learned!
Her store is as varied as her 12 years of teaching have been. She has many desk/center labeling tags to help teachers change the looks of their rooms, packets of 100 standards aligned anytime reading/math/writing/language printables per grade level, yearlong Dolch activity packs, and Christian resources as well. There seems to be something for everyone!

Her current goal, (You can see a sample by clicking on her "superhero theme" category at her storefront, as this category is almost complete) is to create grade level standards aligned themed printables that will assist teachers as they endeavor to incorporate their school’s yearly themes. These will include themed 100th day packs, 100 standards aligned printables, reward coupons, free "getting to know me" pages, as well as end of the year memory books/ writing sets. So if anyone knows their school’s upcoming themes and would love these types of resources, she would love all your suggestions! Just go to her store and click on “Ask A Question.”