My blog posts will return on Wednesday,

**August 9th**

My blog posts will return on Wednesday,

Jill's TPT Store |

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 |

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

Free 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!

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!

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

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!

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).

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!)

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

Martian Fingers |

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

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

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!)

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!

Lindsay's TPT Store |

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

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.

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!

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.

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 **4**1 by the first digit of **1**2 to get the first digit of our answer. We then multiply the second digit of 4**1** by the second digit of 1**2** 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.

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

Let's assume we have the multiplication problem of

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.

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.

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 was first introduced to it on the Teachers Pay Teachers blog. Since I use

I saw several benefits right away! More traffic was coming to my **Pinterest boards** as well as to my **Teachers Pay Teachers Store. **I 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:

- To schedule pins
- To know when the best time to pin is using the Smart Calendar
- To schedule multiple pins to different boards at the same time
- To use interval pinning
- To use the Tailwind Analytics - to know which are my best pins and where my repins are going
- 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.

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**.

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

Her TPT store is called

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!

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.

Here is what I purchased to complete the giant card.

- A large folding poster (You need heavy poster board to hold all of the candy!)
- A Nestle's Symphony Bar
- A Snickers Bar
- Nestle Crunch
- One package of EXTRA chewing gum
- 100 Grand Candy Bar
- Butterfinger
- Skor Candy Bar
- Mr. Goodbar
- Package of Milk Duds
- 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!

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.

With that said, I have discovered that my college students

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?

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 90^{○ }is called a __right angle__.

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,

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

Lauren's Store |

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,

Free Resource |

Only $3.00 |

Her Blog |

Happy Earth Day Everyone! |

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,

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

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

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.

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?

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.)

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.

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 Beamwww.borenson.com |

One Unknown |

First, I instruct the students to look at the equation and determine which terms are out of place. (

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.

What if the equation is: 3 =

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.

Unknown on both sides of the equation |

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.

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.

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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