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Amber Alert! The Baby is Missing!

This will be my last blog article until January 1st. I want to take a much needed break from teaching, blogging and technology to have an old fashioned Christmas with my family - my husband, three grown children and 11 grandchildren. 

There is a 2000 devotional in Our Daily Bread (a daily devotional booklet) entitled Where's the Baby? which I think is excellent, and I wanted to share it with you this Christmas season. It goes like this.

*Two women, who were dressed in their finest, were having lunch together in a very exclusive restaurant. A friend saw them and came over to their table to greet them. "What's the special occasion?" she asked. One of the women said, "We're having a birthday party for the baby in our family. He's two years old today." "But where's the baby," the friend asked. The child's mother answered, "Oh, I dropped him off at my mother's house. She is taking care of him until the party is over. It wouldn't have been any fun with him along."

How ridiculous! A birthday celebration for a child who wasn't welcomed at his own party!?! Yet, when you stop to think about it, that's no more foolish than going through the Christmas season without remembering the One whose birth we are supposed to be honoring! And that's how many people celebrate Christmas. In all their busyness - the party going, gift shopping, decorating, and family gatherings - the One whose birthday they are commemorating is almost completely forgotten.

Jesus Christ, the Greatest Gift of All!
As you move through the holiday season, in all of your good times with your family and friends, make sure you don't leave out the Lord Jesus. Give Him the honor He deserves.

Christmas blessings to each of you.  May God abundantly bless you in the new year of 2020 with much joy and contentment.

*DeHaan, Richard, Where's the Baby? Our Daily Bread, Dec. 14, 2000, RBC Ministries,

A Go Figure Debut for a Creative Math Teacher Who Is New

Kate's Math Lessons
Even though her TPT store is called Kate’s Math Lessons, her real name is Sarah, not Kate. She named her website after her daughter, because she figured her students would respond better if they didn't know she had made it! She married her high school sweetheart, and they have two little girls. She taught for 11 years before choosing to stay home with her two young daughters.

Sarah says that her favorite part of teaching was playing math games with her 8th graders. Middle school is exhausting to teach, but the kids are so fun. Sarah loves to read (James Patterson is her favorite author) and play the piano in her free time. She also loves board games; her family gets competitive when they play Settlers of Catan!

Sarah loves creating printable and digital resources for secondary math teachers and students! Her website (also called Kate's Math Lessons) has Pre-Algebra, Algebra 1, Geometry, and Algebra 2 on-line lessons with examples, videos, and practice quizzes that are all free for students and teachers to use. She wants students to understand WHY math works instead of trying to memorize tricks or little sayings that are easily forgotten. Sarah focuses on conceptual understanding and prefers anything with instant feedback to prevent students from practicing a skill incorrectly. (She is my kind of math teacher!)

Her store currently contains 246 resources; 17 of those are free. They are geared for middle school math through Algebra 2. Sarah wants students to know right away if they're on the right track when practicing a new skill, so most of her resources are self-checking or graded on-line automatically. Truly, it is a win-win situation: immediate feedback for students and less time spent grading for teachers! Sarah loves using QR codes, Google quizzes that can be edited and graded automatically, and digital Boom Cards that give students instant feedback on their answers.

Free Item
Sarah’s featured free item is Order of Operations Boom Cards (digital task cards). Maybe you have never tried Boom Cards and have no idea what they are. In a nutshell, Boom Cards are digital, self-checking, interactive activities. Students are shown one question at a time and get instant feedback on their answers! Check out a short video on Kate’s Blog to see a few examples. Also, here's a blog post Sarah wrote that's helpful for people new to Boom Cards: What are Boom Cards? 

Algebra 1 Review Google Drive Activity is Sarah’s featured paid item. This is an editable activity and is set up to be graded on-line automatically. The activity includes 30 review questions which are a great way to help students get ready for a final exam or a state test! Since it is editable, you can add or delete questions, change the answer type or even the order of the questions.

Check out Kate’s math lessons on YouTube. As a college math teacher, I am more than impressed!  Her YouTube Channel was recently named one of the top 100 Math YouTube channels! Watch just one video, and you will understand why.

Free Winter Ebook for Grades Pre-K-High School - Filled With Ideas and Lessons for the Winter Holidays

Free Resource
Each year, the members of The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC) put together free Ebooks which contain an assortment of ideas, lessons and free handouts for grades PreK-High School.

Our newest Holiday Ebook contains free Christmas lessons as well as handouts and ideas for Hanukkah, Kwanzaa and Martin Luther King, Jr. Day. Just click on the link under the Ebook cover on your left to download the Winter Ebook. Then peruse the book and click on any of the links to the free 20 holiday lessons in which you have an interest.

In addition, our previous Ebooks are still available for downloading. By doing so, you will receive hundreds of free lessons that you can use throughout the school year!

Happy Thanksgiving!

If you can't thankful then you will just be full!
My wish is that you will enjoy time with your family and your friends!

Science Investigations Packet for Grades 3-4

Learning to love math and science is important for so many reasons as our world becomes more dependent on technology. Science can spark imagination, initiate problem solving, require logical thinking, and so much more.  As any scientist knows, the best way to learn science is to do science. This is the only way to get to the real business of asking questions, conducting investigations, collecting data, and looking for answers. Active, hands-on, student-centered inquiry is at the core of good science education.
Only $4.30

Having children do science investigations can be fun, but having the students accurately record things can be extremely difficult. Since my husband teaches science, he helped me to create my newest product on Teachers Pay Teachers - a 12 page generic science investigation packet for grades 3-4. The inquiry packet guides the student through the six steps of the scientific method: 
  1. Investigating Properties 
  2. Interactions
  3. Making a plan 
  4. Determining the Investigative Question 
  5. Prediction and Data Collection 
  6. Writing a conclusion based on the data. 
This packet consists of an introduction, simple and clear step-by-step directions on how to use the packet, a three page student investigation packet, a blank graphing grid, a property word list, an optional student checklist and a four point grading rubric for the teacher. I hope you find it to be a valuable classroom resource.

A Go Figure Debut for A Texan Who Is New!

Laura's TPT Store
Laura is a physics teacher that started teaching in 1998. Her undergrad and masters are from Texas A&M University. She is a certified 6-12 Science Composite and 4-8 Math/Science. She originally wanted to be a large animal veterinarian but got the teaching bug after she taught horsemanship clinics for Texas A&M one summer. Laura feels she clearly was born to be a teacher!

She loves students of all ages. One of her biggest thrills is when she hears them use academic language when discussing a problem with each other. Academic language! Willingly! Correctly! She is addicted to hearing students having scientific conversations.

Even as a first year teacher, Laura wrote her own curriculum. The internet was in its early years, and there wasn't a huge amount of resources out there. Even now, she says it is very hard to find physics resources that are ready to use for the classroom. Because she has always written her class notes to clearly defined objectives that are based on the state standards of Texas, everything is in tight alignment with those stated objectives.

Back in the day before standardized testing was such a push, Laura had a tremendous amount of latitude to get her students researching and learning. They took a field trip to AstroWorld (now defunct) to do physics experiments. She took her Chemistry class to a SCUBA center and learned about SCUBA diving in correlation with her Gas Law unit. The students even got to dive in the center pool, so they were able to make those real life connections to science.

As you can tell, her teaching style is quirky, fly by the seat of her pants. Laura is willing to try most ideas at least once! She even made it into the newspaper twice with her zany exploits. In addition, she successfully won two equipment grants.

Fast forward to the increasingly focused high stakes era, and Laura has had to look for other ways to express creativity. To that end, she writes silly problems. Sure, her students learn about what the specific objective is, but she frames it in the zombie apocalypse. She has long thought she could write an entire year's curriculum in the zombie apocalypse as one long PBL. Maybe one day!

Laura’s store, Delzer's Dynamite Designs, contains 150 resources related to science; six of those
Free Resource
products are free. Her featured free resource, It’s a Gas, is the first item she created. It looks basic, but it is honestly a fun, hands-on way to learn about gas molecule movement as you manipulate temperature, volume, moles and measure pressure. The students act like molecules, and music is used to model temperature.

Claim-Evidence-Reasoning Activity and Lab is a paid resource. Enclosed in this resource is a set of
Only $3.50
Doodle Notes over CER (Claim, Evidence, Reasoning). Laura has included a selection of five commercials to practice CER skills as well as one of her super reliable labs to elaborate and practice CER. Doodle Notes act as a CER graphic organizer to help provide visual cues of how each component reinforce each other. This helps students to activate both hemispheres of the brain and make visual connections to the material, while helping to defuse anxiety.

If you are a science teacher, Laura’s Teachers Pay Teachers store is worth checking out. You will find many fun, engaging and creative resources that you can easily adapt to your classroom. AND your students will have a fun and exciting time learning science.

Glyphs Are Really A Form of Graphing - Completing a Turkey Glyph

Only $3.00
Sometimes I think that teachers believe a glyph is just a fun activity, but in reality glyphs are a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and requires a legend/key to understand the glyph. The creation of glyphs requires problem solving, communication as well as data organization.

Remember Paint by Number where you had to paint in each of the numbers or letters using a key to paint with the right color? How about coloring books that were filled with color-by-number pages? Believe it or not, both of these activities were a type of glyph.

For the Thanksgiving, I have created a Turkey Glyph. Not only is it a type of graph, but it is also an excellent activity for reading and following directions.

Students are to finish the turkey glyph using the seven categories listed below.
  1. Draw a hat on the turkey (girl or a boy?)
  2. Creating a color pattern for pets or no pets. 
  3. Coloring the wings based on whether or not they wear glasses. 
  4. Writing a Thanksgiving greeting based on how many live in their house. 
  5. Do you like reading or watching TV the best? 
  6. How they get to school. (ride or walk)
  7. Pumpkins (number of letters in first name)
At the end of the activity is a completed Turkey Glyph which the students are to "read" and answer the questions. Reading the completed glyph and interpreting the information represented is a skill that requires deeper thinking by the student. Students must be able to analyze the information presented in visual form. A glyph such as this one is very appropriate to use in the data management strand of mathematics.  If you are interested, just click under the resource cover page above.

Making Parent Teacher Conferences Meaningful

Are You….....
  • Tired of always talking about grades at parent/teacher conferences? 
  • Tired of feeling like nothing is ever accomplished during the allotted time? 
  • Are you having problems with a student, but don’t know how to tell the parents? 
  • Do you want to be specific and to-the-point? 
When I taught middle school and/or high school, these were the items that really discouraged me. I knew I had to come up with a better plan if I wanted parent/teacher conferences to be worthwhile and effective for both the student and the parents. I created a a checklist that I could follow, use during conferences, and then give a copy to the parents at the end of the conference.  It contained nine, brief, succinct checklists which were written as a guide so that during conferences I could have specific items to talk about besides grades. I found it easy to complete and straight forward plus it provided me with a simple outline to use as I talked and shared with parents.

Since other teachers were able to use it successfully, I took that checklist and turned it into a resource called Parent/Teacher Conference Checklist, Based on Student Characteristics and Not Grades. Nine different categories are listed for discussion.  They include:
  1. Study Skills and Organization 
  2. Response to Assignments 
  3. In Class Discussion 
  4. Class Attitude 
  5. Reaction to Setbacks 
  6. Accountability 
  7. Written Work 
  8. Inquiry Skills 
  9. Evidence of Intellectual Ability 
To get ready for conferences, all you have to do is place a check mark by each item within the category that applies to the student. Then circle the word that best describes the student in that category such as "always, usually, seldom". (See example above.)

Finally, make a copy of the checklist so that the parent(s) or the guardian(s) will have something to review with their student when they return home.

Now you are ready for a meaningful and significant conference.

A Go Figure Debut from a New Yorker Who Is New!

Jillian has been an educator for over 11 years. She has her bachelor’s
degree in Childhood Education and her Master's in Mathematics. Before starting her career as an educator, she worked for a nutraceutical marketing and sales company which was geared towards selling all-natural vitamins and supplements. Shortly after being hired in sales, she became the training manager for the company which gave her invaluable experience in the business world! She has taught grades 1-3 as well as 6-8 grade math. In addition, she has had the privilege of being a technology consultant where she gained extensive knowledge on how to train teachers and administrators on how to use various types of technology. She is currently on maternity leave, taking care of her amazing daughter. She also has two fur babies, Rambo and Debo who are the best big brothers ever!

Jillian’s Teachers Pay Teachers store called Count on Me contains 361 resources, with 15 of the
items being free. She offers a free template for a square cover to TPT sellers. If you are just starting out on TPT or if you want to give your products an awesome update, use this template. The template has a clean and chic look that will make your resources stand out to your buyers. It's like going to a store and seeing a familiar brand - you are going to be more likely to buy the brand you've seen before than one you haven't. Branding yourself is the best way to get repeat buyers who know the quality of your resources. The template is easy to edit right in PowerPoint. You can change the fonts, colors and formatting to meet your needs. The best part is you can use this template over and over for all your resources, so you don't have to start from scratch every time!

Jillian’s featured paid resource is a math bundle entitled 7th Grade Math Puzzle Piece Matching Games Bundle. These super engaging low prep matching games will help your students practice 7th
grade math concepts in a fun way! This bundle has a review of all 7th grade math concepts! Jillian’s students really enjoyed these puzzle pieces and making all the matches. The answer keys and recording sheets are included to keep students on track.

While she is out of the classroom, she is fortunate to be able to work from home creating engaging and fun resources for Teachers Pay Teachers, as well as designing digital resources on Etsy! When creating resources, you will find her either creating engaging math games or products geared towards TPT sellers to help grow their businesses and brands. Her husband is a small business owner with five well established and extremely successful businesses. He has been the inspiration behind her taking the proper steps to grow her business and taking charge of her own destiny. She feels fortunate to have his guidance.

This is why Jillian has ventured into coaching and consulting some AMAZING people looking to grow their brands and businesses. Teachers Pay Teachers is a wonderful way to make money, but it can be super overwhelming to get started. Plus, it can be difficult to understand ways to market yourself if you have already opened your store! Jillian has a passion for helping people and seeing others become successful. She is incredibly proud to see the people she has coached thriving and making huge growth in their stores and online presence. She would love to be that person to help guide you, help you stay accountable, and help you understand how to take that next step on the path of growing your brand and your business. For more information, you also might check out her Instagram account and her website

The Dreaded Math Curse - Linking Literature and Math

I love books that link math and literature, and one of my favorites is Math Curse by Jon Scieszka. Published in 1995 through Viking Press, the book tells the story of a student (I’m not sure from the illustrations if it is a boy or a girl) who is cursed by the way mathematics works in everyday life. It is a tale where everything is a math problem, from tabulating teeth to calculating a bowl of corn flakes. Everything in life becomes a math problem.

First you see the math teacher, Mrs. Fibonacci, (don’t you love that name?) declare, “You know, you can think of almost everything as a math problem.” Then you watch as the student turns into a “raving math lunatic” since s/he believes “Mrs. Fibonacci has obviously put a math curse on me.”

From sunrise to sunset, the student anxiously mulls over the answers to countless calculations such as: How much time does it take to get ready and be at the bus stop? (a problem the reader can solve.). Estimate how many M Ms you would eat if you had to measure the Mississippi River using M Ms. There is even an English word problem: “If mail + box = mailbox, does lipstick – stick = lip? Does tunafish + tunafish = fournafish?” (silly, but funny.) A class treat of cupcakes becomes a study in fractions, while a trip to the store turns into a problem of money. The story continues until the student is finally free of the math curse, but then again Mr. Newton, the science teacher, regrettably says, “You know, you can think of almost everything as a science experiment.”

Math Curse is full of honest to goodness math problems (and some rather unrelated bonus questions, such as "What does this inkblot look like?"). Readers can try to solve the problems and check their answers located on the back cover of the book. The problems are perfect to get students’ minds working and thinking about how math really does apply to their everyday life.

The illustrations by Lane Smith are one of a kind. They are busy and chaotic to reflect the “math zombie” this student becomes. Many resemble a cut and paste project, with some images touching or overlapping others. Mostly dark colors are used especially when the student begins to dream s/he is trapped in a blackboard room covered with never-ending math problems. (a nightmare for many) Smith’s art work makes Scieszka's words come to life and helps to paint a picture of what is going through the mind of the main character as s/he deals with the dreaded math curse.

John Scieszka does a remarkable job of breaking down the typical school day into math problems while also adding some tongue-in-cheek and light hearted humor which every mathphobic needs. The math is perhaps a little advanced for elementary students, but the problems are perfect for middle school or high school students.

Math Curse also demonstrates how a problem may seem difficult, but if you are persistent, you can find the solution to the problem. The book teaches not to fear or be anxious about math or for that matter, any other subject in school. Despite the fact the main character is completely overwhelmed by mathematics, it allows students who struggle with the identical feeling to know they are not alone. Any student who has ever been distressed over numbers, fractions, word problems and the like will certainly identify with the main character.

As a math teacher, I think this book makes math fun as well as interesting. Although I recognize math is everywhere in everyday life, I never realized just how much until I read the Math Curse and mathematically saw the day of a typical student. I believe what sets Math Curse apart from other books is that it accurately illustrates and explains how math is actually used and applied in day-to-day life. I love the story, the message, and especially the content.

October - Is It "Fall" or "Autumn"?

It's finally October, one of my favorite months of the year. October means football (Ohio State, of course), cooler weather and gorgeous leaves. (It is also when my husband and I were married.) In October, we see the leaves turning colors, and the deciduous trees shedding their leaves.

Another name for fall is autumn, a rather odd name to me.  Through research, I discovered that the word autumn is from the Old French autumpne, automne, which came from the Latin autumnus. Autumn has been in general use since the 1960's and means the season that follows summer and comes before winter.
Fall is the most common usage among those in the United States; however, the word autumn is often interchanged with fall in many countries including the U.S.A. It marks the transition from summer into winter, in September if you live in the Northern Hemisphere or in March if you live in the Southern Hemisphere.  It also denotes when the days are noticeably shorter and the temperatures finally start to cool off. In North America, autumn is considered to officially start with the September equinox. This year that was September 23rd.
With all of that said, the leaves in our neighbor's yard have already begun to fall into ours which aggravates my husband because he is the one who gets to rake them. Maybe focusing on some activities using leaves will divert his attention away from the thought of raking leaves to science investigations.  
Remember ironing leaves between wax paper?  We did that in school when I was a little girl (eons and eons ago).  Here is how to do it.
  1. Find different sizes and colors of leaves.
  2. Tear off two sheets about the same size of waxed paper.
  3. Set the iron on "dry".  No water or steam here!
  4. The heat level of the iron should be medium.
  5. Place leaves on one piece of the waxed paper.
  6. Lay the other piece on top.
  7. Iron away!
You can also use this activity to identify leaves.  According to my husband who knows trees, leaves and birds from his college studies, we "waxed" a maple leaf, sweet gum leaf, elm leaf, cottonwood leaf (the state tree of Kansas - they are everywhere), and two he doesn't recognize because they come from some unknown ornamental shrubs.
Leaf Investigation

Maybe you would like to use leaves as a science investigation in your classroom.  I have one in my Teacher Pay Teachers store that is a six lesson science performance demonstration for the primary grades. The inquiry guides the primary student through the scientific method and includes 1) exploration time, 2) writing a good investigative question, 3) making a prediction, 4) designing a plan, 5) gathering the data, and 6) writing a conclusion based on the data. Be-leaf me, your students will have fun!

(A preview of the investigation is available. Just click on the title under the resource cover.) 

Using 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 a Canadian Science Teacher Who Is New!

Mo, of Big Red Science, is heading into her tenth year of teaching. She has taught in Canada, Italy, Micronesia, and on a tall ship while sailing the world!  Like most teachers, she loves the relationships she develops with her students. When a new school year starts, she is always eager to fast forward about two months to a time when she knows that her students and she will have created their own unique environment together full of positivity, comfort and a few ‘class inside jokes’!  Over the years, what she has learned about herself is that she develops these relationships through the learning that takes place. Mo loves the challenge of taking a concept that seems confusing or boring and tackling it in a way that makes students find joy in learning new things. She says that there is something about guiding students in their science and math journeys that really strengthens the relationships that she has with them.
At Mo’s school, each teacher has a desk in their departmental office, and then the teachers float between multiple classrooms each day. (Sounds like what I do on the college level.) This means that her décor is nothing special! (In other words, no bulletin boards to do!)  The vibe of whatever classroom she is in is relaxed because students feel comfortable with her. She also thinks it is important for students to know each other so she encourages numerous group work activities and tries to find ways for her students can talk to each other early and often. 

Bringing variety to her lessons is also a key component of her personal philosophy of education. She believes that if everything is the same day after day, students won’t be able to distinguish one day or topic from the next. Therefore, Mo fills her classes with as many different types of activities as she can find like games, case studies, labs, simulations, models, skits, foldables, watching and making videos and podcasts, debates, ‘speed dating’, question trails, storytelling, typical lectures…all kinds of stuff!  

Mo has lots of interests outside of teaching including singing, playing games, traveling, spending time at her cottage and recently squash. And the one thing that she will always, ALWAYS say yes to is an escape room. She and her partner have probably done thirty of them, and they claim they are pretty good!

FREE Resource
Currently, Mo has 60 resources in her store, Big Red Science, and nine of those items are free. One of her free items Fish and Polar Bear Back to School Inquiry Activity is a great way to get students to work together in a low-pressure situation while at the same time asking questions and using the scientific method intuitively. She uses it as an early ice breaker, but it can be done at any time of the year!

Only $3.00
Her featured paid item, YouTube Alternative Bell Ringer Assignment, is an engaging way to start a class. This assignment has students sift though You Tube to find a video that relates their science class to the real world. Mo has used this assignment in various classes for years, and notices that students always find incredibly interesting and engaging content.

Mo also has a blog called Big Red Science. (Can you guess how she got that name?) I found her articles to be engaging as well as practical. Take some time to check it out as well as her Teachers Pay Teachers store. There are products for general science, biology, chemistry and math. In addition, she has games, diagrams, movie guides, question trails, some décor, and video and podcast assignments. You will discover her products reflect the variety that she values in her classroom. 

The Left Angle Mystery - Does Such an Angle Exist?

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.

Only $3.25
If you would like some different hands-on ways to teach angles, you might look at the resource entitled, Angles: Hands-on Activities.
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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!

Only $3.00
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!)

To help your students learn their multiplication facts, you might like the resource entitled Pattern Sticks. It is a visual way of showing students the many patterns on a multiplication table.

Unlocking Fractions for the Confused and Bewildered - A New Approach to Teaching Fractions

I teach remedial math on the college level, and I find that numerous students are left behind in the mathematical dust if only one strategy is used or introduced when learning fractions. Finding the lowest common denominator, changing denominators, not changing denominators, finding a reciprocal, and reducing to lowest terms are complex issues and often very difficult for many of my students.

I classify my students as mathphobics whose mathematical anxiety is hard to hide. One of my classes entitled, Fractions, Decimals and Percents, is geared for these undergraduates who have never grasped fractions. This article encompasses how I use a different method to teach adding fractions so these students can be successful. Specifically, let's look at adding fractions using the Cross Over Method.

Below is a typical fraction addition problem.  After writing the problem on the board, rewrite it with the common denominator of 6.

1) Ask the students if they see any way to multiply and make a 3 using only the numbers in this problem.

2) Now ask if there is a way to multiply and make 2 using just the numbers in the problem.

3) Finally, ask them to find a way to multiply the numbers in the problem to make 6 the denominator.

4) Instruct the students to cross their arms. This is the cross of cross over and means we do this by cross multiplying in the problem.

5) Multiply the 3 and 1, then write the answer in the numerator.  *Note: Always start with the right denominator or subtraction will not work.

6) Next multiply the 2 and 1 and write the answer in the numerator. Don’t forget to write the + sign. *Note: One line is drawn under both numbers. This is to prevent the students from adding the denominators (a very common mistake).

7) Now have the students uncross their arms and point to the right using their right hand. This is the over part of cross over. It means to multiply the two denominators and write the product as the new denominator.

8) Add the numerators only to find the correct answer.

9) Reduce to lowest terms when necessary.

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It is important that students know the divisibility rules for 2, 3, 5, 6, 9 and 10. In this way, they can readily reduce any problem. In addition, it is extremely important that the students physically do the motions while they learn. This not only targets the kinesthetic learner but also gives the students something physical that makes the process easier to remember. The pictures or illustrations for each technique also benefit the visual/spatial learner. Of course, the auditory student listens and learns as you teach each method. 

I have found these unconventional techniques are very effective for most of my students.  If you find this strategy something you might want to use in your classroom, a resource on how to add, subtract, multiply, and divide fractions is available by clicking the link under the resource cover.

A Go Figure Debut for A Tutor Who Is New!

Caroline lives on the beautiful Wirral Peninsula, in between Liverpool and Chester, in the UK with her husband Ray. They have five grown up children and one grandchild. When they are not working. they love to travel and to spend time with their family and friends.

Caroline left the classroom around five years ago to start her own tutoring business; hence, the name of her Teachers Pay Teachers Store – The Booked Up Tutor. She worked for eight years as a teaching assistant at an inner-city primary school and while there gained a First-Class Honours Degree in Teaching. (An honours degree is a grading classification in the United Kingdom that distinguishes achievements of undergraduates. A degree with honours denotes a degree in a given subject that requires a higher level of academic learning and achievement.) She wanted the freedom to combine her years of experience with her interest in how we all learn differently while at the same time having the freedom to run her own business. She says she has never looked back and now help many students each week to improve their math and English. For her, to be fully booked with a permanent waiting list, is a wonderful feeling because she was just like the kids she now tutors. She could NOT do math and would sit and cry during lessons. Caroline never wants any child that she teaches to feel that way; she wants them to achieve what they can achieve and to be the best possible version of themselves.

Caroline of The Booked Up Tutor
By tutoring, she has become very adept at quickly identifying weak areas in math and subsequently helping students to improve greatly. She teaches her students quick mental math strategies that help them, and always starts by making sure that they know their number bonds (alternatively called an addition fact) to ten. Sadly, she has discovered that even some eight and nine-year olds don’t know them. (I teach college students who don’t know them!) Once they know these, it is a smooth transition to learn them to 100 and then 20 and then beyond that. She is also a huge multiplication fan. She believes times tables are the golden key to math in primary school and if a student doesn’t know them then obviously, they will struggle with division, fractions, prime numbers, area of shapes and many other things. (I see this all the time as I tutor college students in the Math Lab at the college where I teach.) 

Caroline has 385 diverse and assorted resources in her store. Her resources have all been developed from the ground up thanks to her students who range in age from 5 to 11 and sometimes older. Her products tend to share the theme of over-learning as that is what students often must do, but it works, and it helps her struggling students with reading and math.

One of her free items is called Number Bonds to 10. This FREE pack contains her number bonds rhyme that help students remember the number facts to ten plus color-coded support worksheets that teach the fact families. Help your students easily learn the addition and subtraction facts within ten by downloading this free item. 

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If you would like another resource for multiplication, check out her bundle called Multiplication Worksheets Bundle. Master multiplication worksheets, multiplication facts and division facts 1 to 12 with these 12 x 34-page booklets of multiplication worksheets. Self-paced times tables booklets (with answers) help students understand and secure basic math mastery of times tables and multiplication fluency through skip-counting, arrays, multiples, fact families and self-assessment. Use for extra practice, math homework, in remediation groups, for special education, math intervention or math centers.

As a late-comer to Math, Caroline really enjoys making sure no child is left behind with poor teaching, as she was. She never stops learning; her experience grows every single day and her students benefit from that. This is evident in the resources she creates; so, be sure to take some time to check them out.

Developing and Writing Effective Lesson Plans for Math

We often hear of research based strategies and how to use them in our classrooms. Having worked at two colleges in the past ten years, I have discovered that some who are doing this research have never been in a classroom or taught anyone under the age of 18!  (Sad but True)  Then there are others who truly understand teaching, have done it, and want to make it more effective for everyone. That's the kind of research I am anxious to use.  I came across the Conceptual Development Model while teaching a math methods class to future teachers. It was one of the first research models that I knew would work. 

The Conceptual Development Model involves three stages of learning: 1) concrete or manipulative, 2) pictorial, and 3) the abstract.  The concrete stage involves using hands-on teaching which might involve the use of math manipulatives or real items. Next, the pictorial stage utilizes pictures to represent the real objects or manipulatives. A visual such as a graphic organizer would also fit in this stage. Last, the abstract stage of development entails reading the textbook, using numbers to compute, solving formulas, etc. Let's look at two classroom examples.

Example #1:  You are a first grade teacher who is doing an apple unit.  You decide to have the children graph the apples, sorting them by color.

Concrete:  Using a floor graph, the children use real apples to make the graph.

Pictorial:  The children have pictures of apples that they color and then put on the floor graph.

Abstract:  The children have colored circles which represent the apples.

Example #2:  You are a fifth grade teacher who wants to teach how to find the volume of a cube or rectangular solid.

ConcreteBring a large box into the classroom, a box large enough for the children to climb inside, OR have the students build 3-D objects using multi-link cubes.

PictorialGive the students pictures of 3D objects which are drawn but shows the cubes used to make the solid. Have the students count the cubes to determine the volume.

AbstractHave students use the formula l x w x h to find volume.

Requiring my perspective teachers to think about this model and to use it when planning a math unit dramatically changed the quality of instruction which I observed in the classroom. 

Writing Math Lesson Plans
Now that I teach mathphobics on the college level, I am finding this model to be a crucial part of my planning.  Most of my students started math at the abstract level, "Open your books to page...." without any regard to the other two stages of development. Using manipulatives and graphic organizers have changed my students' ability to learn math, and some have even ended the semester by saying, "I like math". Maybe this is a model we should all consider implementing.

If you want more examples and suggestions about using this model to write math lesson plans, click on the link below the resource cover

Also look at the resource entitled Graphing without Paper or Pencil in which is appropriate for grades K-5 and is based on the Conceptual Model of Development: concrete to pictorial to abstract.

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