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Taking A Summer Three Week Break

Since my husband and I are both teachers (80+ years together), we usually have the same time off. Since we would like some time to relax and rejuvenate, for the next three weeks, I am setting aside all technology and work related items to focus on my family, grandkids (11 of them) and friends. In the meantime, if you really want something to read, choose one of my older posts. My blog posts will return on Wednesday, July 31st.

Ten Black Dots - Linking Math and Literature

I am an avid reader, and I love books that integrate math and literature. Occasionally, my blog will feature a book that links the two.  I will summarize the book, give its overall mathematical theme, as well as list various activities you can use in your classroom.

Today's featured book is Ten Black Dots by Donald Crews (Greenwillow Books, 1986).  This picture book is for grades PreK-2 and deals with numbers and operations. 

The book asks the question, What can you do with ten black dots?  Then the question is answered throughout the book by using  illustrations of everyday objects beginning with one dot and continuing up to ten. Simple rhymes accompany the pictures such as:

"Two dots can make the eyes of a fox, Or the eyes of keys that open locks."

Materials Needed: 
  • Unifix cubes or Snap Cubes (multi-link cubes) as seen on the right
  • Black circles cut from construction paper or black circle stickers
  • Crayons
  • Pencils
  • Story paper
  • Calculators -simple ones like you purchase for $1.00 at Walmart


1)  Read the book a number of times to your class.  Let the students count the dots in each picture. On about the third reading, have the children use the snap cubes to build towers that equal the number of dots in each picture.

2)  Have the children think of different ways to make combinations, such as: How could we arrange four black dots?  (e.g. 1 and 3, 4 and 0, 2 and 2)  Have the children use black dots or snap cubes to make various combinations for each numeral from 2-10.

3)  This is a perfect time to work on rhyming words since the book is written in whimsical verse. Make lists of words so that the students will have a Word Wall of Rhyming Words for activity #4.
  • How many words can we make that rhyme with:  sun?  fox?  face?  grow?  coat?  old?  rake?  rain?  rank?  tree?
  • Except for the first letter, rhyming words do not have to be spelled the same.  Give some examples (fox - locks or see - me)
4)  Have the children make their own Black Dot books  (Black circle stickers work the best although you can use black circles cut from construction paper. I'm not a big fan of glue!)  Each child makes one page at a time.  Don't try to do this all in one day.  Use story paper so that the children can illustrate how they used the dots as well as write a rhyme about what they made.  Collate each book, having each child create a cover.

5)  Have the children figure out how many black dots are needed to make each book. (The answer is 55.)  This is a good time to introduce calculators and how to add numbers using the calculator.

If you can't find Ten Black Dots in your library, it is still available on Amazon.

Tools for Helping Students Graph Equations

I work in the math lab at the community college where I also teach. The math lab is staffed by only math instructors and offers free math tutoring to any of our students. We try to have many resources available for our students. When it comes to graphing, we have found that the computer can be very unfriendly. The graphs are often hard to see, and so finding points is next to impossible. We keep in stock some items that help our students.

First, we have graph paper that is always available. We keep an assortment of different kinds for our students:
  1. 1/4" grid paper
  2. Four co-ordinate graphs per page
  3. Full co-ordinate graph paper
  4. Six small co-ordinate graphs per page
On the right, you see Markwan holding the example of #2.

We also have two-sided white boards. One side is blank while the opposite side contains a coordinate graph outline. Our students make good use of these. They like the fact that they can do the linear or quadratic equation on one side and then construct the graph on the other.  (They don't have to draw the X-Y axes and tick marks for each problem or get out the ruler for accuracy.) Since the white boards are erasable, they can be used over and over again. On the left, Sam is "modeling" the white board. (Both young men wanted to be on my blog and were anxious for me to use their first names.)

Click Here for More Information
BUT my favorite item we have on hand are graphing sticky notes.  I often use them in my math classes because students can take notes while drawing examples of graphs and then stick the example right into their math book.  These post-it-notes are called MiniPLOTs®.  They are a unique brand of Post-It Notes designed for math students, teachers and tutors. MiniPLOTs® are 3x3" paper pads with 50 coordinate grid, polar coordinates, or 3D solid shapes printed on each sheet. They are the perfect size for homework and tests. In addition, the company makes them for algebra, geometry, trigonometry, statistics and K-6 math (provides an innovative method of teaching students the basic multiplication and division factors in about six weeks).

These work great when I am grading math homework. When a student has graphed an equation wrong, I simply take a graphing sticky note, correctly graph the equation and stick it beside their incorrect answer. It's important that students see the correct answer so that the wrong one doesn't remain stuck in their heads!

The Math Lab also supplies a reference sheet entitled Graphs of Some Common Functions. It gives an example of the equation being graphed (i.e. f(x) = x ), a visual of the what the graph should look like, the domain, range, and symmetry origin. The students are free to use the laminated ones in the Math Lab, but can also take home a paper one to place in their math notebooks.

On the reverse side of this reference sheet are examples of: Graph of f(x) = ax and Graph of f(x) = loga(x). Besides a visual of the graph, it includes domain, range, decreasing on and horizontal or vertical asymptote.

 Most students are visual learners and can see lines and curves and project how they behave intuitively. Their brains can easily understand, understand and recognize pictorially better than just remembering abstract equations.  It is therefore important for students to construct and draw graphs so they can picture them in their minds. Hopefully some of these graphing tools will make constructing those graphs easier.

A Go Figure Debut From A Kansan Who is New

Today, my Go Figure Debut is for someone from my hometown, Wichita, Kansas. (I personally have never met Dianna, but I would like to. In fact, we live very close to one another.) Dianna has been in education since 2004. She spent nine years in the classroom teaching different grade levels - PreK through 6th grade. She now works as a success coach (university supervisor) and instructor for Wichita State University (I, too, worked there for five years.).

Dianna likes working with students who are studying to be teachers. She helps them come up with lesson ideas for grades PreK through 6th grade, and she delights in watching these students phase into teachers. Since she teaches online, her home office is her classroom. Right now she is teaching her four year old preschooler; so, she has turned her office into a classroom for her with a calendar, letter of the week, weather, and fun learning activities. She and Evangelene enjoy playing file folder games together.

Dianna has been married for 13 years to her husband Greg. They have two children; Joshua who is nine, and Evangelene who is four. They have two dogs, a Collie named Blue Bell, a silver Labrador named TC and a leopard gecko named Spike. Dianna loves reading, especially romance novels. Her favorite author is Jane Austen, and her favorite TV show is Friends. Spending time with her family, travelling, swimming, fishing, going for walks, etc. is her favorite thing to do.

Teachers R Us
Dianna’s store is called Teachers R Us. Currently her store contains a total of 107 resources with five of those being free. Her resources are suitable for grades PreK-2. 

One of her free items is titled, Kindergarten Popcorn High Frequency Words Activity Freebie. It comes with:
Free Resource
  • 9 High Frequency Words on pieces of popcorn
  • 9 High Frequency Words on popcorn containers  
  • Popcorn High Frequency Words Writing Page 
  • Take Home Word Cards 
This product teaches sight words, nine words from Literacy First. It is a fun way for your students to interact with high frequency words.

Her featured paid item is a $15.00 bundle (you save $2.00) called Long e (-y), ey, and y Literacy Activities Bundled with Assessment. This product teaches Long e (-y). It has puzzle matches, picture and word sorts, word scramble, and worksheets. This product includes: 

Only $15.00
  • 6 worksheets with answer keys
  • Picture Sort Worksheet with answer key 
  • Word and Picture sort 
If you are looking for morning work, center work, or homework, then this product is for you.

Dianna says she loves teaching and believes God has given her the best job she could possibly ask for. If you check out her store, you will observe that she has top ratings (4.0) from her buyers with many of them saying that they “love” her resources! I expect you will, too.

There's A Place For Us! Teaching Place Value

When my college students (remedial math students) finish the first chapter in Fractions, Decimals, and Percents, we focus on place value. Over the years, I have come to the realization how vital it is to provide a careful development of the basic grouping and positional ideas involved in place value. An understanding of these ideas is important to the future success of gaining insight into the relative size of large numbers and in computing.  A firm understanding of this concept is needed before a student can be introduced to more than one digit addition, subtraction, multiplication, and division problems. It is important to stay with the concept until the students have mastery. Often when students have difficulty with computation, the source of the problem can be traced back to a poor understanding of place value.

It was not surprising when I discovered that many of my students had never used base ten blocks to visually see the pattern of cube, tower, flat, cube, tower, flat.  When I built the thousands tower using ten one hundred cubes, they were amazed at how tall it was.  Comparing the tens tower to the thousands tower demonstrated how numbers grew exponentially.  Another pattern emerged when we moved to the left; each previous number was being multiplied by 10 to get to the next number.  We also discussed how the names of the places were also based on the pattern of:  name, tens, hundreds, name (thousands), ten thousands, hundred thousands, etc. 

I asked the question, "Why is our number system called base ten?"  I got the usual response, "Because we have ten fingers?"  Few were aware that our system uses only ten digits (0-9) to make every number in the base ten system.

We proceeded to look at decimals and discovered that as we moved to the right of the decimal point, each number was being divided by 10 to get to the next number. We looked at the ones cube and tried to imagine it being divided into ten pieces, then 100, then 1,000. The class decided we would need a powerful microscope to view the tiny pieces.  Again, we saw a pattern in the names of each place:  tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.

I then got out the Decimal Show Me Boards.  (See illustration on the left.)  These are very simple to make. Take a whole piece of cardstock (8.5" x 11") and cut off .5 inches. Now cut the cardstock into fourths (2.75 inches).  Fold each fourth from top to bottom. Measure and mark the cardstock every two inches to create four equal pieces. Label the sections from left to right - tenths, hundredths, thousandths, ten thousandths. Numbers (see free handout below) will fit into the slots which are the unfolded part of the cardstock. (You can type up the names of the places which then can be cut out and glued onto the place value board).

Here are some examples of how I use the boards.  I might write the decimal number in words.  Then the students make the decimal using their show me boards by putting the correct numbers into the right place.  Pairs of students may create two different decimals, and then compare them deciding which one is greater.  Several students may make unlike decimals, and then order the decimals from least to greatest.  What I really like is when I say, "Show me", I can readily see who is having difficulty which allows me to spend some one-on-one time with that student.

If you aren't ready to do decimals, Show Me Boards can also be made for the ones, tens, hundreds and thousands place.  Include as many places as you are teaching. I've made them up to the hundred thousands place by using legal sized paper. As you can see in the photo above, my two granddaughters love using them, and it is a good way for them to work on place value.

I have attached a link to a number handout which is FREE. Just run it off onto cardstock, laminate, cut apart, and place the numbers into small zip lock bags (one sheet per child). Try using different colors of cardstock, so if a number is lost, it is easier to find the bag from which the number is missing.

Free Resource

Under the resource cover on your right is the link to a free page of numbers which anyone is welcomed to download and use.

Only $3.00
A good way to practice nay math skill is with a game. Your students might enjoy the place value game entitled: Big Number.  Seven game boards are included in this eleven page resource packet. The game boards vary in difficulty beginning with only two places, the ones and the tens.  Game Board #5 goes to the hundred thousands place and requires the learner to decide where to place six different numbers.  All the games have been developed to practice place value using problem solving strategies, reasoning, and intelligent practice.

Let's Go Fly A Kite - Using the Correct Geometry Term for Diamond!

This was a comment I received from a fourth grade teacher, "Would you believe on the state 4th grade math test this year, they would not accept "diamond" as an acceptable answer for a rhombus, but they did accept "kite"!!!!!  Can you believe this? Since when is kite a shape name? Crazy."

First of all, there are NO diamonds in mathematics, but believe it or not, a kite is a geometric shape! The figure on the right is a kite. In fact, since it has four sides, it is classified as a quadrilateral. It has two pairs of adjacent sides that are congruent (the same length). The dashes on the sides of the diagram show which side is equal to which side. The sides with one dash are equal to each other, and the sides with two dashes are equal to each other.

A kite has just one pair of equal angles. These congruent angles are a light orange on the illustration at the left. A kite also has one line of symmetry which is represented by the dotted line. (A line of symmetry is an imaginary line that divides a shape in half so that both sides are exactly the same. In other words, when you fold it in half, the sides match.) It is like a reflection in a mirror.

The diagonals of the kite are perpendicular because they meet and form four right angles. In other words, one of the diagonals bisects or cuts the other diagonal exactly in half. This is shown on the diagram on the right. The diagonals are green, and one of the right angles is represented by the small square where the diagonals intersect.

There you have it! Don't you think a geometric kite is very similar to the kites we use to fly as children? Well, maybe you didn't fly kites as a kid, but I do remember reading about Ben Franklin flying one! Anyway, as usual, the wind is blowing strong here in Kansas, so I think I will go fly that kite!


Only $1.95
This set of two polygon crossword puzzles features 16 geometric shapes with an emphasis on quadrilaterals and triangles. The words showcased in both puzzles are: congruent, equilateral, isosceles, parallelogram, pentagon, polygon, quadrilateral, rectangle, rhombus, right, scalene, square, trapezoid and triangle.  The purpose of these puzzles is to have students practice, review, recognize and use correct geometric vocabulary. Answer keys are included.

Free End-of-the-Year Ebook

FREE Ebook
We hope you and your students will enjoy our "Free End of the Year Lessons" by The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC) for 2019. On each page, you will find links to a free resource as well as a priced resource created by a member of TBOTEMC.

Inside this 2019 edition of the "Free End of the Year Lessons" you will find:

  • French: Les Animaux Marins
  • Nursery Rhymes Activities
  • Beginning Letter Sounds (A-Z) Worksheets
  • Geometry Shapes - Kindergarten, 1st, 2nd
  • "R" Blends Coloring Fun
  • Digital Citizen Pledge
  • Close Reading for LITTLE ONES!
  • End of the Year Activity Booklet
  • Twenty Study Tips to Help Students Succeed in School
  • End of the Year Awards
PLUS much more! Altogether there are 14 free items for grades K-12. All you have to do is download the free Ebook.

TBOTEMC is made up of teachers who work together to market their Teacher Pay Teachers products. Using the power of cross-promotion, TBOTEMC members are able to use their combined social media sites to its full potential. If you are a TPT seller, join The Best of Teacher Entrepreneurs Marketing Cooperative and take your TPT store to the next level. For more information, email Victoria Leon about TBOTEMC. You'll be glad you did.

A Go Figure Debut for an Arkansas Teacher Who is new!

Lynn's TPT Store
Lynn has taught for over 14 years in both public and Christian private schools, and she spent several years homeschooling her own children. She loves to see her students work hard to obtain a goal and succeed, while keeping the learning as fun as possible.  

Lynn studied curriculum and instruction and is finally able to use this degree by being on Teachers Pay Teachers! She loves creating materials, and it has become her dream job, as she is not currently teaching. Her classroom decor has themes and whenever possible, lots of color. (Check out the one below.) She creates theme-based materials, as she feels this works well for many students in the learning process. In her spare time, she likes to read mysteries, garden, cook, and travel.

Free - Just Download It
At this time, Lynn has 292 products in her store with 13 free items. She creates materials for math, ELA, science and social studies. Most of her products are geared for 4th, 5th and 6th grade, but she also has some primary materials. 

One of her free resources is called Happy 4th of July Classroom Banner Decor.   This banner has celebration colors of red, white and blue with a realistic wood whitewash background. This product includes one banner and directions for print-out.

Only $5.00
Lynn's featured paid item is Grocery Store Change from $5.00.  It aids learners in solving money word problems for change given from a $5.00 bill. It can be used as a hands-on math center, an intervention, cooperative learning groups math activity, a class game and an assessment. It includes:
  • Directions
  • 30 Game Task Cards
  • Key
  • Two Student Award Cards
  • Student Recording Sheet
  • Useful Links
Lynn writes a blog she calls Tieplay Educational Resources Blog. Some of her articles are quite interesting and thought provoking. She even has animated pictures on her blog (something I do not know how to do.)

If you like what you see, take some time and check out her store as I am sure Lynn’s quality and reasonably priced products will save you time!

The "Lure" of Fish - The Benefits of Keeping an Aquarium in Your Classroom

I am a critter "wife"; not by choice, but since my husband teaches science, creatures of all kinds enter our home. We have been blessed with hissing cockroaches from Madagascar, (they are huge) tree frogs, meal worms, (they turn into black bugs) red worms, etc. Some have lived in our guest room while others have found a special place in my refrigerator. We've even had horse dung soaking in water so the bacteria could grow. Oh, that was delightful and aromatic! Thank goodness for the invention of "Oust". So after all of those creatures, what kind of a story could I possibly write to make critters attractive? Well, I do have a fish tale, but up front I must disclose that it is not your typical "fish" story.

When I taught third grade in an inner city school, I knew the children needed something to love, but being a city girl, my love of animals was deficient. That is when my husband helped me to set up an aquarium. I purchased a water heater, a bubblier, chemicals, plants, fish food, and of course the fish! Little did I know what effect this would have on my students.
Every day, the children would enter the room, go over to the fish tank, and talk to the fish. Each fish had a name, and being the fish keeper became the prized chore. Even though we couldn't pet the fish, they were loved by every child, and they brought a sense of family to my classroom. Naturally, one of the fish died, but it allowed us, as a class, to mourn together.

When a guest entered our room, s/he had to be formally introduced to the fish. They became the focal point of the classroom. But there was something else that transpired that truly surprised me. The fish had a calming effect on my student who had a behavior disorder. If his desk were moved near the aquarium, he would sit quietly and actually do some of his work without disruption.

At the end of the year, the remaining fish made their way to my home where they spent the summer with my husband's critters. Unfortunately, they failed to calm the cockroaches into silence! But all six survived to be in third grade again!

You are invited to the Inlinkz link party!
Click here to enter

It's a Puzzling Situation! Getting Students to Work Together.

One of my colleagues completed a Leadership Project with her ten students that I want to share with you. She had two ‘alike’ 100 piece puzzles. (The puzzles are fairly inexpensive at Walmart or Dollar General.) Kay took these two similar puzzles which had alike colors/pictures on them and mixed them up. She then separated them into two baggies, and put each baggie in one of the original two boxes.

The class numbered off, 1-2-1-2...and so on, and then separated into two groups. At first, the students thought this was going to be a race to see which group could complete their puzzle first; however, each group started at the same time, writing the starting time on the board. After that, Kay didn’t say a word, and answered no questions! She simply observed the students. The students tried asking her, "Hey we don’t have all the edges; these pieces don’t match; are these the right puzzles?" Something is wrong; what's up?"

Kay waited to see who would take the lead to combine the groups, and how they joined. She wondered, "Would they join peacefully? Would they gather and form one group; two new groups; work together, or divide again?"  As she continued to observe, she began to write names on the board of those who were positive and took leadership. She then wrote the time on the board when they commenced to form one group.

When they finished, she held a Socratic Seminar (an Avid strategy) about how they felt concerning the activity. One student, who did not want to join a group in the beginning, became so involved during the project that he actually was the leader in getting the groups together.  It was one of those fantastic teacher moments!

Kay's students learned quite a bit from the activity since in reality, this is how life, social, and work environments are. She pointed out that they may not have a project that is going well, but by joining together with another group, you can problem solve, gain assistance, and acquire more pieces to your puzzle to accomplish your project.

Since working together doesn't seem to be a skill that comes naturally, I use this activity with my college freshman as they begin their final group projects. Plus, as you think about your class and are puzzled about how you can get your students to work well in cooperative groups, keep this activity in mind.  It might just put the pieces together for you.

In the Hood - An Activity for the Book, "My Side of the Mountain"

Each year, my husband's science students read My Side of the Mountain. The main character in the book is Sam Gribley, a boy in his early teens. For a year, Sam lives in the woods of the Catskill Mountains. One day Sam spies a peregrine falcon pursuing its prey. Sam determines he wants a falcon as a hunting bird; so, he goes to the nearby town of Delhi to learn about falconry (hunting small game by using a trained bird of prey) by searching books at the local library. For several days, he camps near a cliff hoping to find the location of a peregrine falcon nest. While the mother bird attacks him, Sam steals a female chick from the nest. He names the bird Frightful, and it becomes one of Sam's closest companions. 

If you are acquainted with falconry, you know that peregrine falcons will wear a hood to keep them calm and to make certain they are alert for the falconer. The falcons are also trained to go into hunting mode once the hood is removed. A good falcon hood does not bother the falcon. If it fits well, it does not damage the bird’s feathers or hamper its breathing. Under no circumstances does the hood come in contact with the falcon’s eyes. Out of all the falconer's aids, the hood is the most important piece of equipment. In the book, Sam makes jesses (leg straps), leashes and a hood out of deer skin for Frightful. My husband figured if Sam could construct a falcon hood, then maybe his students could as well.

Using the Internet, (Hood Patterns) my husband found several hood patterns. (Most hoods are custom made by hand and can cost $150 or more!) He purchased faux leather from the fabric store as well as special needles and thread. The students practiced sewing on scraps of the material before cutting out their own patterns and sewing them together. Below is a summary of the process in pictures.

What makes every hood unique is that each falconer decorates the hood in an extraordinary way. They may use elaborate feathers, pieces of colored leather, ornaments, etc. Sometimes, they are even hand painted, dyed or uniquely tooled. Here is what a few of the handmade hoods looked like after the students decorated and embellished them.

Overall, this was a successful book assignment which was not only creative and imaginative, but it gave the artistic students a chance to shine. As a result, you might want to try this project in your classroom as well. So I wish you good luck, good reading and good hood making.

If your class is reading this book, here are three supplementary resources for My Side of the Mountain that you might be interested in.

Two Word Searches - This resource contains two different word search puzzles about the survival materials used by Sam, the main character in the book, My Side of the Mountain. Both puzzles include the solutions.

A Crossword Puzzle about Birds - This is a free form crossword puzzle that highlights 16 different birds which appear in the book My Side of the Mountain. The 16 clues are based on the bird’s unique characteristics, color, and song.  A solution key to the puzzle is included.

Crossword Puzzle about Plants - This is a free form crossword puzzle that highlights 18 different plants which appear in the book My Side of the Mountain. The 18 clues are based on the plant’s distinctive characteristics, color, size and physical appearance.  A solution key to the puzzle is included.

A Go Figure Debut for an Elementary Teacher Who is New!

Our newest Go Figure Debut is for a Florida teacher who has been teaching for three years; however, she is currently taking a break from teaching to be a stay-at-home mom. Hannah has two sweet kiddos (a girl and a boy), both under the age of two. Also included in her family is a cat named Tinkerbell who lives up to all the sassiness of her name.

Hannah describes her elementary classroom as organized, energetic, fun and adventurous! She loves seeing the joy on her students’ faces as they learn a new skill that they once struggled with, and then watching their confidence grow a mile!

At the moment, Hannah has 75 products in her store mainly geared for the primary
Free Resource
grades of K-2. Thirteen of her resources are free and include student activities, teacher gifts, and design elements for creating TPT resources. Her featured free item is called Encouraging Bookmarks because sometimes you just need a free bookmark! After purchasing these bookmarks, one buyer left this comment: “These are adorable and sweet bookmarks! I love the fonts and colors you chose for these- simply perfect!”

Any teacher knows that planning a school event can be stressful. Hannah’s Fall Festival Event Bundle helps you put together a memorable event without breaking into a sweat. Planning a Fall Festival for
your school, church, or home-school group has never been easier when you use this bundle of resources! Included in the bundle are:
  • 20 Activities, Games, and Crafts complete with Decorations, Posters, Teacher Directions, Student Directions, and Direct Links to Activity Materials.
  • Ticket Signs
  • Fall Festival Programs (Editable PowerPoint)
  • Fall Festival Flyers (Editable PowerPoint)
  • Social Media Posts and Stories for Facebook, Instagram, and Twitter (Editable Power Points)
  • Fall Festival Event Forms
  • Sign Up Form (For Running Activities)
  • Master Checklist (Stay Organized While Planning Your Event)
  • A "Tips, Ideas, and Suggestions" Note for Your Fall Festival Event

Currently, Hannah runs a home goods business called White Gardenia Company where she sells handcrafted candles, soap, and tea. Although it’s her business, it feels like a hobby to Hannah because she loves getting to work creatively with her hands. Plus it allows her to be her own boss and do what she loves, while giving her the flexibility to stay home with her children and not miss out on those precious, once-in-a-lifetime moments.

Algebraic Terms - Finding the Greatest Common Factor and Least Common Multiple Using a Venn Diagram

I tutor math at the college where I teach. Many of those students have been confused on how to find the greatest common factor for a set of algebraic terms. Having an elementary background, I introduce them to a factor tree which, believe it or not, many have never seen.

When just a rule is given by an instructor, often times, students get lost in the mathematical process. I have found that utilizing a visual can achieve an understanding of a concept better than just a rule. A Venn Diagram is such a visual and helps students to follow the process and understand the connection and relationship between each step of finding the GCF and LCM.

It's important to always begin with the definitions for the
words factor, greatest common factor and least common multiple. If a student doesn't know the vocabulary, they can't do the work! I continue by explaining and illustrating what a factor tree is (on your left) and how to construct and use a Venn Diagram as a graphic organizer.

Let's suppose we have the algebraic terms of 75xy and 45xyz. I have the students construct factor trees for each of the numbers as illustrated on the left.

Then all the common factors are placed in the intersection of the two circles. In this case, it would be the 5 and the xy. 

The students then put the remaining factors and variables in the correct big circle. Five and three would go in the left hand circle and the three 2’s and the z would be placed in the right hand circle.

The intersection is the GCF; so, the GCF for 75xy and 40xyz is 5xy.   To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle.

5 × 3 × GCF × 2 × 2 × 2 × z = 15 × 5xy × 8z = 240. The LCM is 600xyz

Free Item
This method is applicable and helpful in algebra when students are asked to find the LCM or GCF of a set of algebraic terms such as: 25xy, 40xyz. (LCM = 200xyz; GCF = 5xy) or when they must factor out the GCF from a polynomial such as 6x2y+ 9xy2. Using a Venn Diagram is also an effective and valuable tool when teaching how to reduce fractions. 

Are you interested in finding out more about this method?  Then download my newest free resource entitled: Algebraic Terms and Fractions - Finding the Greatest Common Factor and the Lowest Common Multiple Using a Venn Diagram. 

Earth Day - A Time to turn Trash into Classroom Treasures

With Earth Day just around the corner, I began thinking, "What sort of extraordinary things could I create from ordinary things which might otherwise be thrown away?"  Here is just one of my Trash to Treasure ideas.

Go to any Quick Trip or a similar store  and ask if you could have some plastic cup lids, two for each child.  (Stores are usually happy to help out teachers.)  I like the sturdy 4" red ones.  Instead of placing a straw in the designated spot, place a brad to connect two of the lids.  These should be touching each other top to top or flat side to flat side.

After the lids are together, place a few stickers on the outside of the lids.  What do you have?  A card holder!  Just slide the game cards in between the two lids, and they will actually stay there!  These are great for little hands which have difficulty holding several cards, or for older hands which aren't functioning like they use to, or for disabled or crippled hands.  My grandchildren love them because they can now play Old Maid without dropping and showing everyone all of their cards.

FREE Resource
Also, go to my store and download a free version of my resource entitled Trash to Treasure.  It is an eight page handout that features clever ideas, fun and engaging mini-lessons in addition to cute and easy-to-construct crafts made from recycled or common, everyday items. In this resource, discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom.

Do you have a Trash to Treasure idea?  Share it with us by leaving a comment.

Why is 'x' Usually the Unknown in Algebra?

Ted Talk
Again, it's time for some math information you might have missed in school. (Don't worry, I missed a great deal as well.)  Today's question is: Why is the letter "x" the symbol usually used for an unknown?

Even though the letter "x" is commonly used in mathematics, its use often appears in non-numerical areas within different industries such as The X Files or Project X. Terry Moore clears up this mathematical mystery in a TED Talk presentation at Long Beach, California.  In a short and funny four minute talk, he gives an unexpected answer to "why." Just click under the illustration to find out the reason!

What Is Your Mindset?

In the fall, I taught a new course entitled Conquering College. We have found that many students entering college are not prepared, lack study skills as well as the soft skills of being on time, regularly doing homework, turning in assignments - on time, etc. This class is required for every student who tests into developmental math and/or reading.  It has three purposes:
  1. To enable students to learn and use Advancement Via Individual Determination (AVID) strategies necessary for persistence and success at the college level, 
  2. To develop a learning plan based upon personal abilities and goals, and 
  3. To become more self-reliant in fulfilling academic goals.
During the sixteen weeks, we spent time focusing on the the growth and fixed mindset. If you haven't heard of the fixed mindset and the growth mindset, I'll summarize it this way - it is our attitudes, thoughts and beliefs about something.

Study the two charts below. In which category do you fit? Where would you place many of your students?

Carol Dweck has done a great deal of research on Growth Mindset. There is a ten minute video on You Tube which is well worth watching and sharing with your fellow teachers. It is called How To Help Every Child Fulfill Their Potential. (click on title) If for no other reason, watch it to discover what 15 years of praising children for their intelligence has done to our students. It is definitely eye opening!

A Go Figure Debut for An Idaho College Teacher Who is New!

Dr. Jan's Math & Science Lab

Jan has been teaching for one million years. (Of course that is better than "since the earth cooled," like me.)  This is her 27th year of teaching, which includes 21 years at the elementary level, and the last six at the college level.  She currently works in a STEM teacher preparation program at Boise State University; so, she teaches future teachers.  

This semester she is teaching the Elementary Science Methods course for the first time, and she LOVES it! The main thing she enjoys is giving future teachers experiences in classrooms to boost their confidence and to show them that teaching science is engaging for kids and so worth squeezing into the busy school day.  For her job, Jan has the unique experience of teaching future teachers student-centered practices, and then going out to local schools to watch them try out teaching.  It is super rewarding when they have positive experiences and decide that teaching might be right for them. 

Jan has three "young" adult children; Zoe who is 23, Drew who is 20, and her youngest Alex who is 18.  Alex will be graduating from high school this spring and heading to college.  She and her husband of 26 years are excited about the next chapter in their lives and officially being empty nesters.  Jan also has two fur babies that she adores.  Ari is an Australian Shepherd, and Mia is a French Brittany.  In her free time, Jan enjoys traveling,  skiing, camping and going to outdoor concerts.  

Jan has 167 products in her store, seven of which are free.  Her focus is on math and science, mostly for grades K-8.  Currently, she is working on creating more middle school level products.  Since she loves inquiry based instruction and Project Based Learning, many of her products promote these practices. 

Only $4.00
One of Jan's paid items is entitled, Design A Dog Park.  It is a fun project based learning project that engages students! Students work in teams to design a dog park. A variety of math skills are practiced including area, perimeter, addition, subtraction, multiplication. ELA skills are also integrated as students write persuasive letters and give oral presentations on their proposals. Giving students relevant contexts to apply skills is a meaningful way for students to construct conceptual understanding and see a useful application.


Jan's FREE item is called Science in a Bag.  It is the perfect birthday gift for students! Simply gather the easy to find supplies, print it off then staple the activity booklet pages and put everything into a quart or gallon sized Ziploc bag. Staple the birthday topper, and you're done! (Better yet, have a parent helper put these together.) The kit includes a mini booklet with directions and questions for three different activities that can be done with little supervision on the teacher's part. If you teach grades 3-6, download it for your classroom.

Jan also writes a blog called Dr. Jan's Math and Science Lab.  (What else?) As an educator, her goal is to share her passion for math and science with as many educators as she can! By having a blog, she hopes to give teachers tools and resources to enhance the math and science education of their students. Be sure to check it out!