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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.


Free Back to School Ebook - Includes Activities for Grades PreK-12

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We hope you and your students will enjoy our "Free Back to School 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 resources created by a member of TBOTEMC.

Inside this 2019 edition of the "Free End of the Year Lessons" you will find resources like:
  • Italian: In Autunno Coloring
  • FREE /Back to School English Number Match
  • Interactive Emergent Reader: Toys - FREE Open Dyslexic Font
  • Free Fun Back-to-School Explanatory Writing Activity Using Similes and Hyperbole
  • FREE Back to School Math Review
  • Twenty Study Tips to Help Students Succeed in School
  • Back to School FREE Music Rules Poster
PLUS much more! Altogether there are 24 free items for grades PreK-12. All you have to do is download the free Ebook. Here are just three samples of the 24 items available in this Ebook.

All American Teacher Tools
Brain Ninjas
Scipi

The Best of Teacher Entrepreneurs Marketing Cooperative
 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, consider joining The Best of Teacher Entrepreneurs Marketing Cooperative and take your TPT store to the next level. For more information, email Victoria Leon at vleon999@yahoo.com about TBOTEMC.  You'll be glad you did.


How Many Classroom Management Rules Does A Teacher Really Need?


Now that most of us are getting geared up for a new school year, it's time to think about what classroom rules need to be established. Maybe the ones you had last year just didn’t work, and you are looking for a change. I could recommend many "Do this or this will happen" or "Please don't do this as it will break my heart" statements, but lists can become very long and mind-numbing. Maybe that is why God only gave Ten Commandments. Fewer rules means less has to be memorized. So, maybe we need to ask ourselves: “How many classroom rules are really needed?” 

I would suggest making a few general rules that are clear and understandable since being too specific often leads to complicated, wordy rules that might cover every possible situation. Most of the time, I post six simple classroom rules (only two words each) in my room which encompass my main areas of concern. I find them to be more than sufficient to govern general behaviors, and because alliteration is used, the rules are easy for all of my students to remember.

1.  Be Prompt – In other words, be on time to school/class/group.

2.  Be Prepared – Bring the items you need to class or to a group. Study for upcoming tests. Have your homework completed and ready to turn in. 

3.  Be Polite – This rule focuses on how we treat each other. Show respect for your teacher(s) and your fellow students in the classroom, in the school, and on the playground.

4.  Be Persistent - The final rule spotlights the need to stay on task and complete an assignment even though it might be difficult. 

5. Be Productive - Always put forth your best effort! Grades are achieved; not received; so, do your best at all times.

6. Be Positive – Bad days happen! If you are having one of those days, I do understand. Please just inform me before class that you are having a bad day, and I will try to leave you alone during class discussion. This is not to be abused.

I firmly believe that class rules must cover general behaviors, be clear as well as understandable. Being too specific often leads to complicated, wordy rules that might cover every possible situation, but are impossible to remember.  (A good example are the IRS tax rules which I still have difficulty comprehending). 
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Here are a few things to consider when communicating your classroom rules.
  • Establish clear expectations for behavior from day one.
  • Use techniques such as interactive modeling to teach positive behavior.
  • Reinforce positive behavior with supportive teacher language.
  • Quickly stop misbehavior.
  • Restore positive behavior so that children retain their dignity and continue learning.
If you are interested in using these six rules in your classroom, check them out on Teachers Pay Teachers. Each two word rule is written as a one page chart, and are ready to download and laminate to hang in your classroom.


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

Activities:

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.