Thursday, November 15, 2012

Two Methods to Teach Prime Factorization

As we are all discovering, the new Common Core Standards for Math stress the importance of teaching students a variety of strategies for a particular skill.  It is then up to the student to choose which strategy they feel most comfortable using.

I have used two different strategies to teach prime factorization in my classroom.  The ‘tree method’ works from the top down and focuses on factors.  The ‘birthday cake method’ works from the bottom up and focuses on division.

The tree method is most widely taught and used.  It is the way you and your parents will be most familiar with.   I have found, however, that the ‘birthday cake method’, while not as widely used, seems to be the method my students prefer and have the most success with.

We, the teacher, have a choice to make.  Do we choose to teach just one and not the other?  Which one?  Or, do we introduce our students to both?  Each teacher needs to decide what is best for the students in their classroom.  Regardless of what you decide, I have created a packet that will provide you with the necessary resources.

Included in this packet are two matchbook foldables--one for each method, a minibook for each method and a two-sided practice page for each method.  Detailed answer keys for practice pages and both mini-books are included as well.

Birthday Cake Method Resources

Birthday Cake Method Matchbook Foldable (cover).
Birthday Cake Method Matchbook Foldable (inside).
Birthday Cake Method Matchbook Foldable (assembled & folded).

There is also a mini-book foldable for each method.  For information on how to fold a mini-book, I would highly recommend viewing the following video.  Unfortunately, I can not adequately show the process with pictures so viewing the video is very necessary.

Unassembled mini-book page (mini-book with answers included).
Assembled mini book.
2-sided practice page (detailed answer key included).
All materials described above are available for the 'tree method' as well.

This product is available at my TpT Store and my Teacher's Notebook Shop.  Happy Factoring :)

Saturday, November 10, 2012

Structuring "Problem of the Day" in 5th Grade

Ask a student to make a list of what they like least about math and it’s likely that ‘story problems’ will be pretty high on that list.

So, for the past 4 years, I have made it a point to include a ‘Problem of the Day’ in my math lesson plans. The past two years, I have shifted more towards a ‘model-drawing’ method.  I have to say I have been quite pleased with the results.  I am currently using a Frank Schaffer resource titled Singapore Math:  70 Must Know Word Problems, Level 3.  While Level 3 is suppose to be for 4th grade, I found it best met the needs of the 5th graders I teach.  Once we finish with Level 3, we will move into the 5th grade book...Singapore Math:  70 Must Know Word Problems, Level 4. 

I'm not going to lie, many of these story problems will challenge even your best math students.  I decided to go with this series, after seeing some sample questions that may be on the new Common Core Math Assessments in the near future.  I felt the problems in these books were a good match and an excellent way to get students comfortable with tackling even the most challenging of word problems.

I also like the fact that a detailed solution can be found at the back of the book for each problem.  The focus of this series is using model drawing to visually solve a problem.  I have to admit, sometimes I look at the solution and it visually works for me and other times it simply doesn't.  I don't get to hung up on whether or not I am doing the model drawing correctly.  I figure if the picture I create makes sense to me, than it's likely that it will for my students too.

So, how do I structure the use of this in my classroom?  We start with Question 1 in the Level 3 book on the first full day of the first full week of school.  I tell the students the "Problem of the Day" is something we will be doing pretty much every day of the school year (Note that there are no cheers of joy at this announcement, lol!)  We do the first 10 problems, one per day, together as a class.  I project the question up on the screen using my Elmo.  We read it together.  Record data (I on the white board, the kids on their papers.)  I model how to take the information and put it into a picture.  Once the picture is made, students can generally see what the first step in solving the equation is.  We then solve together.

After 10 questions, I change things up a bit.  Beginning with question 11, students read the information and come up with a solution on their own.  After they've answered, they turn their paper in.  I check the work by simply starring if correct or marking with an 'x' if it is wrong.  Sometimes I do allow them to work with a 'side partner'.

The following day, I pass the papers back out and I model how to solve the previous day's question.  Students use a colored pen or marker and make changes to their work if needed.  Then I project the next question on the screen and students attempt on their own and then turn in.  The next day we repeat the process.

In this way students are always getting a chance to try their hand at solving but also seeing how I would solve it.  And, believe it or not, the students are not only becoming more and more successful with solving their problems but actually seem to be enjoying the challenge!  I have also seen carryover when solving problems in our other math curriculum.

Oh, one additional thing I have started to do when reviewing the problem, is to have the students help me write the numerical expression one could use to solve the problem...this is only after we've already found the correct answer.  I figure since writing numerical expressions and then evaluating them are included in our 5th grade Common Core Standards, I may as well throw it in whenever I can, lol!   

Because of the success I am having, I decided to create a recording sheet.  I find that having an organized work space on paper gives students structure and actually aids their ability to solve problems.  I just uploaded a copy of the template I use to my TpT Store and Teachers Notebook Shop.

Thursday, November 8, 2012

Division Strategy: Decomposing the Dividend

The new Common Core Standards for Math prompted me to create this Decomposing the Dividend Strategy pack for use with students and with parents.

I am quickly finding out that Common Core stresses not only arming students with a variety of strategies to solve a problem, but also stresses fostering the use of mental math whenever possible.

The Decomposing the Dividend Strategy encourages students to break the dividend into parts that can be divided  easily.  The long-term goal of this method is for students to solve the division problem mentally.  In my experience, it will take a great deal of practice before students will master the ability to solve the problem mentally using this method.   I do find, however, that with modeling and a great deal of practice that my higher achieving math students will pick up on the strategy and  choose to use it. 

 I have also sent a foldable home for parents to have available as a resource they can use when working with their child.

This newly created packet contains a tri-fold foldable (front and back) that shows how the strategy works. It would make a wonderful resource for both students and parents.
Tri-Fold Foldable (Front cover is upside down for easier copying).

Foldable all assembled and folded.  Ready for a math journal.
 Also included is a 2-sided practice page as well as a detailed answer key.
Front and back of 2-sided practice page.  The front side of practice page provides the student with some information so as to guide them through the steps.

Also included is a detailed answer key.

Complete Decomposing the Dividend Packet.
If you are interested in purchasing a Decomposing the Dividend Strategy pack for use in your own classroom, please visit my Teachers Pay Teachers Store or my Teacher's Notebook Shop.

Monday, November 5, 2012

Teaching A New Division Strategy - Partial Quotients

The new Common Core Standards for Math prompted me to create this Partial Quotient Strategy pack for use with students and with parents--yes, parents !

I will get to parents shortly, but first...Common Core stresses arming students with a variety of strategies to solve a problem.  This includes division.  Now, I’m an old-timer, and as an old-timer, I believe that every 5th grader should know how to do long division.  I’ve spent countless hours trying to teach the algorithm to each and every student.  The truth is, some kids JUST DON’T GET IT!  Common Core gives the teacher permission to try teaching the concept using a different strategy.  Amazingly, these struggling students seem to catch on fairly quickly to the Partial Quotient Strategy.  Does it still bother me that they aren’t using the long division algorithm?  Yes, quite honestly it does, but I am slowly changing my thinking--us old-timers can be pretty set in our ways.

I do teach the Partial Quotient Strategy to all my students.  I find that those who understand long division, will practice this new strategy with me, but revert to the long division algorithm when given the choice.  This suits me fine.

Now for parents.  At nearly every parent/teacher conference I had this year, I heard how challenging the math was.  How the parents could not even help their child with their math because the way we are solving problems is ‘not the way they learned it’.  So, my thought for next year, is to have a math night.  Invite parents into the classroom and show ‘new’ strategies such as this.  I think the foldable would make a good resource and wouldn’t solving the problems together be fun, lol?  And, even if you aren’t quite ready for a ‘math night’, just sending the foldable resource home would be beneficial.

Included in this packet is a one-fold foldable. The cover gives a brief explanation of the partial quotient method. The inside gives two detailed examples.

I have also included to 2-sided worksheet to use with students. Also, included is a detailed answer key.

If you would like to purchase this packet for use in your classroom please visit my TpT Store or my Teacher's Notebook Shop.

Saturday, November 3, 2012

Divisibility Rules

The new Common Core Standards for Math prompted me to create this Divisibility Rules Pack for use in my own classroom.

Common Core emphasizes the need to develop mental math strategies with students.  Understanding the divisibility rules will allow students to begin the process of making math connections and help to strengthen mental math skills.

My 5th grade students had never been introduced to most of these divisibility rules, so I chose to teach them one at a time.  Slowly, over the course of a semester, I introduced each one, giving them time to practice and master each before moving on to the next.

Some are obviously easier than others, so I chose to start with those (divisibility rules 2, 5, 10) first.  I did not teach the rules in numerical order, but rather by order of difficulty.

This pack includes 10 single-flap, Individual Divisibility Rules Foldables.  Rules include, divisibility rule for 2, 3, 4, 5, 6, 7, 9, 10, 11, and 12.  The inside of all of these foldables could be enlarged and used as a poster for your classroom.  To learn how to make a poster be sure to visit my Making Posters post.
Inside of each Individual Divisibility Foldable (2 per sheet).
Outside of each Individual Divisibility Foldable (2 per sheet).
Each Individual Divisibility Foldable Assembled and Folded
Each Individual Divisibility Foldable Cut Apart

Also included are two foldables that summarize five divisibility rules each.  These foldables would work well with older students that have already been taught the divisibility rules, but just need a resource to refer to.
Inside Combined Divisibility Rules (5 per foldable)
Outside Combined Divisibility Rules (5 per foldable)
Assembled and folding begun.
Assembled, Folded and Cut
I have also included ten, 18 question, worksheets to accompany each divisibility rule. An answer key is also provided.
18 question practice page for each rule (2 per sheet).  Answer Key provided.
Individual practice pages cut apart.
 If you are interested in purchasing a Divisibility Rules Pack for your classroom, please visit my TpT Store or my Teacher's Notebook Shop.