Pick Up Sticks!

My students are now half way through the chapter on fractions.  They seem confident in performing the different operations, but a few are still unsure of how to reduce fractions. 

Although I have stressed learning the Divisibility Rules for 2, 5, 10, and the digital root for 3, 6, 9, (September 21st posting) some still have difficulty since they do not know their multiplication tables.  This week we made Pattern Sticks, a visual and kinesthetic aid, similar to a multiplication chart like the one on the left. Notice that an extra column (blue) has been added to the chart. (In this space, a hole is punched so that a 1" ring can be inserted to store all of the sticks in one place.) .

On the right are the directions for making the Pattern Sticks using a multiplication chart. 

(Side note:  My students cut out individual Pattern Sticks which I prefer over cutting a multiplication chart apart.  If you are intetested in these, see the link under the scary fingers.)

I then gave the students fractions such as 9/36 to reduce.  Using the Pattern Sticks, they looked for a column where a 9 and a 36 were lined up in the same one.  They easily found it on the 1 strip and the 4 strip.  They then took the two strips and lined up the two so that the 9 was over the 36.  (see illustration above)  By going to the left, they discovered that 9/36 is the same as 1/4.  This is 9/36 in its lowest terms. Also notice that all the fractions in the illustration above are equivalent fractions: fractions that have the same value.  We also used the Pattern Sticks to determine what number to divide by and to change improper fractions to mixed numbers.

Pattern Sticks

On a more elementary level, the Pattern Stricks can be used to practice skip counting.   I purchase those scary, wearable fingers at Halloween time. (You can purchase them in bulk from the Oriental Trading Company.)  My students wear one for such activities as this.  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.  (If you like this idea, be sure that each student uses the same finger every time to avoid germs, etc.  Keeping it in a zip lock bag with the child’s name on the bag worked best for me. Believe it or not, when I taught middle school, the students would paint and decorate the fingernails!) 

If you are interested in learning more about Pattern Sticks and how to use them in your classroom, check out the resource entitled Pattern Sticks: A Math Tool for Skip Counting & Reducing Fractions at Teachers Pay Teachers.  Just click on the link under the scary fingers.

The ROOT of the Problem

When students skip count, they can easily say the 2's, 5's, and 10's which translates into easy memorization of those particular multiplication facts.  Think what would happen if every primary teacher had their students practice skip counting by 3's, 4's, 6's, 7's, 8's and 9's!  We would eradicate the drill and kill of memorizing multiplication and division facts.

Since many of my college students do not know their facts, I gravitate to the Divisibility Rules.  Sadly, most have never seen or heard of them.  I always begin with dividing by 2 since even numbers are understood by almost everyone.  (Never assume a student knows what an even number is as I once had a college student who thought that every digit of a number must be even for the entire number to be even.) We then proceed to the rules for 5 and 10 as most students can skip count by those two numbers. 

Finally, we learn about the digital root for 3, 6, and 9.  This is a new concept but quickly learned and understood by the majority of my students.  (See the definition below).

 Here are several examples of finding Digital Root:

1)   123 = 1 + 2 + 3 = 6.  Six is the digital root for the number 123.  Since 123 is an odd number, it is not divisible by 6.   However, it is still divisible by 3.

2)   132 = 1 + 3 + 2 = 6.  Six is the digital root for the number 132.  Since 132 is an even number, it is divisible by 6 and by 3.

3)   198 = 1+ 9 + 8 = 18 = 1 + 8 = 9.  Nine is the digital root for the number 198; so, 198 is divisible by 9 as well as by 3.

4)   201 = 2 + 0 + 1 = 3. Three is the digital root for the number 201; so, 201 is divisible by 3.

  



      The first time I learned about Digital Root was about six years ago at a workshop presented by Kim Sutton.  (If you have never been to one of her workshops - GO!  It is well worth your time.)  Anyway, I was beside myself to think I had never learned Digital Root.  Oh, the math classes I sat through, and the numbers I tried to divide by are too munerous to mention!  It actually gives me a mathematical headache.  And to think, not knowing Digital Root was the ROOT of my problem!

      A teacher resource on Using the Divisibility Rules and Digital Root is available at Teachers Pay Teachers. If you are interested, just click here.  Divisibility Rules

The Groupies

My college students are like charter members of a church. They claim their seat on the first day of class, and from then on, no one else better take it! Since we journal every day, often in groups, the same people were sharing with the same people day after day. This meant the students were not getting to know each other; they were unaware of how others were problem solving, and they were way too comfortable in their group. Things had to change!

This semester, I asked the students to make name cards. (I know it sounds elementary, but it does help this "old" teacher to quickly learn who is who). On the name tags, I placed a variety of stickers (my students didn't seem to mind). Based on the stickers, the students would group by pairs, threes, fours or groups of eight.  Now, the students would divide up into groups based on something other than their preference.

Sample of Grouping by Stickers

On Monday, we grouped by 2's according to the color of the dog and cat stickers. Right away I noticed that the dominance of the group had changed, and more dialogue was going on between the partners. We then grouped again to present problems using the order of operations, only this time I used the stars to make groups of 3's. (I used this same idea when I taught math in middle school and high school only the stickers were put directly onto the journals which always stayed in the room with me.)  

I also used this strategy when I taught elementary (back in Noah's Day, after the flood), but there was always one or two "sticker pickers" in my class. To alleviate this problem, I placed the stickers on the desks and covered them with clear packing tape or contact paper which was not easily removed. If a student moved away, I simple gave the new student the vacant desk or grouped the remaining students according to a different number.

Want to try this in your classroom? Just purchase a variety of stickers. Decide on the groups you want such as 2's, 3's, 4's, 5's etc. and get to work!

There's A Place For Us!

My college students just finished the first chapter in Fractions, Decimals, and Percents where the focus was 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 found 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.

Not doing 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 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.

Below is the link to a free page of numbers which anyone is welcomed to download and use.

Free Sheet of Numbers

Meet the Parents!

In preparing for parent/teacher conferences, what can be done a daily basis?  Is the conference based on simply talking about grades or are there additional items that need discussing?  How can an observation be specific without offending the parent or guardian?  Is it possible to remember everything?

My student teachers were required to keep a clipboard on which were taped five 6” x 8” file cards so they overlapped - something like you see in the two pictures above.  Each week, they were to evaluate five students, writing at least two observations for each child on the cards.  At the end of the week, the cards were removed, and placed into the children's folders.  The next week, four different students were chosen to be evaluated.  In this way, the student teacher did not feel overwhelmed, and had time to really concentrate on a small group of children.  By the end of 4-5 weeks, each child in the class had been observed at least twice.  By the end of the year, every child had been observed at least eight different times.

Below are sample observations which might appear on the cards.

Student	Date	Observation	IEP	ESL
Mary Kay	2/18 2/ 20	Likes to work alone; shy and withdrawn; wears a great deal of make-up. She has a good self concept and is friendly.  Her preferred learning style is visual based on the modality survey.	X
Donald	2/19 2/21	Leader, at times domineering, likes to play games where money is involved. His preferred learning style is auditory (from the modality survey).  He can be a “bully,” especially in competitive games.  He tends to use aggressive language with those who are not considered athletic.

By the time the first parent/teacher conferences rolled around, the student teacher had at least two observations for each child.  This allowed them to share specific things (besides grades) with the parents/guardians.  As the year progressed, more observations were added; so, that a parent/guardian as well as the student teacher could readily see progress in not only grades, but in behavior and social skills.  The cards were also an easy reference for filling out the paperwork for a 504 plan or an IEP (Individual Education Plan).  As a result of utilizing the cards, the student teachers learned pertinent and important facts related to the whole child which in turn created an effective and relevant parent/teacher conference.

Are you a parent or a teacher?  Do you need some tips for parent/teacher conferences?  Check out one of my best selling products on Teachers Pay Teachers entitled: Checklists for P/T Conferences Based on Characteristics, NOT Grades! Just click on the link below!

Checklist for Parent/Teacher Conferences