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Let's Go Fly A Kite!


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 (see Nov. 20, 2014 post entitled Faux Diamonds), 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!

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 eight 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!

Divisibility Rules



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

A Go Figure Debut for an Ontarian That's New


Mrs. Teacher's Store
For our Go Figure Debut this month, we head north....way north to Ontario, Canada. Pat has been an active member of Teachers Pay Teachers for about a year and a half. She states that creating and selling resources on this site has been a steep learning curve but a delightful adventure. Her TPT store is called Mrs. Teacher, and it contains 88 different resources for many grade levels and various disciplines.

Pat's background experience is actually in finance, but she has always created her own worksheets to supplement her sons' learning materials from school. When her two sons were in school, she would teach them during the summer months so that there was a minimal "summer slide" before school began again. She discovered that she enjoyed teaching so much that she now volunteers at a literacy center where she teaches basic reading, writing and math skills to adults.

She enjoys playing the flute and also has a flare for art.   She loves doing watercolor painting. In addition, Pat dabbles in creating frames, stationery, etc. although she claims that she still has much to learn in that area. In the future, she would love to create clip art, but right now, she has no clue how to even begin!

She characterizes her teaching style best as facilitating because she leans towards student-centered learning. She likes to allow the students to take the initiative for meeting the demands of the various learning tasks. She believes it is important for learning to be both fun and challenging.

In her store, Pat has a variety of math resources.  I particularly like her 41 page linear measurement package that I believe would be a wonderful addition to your math centers! It covers both the Imperial System and the Metric System and is appropriate for grades 3-5

Measuring Up contains:
  • a brief history of linear measurement
  • a test and answer key
    Linear Measurement Package
  • explanations and worksheets in both Imperial and Metric systems
  • measuring worksheets for both non-standardized and standardized units
  • worksheets for independent work and activities for working with a partner
  • problem solving
  • estimating
  • rounding off measurements 
  • working with rulers
  • measurement conversions
  • blank templates for additional practice 
  • worksheets using standard units to find the perimeter of shapes 
**Spellings are given in both American and Canadian English.

Free Resource
Pat also has an unique free resource about different kinds of lighthouses and their history. The easy-to-understand information makes the content understandable even for a young audience. (appropriate for grades 3-5)  Using this resource, a teacher might explore the dangers and challenges of life at sea, the importance of being responsible at work, etc. The students are introduced to new nautical terminology, and the included activity helps them to remember the new words.

So take a few minutes to check out Mrs. Teacher's store.  While you are there, become a follower, or download a freebie or better yet, purchase a resource for your classroom.