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"Sum" Trick

In the book Ten Black Dots book, there are a total of 55 black dots. Normally, to find that answer, you would add the numbers together.

But did you know there is an easier way? Take 10 and divide it by 2. That equals 5. Multiply 10 x 5 and you get 50 then add in the 5 which equals 55. Too confusing? Well let's look at it in groups that equal 10.

As illustrated above, 10 is by itself so it is 10. Then if we group the numbers so that each group equals ten, we have four additional sets. All together, we have five groups of ten with five left over which equals 55.   5 x 10 = 50 + 5 = 55

This will work for every sequence of consecutive numbers which begins with one and contains an even set. In other words, sets that contain 2, 4, 6, 8, 10, 12... numbers. Merely divide the largest number by 2; multiply the largest number by the quotient, and then add the quotient.

Example:  14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2, 1

This will also work for an odd numbered sequence like 11 but the formula or quick trick for finding the sum is a little different. As seen below, we again divide 11 by 2, which 5.5 or rounded up equals 6. Again we group sets of two that equal 11. There are five groups plus 11 by itself so that makes a total of six groups.
Since there are no numbers left by themselves, simply multiply 11 by 6 (the rounded up quotient) to get the sum which is 66.

I love to write a series of consecutive numbers which begin with one on the board, and have the students find the answer using their calculators while I do the math in my head. Of course, they are amazed and swear that I have memorized the answer. I then ask me to give me a series (not off the wall or so large that it would take forever to use the calculator) and again I quickly give them the answer. I then teach them that math trick.

Students love "tricks" like this, but I always burst their bubble by telling them mathematicians are astute people. That's why they are always looking for faster, quicker, and smarter ways to do math!

A Go Figure Debut for A Poet Who Is New!

Theresa's TPT Store
Today’s post features a Board Certified Teacher from North Carolina. (As most of you know, Board Certification requires a great deal of work!) Theresa has taught Reading Recovery, been a third grade resource teacher, has taught first and second grade, as well as a first and second multi-age class. She has been teaching for 19 years and says she still loves what she does!!! Besides teaching, she enjoys spending time with her family and taking care of her two cats that are named Cindy Lou Who and Boots.

Her Teachers Pay Teachers store, Theresa’s Teaching Tidbits, is unique in that it contains several resources that showcase poems. Theresa even features a poem of the week and offers a bundle of these poem activities in the resource entitled: Poem of the Week Bundle. It includes all four of her Poem of the Week elementary products at a discounted price. They are:
Discounted Bundle
  • A Kind and Caring Classroom: Poems of the Week that Promote Good Character
  • Science Poems and Activities for Primary Grades
  • Patriotic Poems and Activities for Primary Grades
  • Fall Poems and Activities for Primary Grades
She suggests using these poems as a part of your weekly routine to teach comprehension, phonemic awareness, phonics, vocabulary and fluency.

Free Resource
Since her students love word searches, Theresa has created a ten page freebie called Word Searches: Fry Word Finds. She uses word searches to help early readers increase instant recognition of high-frequency words. Each word search in this free resource features ten of the 100 most used words in reading and writing and includes three different word searches with answer keys. These would be perfect for a center or for those who finish early!

Additionally, Theresa has a blog that bears the same name as her store. I loved reading her August 27th post about having a school garden. Since I teach at a college, we have gardens everywhere, but they aren’t created or maintained by the students which might be a good thing. If you take time to look at her blog, you will see pictures of her current classroom which might give you some ideas for arranging yours. In addition, she shares some books that made it to her front porch over the summer. I get the idea she loves reading books to her students!

In her August 20th post, Theresa gives you a step-by-step picture tutorial on how to make four-pocket folders that she uses in her writing workshop. (You’ll have a good laugh on why she didn’t make a video tutorial.) She even has free labels for these folders that you can download. You’ll just have to check out her blog to find out where and how…something I highly recommend that you do!

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.

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 on the left, my 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.

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.