While the other gnomes happily added up piles of gemstones, the blue gnome had slipped off by himself with a handful of gemstones.
He loved all the beautiful colors of the gemstones, but had decided he could do without orange. His plan was to start taking away the orange ones and count how many were left.
He pulled out a handful of gemstones and began taking away the orange ones.
"Let's see…take away one orange, take away one orange, take away one orange…" he continued for some time.
Soon he had two piles of gemstones. One pile was just orange and the other pile had the rest of the colors. By this time his friends, including Old Dismas, curious where he had gone, were watching quietly.
"Huuuuumph. Subtraction." said Old Dismas.
Startled, the blue gnome looked up and realized he was no longer alone.
"I'm not sure…I'll just take away another one and another one…" He realized he was no closer to knowing how many were left.
Now, King Equals came over. The blue gnome hoped he might have a way to help him just as he had helped the green gnome.
"I certainly can," replied the King. "I have a gift for you as well," he said as he pulled out his wand. The King waved his wand at the blue gnome's chest and suddenly a symbol appeared there. It was one line going side to side.
"Whenever you want to find out how many, just remember to use this sign between each number. And when you have finished, call on me and you will find your answer," finished King Equals.
Now the blue gnome understood. The little sign took away the gemstones he didn't want and left him with fewer gemstones. And just like Plus, King Equals' answer told him just how many were left.
"Oh! I get it. Three gemstones take away one gemstone is two gemstones." He was so relieved that he wouldn't have to count all those orange gemstones he jumped up and down with glee.
"Excellent work! You have understood well. Because you have also figured out a mystery of counting you too shall have a new name. From this time forth you will be known in Numeria as Minus." King Equals tapped the shoulder of the gnome, granting him his new name.
"Hah! Of course, Subtraction must be the secret of numbers," the blue gnome said with pride.
The yellow gnome spoke up. "I think I would like to subtract all the blue gemstones from my pile." So off he went. Minus kept busy taking away the orange gemstones. Plus decided he would keep adding his.
But Red had an idea that just might help him add up more gemstones quicker than any of them imagined. He went off by himself and started making piles.
You can Download Subtraction.pdf here.
The next few weeks will be spent working with Minus. Take this time to really master basic subtraction. For now there will be no borrowing or regrouping. You should continue to review and reinforce lessons on place value to prepare for the next step in subtraction. Use whatever manipulatives you know and love. As stated before in the Gnomes and Gnumbers lessons, they are an essential element in presenting an abstract concept in a concrete way.
For younger children start with a small pile of gemstones in two different colors. For example, three red gemstones and two blue gemstones. Count the whole group-five. Next have the child "take away" the blue gemstones. Ask, "How many are red gemstones are left?" Then "say" the equation, "Five minus Two equals Three." This can then be illustrated in the main lesson book with the equation written below. As you practice, write and illustrate. Switch to using just one color of gemstone. An older child could probably start using just one color. Work up to as large a number as your child is comfortable with. Remember, don't worry about borrowing just yet.
For an older child you can begin working in the orange band of the rainbow. That is, using a base ten set, take the ten rods and practice subtracting tens. For example, fifty minus ten equals forty. The same can be done working in the yellow band, the hundreds. Keep illustrating and recording work in the main lesson book.
Use a chalkboard to practice. Write a subtraction problem. Let's say, 6-4=___. Draw six gemstones. Show your child how to carefully erase four gemstones. The remaining gemstones is the answer. These problems can be copied into the main lesson book.
Revisit the Number Ladder. When we go down the right side, the numbers get smaller. Practice walking down a certain number of steps starting anywhere on the ladder. For example, "What if we start on the fifth rung a step down three rungs. Where are we now?" This could be made into a simple game to race to the bottom by just taking turns rolling a dice and stepping down however many steps each turn.
In one sense, subtraction undoes addition. Helping your child to understand how parts relate to a whole will help them to understand this. Using Cuisenaire rods or Math-U-See blocks would be the best way to illustrate this in a concrete way. If you take a block five units long and line it up with a two unit block and a three unit block, your child can see the relationship between 3+2=5 and 5-3=2 as well as 5-2=3. Working with different lengths and different equations. For example, you can use a four unit block and a one unit block lined up with a five unit block. This will help reinforce the earlier concept of the many ways to add up to a number. To extend this further with an older child, challenge them to use three different lengths to add up to and then take away from a number. For example, 2+2+1=5 and 5-2-2=1 and so on.
Let's Have SUM Fun with PLUS!
The exciting mathematical tale of Gnomes and Gnumbers will continue in January 2008, but that doesn't mean our work is done. Far from it! From now until then we have much work to do with our new friend Plus. Our clever green friend has made an important discovery and for the following four weeks, assuming that you will be breaking for the weeks of both Thanksgiving and Christmas, we offer the following extensions to further the study of the process of Addition.
For the child who is just beginning her study of addition, you will want to spend the next month working with simple addition equations and memorizing the addition tables. Begin with the +1 table and continue up until +9. The use of manipulatives, whether the gnomes' gemstones or a Base Ten set, is an essential element in presenting an abstract concept in a concrete way.
Older children who already have a solid understanding will benefit from the Whole to Parts exercises listed below and can increase their skills by working on Addition with Regrouping topics using a Base Ten set. If you do not already own a Base Ten set, a gemstone base ten set for download was offered in Lesson Three of Gnomes and Gnumbers. If you have not already, you may want to download those files and prepare them.
Don't forget to review the concepts we've covered in the first four lessons of Gnomes and Gnumbers. For Roman Numeral practice, write a Roman Numeral on a piece of paper or blackboard and ask your child to write or say the number that it represents. On another day give your child a few different numbers and ask her to write them on paper or the blackboard in Roman Numeral form.
Along with games of bean bag toss, review odd and even numbers by filling baskets with different amounts of gemstones and asking your child to sort the gems in groups of twos. Remind her that if one is left over, the number is odd. An alternative review activity is to write numbers on paper or the blackboard and ask your child to circle all odd numbers in one color and all even numbers in a different color. When analyzing larger numbers, be sure to remind your child that the numeral in the units place is the only numeral that we consider when determining whether or not a number is odd or even.
The Addition Strip Board, a great aid in comprehending and memorizing the addition tables, is a traditional Montessori resource. You can purchase a wooden board and strips for a discounted price at Alison's Montessori or you can download a free PDF from Montessori Materials. (Click on "Addition Strip Board" under the heading "Addition Material.") For maximum durability, we suggest printing on card stock and mounting the print-outs on foam board. As beautiful as the traditional set is, this more economical paper alternative is just as effective as using the more expensive wooden set. You will also want to print out this free set of Addition Equation Slips (Click on "Addition Combination Slips.") or purchase the matching wooden set from Alison's.
To introduce the board to a child, ask him to randomly choose an addition equation slip. In the picture here, the equation "4+3=" was chosen. The equation was built by lining the blue 4 strip on the first line, followed by the red 3 strip. With both strips lined up together, it is obvious by checking the number line that the sum is 7. The number seven tile was placed after the equation and the sum was recorded on graph paper.
Spend the next few weeks introducing and memorizing the addition tables +1 through +9. You can use the equation slips to introduce each table, as well as for daily practice. For instance, if your child is going to be working on the +4 table, collect the equation slips that express the +4 equations. Ask your child to build the equations on the strip board. For further practice, the equations slips can be used as flashcards as your child works on memorizing the addition tables. And if he can't remember the sum, always ask him to build the equation on the board.
Don't forget to add fun and movement by playing games of addition bean bag toss. Using a small bean bag, toss the bag to your child as you say "One plus one equals..." Your child should respond with the sum, "Two," as he tosses it back to you. Continue up to 1+9. Use this game as a memory aid for all 9 addition tables.
Using a Base Ten set, you can teach your older child how to add larger numbers that require regrouping or carrying. Consider printing multiple-digit addition equation sheets from The Math Worksheet Site or write your own on graph paper. Use the Base Ten materials to demonstrate the process, reminding your child of the counsel of King Equals, "Only nine of each kind can fit in one band."
Begin with a problem that requires regrouping such as "35+68=" and build each number with the gemstone materials or your Base Ten set.
Pointing out that we only add together those of like kind and that we always start with the Units, combine the Units into one pile.
Counting the Units we find that there are 13 cubes. Remind your child of the wise counsel of King Equals, "Only nine of each kind can fit in one band." Thirteen is more than nine and cannot fit in the red units band of our place value rainbow. We're going to have to do some trading. Get out a Ten Bar and line up ten of the thirteen units against it. Trade then Ten Bar for the ten Units.
Remind your child that we can only add those of like kind, therefore the Ten Bar must be added to the pile of Tens and not the Units. We now only have three Units and move on to adding the Tens together.
"Only nine of each kind can fit in one band." Since we have ten we'll have to trade again. Get out a Hundred Flat and trade the ten Ten Bars for one Hundred.
This example is one in which there is a zero in the Ten's place. It is important to point out that when we trade the different values and end up with nothing in one of the places, we need to make sure that we use a zero to hold the place. Demonstrate with this example that if you didn't use the zero to hold the Ten's Place, the number would no longer be one hundred and three, but thirteen. The child can clearly see that more than 13 is represented by the blocks.
The following exercise is recommended for all children, even those who have experience working with addition equations.
Rather than simply memorize addition equations and their sums, it is important to study numbers in a holistic way by considering them from the whole to the parts. What is the number 12? It can be many things, such as 6+6 or 9+3; but 6+6 can only ever be 12, just as 9+3 can only ever be 12. The focus in this study is to consider what makes up the WHOLE number and for this reason, even a child who has memorized the addition tables can benefit from this exercise. An understanding of the whole of numbers serves in building a stronger foundation for more advanced work in the future.
Over the course of the next month spend a separate day on each of the numbers, 1 through 12. Consider each number as a whole and from that starting point, pick out its parts. There are two ways to have fun with this exercise. The first is to draw Number Ladders.
By drawing a simple ladder we can imagine that the number we are considering is walking up its rungs. Each rung represents a different way to make up that number. Twelve can be eleven and one or it can be five and seven. The ladder shows the many parts of the number. Point out the patterns that numbers make. Going down the left side of the ladder we see that the numbers increase from zero to twelve, while on the right side the numbers decrease from twelve to zero.
Ask you child to make a number ladder for the numbers one to twelve. When he has finished this over a series of many days, consider the twelve number ladders together and compare them. For instance, the eight ladder has many more rungs than the two ladder. Pointing out these patterns and differences transforms an abstract concept into a concrete reality.
A book such as 12 Ways to Get 11 is a great example of expressing the parts of numbers in pictoral form. Make a number picture for each of the twelve numbers. Perhaps seven is a scene of a house with one door, two windows, two trees, one sun, and one chimney. (1+2+2+1+1=7) If your child enjoys this activity, consider using the blackboard for repeated play or maybe he'll want to make his own number picture book.
This week we will continue our study of numbers by considering the number four. Ask your child to think of things that are four. The four inspired authors of the Gospels, Saints Matthew, Mark, Luke and John; the four cardinal directions, north, south, east and west; and the four sides of a square or rectangle are all possible examples. Have your child make a Number Four page for his Main Lesson Book.
Shaping the numerals out of modeling clay is a beneficial tactile experience for all learners, but especially for those with learning challenges such as dyslexia. Later this week Elizabeth will be posting about modeling the numbers as well as modeling representations of number sentences.
When considering an equation, such as four plus two, it is helpful for a child to model the numeral four, an addition symbol, the numeral two and an equals symbol and answer the question by rolling out small balls to demonstrate the equation. Four small balls grouped with two small clay balls adds up to six. The equation is visually represented and the child has been offered the experience of forming the numerals with her own hands. Just as the exercise of Number Study gives the child an opportunity to contemplate the reality of the number in the created world, so too the exercise of making numbers offers the actual experience of forming the individual numbers and feeling its shape.
Encourage an older child to participate in this activity by pairing him up with a younger sibling. In teaching and directing a younger child, the older child not only increases his understanding, but demonstrates it.
Continue the lessons in Form Drawing by reading the next installment in the tale "The Story of the Great King Equals." Who is King Equals? Where did he come from? And how did he get that funny symbol? The answers to these questions and more will be discovered in this tale. After reading this week's portion of the story, draw with your child and allow her to imitate you. Don't hesitate to draw a form for a young child, allowing her to trace your work. Soon she will learn the movement and pattern and be able to work independently. Encourage your child to draw this form using a stick crayon with a continuous and uninterrupted motion.
Descending toward the base of the misty mountains, the Purple Prince looked out upon the vast land. As far as the eye could see were rolling hills covering the land. Spurring his loyal horse to continue on their journey, with great difficulty the purple prince rode over large hills. He was greatly relieved to discover a stretch of small hills. At last he came to a series of medium-sized hills. Finishing this leg of the journey and dismounting his horse, the purple prince was dismayed at what lay before him. Would he ever find a wise man to help him unite his kingdom?
In which the green gnome learns that counting is a PLUS.
Having learned that with the help of a beautiful rainbow it was easy to recognize even the largest of numbers, the four gnomes went back to their work of trying to unlock the secret of numbers.
"We now know that some numbers are odd, while others are even," recalled the yellow gnome. "And we also know that no matter how large a number is, we can figure it out with the help of the bands of the rainbow. But the enchantment has not yet been broken. We obviously haven't figured out the secret of numbers. What else could there be?"
"One gemstone and one gemstone and one gemstone..." he continued for quite some time.
Curious and confused, the other three gnomes sat down and watched their green friend continue. Soon the silence was broken by the woodsy "Huuuuumph!" of Old Dismas.
The green gnome didn't hear the Ancient Tree and continued, "...and one gemstone and one gemstone."
Old Dismas spoke up, "Did you know that what you are doing has a name?"
Suddenly the green gnome stopped. He had been certain that what he was doing was something very new and had been discovered by him alone.
"Addition. What you are doing is called Addition" repeated Old Dismas. "You see how you are adding the gemstones, one gemstone and one gemstone and so on and so forth? That is called Addition. How many gemstones do you now have?" asked Old Dismas.
"Well, let's see. I...I don't know. One gemstone and one gemstone and one gemstone..." The green gnome realized that while he could continue to add one gemstone after another to his long line, he was no closer to knowing how many he had counted.
Walking over to the green gnome, King Equals once again reached inside his cape and pulled out his magic wand.
"I have a gift for you that will help you to answer your question." The purple king waved his wand and pointed it towards the chest of the little green gnome. Suddenly a strange symbol appeared. It was made up of two lines, one going up and down and the other going side to side. And while the little lines went in opposite directions, they crossed exactly in the middle.
"Whenever you want to find out how many, just remember to use this sign between each number. And when you have finished, call on me and you will find your answer" finished King Equals.
The green gnome looked again at his long line of gemstones and this time he traced his new sign in the earth between each gemstone. "One gemstone + one gemstone. King Equals?"
The king approached the gnome and answered, "Two gemstones. One gemstone and one gemstone equals two gemstones."
The green gnome continued, "Two gemstones + one gemstone. Equals?"
King Equals answered, "Two gemstones and one more gemstone is the same as three gemstones."
The little green gnome soon understood that the funny little sign joined the gemstones together and made them one. Not only that, but King Equals' answer told him the number that they made.
"Oh! I get it. And three gemstones and one gemstone is four gemstones!" The green gnome was so excited. He merrily danced around his work.
"Very good, my friend. You have understood well. And because you have figured out this mystery of counting, I give you a new name. From this time forth you will be known in all Numeria as Plus." King Equals tapped the shoulder of of the happy gnome, bestowing upon him his new name.
"I guess I've figured it out then. Addition is the secret of numbers" announced Plus, rising from a ridiculously low bow.
"Not so fast," replied Old Dismas, chuckling to himself. "You are one step closer, that is true; but there is still much more to learn. And until then, I suggest that you and your friends practice using your new symbol, for it will help you in unlocking this great secret."
The red and yellow gnomes rushed to Plus' side, ready to play the new counting game. But not the blue gnome. No, he wasn't interested in the game of Plus. Instead, the blue gnome quietly tip-toed around to the back of the mountain of gemstones.
"I have a better way" he laughed to himself as he began filling the pockets of his cape with handfuls of colorful gemstones.
So far we've learned about Roman Numerals, odd and even numbers, place value and the process of addition. At this point the story of the four greedy gnomes stops for a few weeks in order to allow the children an opportunity to absorb the material. During the next three weeks new ideas on teaching the concept of addition and extension activities will be posted, along with the next three installment of the Form Drawing stories and the next three assignments in our Number Study.
Each week we will go more in-depth with the concept of addition, but before we continue in this study it is important to make sure that your child understands the purpose and function of adding and making sums. Explain that the addition symbol shows that we are joining the two things together that are on either side of it and that the symbol for equals simply means "is the same as." Ask your child to make a page in his Main Lesson Book modeled after the one shown above. Concentrate this week on adding 0 and 1 to a number. Depending on the age and ability of your child, you can also make a +1 page in the Main Lesson Book (0+1 through 11+1 is enough). Allow your child to use the gemstones for practice. Fill one basket with a small amount of gems and a second basket with one. Ask your child to count the gems together to find the answer. You can illustrate these problems on the blackboard or let your child use Do-A-Dots to illustrate addition with gemstones on paper.
For extra practice you can design your own worksheets using The Math Worksheet Site's math sheet generator. Now is a good time to begin enjoying resources such a The Quarter Mile Math or Calculadder.
Looking through the parapets of the great stone castle, the prince saw in the distance an immense range of mountains. "I will depart from this divided kingdom and travel to the mountains, in search of a wise man who can tell me how to unite my family's kingdom once again" decided the purple prince. And with much hope, the prince left his home in the great stone castle and set off on his horse over the misty mountains.
The running form in the drawing this week is similar in appearance to a mountain range. Point this out to your child and then practice drawing the form with him. Encourage your child to use these forms when making page borders in their Main Lesson Book.
This week we will also continue our study of numbers by considering the number three. Ask your child to think of things that are three. St. Patrick's 3-leaf clover that signifies the Three Persons of the Holy Trinity, and a triangle are three examples. Have your child make a number three page for her Main Lesson Book.
RAINBOW Last week we used the rainbow as a way to separate place and assign value to numbers. This week you should review place value. And with the rainbow in mind, now would be a fun time to learn more about them. Read The Magic School Bus Makes a Rainbow: A Book About Color, Don Freeman's A Rainbow of My Own or All the Colors of the Rainbow. Spend some time learning about what rainbows are and how they are formed. You can also have fun with color and rainbows. And you may want to read the story of Noah in a children's Bible too.
Continue spending time reading math-themed living books. Last week we suggested a few titles. If you have not yet read them with your child, go back to that list and read through. Now is a good time to review the things we've learned in the past four weeks and reading the concepts in a living picture book will help reinforce the concepts.
Each week during our four-week addition unit, more theme-related books will be suggested. The following books are this week's suggestions for living books on the topic of addition. Try to read one each day.
In which the gnomes learn the VALUE of their PLACE.
By this time the clearing was littered with baskets thrown here and there. Some were filled with gemstones and others had been toppled over. The mountain of gemstones was still high above the gnomes, but gems were now scattered everywhere, some in even numbered piles and some mismatched in odd groupings. The gnomes knew that they must continue counting in order to find the secret of numbers, but they were getting more and more frustrated the longer they tried to count. And while they were happy that Old Dismas had explained the difference between odd and even numbers, they still knew that there were far more gemstones than they were able to count on their own.
The gnomes were surprised when they suddenly saw a purple-clad king come out from behind the great trunk legs of Old Dismas.
"There is someone here for you to meet," the Ancient Tree announced to the gnomes.
The king stepped out in the clearing. He was an odd looking fellow, almost as wide as he was tall. He was dressed in purple robes that seemed to reflect every color imaginable and, instead of a crown, he wore a pointed cap trimmed in gold.
"I am King Equals, King of all Numeria. It was my ancestor who cast the enchantment on the Ancient Tree long, long ago...the enchantment that you have brought upon yourselves because of your greed. And he who cast the enchantment was a great wizard king, one who knew the secret of numbers that you so eagerly seek to discover."
"We know the enchantment. Old Dismas explained it to us. And we know we must count until we discover the secret of numbers. But these gemstones are far too many for us and when we count we soon become confused. Can you help us?"
King Equals nodded his head and pulled a magic wand out from beneath his purple cape.
"You're a wizard too?" gasped the green gnome.
Regal old yellow gnomes buy itchy vests.
Simply repeat this verse and the solution will present itself to you."
"Regal old yellow gnomes buy itchy vests....Regal old yellow gnomes buy itchy vests....Regal old yellow gnomes buy itchy vests..."
Suddenly a radiant light broke through the tops of the trees and shone upon the mountain of gemstones. And then there was a most beautiful sight. The reflection of the gemstones created a brilliant rainbow and a a prism of color filled the sky. Red, orange, yellow, green, blue, indigo, and violet.
"Use these bands of color to help you keep track of your numbers as they grow. But remember, only nine of each kind can fit in one band" instructed King Equals.
Still awestruck by the exquisite color surrounding them, the gnomes were confused by the words, "Only nine of each kind can fit in one band." And anticipating their confusion, the King began to demonstrate.
"Do you see this first band of red? We call this band Units. Each gemstone represents one unit. And we can fill the red band with nine of them."
King Equals picked up a basket and filled it with 9 sparkling gemstones and carefully laid them in the red band of color.
"But there are many more than nine gemstones, Your Majesty. How can this possibly help us? We have a mountain of gemstones to count" remarked the confused green gnome.
"Ah, but don't you see these other bands? There are many places within which you may count. When we fill up the red Units we move on to the orange band. This band is called Tens."
"Oh! I know what ten is. We counted ten and made up a symbol for it in the shape of an X using branches from...Oh. Sorry Dismas. I'm sure it was not pleasant to have your branches broken off" admitted the yellow gnome with great regret.
The Ancient Tree lowered his heavy head and offered a gentle smile.
King Equals continued his explanation, "After 9 gemstones fill the Units band we must continue by grouping them together in families of ten."
As he said this, the King carefully lined up the gemstones in groups of ten and placed them in the orange band of color.
"Now remember, only nine of each kind can fit in one band. So once we have nine groups of ten in the Tens place, we must move on to the yellow band of color. We call this the Hundreds."
Beginning to understand the sorting game, the gnomes began gathering gemstones once again in their baskets. When they filled the Hundreds with nine groups of one hundred gemstones, they moved on to the green. King Equals went on to explain that the green band was called Thousands and the numbers continued far past that. There were blue Ten Thousands, indigo Hundred Thousands and a place in the violet band for a number called Millions. The gnomes continued their work, and stopped only to notice that King Equals had opened his purple cape to reveal a funny little symbol made up of two lines on his chest.
"Excuse me, Your Majesty, but what is that symbol you wear on your chest? Is it some sort of royal family crest?" asked the red gnome.
"Oh, it is much more than that. Much more. But that story if for another time. For now, continue your counting and fill this rainbow with gemstones. Soon you will learn the purpose of the symbol I wear upon my chest" answered the King.
The gnomes whispered among themselves, "Well, I sure hope that mysterious symbol can help us discover the secret of numbers!"
Of course, you know that Ancient Trees can hear the softest, most faintest sound in the forest. And hearing the musings of the silly gnomes, Old Dismas let out a laugh that shook the forest floor.
There is no need to move on to this lesson until the concepts introduced in the previous two lessons have been mastered. Move at your child's pace. The Gnomes and Gnumbers lessons are archived in chronological order on this page for your convenience.
You will need to assemble a Rainbow Tray for this lesson, as well as collect a set of numerals. If you already have a set of moveable numerals like the ones shown in the picture above, use them. If not, and purchasing a set is not in your budget, spend one afternoon baking a set with your child. The easy salt dough recipe is here and a set of cutters can be purchased. Another option is to model the numerals with modeling beeswax (Suppliers are linked on the right sidebar.) or Sculpey Clay.
If you already own a Base Ten set, you can make use of it for place value work. If not, you can download the Ten Bar and Hundred Flat files below. These were made using Do-A-Dot markers on graph paper. Donna Young's site offers graph paper files for download if your child would like to make a set of base ten gemstones. The graph paper used here is the 10 x 14 size.
You can download the story and artwork by clicking on the links below.
We have chosen to present the rainbow in its true order of colors rather than the simplified version used in many children's songs and books. Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Have fun with the mnemonic device created by Marybeth Foss, Regal old yellow gnomes buy itchy vests, for memorizing the colors of the rainbow and their order.
After reading the story and presenting this lesson on place value, have your child use the gemstones to practice identifying the place value of each numeral in a larger number. Depending on the age and ability of the child, you will want to go as high as he or she is able. A younger child may only understand up to the hundreds place, while an older child will enjoy discovering a million.
Ask your child to illustrate a place value page in the Main Lesson Book. The sample rainbow page offered above can be used as a model for your child.
There are three place value activities that you can play this week using the Rainbow Tray and gemstones. First start by filling a small basket with gemstones. For instance, if your basket is filled with 23 gemstones, your child will count nine gemstones and, reminding him that only nine of each kind can be placed in each band, will then cross over to the Tens color band. The remaining 20 should be grouped in two sets of ten gemstones. Then show your child how to swap out 10 gemstones for a ten bar. Continue in this way until your child understands the concept.
Next, make a 2 or 3-digit number (or larger for an older child) using the moveable numerals. For instance, arrange the numerals so that they show 45. Ask you child to build this number with the gemstone materials or a Base 10 set next to the Rainbow Tray and then place the numerals in the correct strips of color on the tray.
Another fun activity is to sort gemstones in different sizes of cups. Begin with 10 small bathroom-sized cups and ask your child to fill each with 10 gemstones. When ten small cups are filled, they can be poured into a larger 8 ounce cup, representing 100 (pictured here). Ten of these 8-ounce cups can then be poured into a large 32-ounce cup to represent 1,000. This tactile experience gives the child the opportunity to see and feel these numbers. The goal is to bring the abstract into the realm of the concrete.
Add movement by playing games of rainbow bean bag toss. Say "Red" and toss your child a bean bag. He should respond by saying, "Orange" and then toss the bag back to you. Continue in order to memorize the sequence of the colors in the rainbow.
Don't forget to review the concepts covered in the previous lessons. Together read your child's entries in the Main Lesson Book and discuss each page. Practice Roman Numerals at least one day this week and use the bean bags to play a game of toss, using odd and even counting as the rhythm.
If you feel that your child would benefit from math sheet review, there is a wonderful math worksheet generator online called The Math Worksheet Site. You can get a subscription for only $2.50 per month. (The price is reduced depending on the length of your subscription.) The subscription gives you unlimited use of the site and allows you to create custom math worksheets for your child. The site is very easy to use. Consider creating sheets on Roman Numerals, odd and even counting, and place value for your child.
Nicholas Foss came up with a fun activity for the little ones. Using rainbow-colored craft sticks, he sorted the different colored gemstones on each stick and made the pattern of a rainbow. Since these were not glued down, a young child can repeat this activity many times.
This week we are adding the element of form drawing. This exercise in creating rhythmic patterns prepares a young child for handwriting and improves handwriting for the older child. When presenting these running forms, allow your child to first practice in a shallow tray of sand or cornmeal. Tracing the form with a finger in the air also helps the child in learning to imitate the pattern. Your child should use stick crayons when drawing the forms. Later in this main lesson we will be painting the geometric shapes and practice in form drawing will help in preparing the child for this activity.
One running form will be introduced each week for a period of nine weeks and we will be using the art of story telling to capture the attention and interest. Read the following story to your child as an introduction to the first running form. If your child has not had much practice in drawing, it may be a good idea to spend some time practicing standing forms such as squares, triangles, circles, rectangles and stars. Draw with your child and allow her to imitate you. Don't hesitate to draw a form for a young child, allowing her to trace your work. Soon they will learn the movement and pattern and be able to work independently.
Our form drawing tale will be centered on the story of King Equals and how he brought peace to the Kingdom of Numeria. Read this story to your child and practice drawing the form before making a main lesson book page (a sample page is shown here). Perhaps after practicing the form each day, the child can draw it in the Main Lesson Book on Friday. Encourage your child to draw this form with a continuous and uninterrupted movement. Have fun with the colors. You can use these forms to practice memorizing the order of the colors of the rainbow too.
Once upon a time there was a sad prince who lived in a great stone castle in a divided kingdom. For many years his ancestors ruled the kingdom in peace; but one day, in the furthest part of the kingdom, a great treasure was discovered in hidden cave. Ever since that day the people of the kingdom argued and quarreled over the question of who was the rightful owner of the cave and the great treasure. As the prince looked out through the parapets of the great stone castle, he longed for the day when his family's great kingdom would be one again.
At this point show your child the sample page of the running form pictured above. (Download great_king_equals.Story 1.PDF ) These lines resemble the parapet of a castle wall. Practice drawing this form each day, retelling the story each time. By the end of the week your child should be able to narrate the story himself as he works on mastering this form.
For those following the Gnomes and Gnumbers lessons, here's a heads-up. Next week we'll be introducing a new character. So after you've put together your rainbow tray, you may want to follow these step-by-step instructions and add the purple king to your collection of gnomes.
Up Gnext for the Gnomes?
Moms who are following the adventures of our mischievous math gnomes might want to buy a simple wooden tray(mine is 10 1/2 X 14 inside the frame) and some felt in rainbow colors and make a rainbow tray this weekend. Be sure to glue the felt in exactly the order shown in order to use the tray with the stories. I used stiffened peel-and-stick felt and stuck it right to the tray in two inch increments. The tray and the felt were at my local Michael's craft store.
In which EVEN gnomes make an ODD discovery.
"You have taken that which does not belong to you" he groaned in his deep, woodsy voice.
"I…I'm...I'm sure I don't know what you mean, thank you," replied the gnome, hoping that being polite would help matters.
The gnome was completely confused by the Tree Man's strange words and, wondering what had happened to his three friends far below, he ignored the woeful words of the Tree Man and begged to be returned to the ground.
With that the gnome heard the familiar groan that had sounded when the branch had been snapped from the tree.
"Huuuummmphh! And neither is it natural for my ancient branches to be broken into bits" replied the Tree Man.
With these words he lowered his enormous wooden hand and soon the gnome was safely back on the ground with his three companions. Suddenly the Tree Man took a step forward into a clearing and the four gnomes could plainly see his enormous stature.
Whosoever shall harm and tear thee asunder, shall forever count until he hath discovered the secret of numbers.
With those words, Old Dismas left the gnomes in the clearing. The earth groaned under the weight of his steps and the quaking sound of the forest floor echoed throughout the woods.
"What are we to do? Oh dear! Oh me! We've brought a terrible enchantment upon ourselves!" cried the blue gnome.
"It sounds as if we will have to find something to count. The Ancient Tree said that the enchantment will not break until we discover the secret of numbers. What shall we count?"
The gnomes confusedly looked around until they again spotted the mountain of gemstones.
"The gemstones! That's what we shall count" shouted the red gnome, with much excitement.
The four gnomes approached the huge mountain of gemstones and noticed that there were small baskets scattered around the ground. Each of them grabbed one and collected as many gems as he could fit in his basket.
After their baskets were filled to the brim, the green gnome asked, "Now what do we do?"
"How about we break a branch off that tree over there and use the sticks to count our gemstones" replied the blue gnome, with a look of enthusiasm.
"No!" shouted the other three. "Don't you remember? That's what got us in this mess in the first place!"
The four gnomes didn't know what to do, so they emptied their baskets of gemstones and began spreading them on the ground in order to count. The blue and green gnomes decided to sort their gemstones into pairs of two, but soon the blue gnome became frustrated.
"Well now, this is rather ODD. Every time I try to sort my gems in pairs, I always find one left over."
"Now, that is not EVEN fair. You do not have any left over. How is it that when I match my gemstones in pairs I always have one left over and you are able to match every last one?"
Soon the crunching and snapping of twigs could be heard again beneath the feet of Old Dismas. As he was approaching the clearing, he overheard the debate and offered an explanation.
"Yes, it is ODD when a group has one left over and for this reason we call those numbers ODD. How many gemstones have you counted?" asked Old Dismas.
"Eleven" replied the blue gnome. "Is eleven an ODD number?"
"Yes" answered the Ancient Tree. "And how many gemstones have you counted?" he then asked the green gnome.
"Twelve. Twelve gemstones" answered the gnome. "Twelve is an EVEN number then because all of my gems have a partner. That's it! I've discovered the secret of numbers!" The silly green gnome began dancing around his sorted gemstones.
"Not so fast," laughed Old Dismas. "The secret is far deeper than the discovery of ODD and EVEN. But don't lose hope. There is someone here to help you."
And suddenly a King dressed in purple was standing before them.
This lesson continues the story from Lesson 1 and introduces the concept of odd and even numbers. If your child has not yet mastered the material presented in Lesson 1, wait before continuing with Lesson 2. Regardless, remember to practice and review Roman Numerals throughout the week. If your child is interested, introduce further Roman Numerals such as L equals 50 and C equals 100. Use your child's work in the Main Lesson Book as a springboard for review. By creating a Main Lesson Book, your child is writing and illustrating his own Math book!
If you are continuing with a 5 to 6 year old, rely heavily on the manipulatives (the gemstones) to teach this concept. Talk to your child about the things around her that naturally exist in pairs: two eyes, two ears, two feet, two socks or shoes. Then proceed to group the gemstones in pairs of two. Fill up the miniature baskets with gemstones (keep it under 10 for a young child) and ask him to sort them in pairs. If one is left over you can make a game of saying, like the blue gnome, "Well, isn't this ODD!" Point out that when all the gemstones have a partner, they are all EVEN. Make an Odd Number and Even Number page in your child's Main Lesson Book modeled after the sample page in the story. Draw with your child if he is having trouble expressing these concepts in writing and allow your child to spend a few days on his page if necessary. Young children learn best by imitation.
If you're working with a 7 to 8 year old, repeat the above activity and review it each day. Create and add the Even and Odd Number pages in the Main Lesson Book. Encourage your child to decorate his page with a border that reflects the story or concept learned. Remember, these pages are to be approached as works of art. When your child has grasped the concepts of even and odd, continue the work by using the blackboard. Write a random number and ask your child to tell you if it is even or odd. Allow her to use the gemstones to find the answer.
Continue to combine movement with your child's learning. Games of bean bag toss are a fun way to practice numbers. This week, play games of Even and Odd toss. As you toss the bean bag to your child say, "One!" and as your child catches it, he responds, "Three!" Continue through the odd numbers as he is able and then try the even numbers. Weather permitting, take your lessons outside. Use stones or acorns and sidewalk chalk to make number pictures on the ground.
Beginning this week we are going to concentrate on a different number each week. Don't skip this activity, even if your child knows his numbers well and can work basic math equations. We're going to be considering the concrete reality behind the very abstract idea of numbers. This week we'll begin with Number 1.
Consider the world and its Creator. What exists that expresses oneness? Some answers could be one God, one sun, one moon, one nose, etc... (Remember these answers are taken from the experience of a young child. There is no need to correct him and point out that the sun is a star and there are many in the universe, etc...) Ask your child to make a Number 1 page in his Main Lesson Book.
I ordered all of our supplies from A Child's Dream Come True, one of my favorite sources of quality, natural fiber handcraft materials. The felt is 70% wool and 30% rayon and is a pleasure to work with (Of course, if you're like Elizabeth and are allergic to wool, you'll have to order some Benadryl as well ;-) The variety of beautiful plant-dyed colors make working with the felt a lot of fun for the children. The wooden body is listed at the bottom of this page as the "Wood Angel/Fairy Folk" and the cotton skeins of embroidery floss can be found here.
As far as the patterns for the robe, cape and hat, I just drew them on card stock and pinned them to the felt for cutting. Only two shapes are necessary to make the three pieces for the gnome.
I used the embroidery floss to create the details on the clothing. The names and characteristics of each of the four gnomes will be revealed in the stories over the next weeks, but if you are embroidering the details on your gnomes, it is necessary to do so before putting them together. The green gnome that I am working on in these pictures is the Addition Gnome. His clothing is detailed with addition signs.
Here is the detail work on the Multiplication Gnome.
The two identical pattern pieces are used for the robe (front) and cape (back) of the gnome. After you have added the details and designed your gnome's robe, you simply use a small amount of Tacky Glue and attach the piece of felt to the front of the wooden body.
The gnome's hat is made by rolling the semi-circle pattern piece. Just use a bit of glue at the seal and allow it to dry. We kept our hats simple, but these could be detailed as well.
The colors are important if you want your gnomes to match the descriptions in the Gnomes and Gnumbers stories. Addition is green, Subtraction is blue, Multiplication is yellow and Divide is red.
Here are a few more pictures of our new set of Math Gnomes.
Subtraction and Addition ready to count their baskets filled with gemstones.
Division Gnome waiting to divide his basket of gemstones. The baskets can be found here.
More Gnomes and Gnumbers stories coming on Sunday!
Elizabeth and I were discussing our little ones and how they would enjoy having coloring pages. I tweaked around with Photoshop and saved this week's Gnomes and Gnumbers illustrations as line drawings. We'll be adding them to our Main Lesson Book and you can download them here for your child's book as well.
Once upon a time, in the deepest, darkest recesses of the earth, there lived a clan of four greedy gnomes. The first was as blue as a crisp, clear sky. The second was the shade of a red apple in autumn. The third was as yellow as the sun and the fourth was greener than a blade of grass.
Now gnomes are a curious folk. Burrowing deep in the ground, they build hidden cities that guard the treasures of the earth. Of course you already knew that, but these gnomes were particularly curious folk. Not content to work with their fellow earth-dwellers, they wanted to make a name for themselves and build up a treasure greater than any the world had ever known. So these four miserly gnomes dug and burrowed and tunneled until they reached the middle of the earth where they believed their treasure would remain protected.
Days and weeks and months went by and the four gnomes came to realize that they had nothing to do but count and sort their mounds and mounds of jewels all the day long. It wasn't long before the gnomes began arguing among themselves about the true owner of the treasure.
"It is all mine!" squeaked the small yellow gnome as he scooped great piles of rainbow-colored gems toward himself. "I am the one who found the way to the middle of the earth. The jewels belong to me."
After many days of bickering and quarreling, each of the four gnomes had clearly argued their reason for being the rightful owner of the treasure. Finally, the red gnome offered a solution.
"But how shall we know if we have divided the treasure evenly?" asked the green gnome.
The gnomes fell silent, each trying to think of a way to be absolutely certain that their pile was equal to the piles of the other gnomes.
After what seemed like hours upon hours, the yellow gnome suggested that they take a trip back up through the winding tunnels to the surface of the earth in search of someone with wisdom who could solve their problem. The others reluctantly agreed and soon they were on their way.
The gnomes made their way through a tunnel which led to a secret hollow in a magnificent, ancient tree. Climbing out of the hollow, they tripped over the gnarled feet of the tree and looked around hoping to find someone to direct them to the dwelling place of a wise one who would offer a solution to their problem. Suddenly a sparkle of brilliant color caught the eye of the green gnome.
"What is that?" he asked in a whisper.
The gnomes turned and together discovered a pile of the most beautiful gemstones.
"They are mine!" shouted the green gnome. "I spotted them first!"
Before he had a chance to dive upon the pile of gems, the red gnome held up his wee hand and interrupted. "Let us use sticks to count how many gems there are and then we shall share them. Surely this is a great treasure which we must carefully guard." Then reaching up to the tree above him, he pulled down on a branch and snapped it off.
"What was that?" asked the blue gnome.
The other gnomes ignored the deep and unusual sound and went about their work of counting.
After spreading the gems on the ground, the gnomes laid down the branch next to the first stone. And when they added a second gem they broke the branch in two. For the third stone they broke one of the two branches again and saw that they had three stones and three sticks. Then a fourth gem was moved but the sticks were becoming hard to keep track of and they stopped to find a solution.
"Let us use two of the pieces of the branch to make the shape of the Letter V. That looks like the "V" between our thumb and other fingers when we hold up our hand. That will help us to remember the number five" suggested one of the gnomes.
Placing one of the leftover sticks before the V-shaped pair, the gnomes counted four.
"One before five is four."
The gnomes continued to count the gems in this way. The V-shaped formation showed five and then adding a stick after it made six.
"One after five is six." The gnomes were rather pleased with themselves.
Pulling a seventh gem from the group, they decided to break the single stick in half to make seven. One of those was broken again to make eight.
"This is getting confusing again," sighed the red gnome. "What can we do to count so many gemstones?
"I know," boasted the greedy yellow gnome. "Let's cross two sticks together, like our arms crossed in front of our chest. This will remind us that the gems are all mine!"
The other three were not happy with his solution, but not being able to come up with a better one, they agreed. It was true, when both hands are crossed together they counted ten fingers. The sticks in the shape of a V were rearranged to form an X.
"One before ten is nine" said the yellow gnome.
Again the gnomes continued moving the gems and counting. The X-shaped sticks by themselves represented ten gems and then one more was added in front of it.
"One after ten is eleven. And two after ten is twelve."
The gnomes were tired and sat down to rest.
"We have so many more gems to count. We will most definitely need another branch" announced the yellow gnome.
And just as he raised his arm to grab the nearest branch..."Huuuummmphh!" An enormous woody hand swooped down and scooped him up high above the green ceiling of the forest.
According to the age and ability of your child, this lesson could be used over a period of one week or up to one month. All work should be done in a Main Lesson Book with both stick and block crayons. Recommended resources and suggested sources are linked below. The lesson plans are suggested for two different age groups. The ages are only offered as a general estimate but, of course, the parent will be able to best identify the work which will most benefit her own child.
Along with a variety of math-related games and fun, the scope and sequence of the Gnomes and Gnumbers Main Lesson covers the four mathematical processes (addition, subtraction, multiplication and division), counting to 1,000, place value, both horizontal and vertical operations, identifying odd and even numbers, multiplication work up to the 12 times table, mental math, borrowing and carrying work, multiple digit and multiple operation problem solving.
The original art work can be downloaded and reprinted for use as a visual in telling this story.
If you are using this math story with a 5 or 6 year old (or a child with little or no previous math experience), you may want to consider introducing one Roman Numeral per day. Before you tell this story, go outside with your child and find a stick to use for story time. The child can break it apart as the gnomes break their stick. (Rather than breaking a stick, using toothpicks is another option.) The illustration offered above of the gemstones, sticks and Roman Numerals is a sample page of a Main Lesson Book. For a young child you will want to demonstrate drawing this page and allow your child to imitate you.
After the Roman Numerals I through XII are introduced, you will want to spend a few days writing the numbers 1 through 12 on another page of the Main Lesson Book. Ask your child to draw a different colored gemstone between each number to keep them from running together into one huge number.
As you work through this introduction you should spend some part of your lesson playing counting games. Find creative ways of reinforcing number recognition. Model numbers one through twelve out of modeling beeswax or instead, cut them in salt dough with number cookie cutters, which can be baked and later painted.
Add movement to your child's learning and take time to play number games. Toss a bean bag back and forth while taking turns counting the next number. (Say "One" and toss the bean bag to your child. He or she will respond "Two" and throw it back to you as you say "Three" and so on.) The early learning game of Walking the Line can offer another fun exercise in counting. Mark a line with masking tape or use a grout line on a tile flour. As your child walks forward, together count forward to twelve and as he or she walks backwards, count the numbers backwards with your child from twelve to one.
If you are using this math story with a 7 or 8 year old (or a child who has a basic understanding of numbers and familiarity with one or two of the four basic math processes), you may be able to tell this story in one day. Have your child complete the entire Main Lesson Book entry of Roman Numerals I through XII on the same or following day. (As with a younger child, some children will need to imitate your example. Don't hesitate to draw with your child.) On the following day ask your child to narrate the story as you look at yesterday's drawing in the Main Lesson Book.
According to the ability of your child, have him write (in crayon) the numbers one through one hundred in his Main Lesson Book. (You can spread this exercise out of several days if necessary.) Ask him to change colors every tenth number. (For example, 1 through 9 are green, 10-19 are red, 20-29 are blue, etc...) This will help in preparation for learning place value. Have him separate each number by drawing a gemstone between each number to keep the numbers from running together.
One day, or if necessary over the course of several days, have your child model the numbers one through twelve using beeswax or use cookie cutters and salt dough and bake.


In the most recent month of electricity data, February 2019, Little Ferry's average rate of 16.24¢/kWh -- a difference of about +28% from the U.S. average of 12.70¢/kWh that month.
Year over year in Little Ferry (NJ), electricity rates increased an estimated 2 percent -- from 15.86¢/kWh (February 2018) to 16.24¢/kWh (February 2019).
In February 2018, the average electricity rate in Little Ferry (New Jersey) of 15.86¢/kWh -- a difference of about +25% from the United States average of 12.66¢/kWh that month.
The average amount of solar radition in Little Ferry (measured on a monthly basis) is 33 percent lower than an area of the U.S. (Nevada) with historically high levels of solar radiation.
May is historically the month that will have the highest solar output (AC) values in Little Ferry -- averaging an estimated 545 kWhac. December typically has the lowest output (314 kWhac).
The average amount of solar radition in Little Ferry (measured monthly) is 19 percent higher than an area of the U.S. (Washington) with historically low levels of solar radiation.
The average monthly solar radiation level in Little Ferry, NJ is 4.45 kilowatt hours per square meter per day(kWh/m2/day). See the chart below for monthly comparisons.
The average monthly solar system output (AC) in Little Ferry, NJ is 5462 kilowatt hours (AC). See the visualization below for month-by-month averages in Little Ferry.
In the most recent month of natural gas data, January 2019, Little Ferry's average rate of 9.21$/Mcf -- a difference of about -2% from the U.S. average of 9.43$/Mcf that month.
On a year-over-year basis in Little Ferry (NJ), natural gas rates increased about 4 percent -- from 8.87$/Mcf (January 2018) to 9.21$/Mcf (January 2019).
In January 2018, the average electricity rate in Little Ferry (New Jersey) of 8.87$/Mcf -- a difference of about -0% from the United States average of 8.91$/Mcf that month.
Average natural gas rates in Little Ferry, NJ in January 2019 were 9.21$/Mcf -- an estimated 2 percent less than that month's average U.S. rate of 9.43$/Mcf.
Comparison of Little Ferry natural gas rates versus national average rates.
Electric companies providing service in or near Little Ferry, NJ.
Our search for electric companies located in Little Ferry produced no matches.
Gas companies that offer service in or near Little Ferry, NJ.
Our search for gas companies located in Little Ferry produced no matches.
Builders that specialize in solar energy in or near Little Ferry, NJ.
Our search for solar contractors located in or near Little Ferry produced no matches.
One particular type of solar energy imitative has been making waves in multiple countries across the globe: floating solar panel installations.
Little Ferry (NJ) is a borough in Bergen County with an estimated population of 10,626.
For more information on energy in Little Ferry, NJ, or for additional resources regarding Little Ferry energy, visit the EIA.


So how do you go about training a new advisor? Nicely, it is not straightforward. In response to Sarah Chandler, writing for Investopedia , the success charge for bigger brokerage firms to create a worthwhile monetary advisor is around 30%. Now, in case you're looking to retire, this may be less related to you. You're not trying to hire a junior to construct a brand new e-book of enterprise, but to take over yours. This implies the main focus is totally different. You are not spending time training your alternative to prospect and cold name. You are not even training your junior to construct an independently profitable ebook of business. As a substitute you're specializing in having your junior shadow you, study your shoppers, and perceive the right way to preserve these relationships. Over time, your junior will be able to take this skillset and develop her personal book of enterprise, but, early on, her job is to make your current purchasers love and need to work along with her.
A company with shares or debt admitted to trading on a regulated market is (topic to certain exceptions) required to prepare a half-yearly report which units out specific info regarding the corporate's actions and revenue and loss through the relevant 6-month interval. The half-yearly report have to be printed inside 2 months of the tip of the interval ( DTR four.2, and see DTR 6 and Listing!14 and Checklist!sixteen 41 for necessities and guidance for publication). It ought to include a condensed set of financial statements (in accordance with IAS 34 42 ) an interim administration report and responsibility statements. In addition (where the traded securities are shares), approximately at the end of the first and third quarter there needs to be an interim administration statement. No monetary statements are required but some firms, significantly those with US shareholders, present quarterly interim statements.
There are three categories of monetary worth risk; rate of interest danger, Change Rat threat, and commodity costs risk. Each can have potentially optimistic or unfavourable impacts on the profitability or worth of the agency. If the dollar have been to appreciate against different main currencies just like the Japanese yen, Kodak's merchandise would be costlier to overseas buyers, and it may lose market share to overseas competitors.
Now Alice has a much clearer view of what is going on on in her monetary life. She will see, for instance, that dwelling bills take the most important chunk out of her revenue and that hire is the most important single expense. If she needed to lower expenses, finding a spot to reside with a less expensive hire will take advantage of impression on her backside line. Or maybe it will make extra sense to make many small changes fairly than one giant change, to chop again on several other expenses. She could begin by chopping back on the expense gadgets that she feels are least crucial or that she may most simply dwell without. Maybe she might do with much less leisure or clothes or travel, for example. Whatever choices she subsequently made would be mirrored in her revenue assertion. The value of the earnings assertion is in presenting revenue and bills intimately for a particular period of time.


Ready to Get to the Root of Your Health Issues?
The First Step to a Healthy Life is a Healing Diet.
What is the Healing Diet Reset Program all about?
Are you putting up with symptoms that are cramping your style, zapping your vitality, snuffing out your joy? Maybe you chalk it up to being over 30, getting older, having food allergies? Maybe you're just accepting this as your new reality?
Don't settle for low energy, low libido, poor digestion and all the problems that are slowly leading you down the path to chronic illness.
Ask yourself, how would your life be different if you had lots of energy, less pain, needed no prescriptions, could stay 'in the zone' with a clear, focused mind?
The key to healing lies in your diet. Our Standard American Diet is highly inflammatory, largely devoid of nutrients, high in refined sugars, low in critical fats and full of toxins, pesticides, herbicides and hormones.
Even if you aren't yet suffering from a degenerative disease, if you are just following what the masses are doing, you are at high risk for developing heart disease, cancer, diabetes, Alzheimer's and autoimmune disease.
We want to help you get off of that path and on to a path that promises abundant energy and health.
We've taken all of the resources that we've developed over the years in our practice and assembled them into a powerful program that is designed to help you take control of your health by taking control of your diet.
We believe that if we could all just go back to a diet that is more like our ancestors, we would be a much healthier nation and a growing body of scientific evidence supports that idea. This diet goes by many names like "Paleo", "primal" or "ancestral" but whatever you call it, this focus on a diet full of foods that are free of processed and refined ingredients and other by-products of modern food production is turning out to be the answer to the modern health challenges.
On the Healing Diet Reset program, you'll get to eat real foods bursting with flavor and nutrition. No counting calories or carbs and fat, no starving yourself, no bland powders or shakes, no disgusting packaged meals. You just eat the delicious foods that are part of the plan, and your body takes care of the rest.
We'll provide you with all the meal plans, recipes, shopping lists, and other tools you need to do the reset program for a minimum of 30 days and in that time, you'll learn how to reboot and jumpstart your health.


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A near-capacity audience at Tacoma's historic Pantages Theater Friday night was treated to a diverse concert band program, skillfully presented by the 60-piece Tacoma Concert Band under the direction of Robert Musser.
The program included band classics such as "Fame and Fortune" by Karl King, "The Thunderer" by John Philip Sousa, and even "A Leroy Anderson Portrait", arranged by James Barnes. Two soloists were featured as well. Local student saxophonist Erik Ibsen-Nowak performed the Glazunov saxophone concerto as winner of the Tacoma Concert Band Student Soloist Competition, an annual opportunity for local student musicians. Soprano soloist Edie Delegans shared lovely renditions of two traditional songs, "Down by the Sally Gardens" and "Gypsy Love Song".
The program also included two contrasting contemporary works for concert band, both of which were given a very committed and convincing performance. The first was Philip Sparke's "Dance Movements", a work commissioned by the United States Air Force Band and premiered by them in 1996. The four-movement work demonstrated superb writing for concert band, with excellent solo use of several instruments as well as wonderful layered ensemble writing. As the composer himself describes, "the four movements are all dance-inspired, although no specific dance rhythms are used". Perhaps most striking in this performance was the brass movement which Sparke describes as a "love duet". The tremendous strength and warmth of the Tacoma Concert Band brass were shown off in this touching brass chorale.
The true gem of the program was Aldo Rafael Forte's "Van Gogh Portraits", a five-movement work based on famous paintings by the great Dutch artist. Forte was born in Havana, Cuba, in 1953, and moved to the United States in 1962. The highly programmatic movements are unified by the use of the three notes B-flat, D, and A. This "Van Gogh motif" develops and transforms through the course of the work, but is always recognizable as a unifying theme. Throughout the work, new sounds and textures are explored as a means of expressing the theme of each painting. The third movement, "Zouave", which features the percussion, and the fourth movement, "The Drawbridge", in which clarinets and bass clarinet establish a remarkably suggestive foggy water scene, were particularly striking examples of the tone painting achieved by Forte in this work.
While it might be said that the program had "something for everyone", the bulk of the audience was attentive and receptive throughout the evening. The same folks who applauded the "Leroy Anderson Portrait" also enjoyed the "Van Gogh Portraits". Such programs are rare musical experiences, and are only possible when the ensemble as a whole has real commitment and skill on which to draw; this is obviously the case with the Tacoma Concert Band.
Kim Davenport
Puyallup Blog

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https://www.incomeinvestors.com/vz-stock-verizon-communications-inc-is-a-top-dividend-stock-for-2017/24331/ VZ Stock: Verizon Communications Inc. is a Top Dividend Stock for 2017 Jing Pan, B.Sc., MA Income Investors 2017-07-12T07:00:25Z 2017-07-12 07:49:33 Verizon stock VZ stock Verizon Communications Inc. NYSE:VZ top dividend stock VZ dividend Verizon dividend income investing Even though Verizon Communications (NYSE:VZ) has seen low share price performance recently, it has increased its quarterly dividend rate in each of the last 10 years. Dividend Stocks,News https://www.incomeinvestors.com/wp-content/uploads/2017/07/Verizon-Top-Dividend-Stock-150x150.jpg
VZ Stock: Verizon Communications Inc. is a Top Dividend Stock for 2017
By Jing Pan, B.Sc., MA | July 12, 2017
Own Verizon Stock for Dividends
As a mega-cap company, Verizon Communications Inc. (NYSE:VZ) stock is not known for making big moves. Yet in the past three months, Verizon stock dropped 11.2%. Does that mean it's time for investors to reconsider their position in the American telecom giant?
Not really, especially for income investors with a long-term horizon. In fact, because a company's dividend yield moves inversely to its share price, the recent downturn in Verizon stock could represent an opportunity.
Verizon is a multinational telecom company. In particular, it is the largest wireless communications service provider in America. In the first quarter of 2017, Verizon had a 35% market share in terms of the number of wireless subscribers. (Source: "Market share of wireless subscriptions held by carriers in the U.S. from 1st quarter 2011 to 1st quarter 2017," Statista, last accessed July 10, 2017.)
Today's Verizon operates through a number of segments, but being a wireless carrier is by far its biggest business. In 2016, Verizon Wireless generated $89.2 billion in revenue, accounting for 70.8% of the company's total revenue. (Source: "Verizon grows its strong customer base profitably in 4Q," Verizon Communications Inc, January 24, 2017.)
Providing wireless communications services is quite a profitable business, too. In 2016, Verizon's wireless segment achieved earnings before interest, taxes, depreciation, and amortization (EBITDA) margin of 43.8%, representing a 130-basis point improvement from the prior year.
Of course, there are plenty of lucrative businesses out there. What's special about Verizon is that its business has high barriers to entry. If one company is making a lot of money, others will notice. And before long, the industry will be filled with new entrants. As competition increases, existing players will see their profitability decline. As taught in Economics 101, firms under perfect competition are price takers and make zero economic profit in the long run.
High barriers to entry prevent this from happening in the wireless carrier business. You see, building enough cell phone towers to cover a service area large enough to compete with Verizon would require billions of dollars. And that's only if you could get the permission to build them. These days, new cell tower proposals are often met with strong protests from nearby residents.
Mike Mozart/Flickr
That's why in the U.S., the wireless carrier business has just four main players. Verizon is the biggest one, followed by AT&T Inc. (NYSE:T), T-Mobile US Inc (NASDAQ:TMUS), and Sprint Corp (NYSE:S). Together, these four companies account for over 95% of the number of wireless subscriptions in America.
Limited competition in the wireless services industry is a key reason behind your rising cell phone bills. For companies in the industry, though, less competition means a perpetual cash cow business.
This is also great for Verizon stock investors. Because the company has a stable and recurring business, it can afford to return some of the profits to shareholders. Verizon stock currently pays $0.5775 per share on a quarterly basis. At today's price, that translates to a handsome annual dividend yield of 5.34%.
Verizon stock has also been raising its payout. The company has increased its quarterly dividend rate in each of the last 10 years.
Source: "2016 Annual Report," Verizon Communications Inc, last accessed July 10, 2017.
The Bottom Line on Verizon Stock
Other than its core wireless business, Verizon also has a few projects that could turn into powerful catalysts. It recently launched a pilot program for its 5G wireless technology, has made multiple investments in the "Internet of Things," and could significantly boost its digital advertising revenue with the Yahoo acquisition.
Bottom line: Verizon is a solid company. Even though its share price performance has been lackluster in recent months, Verizon stock still offers value to income investors.


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Peter Wentworth Bucknell (born 1967) is a filmmaker, author and classical violist residing in Barcelona.

Film
Known best for his underwater films, Bucknell is a commercial and documentary film maker. In 2014 he wrote The Underwater GoPro Book: an instructional book on the use of the GoPro. He is an underwater cameraman known for his work on New York's shipwrecks and in Mexico's caves.

Performing arts
Author of Violin is Easy, a pedagogical book for teachers and students, Bucknell began in the performing arts as a classical musician. He performed the Australian premiere, broadcast live by the Australian Broadcasting Corporation, of Chaconne for Viola and Orchestra by Michael Colgrass. He performed and recorded as solo violist with Apollo's Fire, the Los Angeles Baroque Orchestra, Les Concerts du Monde, and Los Angeles Musica Viva. He was the principal violist with the Rebel Baroque Orchestra from 1998 - 2009. He appeared as a guest on Jim Henson's The Ghost of Faffner Hall as a member of the Como String Quartet in 1988.

As a member of the Danel Quartet, specialising in the string quartets of Dmitri Shostakovich, Bucknell has appeared at Wigmore Hall and in many other European halls, and on Radio France. As a member of the Stradivari Sextet, Bucknell was loaned the "Mahler Stradivarius."

He was a founding member of the Raw Fish Quartet performing at the George Crumb Festival in New York, concerts in Taiwan and La Jolla and at the Santa Fe Chamber Music Festival, playing George Crumb's Black Angels and Steve Reich's Different Trains. He was a member of the Munich Chamber Orchestra, he recorded with Concerto Köln, and performed with Musica Antiqua Köln.

Background
A documentary film maker, Bucknell is known for his factual short films and environmental films shot underwater. A classical viola player, Bucknell was for several years the Professor of viola at the Crane School of Music, State University of New York at Potsdam.

Bucknell's early studies on violin were with Russian pedagogue Nelli Shkolnikova. In 1991 he won the Auckland International Viola Congress Competition and the Queen Elizabeth II Silver Jubilee Award. His Quartet won the Interpretation Prize in the Osaka International Chamber Music Competition.

He studied music in Melbourne at the Victorian College of the Arts with Nathan Gutman; in Los Angeles, California with violist Donald McInness; in Siena, Italy at the Accademia Musicale Chigiana with Yuri Bashmet; and in Cologne, Germany with Rainer Moog, a student of Walter Trampler at the Juilliard School, the principal violist of the Berlin Philharmonic Orchestra under Herbert von Karajan.

Bucknell holds a Bachelor of Economics and Commerce degree from the University of Melbourne and a Doctor of Music degree from the State University of New York at Stony Brook where he studied with professor Mitchell Stern.

Bucknell is the son of Tasmanian-born painter Toni Bucknell of Melbourne, Australia. He is married to mezzo-soprano Rinat Shaham.

Discography
Recordings include two chamber music CDs on the classical music label, Musica Omnia, with the Atlantis Trio and the Atlantis Ensemble:
 Felix Mendelssohn's Piano trio No. 1, Op.49 and Piano sextet, Op. 110
 Robert Schumann's Piano Quintet Op. 44, Franz Schubert's Trout Quintet and song "Die Forelle." (Eighth release in "The Romantics" series.)

See also
 Early music
 Baroque music
 Historically informed performance

References

External links
 History of la Grange de Meslay

 Osaka International Chamber Music Competition

1967 births
Living people
Stony Brook University alumni
People educated at Trinity College (University of Melbourne)
University of Melbourne alumni
Australian classical violists
Australian filmmakers

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__writing is a lonely job
community, friends and family, having someone believe in you makes all the difference, quotes, stephen king, support for writers, writing, writing is a lonely job
As Stephen King says, writing can be a lonely job. Having people believe in you can make such a big difference. While I have strong ambitions and a passion for writing, the people who have supported me have equally contributed to my progress as a writer. I'd like to take a quick moment to thank people who actively support me and my writing ventures. Thank you to my partner, Eliabeth, Samantha and Anne!
Who has supported you throughout your writing process? Who has believed in you?
– Ermisenda Alvarez
19 thoughts on "__writing is a lonely job"
prisailurophileblog said:
My best friend. My parents aren't really interested in my writing
Ermilia said:
My parents support me passively. Like they are happy I'm doing things that make me happy but…they just keep reminding me to keep studying psychology (to get a secure job). 😛 At least your best friend actively supports you. That's great. 😀
gotmeghan said:
My nana, mom, and my aunt Kat are probably more supportive of my writing then anybody else in my family. I have some friends who support it, but nobody really seems to care about my stuff anymore. 😦
You have a lovely bunch of people who support you. 😀 The issue is that people lose interest if they're not personally interested. My friends care but kind of in a 'oh, so how's that going?' I was lucky enough to find someone who lives in my area who I get along with and she loves to write herself, that's Samantha. Maybe check if there are writing groups in your area? Having a friend who also loves writing helps a lot!
I live in such a small town that there's hardly anything here. I used have people like your friend Samantha, but I think after time and time again of saying I didn't want to make a career out of it like doing my artwork, I think everybody just kind of gave up on me and my stuff altogether.
😦 That's a shame to hear. Maybe you can reconnect with them? Even if you don't want to make a career of writing, it's good to stay positive about your hobby. Even if you don't make it a career, it's still a valid way of spending your time.
The Real Cie said:
My son does, but he has his own problems. I don't even bother mentioning writing to my mother. She'd just squash what little enthusiasm I have left. I really don't have any friends, so no help there.
Anne Schilde said:
This made me think a bit. I made up a best friend and wrote stories about how she supported me. I'm not necessarily suggesting that. It makes me realize though how important is the support we get from ourselves.
It's a shame that your mother doesn't support your work. As Anne said, your own support is so important. In fact I'd argue it's the most important because without it we wouldn't write at all. Btw, we support you here at Ermilia. 🙂
No one has ever been any more supportive than you, Ermi. Thank you!
Naw, thank you. Keep sharing your amazing stories. 🙂 They inspire me.
kvennarad said:
Actually, my publisher, pretty much. My agent. My pseudo-sister Toni.
I'd love to have the support of a publisher and/or agent. Professional support would really motivate me to keep writing. That's the dream, right?
If you had asked me a year ago, I would have said that neither publisher nor agent affected my motivation to write, which has always been sporadic. Then my publisher asked me to write them a teen-vampire novella, which I did. I've never worked harder or faster on anything!
I would have worked fast and hard on it too! 😀 Enjoy the great opportunity and I hope your relations with the publisher/agent stay this good for a long time.
All you lot! Thanks a bunch.
😀 Thanks to you too Joe for your support and amazing presence on Picture it & write. You're so supportive of other writers which I really appreciate.
Larry Atchley, Jr said:
My wife, Sussie has always been my biggest supporter and has believed in my writing from the beginning through to today. My daughter Alina as well, as she will probably always be my biggest fan. Also friends, and fans, too numerous to list all of them here, but especially Jenn, Tiffany, and Fritz who were my first true fans outside of friends and family when I was first published, and who in turn became great friends in the process.
That's beautiful to hear, Larry. Keep hold of all those wonderful people who contribute to your life and support you writing. 🙂


Music lovers in North-West Wales were treated to a trio of bands performing live last night, as part of Independent Music Venue Week; and all for the price of a couple of High Street coffees. The independent music venue in question was Neuadd Ogwen; situated in Bethesda, on the edge of Snowdonia. It's a tiny town, surrounded on all sides by mountains, forests, rivers, and lakes.
A handful of stragglers missed the start of a captivating opening set from Belfast based septet, Documenta; including four guitarists who blended together gracefully; the instruments caressing each other, creating a shoegazing soundscape awash with atmosphere and melodious noise. Documenta cherry pick from (and experiment with) everything from Can to The Beatles, and it works perfectly.
They opened strongly with "Idle Hands" from the album "Drone Pop #1" and from that moment on, the audience were theirs for the taking. Five tracks from the album were included in the set; as well as an as yet untitled song. A 12" EP is in the pipeline, which vocalist Joe Greene promises will be even more experimental. They closed their set with the grooving beat of "Gentle's Yard", from the album, and left an appreciative crowd hungry for more.
Up next were Manchester's Horsebeach. Manchester isn't renowned for it's sunny climate; neither is North West-Wales for that matter, but from the moment Horsebeach kicked off proceedings with "A Place Like This", you could easily imagine you were sitting on a warm summer beach, sipping a cold drink, and contemplating a siesta before going out to party; no mean feat considering this was a cold, wet, and dark Saturday night in January.
The set was a mix of tracks from the band's prolific back catalogue, plus three new songs from their next album, due out in March.
Ryan Kennedy's dreamy, hazy croon dripped like melting ice cream, and you could see the enraptured audience swaying along to songs like the sublime "It's Alright", as though they didn't have a care in the world. Reminiscent of Aztec Camera at times, Horsebeach took us elsewhere, and Neuadd Ogwen basked in the warm melodies the band created.
Last on stage were local band Yucatan. Being on home turf (vocalist Dilwyn Llwyd runs the venue) they were received with rapturous applause from an anticipatory crowd; and rightly so. The band seduced the audience with songs that felt almost hymn like at times. Minimal, soothing, ethereal, almost childlike, Yucatan's set seemed to reflect the stark beauty of the area that surrounds Neuadd Ogwen; one suspects this is what heaven might sound like if it was a band, and Yucatan's ability to enthral an audience looked almost effortless at times.
The fact that the lyrics were sung in Welsh didn't distract at all, and a number of non Welsh speakers hearing the band for the first time were overheard raving with surprise about how amazing they were; quite right too, because Yucatan are startlingly good.
From the moment the drums pounded the intro to "Ffin", you knew you were in safe hands, and hearing "Cwm Llwm" felt like The Velvet Underground singing you to sleep.
They finished the set with the crowd pleasing "Un Cyfle", which is the only point where the laid back Llwyd finally becomes animated. The song starts slowly but surely, and finishes with a squall of noise as the band exits.
At the end of the gig, one audience member was seen taking a photograph of the empty stage. As this night was a part of Independent Music Venue Week, it seemed appropriate to do so. After all, this week has been an opportunity to celebrate the smaller, intimate, independent music venue, and when all is said and done, it is Neuadd Ogwen that the audience was there to celebrate.
When I was offered the chance to be a Life Model for an Art Group, my first concern was that I might be compared unfavourably to previous models…in the trouser department I mean. Reassurances from my girlfriend that I was "a grower, not a shower" didn't help; the last thing I wanted was to grow, mid pose.
As it turns out, the size of my equipment was the least of my worries.
For a start, coming up with eight different poses was hard enough.
"We require five 5 minute poses from you, two to last 15 minute each, and one you can hold for an hour…with a 5 minute break half way through, should you require it" said the lady in charge.
Another worry was the itch on my nose, which started halfway through the first of my 15 minute poses.
Then there was the wind…not the gale force one blowing outside (they'd provided a wall of heaters for that), but the one threatening to explode from my backside; as I knelt on the floor, with my bum in the air, and my back to the artists.
There was a spot of bother "down below" at one point, but it was due entirely to the coffee I'd accepted, halfway through the session; and not because of any dimensional deficiencies, or unwanted expansions on my part. In short, I was desperate to pee. I managed to hold it off until the end of the session, and it was a blessed relief when I finally let go.
And so I stood, and I knelt, and I lounged, and I hugged myself for two hours; striking poses like a pro (because I'm also an actor, there were a couple of dramatic stances on display too that morning).
At the start of each pose, I would find something new to stare at; anything to help me stay perfectly still; and distract from the fact I was stark bollock naked, in front of a dozen women and three men, halfway up a mountain in North Wales, in a bleak midwinter.
avoid beans, eggs, curries etc. the night before.
Most of all though, don't worry about your tackle. Because if you're lucky like me, you'll come away with a bit of spare cash, a new profile picture, and a nice piece of material for a new blog post.


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Q: CloudSQL Proxy intermittently refuses connection I'm using a Cloud SQL proxy sidecar on my nodejs API service.
It appears to work great, except that approximately 1% of my API requests come back with an error indicating that the DB connection failed with:
connect ECONNREFUSED 127.0.0.1:3306

My backend logs show that this was thrown from my ORM when it attempted to connect to the DB.
Sidecar logs show nothing, and the CloudSQL instance in question shows nothing out of the ordinary (17/4000 connections, <1% CPU usage, 1.5/3.5GiB memory usage, <100KiB ingress/egress per time slice on 6 hour window).
What might be causing this?
Edit: additional information:
All my pods have been up for many hours with 0 restarts, so the intermittent failure isn't a transient startup failure.
Logs show that this has been occurring intermittently since 30 days ago.

A: Here are a few reasons that can cause a Cloud SQL instance to become inaccessible:
1) Connection failure between your instance and the agents Cloud SQL uses to monitor the health of your instance

2) Synchronization of operations between your instance and the Cloud SQL service

3) Underprovisioning of resources, such as CPU cores, RAM, and/or storage, to your Cloud SQL instance (see Cloud SQL's Operational Guidelines [1] for additional information).
Since there are several reasons which could cause connections to be dropped (many of which are intricately related to the specifics of your project's implementation and environment), it's extremely complex to diagnose abnormal connection rejection. Additionally, Cloud SQL continuously monitors for any issues that can make an instance inaccessible and automatically takes action to resolve these issues.
Under normal circumstances, the error rate will not fully go away, but should happen at a very low level [2]. There are, of course, some conditions that can make it worse - both production issues as well as certain combinations of operations.
In any case, the recommendation under such circumstances is to implement a retry strategy for reconnection to the instances with exponential backoff. Some of the client libraries already have supporting code in place, but it depends a bit on what you're exactly using.
[1] https://cloud.google.com/sql/docs/mysql/operational-guidelines

[2] https://cloud.google.com/sql/sla

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text:
DSA Architect Biography Report (January 16, 2022, 7:41 pm)
Basic Biographical Details
Name: John Sutherland Ross
Designation: Architect
Born: 28 June 1904
Died: 30 July 1977
Bio Notes: John Sutherland Ross was born on 28 June 1906, the son of John Ross, painter and his wife __MacLeod. From February 1921 he was articled to Alexander Ross & Son while attending the Royal Burgh of Inverness continuation classes in Building Construction and Architectural Design. He remained with Alexander Ross & Son for five years as an apprentice but it is not yet clear where he worked from 1926 until 1938, though it must be assumed he remained with Alexander Ross. In 1938-39 he was a lecturer in Architectural Design at the Burgh Continuation Classes while having a post as chief assistant to Alexander Ross & Son.
In 1939 Ross was called up and served with an infantry regiment in Cape Town, South Africa, Egypt and North Africa. From 1943-45 he undertook survey work in the Middle East while on military service.
He returned to his previous post with Alexander Ross & Son after the war. He was admitted LRIBA in 1949, proposed by John Alistair Ross, William James Taylor and Alexander Cullen, junior.
He died on 30 July 1977 at his home in Fearn in Ross-shire. He was survived by his wife Alexandrina.
Private and Business Addresses
The following private or business addresses are associated with this architect:
Address Type Date from Date to Notes
28, Queensgate, Inverness, Inverness-shire, Scotland Business 1939 *
3, Ardross Place, Inverness, Inverness-shire, Scotland Private 1949
Castlebrae, Tain, Ross and Cromarty, Scotland Private/business(?) Before 1950(?) After 1952(?)
1, Kingsway House/High Street, Tain, Ross and Cromarty, Scotland Business 1964 *
Commercial Bank Buildings, Tain, Ross and Cromarty, Scotland Business 1970 *
* earliest date known from documented sources.
The following individuals or organisations employed or trained this architect (click on an item to view details):
Name Date from Date to Position Notes
Alexander Ross & Son February 1921 * 1926 Apprentice(?)
Alexander Ross & Son 1926 1938 Assistant
Alexander Ross & Son 1938 Chief Assistant
Buildings and Designs
This architect was involved with the following buildings or structures from the date specified (click on an item to view details):
Date started Building name Town, district or village Island City or county Country Notes
1952 Alness Public Hall Alness Scotland Alterations
The following books contain references to this architect:
RIBA 1939 The RIBA Kalendar 1939-1940 London: Royal Institute of British Architects
RIBA 1964 The RIBA Kalendar 1964-65
RIBA 1970 RIBA Directory 1970
The following periodicals contain references to this architect:
The following archives hold material relating to this architect:
RIBA Archive, Victoria & Albert Museum RIBA Nomination Papers L no6387 (Combined Box 136)