source: The Chuppies Monthly nature calendars from Natural Science Through the Seasons by James A. Partridge |
Our Homeschool From Preschool to High School
Nature Calendar: November
Halloween Week Art and Science: Negative Art and Bones
The boys made negative art by spraying paint on top of their hands. We have done this before years ago when we studied cave art, to simulate cave handprint paintings.
source Cave of Hands, Argentina |
This time we watered down white paint in a spray bottle and sprayed the boys' hands on dark paper.
Black would have worked better, but all we had was gray, so we went with that.
After we had their hands painted in negative space, they glued down cotton swabs to simulate the bones in the hand.
source |
James, age 11 |
Quentin, age 8 |
And so, we got an art and a science lesson in one!
related posts:
Halloween Week Science: Magical Mystery Slime
1 teaspoon Borax powder
1 1/2 cups. water, divided
4 oz. (or 1/2 cup) Elmer's glue--we used clear glue, but you can also use the white.
food coloring
glitter
1 1/2 cups. water, divided
4 oz. (or 1/2 cup) Elmer's glue--we used clear glue, but you can also use the white.
food coloring
glitter
Fill a small bowl with 1 cup of water and add 1 teaspoon of Borax powder. Mix until the Borax is dissolved and set aside. Pour glue into a medium mixing bowl and add 1/2 cup of water. Add four-eight drops of food coloring to the glue mixture. Stir it up a bit and add a bunch of glitter. Now add the Borax mixture to the glue mixture and watch it begin to solidify.
Stick your hands in and and start mixing it all up. Pour out the excess water and knead the mixture until it becomes more firm and dry.
When you're done playing with it, store in a Ziplock bag or other air tight container. We used 2 oz. Multi-purpose mini cups I bought at Wal-mart.
The Science Behind It: This mixture is a polymer. Polymers have long chains of molecules that can slide past each other until some of the molecules come in contact with molecules that stick together at a few places along the strand. Borax is the compound that is responsible for hooking the glue’s molecules together to form the putty-like material. There are several different methods for making this putty-like material. Some recipes call for liquid starch instead of Borax soap.If you are concerned about using Borax, perhaps this article can help reassure you.
Related Posts:
Contractions
We worked on contractions today. (Please pardon the black paint on my fingers.) I wrote out the words used in contractions and he cut them out into rectangles.
He then folded them over, putting the words that are taken out of the words inside the folds...
to make the contractions.
He then taped them into his book. He can refer to them, if he needs to, unfolding and refolding as much as he needs to. When writing the words in his writing assignments, he knows to put the apostrophe where the fold is.
inspiration and sources:
links:
World Geography: India
Next up is India, the second most populated country in the world! In India they speak over 200 hundred languages and three faiths originated there: Hinduism, Buddhism and Sikhism. India is the world’s biggest producer of crops and movies!
image by Arne HÃ¼ckelheim, Wikimedia Commons |
Diwali, Festival of lights
Diwali is celebrated in September–November. This year Diwali will start on Tuesday, the 13th of November and will continue for 5 days until Saturday, the 17th of November. Also called the Festival of Lights, Diwali means "row of lamps" is one of the largest and most important festivals of the year for Hindus. The festival involves lighting small lamps, called divas, filled with oil to signify the triumph of good over evil. It is also celebrated with fireworks, cleaning the home, wearing new clothes and decorating with lots of lights. In business it is often used to start a new accounting year, and it also celebrates a successful harvest. Families and friends exchange sweets and dried fruits.
Rangoli
Rangoli are traditional patterns used to decorate Hindu homes in India on special occasions.
First I helped them trace a plate and using a ruler, draw a geometric design in the circle |
They then glued beans, lentils, pasta and spices on their patterns. |
Quentin's |
Alex's |
James' |
Indian Dal
Dal is the Indian word for lentils. it is cooked almost daily in every Indian home. As a result, there was many different ways to prepare dal. Often they used red lentils and served it over rice.
Dal is the Indian word for lentils. it is cooked almost daily in every Indian home. As a result, there was many different ways to prepare dal. Often they used red lentils and served it over rice.
Taj Mahal
Monsoons
turbans
coriander
rickshaws
rickshaws
mehndi (henna )
East India Company map |
History of India
We reviewed the rise of Islam (570-1258), the battle which added an Indian province to Alexander the Great's empire,
"Treat me as a King ought" said King Porus when he was captured.
"That is understood," said Alexander, "but is there anything I can do for you personally."
"Everything is included in that one request," replied Porus.
James' (age 11) notebook page 1850-1858 Dost Mohammad signs treaty with Great Britain, Sepoys rebel against the East India Company |
And so, we picked up where we had left off in our history studies of India.
Quentin's (age 8) notebook page 1919-1930 |
From Colonies to Countries
1919 The Amritsar Massacre
1920's-1948 The peaceful protests of Gandhi
Alex's (age 18, special education) notebook page 1947-present |
1947 India is divided into Pakistan and India (Partition), India gains Independence from Great Britain
1966 Indira Gandhi becomes Prime Minister of India
1971 Bangladesh (East Pakistan) gains Independence from West Pakistan
1984 Bodyguards assassinate Indira Gandhi, Poisonous gasses leak from Union Carbide factory in Bhopal, India
Arguments between India and Pakistan over Kashmir
To celebrate our studies, we went to an Indian restaurant buffet and then afterwards looked at a selection of clothes from India that were for sale. (The photos of the paintings all come from the restaurant.)
At Sahib |
related posts:
- Marco Polo's (1271-1295) Journey, Part VII: From India to Venice
- Islamic Empires in the Renaissance
- The Rise of the Dutch
- Revolutions and New Nations
- Daughter of the Mountains, Louise S. Rankin, (grade 3/age 8 and up), includes bits about Tibetan Buddhist monks.
- Gandhi : Peaceful Warrior, Rae Bains (grade 4/age 9 and up)
- India: The Culture; India: Lands and India: Peoples, (3 book set), Bobbie Kalman, (grade 4, age 9), non-fiction
- Just So Stories, Rudyard Kipling
- Homeless Bird, Gloria Whelan (age 10 and up)
inspiration:
- Divali Rangoli Pattern at Nurture Store
- Indian Grocery Store Scavenger Hunt at The Golden Gleam
- Slippers of India from Painted Paper
- Sand Painting at The Tiger Chronicle
- Indian doll at Restless Risa
Advanced Multiplication (3-6)
Multiplication with Beans and Cups
For cups and beans, I begin with two cups and a stockpile of beans. I first tell them to start with putting 1 bean in each cup, and I begin recording while they count the beans. 2 (cups) x 1 (bean in each cup) = 2
Then I ask them to put 1 more bean in each cup and I record while they count.
2 x 2 = 4
We continue on like this for a few minutes.
Somewhere along the way, I just give them 1 instead of a set of two beans and ask them what do we do about this?At this point we talk about some numbers not coming out evenly, and then we add 1 more to make a set he can add to the cups, and continue on from there. We can add more beans or more cups as long as there is interest in this activity. In this way, young children can bridge the gap between addition and multiplication seamlessly.
Lattice Multiplication and Napier's Bones
As problems increase in size, the use of these materials becomes impractical. Traditionally an abstract system of long multiplication the distributive process has been taught.
"Research has shown, however, that the lattice system of multiplication allows students to compute multi-digit multiplication problems in significantly less time and with greater accuracy than is possible using the distributive method. "- A Comparison of Two Methods of Teaching Multidigit Multiplication [University of Tennessee, Frank George Hughes]
The lattice method came out of a calculating aid made by John Napier called "Napier's Rods."
"John Napier was a Scottish nobleman who loved mathematics. He invented logarithms, worked in spherical trigonometry and designed "Napier's rods," a mechanical calculating aid...These were an assortment of rods marked off with numbers. When these rods were arranged correctly, they could be used for multiplication and division...They were a sort of movable multiplication table -an early type of slide rule, which is what people used before pocket calculators. Because they were made of bone or ivory strips they were sometimes called "Napier's Bones."
This method can be used for as large a problem as you want. Just make sure you draw the correct number of boxes according to the numerals that are in your problem. Here is the problem 123 x 12. We got out our 1, 2 and 3 rods and made our graph 3 boxes by 2 boxes and wrote the numerals around the top and right hand edges. We then copied what the first (1) and second (2) boxes of the bones had in them. We then added the numerals on a diagonal, getting the correct answer; 1,476.
You have to use a slightly different method of adding up the numbers if you get numbers that have carrying in them. For this problem, for example, 123 x 67, you will get the numerals from left to right, 7 1,14,11 and 7. If you get numerals over 9, you must carry them over into column addition. You write down the numeral(s) and then add the number of 0's after it that corresponds to the number of columns after it. Since 1 is in the first row, it gets no 0's after it. 14 is in the next row, and it has only 1 row after it, so you write down 14 with 1 0 behind it, or 140. The next row has 11 in it (pardon the odd looking numerals; my son made a mistake in his addition the first time and got 10, but then changed it to an 11) so you write 11 with two 0's behind it for the two columns, or 1100. The last row has a 7 in it and it has three 0's behind it for the three rows, or 7000. Add these numbers together and you will get 8,241; the correct answer. This is something that is complicated to explain but easy to use once you understand how it goes. All a child needs to be able to do is add two digit numbers.
You can instead go to Mathwire and print and cut out these Napier's Bones. They can be used on their own or cut out and glued to large craft sticks.
"Students who have difficulty reasoning abstractly with numbers are frequently unable to grasp the numberical logic behind either the distributive or the lattice approach to long multiplication. Knowledge of why an abstract system of producing answers works is not as important as the knowledge that it does wok. For this reason, answers to the initial problems students work using a lattice method are checked against the materials, ususally chips on the chip trading boards."
-Mathematics...A Way of Thinking, Robert Baratta-Lorton
"Research has shown, however, that the lattice system of multiplication allows students to compute multi-digit multiplication problems in significantly less time and with greater accuracy than is possible using the distributive method. "- A Comparison of Two Methods of Teaching Multidigit Multiplication [University of Tennessee, Frank George Hughes]
The lattice method came out of a calculating aid made by John Napier called "Napier's Rods."
"John Napier was a Scottish nobleman who loved mathematics. He invented logarithms, worked in spherical trigonometry and designed "Napier's rods," a mechanical calculating aid...These were an assortment of rods marked off with numbers. When these rods were arranged correctly, they could be used for multiplication and division...They were a sort of movable multiplication table -an early type of slide rule, which is what people used before pocket calculators. Because they were made of bone or ivory strips they were sometimes called "Napier's Bones."
-Mathematicians Are People, Too, Reimer and Reimer
For example if your problem is 298 x 7, you take out the 2 rod, the 9 rod and the 8 rod and lay them down on the table. You can see, if you go down to the 7th row of this set (because 7 is the second number you are working with), on the top of the slashes is 165. Write that down. These are your tens. Below the slashes are the numbers 436. Since these are your ones, you will write them under the 165, but you will indent out one column, to make the number above start in the tens column. Add these two numbers together, and you will get 2086, which is the answer to 298 x 7.
Let's try another problem; 31 x 24. This system is sometimes called the "Lattice System" because when you get to working with larger numbers, it becomes easier to make a grouping of boxes. You make a graph with the number of boxes across as there is in your first numeral; in this case two. You make the number of boxes down as you have numerals in your second numeral; in this case also two. So you have a graph with two boxes going across and two boxes going down for this problem.
Now put diagonal lines going from one corner of each box diagonally to the other corner. I extend my diagonal to make it clear where the answers go. The drawing of the boxes may seem complicated, but it is easy once you have done it a few times and kids find it easy to do on any blank piece of paper. Next, write the digits of your problem along the sides of your boxes. Now, get out your rods for the first two digits of your problem; in this case the 3 rod and the 1 rod. Go down the number of boxes according to the numerals along the side of your graph; in this case, 2 first. Copy down the boxes just as they are on the rods, the numerals above and below the slashes will correspond to the boxes and slashes you have in your graph; in this case 0/6 and 0/2. Continue this way with the next digit; in this case, 4. Now you have numerals all around your boxes. Ignore the numerals along the top and right sides now, and add only the numbers within the boxes on the diagonal. Starting at the bottom corner the one diagonal triangle box has the numeral 4, so I write 4 down below it. The next row of diagonal triangle boxes contain the numerals 2,0 and 2, which if you add them together equal 4, so I write 4 below them. The next diagonal row of numerals are 1,6 and 0, which equals 7, so I write 7 below it. The corner diagonal box contains 0, which I chose to just leave out since it won't affect the answer, but you could have your students write a 0 there just to be consistent and get in the habit of always writing down the numerals so as not to forget any by accident. It depends on how old they are and their understanding of the concepts.
The answer to this problem, reading the numerals from right to left is 744.
Let's try another problem; 31 x 24. This system is sometimes called the "Lattice System" because when you get to working with larger numbers, it becomes easier to make a grouping of boxes. You make a graph with the number of boxes across as there is in your first numeral; in this case two. You make the number of boxes down as you have numerals in your second numeral; in this case also two. So you have a graph with two boxes going across and two boxes going down for this problem.
Now put diagonal lines going from one corner of each box diagonally to the other corner. I extend my diagonal to make it clear where the answers go. The drawing of the boxes may seem complicated, but it is easy once you have done it a few times and kids find it easy to do on any blank piece of paper. Next, write the digits of your problem along the sides of your boxes. Now, get out your rods for the first two digits of your problem; in this case the 3 rod and the 1 rod. Go down the number of boxes according to the numerals along the side of your graph; in this case, 2 first. Copy down the boxes just as they are on the rods, the numerals above and below the slashes will correspond to the boxes and slashes you have in your graph; in this case 0/6 and 0/2. Continue this way with the next digit; in this case, 4. Now you have numerals all around your boxes. Ignore the numerals along the top and right sides now, and add only the numbers within the boxes on the diagonal. Starting at the bottom corner the one diagonal triangle box has the numeral 4, so I write 4 down below it. The next row of diagonal triangle boxes contain the numerals 2,0 and 2, which if you add them together equal 4, so I write 4 below them. The next diagonal row of numerals are 1,6 and 0, which equals 7, so I write 7 below it. The corner diagonal box contains 0, which I chose to just leave out since it won't affect the answer, but you could have your students write a 0 there just to be consistent and get in the habit of always writing down the numerals so as not to forget any by accident. It depends on how old they are and their understanding of the concepts.
The answer to this problem, reading the numerals from right to left is 744.
This method can be used for as large a problem as you want. Just make sure you draw the correct number of boxes according to the numerals that are in your problem. Here is the problem 123 x 12. We got out our 1, 2 and 3 rods and made our graph 3 boxes by 2 boxes and wrote the numerals around the top and right hand edges. We then copied what the first (1) and second (2) boxes of the bones had in them. We then added the numerals on a diagonal, getting the correct answer; 1,476.
You have to use a slightly different method of adding up the numbers if you get numbers that have carrying in them. For this problem, for example, 123 x 67, you will get the numerals from left to right, 7 1,14,11 and 7. If you get numerals over 9, you must carry them over into column addition. You write down the numeral(s) and then add the number of 0's after it that corresponds to the number of columns after it. Since 1 is in the first row, it gets no 0's after it. 14 is in the next row, and it has only 1 row after it, so you write down 14 with 1 0 behind it, or 140. The next row has 11 in it (pardon the odd looking numerals; my son made a mistake in his addition the first time and got 10, but then changed it to an 11) so you write 11 with two 0's behind it for the two columns, or 1100. The last row has a 7 in it and it has three 0's behind it for the three rows, or 7000. Add these numbers together and you will get 8,241; the correct answer. This is something that is complicated to explain but easy to use once you understand how it goes. All a child needs to be able to do is add two digit numbers.
More about how it works here at Math is Good For You!
"The lattice method produces the same kind of understanding as the distributive method but is easier to teach, faster to use, and less prone to error. " -Mathematics...A Way of Thinking, Robert Baratta-Lorton
How to Make Napier's Bones
"The lattice method produces the same kind of understanding as the distributive method but is easier to teach, faster to use, and less prone to error. " -Mathematics...A Way of Thinking, Robert Baratta-Lorton
How to Make Napier's Bones
If you would like to make some Napier Rods, just get 9 wide craft sticks (like tongue depressors) and divide them into 9 fairly even sections. I just eyed mine; I did not measure them. If you are using these with children younger than 3rd or 4th grade, I would divide them into 10 sections and use the top section to put the number of the rod on the top. My Kindergartner can use these, but sometimes has difficulty reading the top number to identify which rod he is using. I ended up putting the number of the rod on the back for him. He chooses the rods by the numbers on the back and then turns them over to use them. My severely dyslexic son has trouble sometimes counting down the blocks correctly. Perhaps using different colors for the block divisions than for the numbers would help with this. (It would also be possible to make a thin column down one side to mark the rows with numbers.) Divide each of these sections with a diagonal line and copy the numbers above. The numbers are just the traditional multiplication tables. I used an Ultra-fine point Sharpie to write with, but it did bleed into the wood a little, making the numerals fuzzy. I am not sure if there would be a better writing instrument to use for this.
"Students who have difficulty reasoning abstractly with numbers are frequently unable to grasp the numberical logic behind either the distributive or the lattice approach to long multiplication. Knowledge of why an abstract system of producing answers works is not as important as the knowledge that it does wok. For this reason, answers to the initial problems students work using a lattice method are checked against the materials, ususally chips on the chip trading boards."
-Mathematics...A Way of Thinking, Robert Baratta-Lorton
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