6.25.13 | Go Fly A Math Kite!
Kites are fun, and so should math be. Step outside the math box of rote learning and worksheets, then make and fly a kite! Grocery bag kites are easy to create and fun to fly.
Have your child(ren) decorate their kites with whatever wonderfully colorful math patterns they’re learning at the moment. The brown paper is a good surface for bright, chunky colored pencils (the color can easily be removed or changed with an ink eraser).
For instance, this is a mirror image of the first 4-5 lines of the wonderful number pattern, Pascal’s triangle:
And here are the first 5 triangular numbers, 3, 6, 10, 15, and 21.
The top image shown here is the pentagon created by the 2 and 8 times tables and the pentagram created by the 4 and 6 tables. (The numbers on the circle represent the 2nd digit of 2-digit numbers.)
The 2’s: start at 0 then proceed to the right: 2-4-6-8-10.
The 8’s: start at 0 then proceed to the left: 8-16-24-32-40.
The 4’s: start at 0 then proceed to the right: 4-8-12-16-20.
The 6’s: start at 0 then proceed to the left: 6-12-18-24-30.
The bottom image is diamond square numbers for 4, 9, and 16. If you count the rows of dots, you have the odd numbers: 1-3-5-7. You can go on building these diamond shaped rows to access all of the square numbers. Try it!
To make a grocery bag kite, you’ll need:
A large brown paper grocery bag
Paper ring reinforcement circles (used for 3-hole binder paper)
Glue or paste
Chunky colored pencils
Paper streamers or crepe paper cut into strips
And here’s how to make it:
1) Make 4 holes in the top of the bag, one at each corner. Add the paper ring reinforcements to each of the holes (one on each side) to ensure that the holes don’t tear through.
2) Cut 2 lengths of string, about 30” each.
3) Tie each end of the strings through a hole in the bag, making 2 loops.
4) Cut another piece of string, again about 30” and tie one end around the middle of the 2 loops and tie a knot. This is the “flying” string or handle.
5) Decorate with colorful math patterns!
6) Cut the crepe paper into strips for the streamers or kite tails, and glue them to the open end of the bag around the strings you attached earlier.
7) When the glue is dry, the kite can fly. Hold tightly to the string handle and run so the wind catches the kite. When the bag fills with air it will float and flutter behind you. Add more string to the handle to fly the kite higher.
Creation stories are told in Grade 3, and many examples given of how we humans as a whole have “gotten on” in the world. As the gate to the garden of childhood begins to close, the joys of newfound independence and self-reliance mix with some sadness around an accompanying loss of innocence. Hearing stories of how humanity as a whole has surmounted this archetypal loss can lessen these often tumultuous feelings. It’s reassuring to the 9 year old, as s/he faces the daunting task of growing up, to know that others have succeeded at it, gaining independence and freedom in the process. Time and measurement are helpful tools at this stage , and so are taught in depth now.
Learning about housebuilding, or how people around the world find and create shelter, is a natural companion to these stories. Gardening and cooking, in the spirit of living independently on the earth, can be brought now as well. Wonderful stories can accompany all of this, for example before teaching time and measurement, tracing its cultural progression, recapturing it and weaving it into what is taught can be magically effective. The resonances between cultural and child development are real, and when tapped into and brought to awareness, can be a wonderful teaching tool.
Imagine a story about Brother Sun and Sister Moon dancing around Earth, pulling down Night’s starry velvet curtain, then gently parting it with the rose light of Dawn. Or a colorful story about how and why the Moon changes her shape. Storytelling, as always, is the best cloak to wrap around these facts or anecdotes. There’s no need for these stories to be elaborate, in fact the simpler the better.
So, go to the library or online to find the surprising, amusing, and informative facts and then teach them in story form. For instance, did you know that the king’s foot was the source of our modern 12 inch foot? Or that our weekdays are named for three heavenly bodies, and various gods and goddesses? SATURN, the SUN, and MOON for Saturday, Sunday, and Monday, and the gods TIU, WODEN, THOR, and the goddess FREYA for Tuesday, Wednesday, Thursday, and Friday.
You’ll find lots of interesting information on weights and measures too. It’s surprising how relatively recently we’ve adopted these standards. When we lived more simply, before commerce and trade, there was little to no need to measure or weigh anything accurately. Many peoples or tribes used individual systems of measurement in their local communities. Barter and trade then demanded that balance scales and weights be used. Making a balance scale with your child(ren) could be a creative, fun, informative project. Keep it simple: seeing the essence of things goes a long way toward enthusiasm and understanding!
The first known unit of universal measurement was the
Egyptian cubit. Its length was based on the length of the
arm and hand, from the elbow to the extended fingertips.
Everyone’s arm measures differently, so in ancient Egypt
the Standard Royal Cubit (used to check the accuracy of
measuring rods) was made of black granite and preserved
at the Royal Court. A wonderful project to illustrate
the length of the cubit is to have your child(ren) make one
and take it to a large, open space to measure the length of
Noah’s Ark! (You can find the length in cubits in the Bible.)
So you can see that there’s a wealth of opportunity to mix math and stories in Grade 3! Find all of the above and much more in the Math By Hand Grade 3 materials, and have a wonderful year while including many, many practical arts and crafts as well. The list is endless!
Build a garden cart
Plant a “soup and salad” garden
Make a simple churn and then churn butter
Go to a sheep farm at shearing time and gather wool
Wash the wool and use it for felting, or card, spin, and knit it
Find SO many more wonderful things to do with your third grader!
The Grade 2 “mood” is one of contrasts. There’s a settling in to the new world of challenges and learning begun in Grade 1, accompanied by a certain restlessness. As boundaries are tested, there’s a desire to take on more, which can be expressed as a somewhat overly confident rambunctiousness. This quality is reflected in the Aesop’s Fables’ brashly bold animal characters, as they repeatedly test any and all boundaries.
So here we have the perfect fit for the typical 8 year old, a way of “laying down the law,” palatable and effective and understandable. Grade 2 is an optimal time for sowing these deeply pedagogical seeds, so they later become the basis for a mature, caring sense of responsibility. Fables are endearingly entertaining as well. Brevity and conciseness underscores their effectiveness, so their messages are easily heard and retained.
In addition to the moral that follows the story, the animals’ rambunctiousness nicely echoes the 8-year-old’s unruly thread of high-spirited boundary testing.
Fables are uniquely adaptable to math lessons, enhancing them with story, movement, and art. The Math By Hand Grade 2 curriculum provides many examples of applying these wonderful tales to your math lessons. It’s a sure-fire way to raise skill levels and improve retention, while providing the most important element for a successful math program: enthusiasm! Here are a couple of examples:
After telling the story, “The Lion and the Mouse” in which a tiny mouse proves his worth to the mighty lion by gnawing at the strings of the net used to capture the lion, thus freeing him, elements of the story are used to teach (and illustrate!) the square numbers.
After telling the story, “The Grasshopper and the Ants” use elements of it to illustrate a movement done large on the floor with a number line, showing patterns found in the 3 and 7 tables. The Math By Hand curriculum provides all the details needed to access this, along with many other ways to combine fables with math lessons.
In stark contrast to the animals’ mischief-making, the legends of saints and heroes paint inspiring portraits of men and women whose lives have made a difference in our world. This contrast of the beastly with the saintly can help to balance polarities your child(ren) may be experiencing at this age.
Find many stories like this one, of exemplary men and women of all times and cultures online or at your library, and share their legendary lives with your child(ren). Your efforts will reap many and varied benefits and rewards.
Though not as directly applicable to math lessons as the fables, the saints and heroes tales provide an essential counterbalance to the animal tales in their inherent goodwill and compassion, while imparting valuable life lessons.
Recognize then the value of stories to any curriculum, including math, and be sure to always include them, along with art and movement.
After the numbers 1-12 have been formally introduced with a story that is fitting to each one, it’s time to bring the numbers together. Relationships are now formed and the numbers’ interactions can be characterized. If all 4 processes are presented together, from the very beginning, it makes this sort of lively exploration possible.
One of the most effective vehicles for this is storytelling, costumes, and plays. When the children are encouraged to role-play the very different nature of each of the 4 processes, math takes on a much deeper value than if the various problems are presented abstractly and the children expected to learn by memorization and drill.
The most commonly used method of characterization for the 4 processes is applying the 4 classical temperaments to each of them, while naming them accordingly and attributing traits, personalities, and appearances that exemplify each of them. Here are some examples:
ADDITION: Addi could be acquisitive, plump, GREEN and growing. She may also be seen as industrious and persevering since she stays with the job to the very end, until it’s finished. The temperament most suited to addition is PHLEGMATIC.
SUBTRACTION: Subtra is sad, BLUE, and always losing things. Other aspects of his personality may be that he is generous, freely sharing and giving things away. The temperament most suited to subtraction is MELANCHOLIC.
MULTIPLICATION: Multi is complex and busy, YELLOW and very happy to be so. He could also be said to be helpful, willing to take on more than his share. The temperament most suited to multiplication is SANGUINE.
DIVISION: Divida is decisive, RED, and definite. she may be called upon to be an impartial judge because of her fairness and accuracy. The most suitable temperament for division is CHOLERIC.
A little costuming and story creation is all that’s needed to convey the “mood” of each of the 4 processes. This concept goes a bit beyond math, since it can also be seen as a window into aspects of personality and character. The traits of the 4 processes can be a mirror, reflecting qualities that resonate on deeper levels.
A bit about the 4 temperaments. An awareness of their qualities in children can be quite helpful in teaching. There are 4 temperaments, and we all have a bit of each one, with one or two that predominate. They are universal qualities or personality traits that tend to be more singularly individual at first. As the child matures, the dominant trait can be modified or balanced, thus blending somewhat with the others. When these qualities are mirrored back, as they can be with the 4 processes characterizations, it can promote deeper understanding and acceptance of self and others.
So do have fun with these personalities, applying them within stories and plays that first show the qualities and interactions and then also bring the computation itself to life, as a lively interaction that every child can appreciate, understand, and comprehend. Numbers and their interactions can then be seen as friendly, approachable, and not least importantly, symbolic of much more than just everyday math.
Fairy tales. They are not to be read or listened to lightly, for they are essential to the young child’s well-being. In a Waldorf kindergarten, there a steeping in these tales, with the same story told again and again, every day for a week. You need only watch the children’s faces as they sit raptly listening, to know how deeply these stories are taken in.
As a Waldorf teacher in the lower grades, I was always amazed at how accurately the story that was told the day before was recounted by the children. No detail was missed, indicating how very enmeshed in the tale they were. Stories are also the perfect medium for learning, as they carry otherwise abstract concepts within a vessel of beauty and grace.
The letters are taught, one by one, when the child is ready to learn them, usually at 6 or 7. Each letter is lovingly cloaked in a story, so the letter “B” for instance might be introduced with the Grimm’s fairy tale, “The Queen Bee.” Then the bee itself could be rendered as a prototype for B. In this way, every letter is livingly brought.
The same process can be followed for the numbers. Even though they will already be familiar to most first graders, this sort of formal introduction, stressing the qualities that are unique to each one, enables the numbers to become good and trusted friends. A deep investment is then made in having an ongoing relationship with these friends!
Each of the numbers from 1 – 12 could be introduced via a fitting fairy tale. The story can be told on day one and retold by the children on day two, before drawing and writing the number along with images from the story and a geometric form. These forms help to express the numbers’ unique qualities while also illustrating geometric relationship.
For the number 1, a fairy tale about the sun or moon (or both) expresses its unique, individual nature. Many sun/moon fairy tales from around the world can easily be found online or at the library. As shown below, a relationship can also be made between the number 1 and the uniqueness of each individual person. The circle could represent the sun or moon as well an important quality of the number 1.
Telling the Grimm’s fairy tale, “The Star Money” for the number 5 could include the obvious relationship to the 5-pointed star. The golden nature of the human being could also be shown as one of the number 5′s qualities. Accompany this with a wonderful movement activity by using a yellow or gold rope to outline the figure of one of the children with his or her arms and legs outstretched. Tracing the figure uses “body knowledge” as an aid for learning how to draw the star. This drawing could accompany an illustration/caption from the story.
After all of the numbers have been introduced, they can come together to interact, with all 4 processes taught at once through story and characterization. See our next post for more on this! And do consider Math By Hand. It’s a child-friendly program that integrates stories, movement, music, poetry and more with math. We guarantee that you and your child will fall in love with math . . . no more math tears or fears! Go to the Shop page, choose from a variety of affordable options, and buy it today!