WEEKLY ACTIVITIES
STARS AND STRIPES: K-2
Flag shapes. Using a U.S. flag as a model, generate a list of the different shapes you see on the flag. In small groups, discuss the similarities and differences between the star and the rectangle. Use a Venn diagram to organize your thoughts.
Making stars. Predict how many stars you can draw in one minute. Practice, and then time yourself for one minute. Count the stars by circling groups of ten. How many stars did you draw? How long would it take you to draw 50 stars? Explain.
How many stars on a flag? Look at a U.S. flag for 10 seconds and then put it away. Estimate how many stars you think were on the flag. How did you arrive at your estimate? Use a flag to check your estimate. Share the strategies you used to count the stars accurately.
Around the flag. Use a flag and Unifix cubes. Estimate how many cubes are needed to go around the outside of the flag. After checking your estimate, make another prediction, but using a different-sized manipulative. Try smaller and larger manipulatives. Does the size of the manipulative make a difference? Explain your answer.
STARS AND STRIPES: 3-4
Point to the stars! Ever wonder why the U.S. flag has 5-pointed stars? Do you know about George Washington's idea of a 6-pointed star? Why did Betsy Ross's idea of a 5-pointed star win over Washington's 6-pointed star? There are many ways to compare the two kinds of stars, such as the following:
Which star has more lines of symmetry?
Which star takes less material to make? Compare the areas of the 5- and 6-pointed stars by using graph paper.
Which star is easier to make? Explore making your own stars using different numbers of points. Supposedly, Betsy Ross's idea of a 5-pointed star won over George Washington's 6-pointed star because she wowed audiences with her ability to create a 5-pointed star by making only one cut into a folded piece of paper. You can make Betsy Ross's 5-pointed star using the steps shown on the Web site www.ushistory.org/betsy/flagstar.html. Do you think a 5-pointed or a 6-pointed star should have been chosen for our flag? Explain.
More than material. The U.S. flag is not just material sewn together but also a symbol for the United States and what it stands for. Many rules and regulations exist regarding the flag, and the simple act of folding the flag is no exception. Brainstorm with your classmates to find different ways to fold a paper model of the flag and create a folded flag 1/4 its original size using the least amount of folds. Try 1/8 the original size. Compare the number of folds made for each flag. Now try folding a U.S. flag following the rules and regulations found on www.usflag.org/fold.flag.html. Compare the shapes made after each fold. Hint: If the end result is not a neat triangle shaped like the recorder hats of our forefathers, it is wrong! Remember that one of the rules for a U.S. flag is that it should never touch anything beneath it, such as the ground, the floor, or water.
Time flies. The current U.S. flag has 50 stars and 13 stripes, but the flag had only 13 stars and 13 stripes in 1777. If a star and stripe were added to the 1777 flag for every tenth year up until the present, how many stars and stripes would there be altogether? Compare your results with the number of stars on the current U.S. flag.
Symmetry. Try to make a symmetrical flag by using cutouts of only one star and one stripe. Is it possible? Continue by adding stars and stripes until 50 stars and 13 stripes appear, while continuing to check for symmetry. Describe any trends you notice.
STARS AND STRIPES 5-6
Patterns. The U.S. flag has 50 stars, to represent each of the 50 states. The rows of stars are two different lengths; each row has one more star or one less star than the row above or below it. Without looking at the flag, draw how the stars are arranged. How could the 50 stars be arranged in 5 rows so that every row has one more star than the row above it?
"Super Flag:' The late Thomas "Ski" Desk of Long Beach, California, owned the world's largest flag, "Super Flag." It was hung on cables across Hoover Dam in 1996 to mark the Olympic Torch Relay. Super Flag measures 505 feet by 225 feet, and each star measures 18 feet across. The flag is made of cloth, with steel grommets, or eyelets, placed every 30 inches along the left edge. Determine the area and perimeter of Super Flag. Determine how many grommets were used to provide support for the flag. Go outside and mark off an area the size of Super Flag.
Historical flags. The Flag Resolution of June 14, 1777, stated, "Resolved: that the flag of the United States be made of thirteen stripes, alternate red and white; that the union be thirteen stars, white in a field of blue, representing a new Constellation. " Since 1795, thirty-seven states have been added, and the design of the flag has changed twenty-six times. Use the data on the chart shown on the Web site www.si.edu/resource/faq/nmah/flag.htm to construct a bar graph showing the changes in the number of stars. Analyze and interpret the data on your graph.
Designing. Robert G. Heft of Napoleon, Ohio, the designer of our country's 50-star flag, hopes that his design of a 51-star flag will be accepted if a new state is ever added to the union. Design a flag with 51 stars that you would submit for the new flag.
Betsy Shreero, Cindy Sullivan, & Alicia Urbano. (2002). Star and stripes. Teaching Children Mathematics, 9(1), 22-23. Retrieved December 15, 2009, from Research Library. (Document ID: 161921151).
Another Month
GROWTH AND THEN SUM: K-2
Dominoes-more or less. Get 20 square tiles (1-inch-- square pieces of paper). Pick up 1 tile, which we will call a monomino. You will combine tiles using this rule: Each tile must share at least one complete side with the side of another tile. Place 2 tiles together to make a domino. Now connect 3 tiles to make a triomino. Make a different-- shaped triomino. Create a tetromino with 4 tiles. How many different tetrominoes can you make?
8
Eggs-actly! A farmer has 2 hens. Every day, each hen lays 1 egg. How many eggs would his hens lay in 3 days? How many hens would he need to double the amount of eggs for 1 day? If the farmer needs 28 eggs each week, could he get that many with only 2 hens? If not, how many hens would he need? Draw a picture that shows your answer or find a way to solve this problem without drawing.
15
Boxes and more boxes. Fold a paper in half; open it, and you have 2 rectangles. Refold the paper and fold it in half again. Open the paper and count the rectangles you have now. Refold and fold the paper in half once more but this time, do not open the paper. How many rectangles do you think your paper will have? Open your paper to check your answer. If you folded the paper one more time, how many rectangles would you have? Tell a friend what is happening to the number of rectangles each time that you fold the paper.
22/29
Flower garden. Hold your hand in front of you and spread your fingers apart. Imagine that your hand is a flower and your fingers are petals. How many petals would each flower have? On a large piece of paper, draw a tall line to be a stem. Place your hand at the top of the stem, spread your fingers apart, and trace around your hand. You now have 1 flower on a stem in your garden. If you drew 3 flowers, how many petals would you have? Make a mural by asking class members to make flowers for the garden. Share different ways to find the total number of petals in the garden without counting each petal. How would your answer change if each flower had only 4 petals?
GROWTH AND THEN SUM: 3-4
1
Spring has sprung. New plants are "springing" up everywhere. Just how fast does a plant grow? Plant a seed that will grow fairly quickly, such as a sunflower, pumpkin, or bean seed, and keep it watered. The first day that you see a plant above the top of the soil, take a ruler and measure the height. You will need to choose the unit you measure with carefully because the measurement will probably be very small. Measure your plant every day and record your findings. Describe any patterns you see with the growth. Use centimeter graphing paper and draw a picture each day to show your plant's growth. What do you notice about the pictures when the rate of growth is highest or lowest? Create a table like the one below that shows how much the height changed from one day to the next.
8
Growing patterns. Draw around one square on a sheet of graph paper to create your first shape, Draw around four squares, creating a 2 x 2 array, for your second shape. Color two of the squares to create a chessboard effect. Make a 3 x 3 array for your third shape. Color the squares again to look like the chessboard.
How large will your next array be? Draw a T table like the one below to record your data. What kinds of patterns do you see? Can you find more than one pattern? How does the number of black squares grow as the shape becomes larger? How does that number compare with the number of white squares? Draw and record the data for your shapes as you work toward the size of a chessboard, which is an 8 x 8 array. Use what you have learned to predict the numbers of squares that will appear each time.
15
A grain to grow on. In The King's Chessboard by David Birch (1988), a wise man performed a service for his king and was asked to choose a reward. When the king's chessboard caught the man's eye, it prompted him to ask for 1 grain of rice for the first square on the first day. He would receive 2 new grains of rice for the second square on the second day, making a total of 3 grains. The next day, he would receive 4 new grains, making a total of 7 grains. For each square, the wise man would receive twice as many grains as he received on the square before. The king agreed to the request, thinking that the wise man was not so wise in asking for such a small reward. Use the chessboard from last week's activity How many new grains would the wise man receive on the eighth day? What would be the total number of grains of rice he would have on the eighth day? How many grains of rice would he receive on the sixteenth day? Record your data to show the number of grains received each day and the total number of grains given to the wise man overall. Who was wiser, the king or the wise man? Why?
22/29
Hold your breath. One species of whale can hold its breath for 25 minutes while another species can hold its breath up to 1 1/2 hours, which is 90 minutes. A sea otter can hold its breath for 4 to 5 minutes. You might think that the larger the animal, the longer it can hold its breath. Try this experiment with a few friends and an adult. Find someone who can time you. Hold your breath three different times. Record how long you can hold your breath each time. Compare your longest time with your friends' longest times. Can an adult hold his or her breath longer? Create a graph that compares how long you can hold your breath with the times for sea otters and whales. Explain how you would use that graph to agree or disagree with the idea that the larger the animal, the longer it can hold its breath. (This activity adapted from Corwin and Russell [1989].)
GROWTH AND THEN SUM: 5-6
1
Growth spurts. The chart below shows the average height for boys and girls ages 6 to 20. Use one color of pencil to graph the line for the boys' height and a different color for the girls' height. Find the growth rate by creating a table that shows how much boys' and girls' heights changed from one year to the next. What do you notice about the shape of the graph when the growth rate is highest or lowest? During which years are boys and girls close to the same height? Do both groups experience rapid growth at certain ages? Does one group grow faster than the other during certain years? At what age does growth stop for each group?
8
Growing wealthy seed by seed. In the book Anno's Magic Seeds by Mitsumasa Anno (1995), a man named Jack gets two golden seeds from a wizard. He plants one seed and eats one. Miraculously, Jack is not hungry for a whole year. The planted seed grows and yields two seeds the next fall. For several years, Jack eats one seed and plants the other. He could live forever this way, but then, he gets smart! One fall, he plants both seeds and eats other kinds of food that winter. The next fall, he harvests four seeds, as shown on the chart below in the column labeled "Year 1." Now he eats one seed and plants the other three. How many seeds will Jack have after five years if he continues to eat one seed and plant the others each year? Without filling in every box, predict the number of seeds that Jack will get from his plants at the end of the tenth year. How did you arrive at your prediction? Be sure to read the rest of the book with its many interesting twists.
15
Don't be square! Use a piece of graph paper to draw some squares that each have an area of 1 square unit. Draw a 1 x 1 square with 1 square unit of area. Label the perimeter and area of your square. Draw 10 squares, making each square larger than the one before. You will have a 1 x 1 square, a 2 x 2, a 3 x 3, and so on. Make a table that shows the perimeter and area of each square. Graph the data representing the area and perimeter. Compare the perimeter graph with the area graph. Write a paragraph describing the shape of each graph.
22/29
Tiny panda cubs. The average weight for a human infant is 7 pounds, compared with about 180 pounds for a full-grown man. The fraction 7/180 can be used to describe this relationship. We might say that an infant boy weighs 7/180ths of his normal adult weight. What decimal amount is this? Panda cubs weigh just 5 ounces, compared with the adult male panda that may weigh 230 pounds (3680 ounces!) or more. What part of its adult weight is the panda cub? Try showing this amount as a fraction and as a decimal. Compare the relative sizes of human infants and panda cubs. As a challenge, try to create a graph that communicates the relative sizes of adults and their young (possibly using the computer). Which form (fractions, decimal, graph) makes your comparison easier or clearer?
Gayle Cloke, Nola Ewing, & Dory Stevens. (2002). Growing and then sum. Teaching Children Mathematics, 8(8), 464-466. Retrieved December 15, 2009, from Research Library. (Document ID: 114173591).
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