Teacher says orally: Our class was wondering whether dandelions are weeds or pretty flowers. They grow in many parts of our schoolyard. They seem to spread a lot of seeds." Cut a piece of string 1 meter long. Tie or tape the ends together. In a space in the schoolyard with many dandelions, spread out your string in the shape of a square. Count the number of dandelion plants inside your square. Record the number on the form I provided, then answer the 3 questions. Form provided to students: My square had dandelion plants. If each plant had 10 leaves, how many leaves would be in your square? There would be leaves in my square. If each plant has 5 flowers, how many flowers would be in your square? There would be flowers in my square. If each flower becomes 100 seeds, how many seeds will the plants spread? seeds would be spread. 1 of 9
Suggested Grade Span K 2 Task Teacher says orally: Our class was wondering whether dandelions are weeds or pretty flowers. They grow in many parts of our schoolyard. They seem to spread a lot of seeds." Cut a piece of string 1 meter long. Tie or tape the ends together. In a space in the schoolyard with many dandelions, spread out your string in the shape of a square. Count the number of dandelion plants inside your square. Record the number on the form I provided, then answer the 3 questions. Form provided to students: My square had dandelion plants. If each plant had 10 leaves, how many leaves would be in your square? There would be leaves in my square. If each plant has 5 flowers, how many flowers would be in your square? There would be flowers in my square. If each flower becomes 100 seeds, how many seeds will the plants spread? seeds would be spread. Alternative Versions of Task More Accessible Version Teacher says orally: Our class was wondering whether dandelions are weeds or pretty flowers. They grow in many parts of our schoolyard. They seem to spread a lot of seeds. Cut a piece of string 1 meter long. Tie or tape the ends together. In a space in the school yard with many dandelions, spread out your string in the shape of a square. Count the number of dandelion plants inside your square. Record the number on the form I provided, then answer the 3 questions. 2 of 9
Form provided to students: My square had dandelion plants. If each plant had 10 leaves, how many leaves would be in your square? There would be leaves in my square. If each plant has 5 flowers, how many flowers would be in your square? There would be flowers in my square. More Challenging Version The original version, and Cut a length of string four meters long and use it to make a square 1 meter long and 1 meter wide. Determine the number of dandelions in this square meter. In an area that is 10 meters long and 5 meters wide, how many dandelions would you predict there would be in all, if the other square areas each contained the same number of dandelions as that in your original square? Context We do a week-long study of dandelions in the spring, when children collect bouquets to bring to their teachers and when people discuss why dandelions are such a nuisance. What This Task Accomplishes This task allows children to measure and cut a meter length of string and use it to collect their own data. Counting strategies will be evident as students find out the number of leaves, flowers and seeds within their own space. As a class this can then be extended to include numbers within the class area for use with another possible task: What is the typical number of dandelions in a 33.3-meter x 33.3-meter space on our playground? What the Student Will Do Students will collect data to provide information on dandelions. Some may draw, tally, graph, use counting strategies or use a combination of these. Students will then use the data to answer the three questions asked. Many strategies will be employed while solving this part of the problem, from counting by 5s, 10s and 100s, to using diagrams, manipulatives and number sentences. Time Required for Task About an hour or longer, as data need to be collected first. For first-grade students we used two shorter class periods, collecting data first and then doing the actual task later. 3 of 9
Interdisciplinary Links This task is just one of many that we do around the theme of dandelions. We explore dandelions as weeds or flowers, nuisance or friend, and how people view and deal with dandelions. We dig up whole plants (roots and all) to measure the lengths of roots, leaves, stems and diameters of blossoms. We also practice counting, using leaves and flowers. We share the story Dandelion, by Don Freeman, do story maps, and write and sing songs about dandelions. In art, we make dandelion puppets, and paint and make collages of dandelions. Teaching Tips We are usually a day or more into our dandelion study before we do this problem. We will have had discussions of why dandelions are pretty or not, where they grow, allergy problems, strategies for getting rid of them, etc. Students also will have had experience counting by 5s, 10s and perhaps 100s, so that the problem is manageable. Students will also have experience using drawings, manipulatives, tallying and counting as problem-solving strategies. Suggested Materials Small manipulatives for representations and counting String Scissors Tape Glue A meter stick Paper Pencils Clipboards Possible Solutions Students will arrive at a variety of solutions based on the number of dandelion plants they count in their sample. Look for solutions that utilize correct mathematics based on the original count. More Accessible Version Solution See the solution to the original version. More Challenging Version Solution See the solution to the original version. Note: Each prediction should be 50 times as big as the original count. 4 of 9
Task-Specific Assessment Notes Novice The Novice will cut a meter length of string and will count the dandelions within the square, but s/he will not have an approach that will work to use that data to solve the rest of the problem. Little or no math language will be used, and no, few or inaccurate math representations will be attempted. Apprentice The Apprentice will cut a meter length of string and will accurately count the dandelions within the square. The Apprentice may also explain or show this process using pictures or words. Evidence will be lacking on how the rest of the problem is solved, and not all parts will be addressed or will be correct. Little math language will be used, but work will be present to support aspects of the solution. Practitioner The Practitioner will cut a meter length of string and will accurately count the dandelions within the square. The Practitioner will use this information to accurately find solutions to all of the parts of the problem. Work will be present, and some math language will be used. Expert The Expert will not only accurately and appropriately collect data but will use an efficient strategy for finding answers to the other parts of the problem. Reasoning will be explained, and all work will be present. Math representations will be labeled and clear. The Expert will also make mathematically relevant comments or observations. 5 of 9
Novice 6 of 9
Apprentice 7 of 9
Practitioner 8 of 9
Expert 9 of 9