Exhausted and hungry from hours of delivering chocolate eggs and yellow marshmallow chicks to children around the world, the Easter Bunny came upon Elmer Fudd's most amazing vegetable garden. 1/6 of the garden was planted with chocolate broccoli. 1/6 was planted with marshmallow cauliflower and 1/8 of the garden was planted with peppermint peppers. 1/2 of the space was planted with the chocolate broccoli (already mentioned) and peanut brittle tomatoes. What part of the garden was planted with his most favorite vegetable, Cherry Garcia carrots?
The class is studying fractions. We have been renaming fractions and adding and subtracting fractions. We started studying fractions using a variety of manipulatives. Some students continue to rely on manipulatives whenever possible.
This was an assessment to see how well students could manipulate fractions with unlike denominators in a non-routine problem. I knew most students could do the computation and the simple addition and subtraction problems in the textbook, but this problem would let me know how well they could plan a strategy that involved work with fractions. I was also curious as to what approach each student would take, as well as which students were more comfortable with a visual (area) approach and which students were more comfortable with a number approach. This knowledge will help me as I introduce new topics. Most students started using a combination of sketches and manipulation of numbers. Some students asked and were given the fraction pieces we had been using. Many students had to confirm that the chocolate broccoli mentioned twice were not two different plantings. 45 minutes Some who wanted to do some representations took a little longer. This task could be linked to a unit on garden and landscape planning. There could be some misunderstanding about the chocolate broccoli planting. Be sure students understand that there is only one section of chocolate broccoli.
- Fraction pieces available
- Graph paper
1/6 broccoli + 1/6 cauliflower + 1/8 peppers + (1/2 - 1/6) tomatoes = 19/24; leaving 5/24 for carrots.
This student does not understand that they need to find the part of the garden that is Cherry Garcia carrots. S/he has what appears to be a completed garden plot that has broccoli, tomatoes, cauliflower, peppers and tomatoes. Although, the tomatoes only take up 1/4 of the space - a most common error - 1/4 being 1/2 of the 1/2. There is no explanation of the solution other than the incorrect diagram.
This student is using a strategy that is partially useful. S/he uses fraction pieces for each of the sections and compares them to the one whole fraction bar. There is evidence of mathematical reasoning as s/he states that the missing piece is smaller than 1/4 and bigger than 1/6. However, s/he could not completely carry out the mathematical procedure and compare the space with 2/12 and 1/2 of 1/12 to come up with 5/24. There is some use of mathematical terminology.
This student has a broad understanding of the problem and the major concepts necessary for its solution. The student uses his/her knowledge of adding and subtracting fractions - finding a LCM of all the fractions (although not necessary for solving the problem if fraction pieces to twelfths are available). The student uses effective mathematical reasoning and procedures. There is a clear explanation and appropriate use of mathematical representation. There also is effective use of terminology and notation (LCM and the addition algorithm).
This student shows a deep understanding of the problem, including the ability to identify appropriate mathematical concepts and information necessary for its solution. Although this student drags out the explanation (something I try to discourage), his/her use of making the circle graph was quite sophisticated. We had worked with central angles, but not formally making circle graphs. His/her explanation here showed refined reasoning. There is a clear (although drawn out) explanation detailing how the problem was solved. His/her mathematical terminology and notation is precise and appropriate and his/her representation was outstanding.
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