Virtual Math Girl: Module 5 (Student) and 6 (Teacher) Working with Common Denominators Assessments Standards Alignment: Grade 5 Ohio State Mathematics Standards Grade 5 Ohio State Mathematics Standards addressed in this Module of Virtual Math Girl Module 5: Number, Number Sense and Operations Students demonstrate number sense, including an understanding of number systems and operations and how they relate to
one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and
mental methods. Students demonstrate number sense, including an understanding of number systems and operations and
how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil,
technology-supported and mental methods. Apply number system properties when performing computations. Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations. Y2003.CMA.S01.G05-­‐07.BG.L05.I05 Y2003.CMA.S01.G05-­‐07.BH.L05.I10 Justify why fractions need common denominators to be added or subtracted. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve, and explain solutions to problems involving integers, fractions, decimals, and percents. Y2003.CMA.S01.G05-­‐07.BF.L05.I08 Identify and use relationships between operations to solve problems. Recognize and identify perfect squares and their roots. Use and analyze the steps in standard and non-­‐standard algorithms for computing with fractions, decimals and integers. Y2003.CMA.S01.G05-­‐07.BI.L05.I12 Use physical models, points of reference, and equivalent forms to add and subtract commonly
used fractions with like and unlike denominators and decimals.
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The level of the complexity of the performance expected from students will depend on their prior preparation and achievement levels in mathematics. A series of assessments will be provided here that start with the simplest tasks and progresses to the more complex. Most often these assessments will be used after students have viewed the video and after the instructor has performed demonstrations and at least some instruction and discussion. The following challenges can be posed to the entire class and students can be asked to respond and then justify or explain their answers. The justification based on evidence and reasoning is the most important part of students’ responses because this reveals the most about what students actually understand. When one student responds, without revealing whether the response is correct, the instructor could ask another student whether he/she agrees or disagrees and to explain and justify his/her conclusion. Other students could also be asked for their conclusion. Then the whole class could be asked to vote by raising their hands or through use of student response devices. This strategy tends to encourage independent thinking and can give a more accurate assessment of the level of achievement Virtual Math Girl: Modules 5 & 6 – Assessment © 2010 WBGU-­‐PBS. Permission is granted for non-­‐profit educational use. 1 •
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of more students in the class than relying on the response of only one or two students for each challenge. Alternatively, various types of cooperative learning strategies could be used with these assessment challenges such as posing the challenges to small groups (pairs, trios, or quartets) of students with the charge that the members of each group should come to agreement on the answers to these challenges. These groups could then report to the whole class and the whole class can then be challenged to reach agreement on the best responses and the evidence and reasoning that justifies those responses as being the best. These challenges could also be used as part of or adapted for a written exam to which each student must respond individually and privately without consultation, or the challenges could be given to the students to complete as an in-­‐class or homework exercise. Depending on how and when these assessments are used in the classroom, the instructor may decide to modify the challenges or formats somewhat to fit the specific circumstances of the individual classroom. Virtual Math Girl: Modules 5 & 6 – Assessment © 2010 WBGU-­‐PBS. Permission is granted for non-­‐profit educational use. 2 Virtual Math Girl -­‐ Assessment Challenge Name_________________________________________ From the map, calculate the length of the bus route from Josh’s home to school. Use the space below for your calculations. Virtual Math Girl: Modules 5 & 6 – Assessment © 2010 WBGU-­‐PBS. Permission is granted for non-­‐profit educational use. 3 Virtual Math Girl -­‐ Assessment Name_________________________________________ 1. Solve these problems in addition of fractions. Don’t forget to find the common denominators and to show your answer in lowest terms. Use the space below for calculations. First fraction 2/25 Second fraction + 1/4 + 1/5 4/10 + 3/12 + 4/16 Third fraction + 2/8 Answer = + 3/15 = 1/5 + 1/20 = 1/4 + 1/3 = 2. Solve these problems in subtraction of fractions. Don’t forget to find the common denominators and to represent your answer in lowest terms. Use the space below for calculations. First fraction 13/25 Second fraction -­‐ 1/4 -­‐ 1/5 8/10 -­‐ 11/12 -­‐ 15/16 Answer = = 3/5 = 3/4 = Virtual Math Girl: Modules 5 & 6 – Assessment © 2010 WBGU-­‐PBS. Permission is granted for non-­‐profit educational use. 4