Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? Wire sells for 97 cents a yard at the hardware store. Zack only wants to spend $4.00 for the wire. Will Zack be able to hang all his airplanes? 1 of 10
Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 4 and 5 Task Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? Wire sells for 97 cents a yard at the hardware store. Zack only wants to spend $4.00 for the wire. Will Zack be able to hang all his airplanes? Alternative Versions of Task More Accessible Version: Zack wants to hang his 8 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 8 inches of wire and the 4th model airplane needs 10 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? How many inches of wire will Zack need to hang all 10 of his model airplanes? More Challenging Version: Zack wants to hang his 10 model airplanes at different lengths from the ceiling of his room with wire. The 1st model airplane needs 4 inches of wire. The 2nd model airplane needs 6 inches of wire. The 3rd model airplane needs 9 inches of wire and the 4th model airplane needs 11 inches of wire. If this pattern continues, how many inches of wire will Zack need to hang the 10th model airplane? Wire sells for 97 cents a yard at the hardware store. Zack pays for the wire with a 5 dollar bill. What are the possible ways he can get change back from his 5 dollars? Find all the ways. 2 of 10
NCTM Content Standards and Evidence Algebra Standard for Grades 3 5: Instructional programs from pre-kindergarten through grade 12 should enable students to... Understand patterns, relations and functions. NCTM Evidence: Describe, extend and make generalizations about geometric and numeric patterns. Exemplars Task-Specific Evidence: This task requires students to continue a pattern to the 10th level. Number and Operations Standard for Grades 3 5: Instructional programs from prekindergarten through grade 12 should enable students to... Compute fluently and make reasonable estimates. NCTM Evidence: Develop fluency in adding, subtracting, multiplying and dividing whole numbers. Exemplars Task-Specific Evidence: This task requires students to find the total length of wire needed in inches and find how much that wire will cost if sold by the yard. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a medium-length task. Links This task can be used in conjunction with a unit on space travel, a science unit on how planes fly or a discussion on hobbies. Common Strategies Used to Solve This Task Most students will begin making a chart to keep track of the 10 lengths of wire. They will add the lengths and then divide that total length by 36 (or make groups of three 12 inches). Possible Solutions The lengths of wire are: 4 + 6 + 8 + 10 + 12 + 14 + 16 + 8 + 20 + 22 = 130 inches The 10th length of wire is 22 inches. 3 of 10
Zack will need 130 inches/36 = 3 feet and 22 inches He will need four yards of wire. 4 yards x $.97 = $3.88 Yes, Zack has enough to buy the wire. More Accessible Version Solution: The lengths of wire are: 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 = 130 inches total The 10th model airplane needs 22 inches of wire. More Challenging Version Solution: The 10th length of wire is 26 inches. The lengths of wire are: 4 + 6 + 9 + 11 + 14 + 16 + 19 + 21 + 24 + 26 = 150 inches 150 inches/36 = 4 yards 6 inches He will need five yards x $.97 = $4.85 Task-Specific Assessment Notes Nickels Dimes Pennies 0 0 15 1 0 10 2 0 5 0 1 5 3 0 0 1 1 0 General Notes Students will need previous experiences with situations where items are sold by a unit and they need to buy more than is needed like in the problem where Zack will need to buy 4 yards of wire and have 14 inches left over. 4 of 10
Novice The Novice will misunderstand the problem and will not be able to find the 10th length of wire, the total length of all the wire or the cost of the wire. There will be no representation or the representation will be inappropriate for finding a solution to the problem. Apprentice The Apprentice will use a strategy that is partially useful, leading someway toward a solution, but not to a full solution. For example, the student may find the length of the 10th wire but not be able to decide if $4.00 is enough to purchase the wire. There is some use, or mostly inappropriate use, of mathematical terminology and notation. There is some use of appropriate mathematical representation. Practitioner The Practitioner will find the length of the 10th wire and the cost of the wire correctly. Correct mathematical reasoning is present along with use of mathematical terminology and notation appropriate to the problem. There is affective use of mathematical representation that clarifies the strategy and solution. Mathematical connections or observations are recognized. Expert The Expert will have a correct solution to all parts of the problem using precise and appropriate mathematical reasoning, terminology and notation. Mathematical generalizations, connections or observations are used to extend the solution. A sense of audience and purpose is communicated. 5 of 10
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