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Bridges

 Use manipulatives in problem-solving Find patterns to organize information Use computation in the service of broader goals

Suggested time allotment

Two class periods

Student social organization

Students working alone

Assumed background: It is assumed that the students have had prior experience with using standard colored centimeter rods (or the equivalent). The task also assumes that the children have had experience with "rules" (functions) that describe a general numerical situation.

Presenting the task: Students are given an assortment of colored rods and a copy of the student pages. As always, calculators should be available. The teacher should present the task essentially as the "script" below specifies.

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OCR for page 43
Measuring Up: Prototypes for Mathematics Assessment Bridges Use manipulatives in problem-solving Find patterns to organize information Use computation in the service of broader goals Suggested time allotment Two class periods Student social organization Students working alone Task Assumed background: It is assumed that the students have had prior experience with using standard colored centimeter rods (or the equivalent). The task also assumes that the children have had experience with "rules" (functions) that describe a general numerical situation. Presenting the task: Students are given an assortment of colored rods and a copy of the student pages. As always, calculators should be available. The teacher should present the task essentially as the "script" below specifies.

OCR for page 43
Measuring Up: Prototypes for Mathematics Assessment "You are an engineer who wants to build different kinds of bridges. The bridges will be made of colored rods. The first bridge you are to build is a 1-span bridge made with one yellow rod and two red rods." (Build the bridge illustrated below, with the students copying.) "The yellow rod is called a span, and the red rods are called supports . Since the yellow rod is 5 cm long, the length of the bridge is 5 cm." "The second bridge you are to build is a 2-span bridge made with two yellow rods and four red rods (as shown below). Note that this bridge is 10 cm long." "As you build bridges in the following activities, think of a way to keep track of the number of rods of different colors you use. Your goal is to find out how many rods of each color you would need to build a bridge of any size." Student assessment activity: Distribute the activity sheet and read through question 1 to be sure that the children understand the basic problem. Note: the bridges have been scaled to fit the 7" × 10" page of this volume. The teacher may choose to redraw the bridges to scale when they are reproduced on standard size paper

OCR for page 43
Measuring Up: Prototypes for Mathematics Assessment Name _________________________________________ Date _____________ Part 1 All of the bridges in Part 1 are built with yellow rods for spans and red rods for supports, like the one shown here. This is a 2-span bridge like the one you just built. Note that the yellow rods are 5 cm long. Now, build a 3-span bridge. How many yellow rods did you use? _______  How long is your bridge? _______  How many red rods did you use? _______  How many rods did you use altogether? _______ Try to answer these questions without building a 5-span bridge. If you want, build a 5-span bridge to check your answers. How many yellow rods would you need for a 5-span bridge? _______  How long would your bridge be? _______  How many red rods would you need? _______  How many rods would you need altogether? _______

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Measuring Up: Prototypes for Mathematics Assessment Without building a 12-span bridge, answer the following questions. How many yellow rods would you need for a 12-span bridge? _______ How long would your bridge be? _______ How many red rods would you need? _______ How many rods would you need altogether? _______ How many yellow rods and red rods would you need to build a 28-span bridge? _____ yellow rods and _____ red rods. Explain your answer. Write a rule for figuring out the total number of rods you would need to build a bridge if you knew how many spans the bridge had. How many yellow rods and red rods would you need to build a bridge that is 185 cm long? _____ yellow rods and _____ red rods. Explain your answer.

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Measuring Up: Prototypes for Mathematics Assessment Name________________________________________ Date _____________ Part 2 The bridges for this part are built like this 2-span bridge: The black rods are 7 cm long, and the light green rods are 3 cm long. Notice that the supports are shared between spans, except at the ends. Build a 3-span bridge of this same kind, with black and light green. How many black rods did you use? _____  How long is your bridge? _____  How many light green rods did you use? _____  How many rods did you use altogether? _____ Try to answer these questions without building a 5-span bridge. If you want to, build a 5-span bridge to check your answers. How many black rods would you need for a 5-span bridge? _____  How long would your bridge be? _____  How many light green rods would you need? _____  How many rods would you need altogether? _____

OCR for page 43
Measuring Up: Prototypes for Mathematics Assessment Without building a 13-span bridge, answer the following questions. How many black rods would you need for a 13-span bridge? _____ How long would your bridge be? _____ How many light green rods would you need? _____ How many rods would you need altogether? _____ How many black rods and light green rods would you need to build a 56-span bridge? _____ black rods and _____ light green rods. Explain your answer. Write a rule for figuring out how many rods you would need to build a bridge if you knew how many spans the bridge had. How many black rods and light green rods would you need to build a bridge that is at least 429 cm long? _____ black rods and _____ light green rods. Explain your answer.

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