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### Bowl-A-Fact

 Work backwards to solve problems Apply exhaustive thinking Use arithmetic operations where calculators are of little help Demonstrate multiple solutions

Suggested time allotment

One class period

Student social organization

Students working alone or in pairs, after short teacher introduction

Assumed background: The problem assumes that the students have had some experience in using parentheses with arithmetic operations.

Presenting the task: The teacher explains that in bowling the objective is to knock down 10 pins with one or two throws of a bowling ball. Knocking down all 10 pins with one throw is called a strike. Knocking down all the pins in two throws is called a spare. The game of Bowl-A-Fact is similar to bowling, except instead of throwing a bowling ball, one tosses three number cubes (numbered from 1 through 6) and makes as many numbers from 1 to 10 as possible by adding, subtracting, multiplying or dividing the numbers showing on the number cubes. Each number showing on a number cube must be used exactly once on one side of an

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OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment Bowl-A-Fact Work backwards to solve problems Apply exhaustive thinking Use arithmetic operations where calculators are of little help Demonstrate multiple solutions Suggested time allotment One class period Student social organization Students working alone or in pairs, after short teacher introduction Task Assumed background: The problem assumes that the students have had some experience in using parentheses with arithmetic operations. Presenting the task: The teacher explains that in bowling the objective is to knock down 10 pins with one or two throws of a bowling ball. Knocking down all 10 pins with one throw is called a strike. Knocking down all the pins in two throws is called a spare. The game of Bowl-A-Fact is similar to bowling, except instead of throwing a bowling ball, one tosses three number cubes (numbered from 1 through 6) and makes as many numbers from 1 to 10 as possible by adding, subtracting, multiplying or dividing the numbers showing on the number cubes. Each number showing on a number cube must be used exactly once on one side of an

OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment equation. For each number that can be obtained, the corresponding circle is shaded. (This indicates a pin knocked down.) Student assessment activity: After explaining the rules of Bowl-A-Fact, the teacher should play one game with the whole class. Pretend that the number cubes on the first toss were 3, 4, and 6. Individual students can devise number sentences to knock down pins that have been drawn on the board, as shown below. Of course the pins will probably be knocked down in some order different from the one shown. Also, depending on a child's strategy, the pin number could be on the right or left side of the equals sign. For example, one child might ask, "What can I do with 3, 4 and 6?" and come up with "4 + 6-3 = 7," while another might ask, "Is there any way to knock down the 7 pin?" and write the equation "7 = 4 + 6-3.'' Note, too, that there are other ways of getting many of the pin numbers; this should be explicitly pointed out.

OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment Now the teacher should ask the class to pretend that the next roll is 3, 3, and 4. This is sufficient to knock down the remaining pins, thus getting a spare. Students are given three number cubes and a copy of the following activity sheets.

OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment Name _________________________________________ Date ______________ 1. Play a game of Bowl-A-Fact. Roll the three number cubes, and write the numbers you get in these spaces: _____ _____ _____. (Roll again if you get 3, 4, 6 or 3, 3, 4) Use the numbers to knock down as many pins as you can. (For this part and the remaining parts, record your figuring in the spaces provided.)   Did you get a strike? ______ 2. If you got a strike, go on to the next page. If you did not get a strike, try for a spare. Roll the three number cubes and write them here: _____ _____ _____. Now use the new numbers to knock down as many of the remaining pins as you can. ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________

OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment 3. Suppose you play again and the numbers you roll are 2, 3, and 6. Knock down as many pins as you can using these numbers.   Did you get a strike? 4. Suppose your next roll is 1, 3, and 5. Try to knock down the rest of the pins (get a spare) using these numbers. ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ ____________________________ Did you get a spare?

OCR for page 65
Measuring Up: Prototypes for Mathematics Assessment 5. What pins can you knock down with this toss? 1, 2, and 4.   Did you get a strike? ______ ____________________________

OCR for page 65