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UA MATH 302A - Homework

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Homework for week 1 Math 302A:pp. 26 -29 #3, 5, 14, 21a, 22d, f, 25, 30c, 393. A Martian farmer looks out into the barnyard and sees tribbles (which have four legs) and chalkas (which have seven legs). She says to her son, “I count 97 heads and 436 feet. How many tribbles and how many chalkas are out there?”5. For a certain event, 812 tickets were sold, for a total of $1912. If students paid $2 per ticket and nonstudents paid $3 per ticket, how many of each were sold?14. A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, wha should be the length and the width of the field?21a. For each of the triangles below: (1) describe as many patterns as you can find in the triangle. (2) Write the numbers that would be in the next row of the triangle, and explain how you arrived at your answer.22 List the next term in each of the sequences below, and verbally describe the pattern that enabled you to predict the next term.d. 2, 6, 18, 54, … f. 1, 2, 4, 7, 11, …25. Examine the following phrase made famous by Fred Flintstone: y a b b a d a b b a d o o. If this pattern is repeated over and over, what letter will be in the 275th position?30c. In how many different ways can you make change for one dollar without using pennies?39. This problem was posed in the April 2001 “Problem Solvers” section of Teaching Children Mathematics: Lori and Betty are pretending to have a garage sale. They found five 30¢ price tags and five 40¢ price tags left over from their mothers’ last sale.If they use these price tags on their sale items, how many different amounts of money could they make from their sale?a. Solve the problem yourself.b. The two tables below illustrate one child’s strategy. Continue this strategy to determine the answer. Describe this strategy as if to someone who missed class and doesn’t understand it. Critique the strategy. That is, cite its strengths and weaknesses 12 43 6 94 8 12 165 10 15 20 25111111111111135571397251141 632594111(limitations).30 30 + 4030 + 30 30 + 30 + 4030 + 30 + 30 30 + 30 +30 + 4030 + 30 + 30 + 30 30 + 30 + 30 + 30 + 4030 + 30 + 30 + 30 + 30 30 + 30 + 30 + 30 + 30 + 40c. The table below shows another student’s solution. Combine this strategy with being systematic to find all solutions.Possibilities for 40¢+ 0 1 2 3 4 50 0 40 80 120 160 2001 30 70 110 150 190 2302 60 100 140 180 220 2603 90 130 170 210 250 2904 120 160 200 240 280 3205 150 190 230 270 310 350d. Use this table to find all the possibilities. Explain this table so that someone who doesn’t understand it could use it.pp. 54-57 #11, 12a, 30a11. A boatman is to transport a fox, a goose, and a sack of corn across the river. There is room in his boat for only one of the three at a time. Furthermore, if the fox and the goose are left together, the fox will eat the goose. If the goose and the corn are left together, the goose will eat the corn. How can the boatman do this job?12a. The following two jar problems have been around for many years. They are contrived problems and promote reasoning. In these problems, a jar must be filled completely and emptied completely. For example, you cannot say, “Fill the big jar half full and fill the second jar half full” to get 4 gallons.a. You are given a 5-gallon pail and a 3-gallon pail, both of which are unmarked. You are asked to fetch 4 gallons of water from the well in one trip. How?30a Variations of the following problems are common in elementary schools: See the 2001 NCTM Yearbook, p. 78, and Teaching Children Mathematics, February 1997, p. 326 for two discussions.a. A frog is climbing out of a well that is 8 feet deep. The frog can climb 4 feet per hour, but then it rests for an hour, during which time is slips back 2 feet. How longwill it take the frog to get out of the well?Possibilities for


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UA MATH 302A - Homework

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