Math Olympiad Strategies

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Presentation transcript:

Math Olympiad Strategies Making a Table

Take a Chance Suppose that you roll two number cubes, each of which has faces numbered from 1 through 6. What is the probability of rolling a sum of 8 in the uppermost faces?

Take a Chance Solution First Cube Second Cube + 1 2 3 4 5 6 7 8 9 10 11 12 The probability of rolling a sum of 8 is 5 chances out of 36 possibilities, or 5/36

Barnyard Brainstorming I know that there are 18 animals in the barnyard. Some are chickens and the rest are cows. I counted 50 legs in all. How many of the animals are chickens and how many are cows?

Barnyard Brainstorming Solution Make a table Number of chickens 1 2 3 4 5 … ? Number of cows 18 17 16 15 14 13 Number of legs 72 70 68 66 64 62 50 Examining the data in the table, a pattern emerges. 62 to 50 requires 6 more columns, so the number of chickens is 5 + 6 = 11 and the number of cows is 13 – 6 = 7. So, there are 11 chickens and 7 cows.

Making a Table Homework NAME________________________________ Due:______________________ 1. Suppose that you roll number cubes, each of which has faces numbered from 0 through 5. What is the probability of rolling a sum of 8? 2. Suppose that you roll two triangular pyramids, each of which has equilateral faces numbered from 1 through 4 ( tetrahedren). Make a table of the possible sums of the two faces that rest on the surface. What is the probability of rolling a sum of 5? 3. This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many chairs did the carpenter make? 4. Using one or more coins, how many different amounts of money can be made from a collection of coins that consists of four pennies, one nickel, and one dime? 5. The toll for an automobile crossing a certain bridge is 50 cents The machines in the “exact change” lanes accept any combination of coins that total exactly 50 cents, but they do not accept pennies or half dollars. In how many different ways can a driver pay the toll in an “exact change” lane? 6. A collection of thirty coins consists of dimes and quarters and has a total value of $4.35. How many of each type of coin are in this collection?