Please attempt all problems

Transcription

1 Please attempt all problems 1. (Algebra I: A Process Approach Set 1-6 #2, modified) For an upcoming sale, a store manager told a clerk to stack cans of peanuts in a single triangle. For example, if you had six cans you would stack them as shown at the right. The clerk was given two cases of peanuts and told to stack as many cans as he could. Each case contained two dozen cans. a. How many cans should the clerk place in the bottom row? b. What would your answer be if the clerk had five cases of peanuts to stack? c. Describe the pattern involved for any number of cans. ALGEBRAIC CONCEPTS AND RELATIONSHIPS Problem Set #2 Page #1

2 2. (Prime Time: Factors and Multiples, The Connected Math Project, Page 20) Venn Diagrams are useful tools for exploring how the factors and multiples of two or more numbers are related. A Venn Diagram uses circles to show things that belong together. For example, the Venn Diagram below shows one way to group whole numbers. 7 Factors of 30 Factors of In the Venn Diagram below. a. Find at least five numbers that belong in each of the four regions of the diagram. Think about what numbers belong in the intersection of the circles and what numbers belong outside of the circles. b. What factors do the numbers in the intersection of the circles have in common? Multiples of 2 Multiples of 3 Problem Set #2 Page #2

3 c. Add a new circle to the diagram with the label Multiples of 5, as shown below. Replace your numbers in the correct regions, and make sure you have at least two numbers in each part of the diagram. Multiples of 2 Multiples of 3 Multiples of 5 ALGEBRAIC CONCEPTS AND RELATIONSHIPS Problem Set #2 Page #3

4 3. (Algebra I: A Process Approach Set 1-1 #4) How many equilateral triangles are there? 4. a. Find three numbers less than 100 whose product ends in four zeros. b. Find another set of three numbers less than 100 whose product ends in four zeros. Problem Set #2 Page #4

5 5. The A, B, O Blood System Human blood can contain either no antigens, the A antigen, the B antigen, or both the A and B antigens. A third antigen called the Rh antigen, is significant in human reproduction, and again may or may not be present in an individual. Blood is called A-positive (A + ) if the individual has the A and Rh, but not the B, antigen. Blood is called A-negative (A ) if the individual has the A antigen, but neither the B-antigen, nor the Rh-antigen. A person having only the A and B antigens is said to have type AB-negative (AB ) blood. A person having only the Rh antigen has O-positive (O + ) blood. (See the table at the right). In a certain hospital the following data on patients were recorded: 25 patients had the A antigen, 17 patients had the A and B antigens, 27 patients had the B antigen, 22 patients had the B and Rh antigens, a. How many are of the following blood types? i. O + iii. B ii. AB + iv. O b. How many total patients are represented here? Blood Types A + B + AB + O + A B AB O 30 patients had the Rh antigen, 12 patients had none of the antigens, 16 patients had the A and RH antigens, 15 patients had all three antigens. Antigens A, Rh B, Rh A, B, Rh O, Rh A B A, B (No antigens) ALGEBRAIC CONCEPTS AND RELATIONSHIPS Problem Set #2 Page #5

6 6. (Algebra I: A Process Approach Set 1-6 #4) Suppose you have an unlimited supply of 5-cent stamps and 11-cent stamps. You can make exact postage of 21 cents with two 5-cent stamps and one 11-cent stamp. You can also make exact postage of 60 cents with twelve 5-cent stamps. You can even make exact postage of $1.14 by using four 11-cent stamps and fourteen 5-cent stamps. But, you cannot make exact postage of 23 cents by using only 5-cent stamps and 11-cent stamps. What is the greatest amount of exact postage you cannot make by using these stamps? Problem Set #2 Page #6

7 7. a. Your seventh-grade class at Westview Middle School worked in pairs on the following problem during the first week of school: Eight members of the Harlem Globetrotters are warming up for their game with the Washington Generals. The players are in a circle. Each player passes the ball to each of the other players. How many times is the basketball tossed? Bill and Monica said they made a drawing to help them solve the problem. How do you think they solved the problem? b. Later, you give a quiz with the following task: There are ten executives in the boardroom of Publishers Inc. for their annual meeting. If each of the executives shakes hands with each of the others exactly one time, how many hand shakes will there be? Write a solution to this problem that reflects what you anticipate Bill and Monica will write. Writing Assignment #2: Many times students say, If only I had a hint I think I could solve this problem. Were there any problems on Problem Set #2, you wish you had a hint for? Which problem(s)? What would you like to know? ALGEBRAIC CONCEPTS AND RELATIONSHIPS Problem Set #2 Page #7