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Understanding Natural Numbers and Basic Statistics in ACT Prep

In this assignment, students will explore the properties of natural numbers, including divisors, factors, and prime factorization. They'll also apply the Divisor Test to identify divisors for given numbers and practice basic probability and statistics concepts such as mean, median, and mode. The assignment requires showing all work on a sheet of paper, ensuring a solid grasp of mathematical principles in preparation for the ACT. By solving various problems, students will reinforce their understanding of essential numerical properties and statistical analysis.

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Understanding Natural Numbers and Basic Statistics in ACT Prep

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  1. Lesson 5 ACT Prep II. Properties of Natural Numbers and Basic Statistics

  2. Assignment • Get out a sheet of paper • Record definitions, and complete problems on this paper. SHOW WORK! • Turn in at the end of the hour.

  3. A. Divisors and Factors Divisor – A divisor of a number is any number which will divide it evenly. EX) 10 is a divisor of 30, since 30/10 = 3 Factors – the factors of a number are all the numbers which divide into it evenly EX) The factors of 50 are: 1, 50, 2, 25, 5, 10

  4. A. The Divisor Test

  5. A. The Divisor Test Using the divisor test, determine what number (between 2-9) is a divisor of the given number. Note: some may have more than one divisor, name them all! 1) 1064 2) 1665 3) 1667 4) 3534

  6. B. Prime, Composite, and Unit ACT Definitions: Unit – The number 1 Prime – any number divisible by 1 and itself Composite – numbers with more than 2 factors

  7. 2. Prime Factorization What is prime factorization? Ex) Use a factor tree to determine the prime factorization of 72

  8. Try These Problems • Determine all the factors of 120 • Write the prime factorization of 100 • Find the least common multiple (LCM) of the following. • 12, 32 b) 8, 50, 120 c) d)

  9. C. Basic Probability and Statistics • Probability P = the number of ways it could occur the total number of possible occurrences Ex1) If there are 10 red balls, 3 green balls, and 2 blue balls in a jar, what is the probability that a green ball will be chosen? Ex2) A die has 6 faces numbered 1 to 6. What is the probability of rolling a 4?

  10. 2. The arithmetic mean (average) Ex1) Find the average of 10, 12, and 23 Ex2) A student needs to average 80% on 5 tests to get a B. If the first 4 tests were 70, 75, 86, and 84, what does this student need on the 5th test?

  11. 3. Median and Mode Median – the middle data point when the numbers are arranged from least to greatest. Note: If there are 2 middle points, find the average of those two Mode – the value that occurs the most Hint: MOde = MOst Note: the might be no mode or multiple modes

  12. Median and Mode cont. Find the median and mode of the following set of numbers { 3, 8, 9, 10, 15, 15}

  13. 4. Counting Problems Whenever you have to count how many ways to make a series of choices do the following: • Determine how many choices have to be made and put down a blank for each choice • Fill in each blank with the number of ways that a choice can be made • Multiply the numbers together

  14. 4. Counting Problems Ex2) How many different sandwiches consisting of one cheese, one meat, and one bread can be made from a choice of 4 cheeses, 3 meats, and 5 breads?

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