4. Look at the number formed by the last two digits in each of the numbers you listed in Exercise 2. What pattern do you see in these digits?

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1 Enrichment 3-1 Divisibility and Mental Math Patterns in Numbers 1. Is each number divisible by 4? Write yes or no. a. 108 b. 212 c. 250 d. 316 e. 625 f. 1, List the numbers in Exercise 1 that were divisible by Choose one of the numbers that was divisible by 4. Change the hundreds digit. Write the new number. Is the number still divisible by 4? How do you know? 4. Look at the number formed by the last two digits in each of the numbers you listed in Exercise 2. What pattern do you see in these digits? 5. Write a divisibility rule for dividing by Test your rule. Is each number is divisible by 4? Write yes or no. a. 111 b. 128 c. 332 d. 548 e. 3,456 f. 65, Kendra has 324 marbles. She wants to use them in a game with three friends. a. Can the group divide the marbles equally? b. Suppose she finds five more marbles. Can she divide all the marbles equally among four players? Use your rule to explain your answer. Enrichment Course 1 Lesson 3-1

2 Enrichment 3-2 Exponents Patterns in Numbers You have learned that repeated multiplication can be represented using exponents. You may discover some interesting patterns when working with these numbers. The table at the right shows powers of 2 from 2 1 to 2 10 in exponential and standard forms. 1. Describe the pattern in the table. 2. Continue the pattern. Write the next two numbers in exponential and standard forms. 3. Complete the chart above to represent the powers of 3 from 3 1 through What patterns do you see in these numbers? 4. Are the patterns the same for the powers of 2 and 3? Why or why not? 5. The speed of light is about km/sec. Write this speed in standard form. Powers of 2 Powers of ,024 Enrichment Course 1 Lesson 3-2

3 Enrichment 3-3 Prime Numbers and Prime Factorization Scrambled Factors 1. In the boxes below, write out the prime factorization for the number In the blanks below, write the digits you wrote in the boxes in Exercise Reorganize the digits and write them into a new prime factorization in the boxes below. 4. What number does your new prime factorization represent? 5. Add 24 to your new number. 6. Write the prime factorization of the sum from Exercise Again, reorganize the factors and exponents into a new prime factorization and write the number it represents. Remember that in a prime factorization, the factors must all be prime numbers, but the exponents do not necessarily have to be primes. Enrichment Course 1 Lesson 3-3

4 Enrichment 3-4 Greatest Common Factor Critical Thinking Use each set of clues to find the number being described. 1. Clues: a. The greatest common factor (GCF) of two numbers is 6. b. The sum of the two numbers is 30. c. The difference between the two numbers is Clues: a. The greatest common factor of two numbers is 8. b. If you divide the sum of the two numbers by the GCF, the answer is 10. c. The difference between the two numbers is Clues: a. The greatest common factor of three numbers is 8. b. The sum of the numbers is 48. The following puzzles have more than one answer. Find as many solutions as you can. 4. Clues: a. The greatest common factor of two numbers is 9. b. The sum of the numbers is Clues: a. The greatest common factor of three different numbers is 5. b. The sum of the numbers is Write your own puzzle like the ones on the page. Check to see how many solutions your puzzle has. Enrichment Course 1 Lesson 3-4

5 Enrichment 3-5 Least Common Multiple Visual Thinking The delivery people for a water supply company make deliveries based on a pattern of days, as shown in the table. Every delivery person made a delivery on January How often will both Norton and Melanie make deliveries on the Landry Melanie Norton Owen Every 5 days Every 2 days Every 6 days Every 4 days 2. List the next three dates in January that Norton and Melanie will make deliveries on the same day. 3. How often will both Norton and Owen make deliveries on the 4. List the dates in January that Norton and Owen will make deliveries on the same day. 5. How often will both Landry and Melanie make deliveries on the 6. How often will Landry, Owen, and Melanie make deliveries on the 7. How often will all the delivery people make deliveries on the Enrichment Course 1 Lesson 3-5

6 Enrichment 3-6 The Distributive Property Decision Making Mandy wants to make a necklace for a friend. She will buy a chain and gold letters to spell out a message. Consonants are on square beads and vowels (a, e, i, o, and u) are on triangular beads. Each consonant costs $4. Each vowel costs $5. Round beads to place between words are $3 each. She can buy a 16-inch chain for $10 or a 20-inch chain for $ Mandy wants the necklace to spell MY BEST FRIEND. Draw the necklace with the appropriately shaped beads. 2. Write an expression for the cost of the beads for the necklace. What is the cost of the beads? 3. Mandy needs to buy a chain for the beads. What will the total cost be for the letters and a 20-inch chain? 4. Mandy decides that the necklace is too expensive. Write a phrase that she could use with a 16-inch chain so that the necklace would cost less than $ Draw the necklace with the phrase you selected. 6. What is the cost of the necklace you drew? Complete each equation. 7. (3 b) (2 3) (2 ) 8. 7(4 x) ( 4) (7 ) Enrichment Course 1 Lesson 3-6

7 Enrichment 3-7 Simplifying Algebraic Expressions Critical Thinking For a school project, you are helping set up three stands at a local farmer s market. Each stand has a tent on the top of it. The dimensions of each stand are shown below. 7x 2 Stand 1 Stand 2 Stand 3 3x 2x 2y 3y 1 Use the information given to answer each question. 1. Each stand wishes to hang a banner around the perimeter of its tent that does not have a side in common with another stand. How many sides of the tent will a banner hang for each stand? 2. Write a simplified expression that represents the total length of the banner for each stand. 3. Explain how you found the simplified expressions for each stand. 4. If x = 2 feet and y = 3 feet, what is the length of the banner for each stand? Enrichment Course 1 Lesson 3-7