Even and Odd Numbers GCF and LCM Word Problems Glossary & - PDF document

Slide 1 / 113 Slide 2 / 113 6th Grade Factors and Multiple 2015-10-20 www.njctl.org Slide 3 / 113 Slide 4 / 113 Factors and Multiples Click on the topic to go to that section Even and Odd Numbers · Divisibility Rules for 3 & 9 · Greatest Common Factor · Least Common Multiple Even and Odd Numbers · GCF and LCM Word Problems · Glossary & Standards · Return to Table of Contents Slide 5 / 113 Slide 6 / 113 Warm-Up Exercise What do you think? Think about the following questions and write your answers in your notes. What happens when 1) What is an even number? we add two even numbers? Will we 2) List some examples of even numbers. always get an even number? 3) What is an odd number? 4) List some examples of odd numbers. Derived from

Slide 7 / 113 Slide 8 / 113 Adding Odd Numbers Adding Even Numbers Drag the paw prints into the Drag the paw prints into the box to model 9 + 5 box to model 6 + 8 + + Circle pairs of paw prints to determine if any of the paw Circle pairs of paw prints to determine if any of the paw prints are left over. prints are left over. Will the sum be even or odd every time two odd numbers Will the sum be even or odd every time two even numbers are added together? Why or why not? are added together? Why or why not? Slide 9 / 113 Slide 10 / 113 Adding Odd and Even Numbers 1 The product of two even numbers is even. True Drag the paw prints into the box to model 7 + 8 False + Circle pairs of paw prints to determine if any of the paw prints are left over. Will the sum be even or odd every time an odd and even number are added together? Why or why not? If the first addend was even and the second was odd, then would your answer change? Why or why not? Slide 11 / 113 Slide 12 / 113 2 The product of two odd numbers is 3 The product of 13 x 8 is A odd A odd B even B even Explain your answer. Explain your answer. Multiplication is repeated addition. If you add an odd number 13 x 8 is equivalent to saying 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13. over and over, then the sum will switch between even and Click to Reveal Since you are adding it an even number of times, the product will Click to Reveal odd. Since you are adding the number an odd number of times, be even. your product will be odd.

Slide 13 / 113 Slide 14 / 113 4 The sum of 32,877 + 14,521 is 5 The product of 12 x 9 is A odd A odd B even B even Explain your answer. Explain your answer. If you model the numbers using dots and circle all the pairs, the 12 x 9 is equivalent to 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12. Click to Reveal single dots leftover from each number will create a pair and none Click to Reveal No matter how many times you add 12, since it is even the sum will be leftover making the sum an even number. will always be even. Slide 15 / 113 Slide 16 / 113 6 The sum of 8,972 + 1,999 is 7 The sum of 9 + 10 + 11 + 12 + 13 is A odd A odd B even B even Explain your answer. Explain your answer. The first two addends will result in an odd number. By adding If you model the problem using dots and circle all the pairs, then another odd number, the sum is even. Adding an even number Click to Reveal Click to Reveal there will be one dot leftover since one of the addends is odd. will result in an even number. Since the last addend is odd, the final answer will be odd. Slide 17 / 113 Slide 18 / 113 8 The product of 250 x 19 is 9 The product of 15 x 0 is A odd A odd B even B even Explain your answer. Explain your answer. The product of an odd and even number will always result in an 0 is an even number and the product of any even number and Click to Reveal even number. odd number is always even. Click to Reveal

Slide 19 / 113 Slide 20 / 113 Let's review! Below is a list of numbers. Drag each number in the circle(s) that is a factor of the number. You may place some numbers in more than one circle. 24 36 80 115 214 360 975 4,678 29,785 414,940 Divisibility Rules 4 5 2 for 3 and 9 8 10 Return to Table of Derived from Contents Slide 21 / 113 Slide 22 / 113 Divisibility Rule for 3 Divisibility Rules What factor do the numbers 12, 15, 27, and 66 have in common? They are all divisible by 3. Click 2: If and only if its last digit is 0, 2, 4, 6, or 8. Now, take each of those numbers and calculate the sum of its digits. 4: If and only if its last two digits are a number divisible by 4. What do all these sums 12 1 + 2 = 3 5: If and only if its last digit is 0 or 5. have in common? 15 ________ 8: If and only if its last three digits are a number divisible by 8. They are all divisible by 3! Click 27 ________ 10: If and only if its last digit is 0. 66 ________ A number is divisible by 3 if the sum of the number's digits is divisible by 3. Click Slide 23 / 113 Slide 24 / 113 Divisibility Rule for 9 Try these! What factor do the numbers 18, 27, 45, and 99 have in common? Check if the numbers in the chart are divisible by 3 or 9. They are all divisible by 9. Click Put a check mark in the box in the correct column. Now, take each of those numbers and calculate the sum of its digits. Divisible by 3 Divisible by 9 228 What do all these sums 18 1 + 8 = 9 531 have in common? 735 27 ________ They are all divisible by 9! Click 1,476 45 ________ 99 ________ A number is divisible by 9 Click if the sum of the number's digits is divisible by 9.

Slide 25 / 113 Slide 26 / 113 10 468 is divisible by: (choose all that apply) 11 Is any number divisible by 9 also divisible by 3? Explain. A 2 Yes B 3 No C 4 D 5 E 8 F 9 G 10 Slide 27 / 113 Slide 28 / 113 12 Is 135 divisible by 3? 13 Any number divisible by 3 is also divisible by 9. Yes True No False Slide 29 / 113 Slide 30 / 113 15 Is 24,981 divisible by 3? 14 The number 129 is divisible by 9. If it is, type the quotient. If it is not, type 00. True False

Slide 31 / 113 Slide 32 / 113 Discussion Questions Discussion Questions Continued 1. Make a table listing all the possible first moves, proper factors , your score and your partner's score. Here's an example: 5. On your table, circle all the first moves that only allow your partner to score one point. These numbers have a special Proper Partner's First Move My Score name. What are these numbers called? Factors Score 1 None Lose a Turn 0 Are all these numbers good first moves? Explain. 2 1 2 1 6. On your table, draw a triangle around all the first moves that 3 1 3 1 allow your partner to score more than one point. These 4 1, 2 4 3 numbers also have a special name. What are these numbers called? 2. What number is the best first move? Why? Are these numbers good first moves? Explain. 3. Choosing what number as your first move would make you lose your next turn? Why? 4. What is the worst first move other than the number you chose in Question 3? more questions Slide 33 / 113 Slide 34 / 113 Activity Greatest Common Factor Party Favors! You are planning a party and want to give your guests party We can use prime factorization favors. You have 24 chocolate bars and 36 lollipops. to find the greatest common factor (GCF). Discussion Questions 1. Factor the given numbers into primes. What is the greatest number of party favors you can make if each bag must have exactly the same number of chocolate bars 2. Circle the factors that are common. and exactly the same number of lollipops? You do not want any 3. Multiply the common factors together to find the candy left over. Explain. greatest common factor. Could you make a different number of party favors so that the candy is shared equally? If so, describe each possibility. Which possibility allows you to invite the greatest number of guests? Why? Uh-oh! Your little brother ate 6 of your lollipops. Now what is the greatest number of party favors you can make so that the candy is shared equally? Slide 35 / 113 Slide 36 / 113 17 Is 15,516 divisible by 9? 16 Is 54 divisible by 3 and 9? If it is, type the quotient. If it is not, type 00. Yes No

Slide 37 / 113 Slide 38 / 113 18 Which of the following numbers is divisible by 3, 4 19 The number 126 is divisible by: (choose all that apply) and 5? A 2 A 45 B 3 B 54 C 4 C 60 D 5 D 80 E 8 F 9 G 10 Slide 39 / 113 Slide 40 / 113 20 The number 120 is divisible by: (choose all that apply) A 2 B 3 C 4 Greatest Common D 5 E 8 Factor F 9 G 10 Return to Table of Contents Slide 41 / 113 Slide 42 / 113 Another way to find Prime Prime Factorization Factorization... Use prime factorization to find the greatest common Use prime factorization to find the greatest common factor of factor of 12 and 16. 12 and 16. 2 1 6 12 16 2 12 8 2 3 4 4 4 6 2 4 2 3 2 2 2 2 2 2 3 3 2 2 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 1 1 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 The Greatest Common Factor is 2 x 2 = 4 The Greatest Common Factor is 2 x 2 = 4