2) There are 7 times as many boys than girls in the 3rd math class. If there are 32 kids in the class how many boys and girls are there?

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1 Word Problem EXTRA Practice 1) If Fay scored 78 more points last season, she would have tied the school record. She scored 449 points last season. What is the school record for most points scored? points 2) There are 7 times as many boys than girls in the 3rd math class. If there are 32 kids in the class how many boys and girls are there? Boys Girls 3) Ezekiel rode his bike 2 times as far on Wednesday as he did on Tuesday, and four times as far Tuesday than he did on Monday. If he rode 32 miles on Wednesday, how far did he ride on Monday? miles 4) 45 students were offered potato chips and a drink. There were a total of 31 students who chips. There were a total of 28 students who had a drink. 24 students had both chips and a drink. How many students chose to have neither chips or a drink? students 5) A rectangle has an area that is 527 square inches. The length is 31 inches. What is the width of the rectangle? Width in. 6) There are 40 marbles in a bag. 20 are green, 12 are red, and 8 are blue. What is the probability as a fraction in simplest form of picking a marble that is NOT blue? 7) A rope was cut in half, then each half was again cut in half. Each remaining piece was cut in half again. If each of the remaining pieces is 4 centimeters in length, how long was the original piece of rope in centimeters? centimeters 8) What two numbers have a sum of 42 and a difference of 14? and 9) I am a number. If you multiply me by 8, then add 7, I ll be equal to 55. What number am I? I am

2 10) 7 coins equal 72 cents. What coins are they? Name the coin and how many for each coin you name. You may use Quarters, Dimes, Nickels, or Pennies only, and must use at least 1 of each coin. 11) Using only a 7, 8, or 9, how many different 3-digit numbers can you make? You CANNOT use the same digit more than once in a number. numbers 12) There is a room with some people and dogs. There are a total of 32 eyes and 40 legs in the room. How many people and dogs are there? people dogs

3 Word Problem EXTRA Practice ANSWER KEY AND STRATEGIES 1) If Fay scored 78 more points last season, she would have tied the school record. She scored 449 points last season. What is the school record for most points scored? Simply add the 78 to the points 2) There are 7 times as many boys than girls in the 3rd math class. If there are 32 kids in the class how many boys and girls are there? Since there are 7 times as many of one thing than another, you can divide the boys and girls into 8 parts (7 parts boys and 1 part girls). Then divide the 32 by 8 to get 4. The 4 is one part which is the number of girls. Then multiply 4 by 7 to get 28 or the number of boys. Boys 28, Girls 4 3) Ezekiel rode his bike 2 times as far on Wednesday as he did on Tuesday, and four times as far Tuesday than he did on Monday. If he rode 32 miles on Wednesday, how far did he ride on Monday? Work backwards. Since he rode twice as far on Wednesday as he did on Tuesday, DIVIDE 32 by 2 to get 16. So he rode 16 miles on Tuesday. Then, DIVIDE the 16 by 4, since he rode 4 times as far Tuesday than Monday. He rode 4 miles on Monday. Also, Jake Gooden figured out that since 2 times as far one day, and 4 times as far the other that 2x4=8 and you can just divide the 32 by 8 to get the 4 miles for Monday. 4 miles 4) 45 students were offered potato chips and a drink. There were a total of 31 students who chips. There were a total of 28 students who had a drink. 24 students had both chips and a drink. How many students chose to have neither chips or a drink? Make a Venn Diagram by making 2 overlapping circles and label one as Chips and the other as Drinks. Put the 24 who had both in the middle first. Then, since only 28 had a drink, and you already have 24 in the Drink circle only put 4 in the other part of that circle. And since 31 students had chips, but there are already 24 in the Chip circle only put 7 in the other part of that circle. Now add all the numbers together to get 35. Subtract 35 from 45 to find that 10 students had neither a drink or chips. Chips Drink students

4 5) A rectangle has an area that is 527 square inches. The length is 31 inches. What is the width of the rectangle? Since you know the area, simply divide the area by the length to get the width. 527 divided by 31 is equal to 17. You d do the same if you knew the area and width and needed to find the length. You d divide the area by the width to get the length. Width 17 in. 6) There are 40 marbles in a bag. 20 are green, 12 are red, and 8 are blue. What is the probability as a fraction in simplest form of picking a marble that is NOT blue? Find the number of marbles that ARE NOT blue which is , or 32. Than make a fraction with 32 over 40. Simplify the fraction using your calculator or dividing the numerator and denominator by 4, which is 4/ ) A rope was cut in half, then each half was again cut in half. Each remaining piece was cut in half again. If each of the remaining pieces is 4 centimeters in length, how long was the original piece of rope in centimeters? Each time the rope is cut in half and each remaining piece is also cut in half, the number of pieces doubles. So with 3 cuts in all there are 2 pieces, then 4 pieces, then 8 pieces. Multiply the 8 remaining pieces by 4 centimeters to get centimeters 8) What two numbers have a sum of 42 and a difference of 14? You can first find any two numbers that add up to 42. I ll provide 2 different examples. Example 1: Let s say you chose 30 and 12. Now find the difference of 30 and 12, which is 18. The difference needs to be 14. Since you are 4 away from the difference, you only have to add 2 to one number, and subtract 2 from the other. That gives you 28 and 14. Example 2: Let s say you chose 21 and 21. Now find the difference, which is zero. The difference needs to be 14. You are 14 away from the difference, so you need to add 7 to one number, and subtract 7 from the other. That gives you 28 and 14. NOTE: When you find how far off you are from the difference you need take half of that amount and add that to one number and subtract it from the other. Today in class I figured out a cool other way to do this type problem and can guarantee it will work every time! Step 1: Subtract the smaller number from the bigger number = 28. Step 2: Divide the answer by 2: 28 divided by 2 = 14. Step 3: That answer is the smaller number: 14. Step 4: Now subtract the smaller number from the larger number: = is the bigger number. 28 and 14

5 9) I am a number. If you multiply me by 8, then add 7, I ll be equal to 55. What number am I? Work backwards. Start with 55. Since it says ADD 7, you ll SUBTRACT 7 to get 48. Then since it says MULTIPLY by 8, you ll DIVIDE by 8 to get 6. Notice that when working backwards, you always use the inverse operation of what s in the problem. Adding and subtracting are inverse, and multiplying and dividing are inverse. I am 6 10) 7 coins equal 72 cents. What coins are they? Name the coin and how many for each coin you name. You may use Quarters, Dimes, Nickels, or Pennies only, and must use at least 1 of each coin. Since there is 72 cents, there must be only 2 pennies. This reduces the problem to now needing 5 coins equaling 70 cents. Since you need one of each coin a quarter, dime, and nickel equal 40 cents. Now you only need 2 more coins that equal 30 cents. It must be a quarter and a nickel. The total is now: 2 quarters, 1 dime, 2 nickels, and 2 pennies 11) Using only a 7, 8, or 9, how many different 3-digit numbers can you make? You CANNOT use the same digit more than once in a number. Make a list. When you make it try making it in an organized, logical way. I d begin with the 7. The numbers beginning with 7 would be 789 and 798. Then do the same starting with 8, and then starting with 9. The full list would look like this: 789, 798, 879, 897, 978, 987. There are 6 numbers in all. Also a shortcut would be to just find how many number you can begin with the digit 7. Since there are only 2 you can then tell that there will be the same amount that begin with each other digit so 2 x 3 = 6. 6 numbers 12) There is a room with some people and dogs. There are a total of 32 eyes and 40 legs in the room. How many people and dogs are there? Here is Mr. Binder s secret way (I guess it s no longer a secret!) to solve this type of problem. Step 1: Find out how many things there are by dividing the number of eyes by divided by 2 is 16 so there are 16 things in all. Step 2: Subtract the number of eyes from the number of legs = 8. Step 3: Take half of that difference by dividing 8 by 2 to get 4. Step 4: The 4 from the last step is the number of 4-legged things so you have 4 dogs. Step 5: Subtract the 4 from the total number of things to get 12 people. To check your answer: 16 total things times 2 gives you 32 eyes. And 12 people have 24 legs, and 4 dogs have 16 legs so = a total of 40 legs.

6 12 people and 4 dogs

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