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7 th Grade

7 th Grade. October 23, 2012.

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7 th Grade

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  1. 7th Grade October 23, 2012

  2. A company plans to donate 640 packs of instant noodles, 320 bottles of mineral water, and $800 in cash to a homeless shelter. The items will be placed in gift bags so that the contents of all bags are identical. If the company wants to donate the maximum number of gift bags: a. How many gift bags are needed? b. List the contents of each bag. Adapted from: DM Workbook 1, page 4 problem 22

  3. A company plans to donate 640 packs of instant noodles, 320 bottles of mineral water, and $800 in cash to a homeless shelter. The items will be placed in gift bags so that the contents of all bags are identical. If the company wants to donate the maximum number of gift bags: a. How many gift bags are needed? b. List the contents of each bag. What is the underlying question? What is the greatest common factor of 640, 320, and 800? They will fill 160 gift bags. b. Each bag will contain 4 packs of instant noodles, 2 bottles of mineral water, and $5. Adapted from: DM Workbook 1, page 4 problem 22

  4. A company plans to donate 640 packs of instant noodles, 320 bottles of mineral water, and $800 in cash to a homeless shelter. The items will be placed in gift bags so that the contents of all bags are identical. If the company wants to donate the maximum number of gift bags: a. How many gift bags are needed? b. List the contents of each bag. What is the underlying question? What is the greatest common factor of 640, 320, and 800? 640 10 x 64 10 x 8 x 8 10 x 8 x 2 x 4 10 x 16 x 4 160 x 4 320 10 x 32 10 x 8 x 4 10 x 8 x 2 x 2 10 x 16 x 2 160 x 2 800 10 x 80 10 x 8 x 10 10 x 8 x 2 x 5 10 x 16 x 5 160 x 5 Adapted from: DM Workbook 1, page 4 problem 22

  5. The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively. • Suppose identical cubes are placed within the container such that they fill up the container completely. • What is the greatest possible length of each cube? • What is the corresponding volume of this cube? • How many cubes described in part a are placed inside of the container? Adapted from: DM Workbook 1, page 4 problem 21

  6. The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively. • Suppose identical cubes are placed within the container such that they fill up the container completely. • What is the greatest possible length of each cube? • What is the corresponding volume of this cube? • How many cubes described in part a are placed inside of the container? The largest cube would have a length of 15 cm. The volume of the cube would be 3,375 cubic cm Adapted from: DM Workbook 1, page 4 problem 21

  7. The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively. • Suppose identical cubes are placed within the container such that they fill up the container completely. • What is the greatest possible length of each cube? • What is the corresponding volume of this cube? • How many cubes described in part a are placed inside of the container? It will take 36 of these cubes to completely fill the box. 6 x 3 x 2 Adapted from: DM Workbook 1, page 4 problem 21

  8. Mrs. Shute bought x chairs at $15 each. She bought y tables at $24 each. • Express the total cost of x chairs and y tables in terms of x and y. • Evaluate the total cost of 4 chairs and 7 tables. x $15 Chairs $15 $15 $15 $24 $24 $24 $24 Tables y The cost of x chairs and y tables is 15x + 24 y Adapted from: DM Workbook 1, page 20 problem 7

  9. Mrs. Shute bought x chairs at $15 each. She bought y tables at $24 each. • Express the total cost of x chairs and y tables in terms of x and y. • Evaluate the total cost of 3 chairs and 5 tables. Chairs $15 $15 $15 ? $24 $24 $24 $24 $24 Tables The cost of 3chairs and 5 tables is Cost = 15(3) + 24(5) Cost = 45 + 120 Cost = $165 Adapted from: DM Workbook 1, page 20 problem 7

  10. Last year, Mrs. Hossler borrowed (6x + 12y) books from the library. Mrs. Norwood borrowed 2/3 as many books as Mrs. Hossler and Mrs. Kersch borrowed ½ as many books a Mrs. Norwood. a. Find, in terms of x and y, the number of books borrowed by i. Mrs. Norwood ii. Mrs. Kersch b. Find the total number of books borrowed by all three. c. If x = 3 and y = 1/2 , find the total number of books borrowed by Mrs. Kersch. 4x + 8y 2x + 4y 6x + 12y Number of books Mrs. Hossler borrowed 2x + 4y 2x + 4y 2x + 4y Number of books Mrs. Norwood borrowed Adapted from: DM Workbook 1, page 29 problem 22

  11. Last year, Mrs. Hossler borrowed (6x + 12y) books from the library. Mrs. Norwood borrowed 2/3 as many books as Mrs. Hossler and Mrs. Kersch borrowed ½ as many books b. Find the total number of books borrowed by all three. c. If x = 3 and y = 1/2 , find the total number of books borrowed by Mrs. Kersch. 2x + 4y 6x + 12y 4x + 8y 2x + 4y 2x + 4y 2x + 4y 2x + 4y 2x + 4y 2x + 4y Mrs. Hossler’s books Mrs. Norwood books Mrs. Kersch’s books The total number of books borrowed by all three is 12x + 24y Mrs. Kersch= 2x + 4y = 2(3) + 4(1/2) = 6 + 2 = 8 books Adapted from: DM Workbook 1, page 29 problem 22

  12. = =

  13. Differentiating: There are 6 boys and 9 girls in a class. Find the ratio of The number of boys to the number of girls The number of girls to the total number of students in the class

  14. A bag contains 25 green balls and 15 red balls. Find the ratio of a) The number of green balls to the number of red balls. b) The ratio of red balls to the total number of balls

  15. 15 5 5 5 Number of red balls Number of green balls 5 5 5 5 5 25 The ratio of red balls to green balls is 3 : 5

  16. 15 C 5 5 5 Number of red balls C Total number of balls 5 5 5 5 5 5 5 5 15 25 40 The ratio of red balls to the total number of balls is 3 : 8

  17. Granny is making dinner using a recipe that calls for 1 egg for each 1/3 cup of flour. Write the ratio of eggs to cups of flour. 3:1 3 eggs 1 cup

  18. Simplify the ratio 0.280 : 0.182 : : : :

  19. Simplify the ratio 2 : 3 9 :13 : All of the parts must be the same size.

  20. Simplify the ratio 2 : 3 : : All of the parts must be the same size. :

  21. A right angle is divided into three angles in the ratio of 1:2:3. What is the measure of each of these angles? 15 15 15 15 15 15 30 degrees 15 degrees 45 degrees 90 degrees 6 units = 90 1 unit = 15

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