7 th Grade

October 23, 2012

7th Grade

Adapted from: DM Workbook 1, page 4 problem 22

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.

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

What is the greatest common factor of 640, 320, and 800?

What is the underlying question?

a. They will fill 160 gift bags.

b. Each bag will contain 4 packs of instant noodles, 2 bottles of mineral water, and $5.

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

What is the greatest common factor of 640, 320, and 800?

What is the underlying question?

64010 x 6410 x 8 x 810 x 8 x 2 x 410 x 16 x 4160 x 4

32010 x 3210 x 8 x 410 x 8 x 2 x 210 x 16 x 2160 x 2

80010 x 8010 x 8 x 1010 x 8 x 2 x 510 x 16 x 5160 x 5

The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively.

a. Suppose identical cubes are placed within the container such that they fill up the container completely.

i. What is the greatest possible length of each cube?ii. What is the corresponding volume of this cube?

b. How many cubes described in part a are placed inside of the container?

Adapted from: DM Workbook 1, page 4 problem 21

The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively.

a. Suppose identical cubes are placed within the container such that they fill up the container completely.

i. What is the greatest possible length of each cube?ii. What is the corresponding volume of this cube?

b. How many cubes described in part a are placed inside of the container?

Adapted from: DM Workbook 1, page 4 problem 21

The largest cube would have a length of 15 cm.

The volume of the cube would be 3,375 cubic cm

The length, width, and height of an open box are 90 cm, 45 cm, and 30 cm respectively.

a. Suppose identical cubes are placed within the container such that they fill up the container completely.

i. What is the greatest possible length of each cube?ii. What is the corresponding volume of this cube?

b. How many cubes described in part a are placed inside of the container?

Adapted from: DM Workbook 1, page 4 problem 21

It will take 36 of these cubes to completely fill the box. 6 x 3 x 2

Mrs. Shute bought x chairs at $15 each. She bought y tables at $24 each. a. Express the total cost of x chairs and y tables in terms of x and y.b. Evaluate the total cost of 4 chairs and 7 tables.

Adapted from: DM Workbook 1, page 20 problem 7

$15$15$15$15Chairs

Tables $24$24$24$24

x

yThe cost of x chairs and y tables is

15x + 24 y

Mrs. Shute bought x chairs at $15 each. She bought y tables at $24 each. a. Express the total cost of x chairs and y tables in terms of x and y.b. Evaluate the total cost of 3 chairs and 5 tables.

Adapted from: DM Workbook 1, page 20 problem 7

$15$15$15Chairs

Tables $24$24$24

The cost of 3 chairs and 5 tables isCost = 15(3) + 24(5)Cost = 45 + 120Cost = $165

$24 $24?

Adapted from: DM Workbook 1, page 29 problem 22

6x + 12y

Number of books Mrs. Hossler borrowed 2x + 4y 2x + 4y 2x + 4y

Number of books Mrs. Norwood borrowed

4x + 8y2x + 4y

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. Norwoodii. 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.

Adapted from: DM Workbook 1, page 29 problem 22

Mrs. Hossler’s books

4x + 8y 2x + 4y6x + 12y

Mrs. Norwood books Mrs. Kersch’s books

2x + 4y2x + 4y2x + 4y2x + 4y2x + 4y2x + 4y

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

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.

1620

= =

Differentiating:

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

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.

2515 ¿

𝟓𝟑¿

5 𝑥55𝑥 3

b) The ratio of red balls to the total number of balls

Number ofred balls

Number ofgreen balls

15

25

5

5

55

5555

The ratio of red balls to green balls is 3 : 5

C

Number ofred balls

Total number of balls

15

25

5

5

55

5555

The ratio of red balls to the total number of balls is 3 : 8

15

5 55

C

40

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 eggs

1 cup

3:1

Simplify the ratio 0.280 : 0.182

:

:

::

Simplify the ratio 2 : 3

: 9 :13

All of the parts

must be the same

size.

Simplify the ratio 2 : 3

:

All of the parts

must be the same

size.

:

:

𝟒𝟓 :𝟕𝟐

A right angle is divided into three angles in the ratio of 1:2:3. What is the measure of each of these angles?

90 degrees6 units = 90

1 unit = 15

15 1515 1515 15

15 degrees

30 degrees

45 degrees