ausd grade 6 benchmark 3 study guide - west contra … · ausd grade 6 benchmark 3 study guide page...

AUSD Grade 6 Benchmark 3 Study Guide

of 15 MCC@WCCUSD (AUSD) 05/05/15

1 Find the area of the triangle below.

6.G.1

2 Find the area of triangle ABC.

6.G.1

1´ You try:

Given the triangle above, choose True or

False for the following:

1) The triangle is a right triangle.

Ⓐ True Ⓑ False

2) The height of the triangle is 5 inches.

Ⓐ True Ⓑ False

3) The perimeter is 12 inches.

Ⓐ True Ⓑ False

4) The area is 60 square inches.

Ⓐ True Ⓑ False

2´ You try:

Find the area and perimeter of triangle ABC.

2ft 30

ft 5ft 6

ft 5ft 122

1

2

1

bhA

2cm 12

cm 4cm 3

cm 4cm 62

1

2

1

bhA

5 ft

12 ft

13 ft 3 in

4 in

5 in

5 cm 4 cm

6 cm

5 cm

A

B

C 17 yd

8 yd

30 yd

17 yd

A

B

C



3 Find the area of parallelogram ABCD below.

The area of any parallelogram (including a

rectangle) is base height.

6.G.1

3´ You try:

Given parallelogram ABCD above, choose

True or False for the following:

1) Figure ABCD is a rectangle.

Ⓐ True Ⓑ False

2) Figure ABCD is a quadrilateral.

Ⓐ True Ⓑ False

3) The perimeter is 42 cm.

Ⓐ True Ⓑ False

4) The area is 60 square centimeters.

Ⓐ True Ⓑ False

feet square 16

feet 2feet 8

bhA

2 feet

8 feet

3 feet

A

C B

D 6 cm

10 cm

8 cm

A

C B

D



4 Find the area of the trapezoid below.

Decomposing the trapezoid into 2 triangles.

Formula for the area of a trapezoid.

Decomposing the trapezoid into a

triangle and a rectangle. Area of

Trapezoid Area of

Rectangle Area of

Triangle

6.G.1

4´ You try:

Find the area of the trapezoid below 2 ways.

2

22

21

yd 54

yd 24yd 30

yd 4yd 122

1yd 4yd 15

2

1

2

1

2

1

AA A

hbhb

2

21

yd 54

yd 27yd 2

yd 12yd 15yd 42

1

2

1

bbhA

2

22

2

yd 54

yd 6yd 48

yd 3yd 2yd 48

yd 4yd 32

1yd 4yd 12

2

1

AA A

bhbh

15 yards

12 yards

4 yards

A

C B

D

= +

7 cm

5 cm

4 cm

A

C B

D



5

a) What size cubes would you choose to perfectly fill the rectangular prism shown?

I would choose 4

1cm cubes. This would allow me to fill the prism completely, because

4

1is the

largest unit cube that goes into the three dimensions an equal number of times.

b) How many cubes are needed to fill the rectangular prism?

To fill the height I would need 5 cubes because . To fill the front of the prism I would

need to use 10 cubes because . And, for the last dimension I would need 24 cubes

because . To find the number of cubes I need to fill the prism, I can see there will be 24

times 10 in the bottom layer. So it would take 240 little cubes to fill the bottom. Because there

are 5 layers up, I would multiply that by 5. So, 240 times 5 is 1200.

ஃ 1200 quarter cm cubes are needed to fill the prism.

c) Use the volume formula to calculate the number of 1 cm cubes needed to fill the prism.

3

3

4

75V

42

5235V

4

56

2

5V

4

116

2

12V

V

cm

cm

cmcmcm

cmcmcm

lwh

3

3

2

4

75V

4

515V

4

1115V

V

cm

cm

cmcm

Bh

6.G.2

11

4=

5

4

21

2=

5

2=

10

4

6 =24

4

1

1

4 cm

2

1

2 cm



5´

a) What size cubes would you choose to perfectly fill the rectangular prism shown?

Ⓐ4

1in cubes Ⓑ

2

1in cubes Ⓒ

4

3in cubes

b) How many cubes of the size you chose are needed to fill the rectangular prism?

c) Use a volume formula to calculate the number of 1 in cubes needed to fill the prism.

6.G.2

11

2 in

5 in

21

2 in



6 Classify the nets below as representing a

rectangular prism, triangular prism, triangular

pyramid, or rectangular pyramid.

Rectangular Prism

Triangular Pyramid

6.G.4

7 Draw a net for the rectangular prism shown.

Label the measurements on your net.

6.G.4

6´ You try:

Classify the net below as representing a

rectangular prism, triangular prism, or

pyramid.

7´ You try:

Draw a net for the triangular prism shown.

Label the measurements on your net.



8

Given the figure on the coordinate plane

above, what is the distance (in units) from

point A to point B?

Since point A is at and point B is at

, we know that they have the same y-

coordinate. We can count the units between

the x-coordinates.

Therefore, the distance between point A and

point B is 8 units.

6.G.3

8´ You try:

On a grid map, the school is located at ,

the grocery store is located at , the library

is located at , and the Boys and Girls

Club is located at .

a) Represent the locations as points on the

coordinate grid below with a unit of 1 mile.

b) What is the distance, in miles, from the

school to the Boys and Girls Club?

c) What is the area of the shape created by the

four points?

3,4

3,4

2,2

2,0

2,0

2,2 • A B

C

•

•



9 Find the surface area and volume of the

rectangular prism below:

Surface Area

Volume

6.G.4

9´ You try:

Find the surface area and volume of the

triangular prism below:

2

222

ft 52

ft 12ft 16ft 24

ft 2ft 32ft 2ft 42ft 3ft 42

222

SA

SA

SA

hwlwlhSA

3

2

ft 24

ft 3ft 8

V

V

BhV

3 feet

2 feet

4 feet

10 ft

4 ft

6 ft

5 ft

5 ft



10 Create a box plot for the data below.

How many times did you drink water

yesterday? 2, 2, 3, 3, 3, 5, 5, 7, 8, 9

The minimum and maximum are the smallest and

largest numbers in the data set. Minimum is 2,

Maximum is 9.

To find the median, I find the middle number.

Because there is an even number of responses to the

question, I need to take the average of the middle two

numbers. Median is 4.

The lower quartile and upper quartile are the numbers

in the middle of the lower half and the upper half.

Lower quartile is 3. Upper quartile is 7.

Then, I draw a number line put the points above it at

the five values, and draw my box.

6.SP.4, 6.SP.5

11 What is the lower quartile of the box plot?

Minimum is 153.

Lower quartile is 192.

Median is 207.

Upper quartile is 221.

Maximum is 234. 6.SP.4, 6.SP.5

10´ You try:

Create a box plot for the data.

How many pairs of socks are in your drawer?

0, 1, 3, 3, 6, 8, 8, 9, 10, 16

11´ You try:

What is the median of the box plot?

61 2 3 4 5 7 8 9 10



12 Find the mean, median, range, and mean

absolute deviation for the following dot plot.

Number of Pets at Your Home

●

● ●

● ●

● ● ●

● ● ●

● ● ● ●

0 1 2 3 4 5 6

The Mean of a data set is the sum of the

values divided by the number of values.

The mean is .

The Median is the middle value when the

values are in order from least to greatest or

greatest to least.

The median is 1.

The Range is the difference between the

largest and smallest values.

The range is 3.

The Mean Absolute Deviation is the mean of

the absolute deviations of a set of data about

the data's mean.

The absolute deviations from the mean for

each value of the data are:

1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, and 2

The mean of these absolute deviations is:

The mean absolute deviation is .

6.SP.5

12´ You try:

Find the mean, median, range, and mean


Number of Siblings

● ● ●

● ● ● ● ●

0 1 2 3 4 5 6

1) The mean is 1. Ⓐ Yes Ⓑ No

2) The median is 2. Ⓐ Yes Ⓑ No

3) The mean absolute deviation is .

Ⓐ Yes Ⓑ No

4) The range is 6. Ⓐ Yes Ⓑ No

End of Study Guide

1

15

15

15

322211111100000

=

=

++++++++++++++=

1

3

2

15

10

15

211100000011111

=

=

++++++++++++++=

3

2

2

11



You Try Solutions:

1´ You try:

1) The triangle is a right triangle.

True Ⓑ False

2) The height of the triangle is 5 inches.

Ⓐ True False

3) The perimeter is 12 inches.

True Ⓑ False

4) The area is 60 square inches.

Ⓐ True False

2´ You try:

Find the area and perimeter of triangle ABC.

3´ You try:

Given parallelogram ABCD above, choose

True or False for the following:

1) Figure ABCD is a rectangle.

Ⓐ True False

2) Figure ABCD is a quadrilateral.

True Ⓑ False

3) The perimeter is 42 cm.

Ⓐ True False

4) The area is 60 square centimeters.

True Ⓑ False

2yd 120

yd 8yd 15

yd 8yd 302

1

2

1

bhA

yd 64

yd 17 yd 17 yd 30

around distance

P

17 yd 8 yd

30 yd

17 yd

A

B

C

6 cm

10 cm

8 cm

A

C B

D



4´ You try:

Find the area of the trapezoid below.

Formula for the area of a trapezoid.

Decomposing the trapezoid into a

triangle and a rectangle.

Area of

Trapezoid Area of

Rectangle Area of

Triangle

5´

a) What size cubes would you choose to

perfectly fill the rectangular prism shown?

Ⓐ4

1in cubes

2

1in cubes Ⓒ

4

3in cubes

b) How many cubes of the size you chose are

needed to fill the rectangular prism?

10 along the front edge, 5 up, and 3 back. The

bottom layer will have 30 cubes. There are 5

layers so that will be 150 cubes.

ஃ 150 half in cubes are need to fill the prism.

c) Use the volume formula to calculate the

number of 1 in cubes needed to fill the

prism.

33

3

2

4

111or

4

45V

2

3

2

15V

2

12

2

15V

V

inin

in

inin

Bh

6.G.2

2

21

cm 24

cm 12cm 2

cm 5cm 7cm 42

1

2

1

bbhA

2

22

2

cm 24

cm 4cm 20

cm 4cm 1cm 20

cm 4cm 22

1cm 4cm 5

2

1

AA A

bhbh

+ =

7 cm

5 cm

4 cm

A

C B

D

1

1

2 in

5 in

2

1

2 in



6´ You try:

Classify the net below as representing a

rectangular prism, triangular prism, or

pyramid.

Triangular Prism

7´ You try:

Draw a net for the triangular prism shown.

8´ You try:

On a grid map, the school is located at

, the grocery store is located at ,

the library is located at , and the Boys

and Girls Club is located at .

a) Represent the locations as points on the

coordinate grid below with a unit of 1

mile.

b) What is the distance, in miles, from the

school to the Boys and Girls Club?

The distance from the school to the Boys

and Girls Club is 4 miles.

c) What is the area of the shape created by

the four points?

The shape formed is a rectangle with a base

of 2 miles and a height of 4 miles.

2,2 2,0

2,0

2,2

miles square 8

miles 4miles 2

A

A

bhA

• School Store

Library

•

• • Boys & Girls Club

4 cm

4 cm

3 cm

5 cm

4 cm

5 cm

4 cm



9´ You try:

Find the surface area and volume of the

triangular prism below:

Surface Area

Volume

10´ You try:

Create a box plot for the data.

How many pairs of socks are in your

drawer?

0, 1, 3, 3, 6, 8, 8, 9, 10, 16

11´ What is the median of the box-and-whisker

plot?

Minimum is 300.

Lower quartile is 430.

Median is 570.

Upper quartile is 710.

Maximum is 1120.

2

22

22

22

ft 184

ft 160ft 24

ft 160ft 122

ft 160ft 242

12

ft 10ft 16ft 4ft 62

12

ft 10ft 5ft 5ft 62

12

2

SA

SA

SA

SA

SA

bhSA

hPBSA base

3

2

2

ft 120

ft 10ft 12

ft 10ft 242

1

ft 10ft 4ft 62

1

2

1

V

V

V

V

hbhV

BhV

10 ft

4 ft

6 ft

5 ft

5 ft

80 2 4 5 6 10 12 14 16



12´ You try:

Find the mean, median, range, and mean


Number of Siblings

● ● ●

● ● ● ● ●

0 1 2 3 4 5 6

1) The mean is 1. Ⓐ Yes No

2) The median is 2. Ⓐ Yes No

3) The mean absolute deviation is .

Yes Ⓑ No

4) The range is 6. Yes Ⓑ No

2

11

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