SOLVING MULTISTEP PROBLEMS 6TH GRADE

The following points will be useful to solve multi step problems for grade level 6. 

(i) First, read the problem carefully. 

(ii) List out the important information.

(iii) If it is required, we have to draw a picture.

(iv) From this we can come to know what has to be found.

(v) If it is necessary,  we can use the formula to solve the given problem. 

Problem 1 :

John and Mary are using rolls of fabric to make a rectangular stage curtain for their class play. The rectangular piece of fabric on each roll measures 2.5 feet by 15 feet. If the area of the curtain is 200 square feet, what is the least number of rolls they need?

Solution :

List the important information.

Each roll of fabric is a 2.5 foot by 15 foot rectangle.

The area of the curtain is 200 square feet.

What has to be found ?

Find the least number of rolls of fabric needed to cover an area of 200 square feet

To find this  

Write an equation to find the area of each roll of fabric.

A  =  lw

A  =  15(2.5)

A  =  37.5 square feet

Write an equation to find the number of rolls needed.

n  =  200 ÷ 37.5

n  =  5.33

The problem asks for the least number of rolls needed. Since 5 rolls will not be enough, they will need 6 rolls to make the curtain. 

The least number of rolls John and Mary will need is 6.

Problem 2 :

The area of a triangular block is 64 square inches. If the base of the triangle is twice the height, how long are the base and the height of the triangle?

Solution :

By analyzing the given information, we come to know that, 

The area of a triangular block is 64 in². 

The base of the triangle is twice the height

What has to be found ?

We have to find the base length and height of the triangle.

Let "h" be the height of the triangle

"2h" be the base 

(1/2) x b x h  =  64

 (1/2) x (2h) x h  =  64 

  h²  =  64

  h²  =  8²

  h  =  8

Problem 3 : 

Alex needs to varnish the top and the bottom of a dozen rectangular boards. The boards are 8 feet long and 3 feet wide. Each pint of varnish covers 125 square feet and costs $3.50. 

a. What is the total area that Alex needs to varnish?

b. How much will it cost Alex to varnish all the boards?

Solution :

By analyzing the given information, we come to know that, 

Alex needs to varnish a dozen rectangular boards.

What has to be found ?

From this first we have to find area of one rectangle board, then we have to multiply it by 24 in order to get the total area to be varnished

Also we have to find the required cost of varnish.

1 dozen = 12

Length = 8 feet and width = 3 feet

Area of one rectangle board = L x w

  =  8 x 3

=  24 square feet

24 ft² x 2 sides of a plank  =  48 ft²

48 ft²/plank x  12 planks  =  576 ft²

576 ft² is the total area Alex needs to varnish.

576 ft² ÷ 125 ft²  =  4.608 pint or round to 5 pints

5 pints x 3.50  =  $17.50

Total cost that Alex has to spend to varnish is $17.50. 

Problem 4 :

Leia cuts congruent triangular patches with an area of 45 square centimeters from a rectangular piece of fabric that is 18 centimeters long and 10 centimeters wide. How many of the patches can Leia cut from 32 pieces of the fabric?

Solution :

Area of rectangular piece of fabric

=  Length x Width

=  18 x 10

 =  180 square centimeters

Area of 32 piece of fabric = 32 x 180

  =  5760 square centimeter

Area of one triangular piece of patch

=  45 cm²

Total number of patches that she can cut

=  5760/45

  =  128

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