Many students have difficulty solving worded Mathematics questions. Here is a guide that may be used to help solve your problems.

Strategies include:

Understanding the question may involve drawing a diagram

Making the question easier by using smaller values

Guess and check

Write an equation and solve

There are five steps to solve any worded question.

We will go through each step to solve the following non-routine worded question:

Ms. Rivera wishes to tile her classroom floor with square tiles.  She wants to be able to use whole tiles, without cutting any pieces.  The rectangular floor has dimensions 8.4 meters by 7.2 meters.  What is the minimum number of whole identical square tiles required and what are the dimensions of each tile?

Step 1 – Read the entire question and underline all important information given.

Ms. Rivera wishes to tile her classroom floor with square tiles.  She wants to be able to use whole tiles, without cutting any pieces.  The rectangular floor has dimensions 8.4 meters by 7.2 meters.  What is the minimum number of whole identical square tiles required and what are the dimensions of each tile?

Step 2 – Box what you want to find? What does the question want you to determine?

Ms. Rivera wishes to tile her classroom floor with square tiles.  She wants to be able to use whole tiles, without cutting any pieces.  The rectangular floor has dimensions 8.4 meters by 7.2 meters.  [What is the minimum number of whole identical square tiles] required and [what are the dimensions of each tile]?

There are two sets of information required (in red)

Step 3 – Analyse the information given and see if you can find any connections that will help to solve the question.

Ms. Rivera wishes to tile her classroom floor with square tiles.  She wants to be able to use whole tiles, without cutting any pieces.  The rectangular floor has dimensions 8.4 meters by 7.2 meters.  [What is the minimum number of whole identical square tiles] required and [what are the dimensions of each tile]?

so we are dealing with covering a floor i.e. area

we are to use square tiles, so what’s the area of a square tile? area = side squared or side times side

Do we know the area we want to cover?

Can we find it?

If we know this area how can we determine the smallest number of square tiles needed to cover this area?

Would changing the units of the room help to make the question easier? Would working in centimeters be easier than working in meters with decimals?

Let’s answer these questions and see if they help.

Step 4 – Devise a strategy and Solve the problem

Ms. Rivera wishes to tile her classroom floor with square tiles.  She wants to be able to use whole tiles, without cutting any pieces.  The rectangular floor has dimensions 8.4 meters by 7.2 meters.  [What is the minimum number of whole identical square tiles] required and [what are the dimensions of each tile]?

The clue is area. so area of the floor must be equal to the area of the tiles used.

Area to be covered = 8.4 m x 7.2 m = 840 cm x 720 cm

Since we can only use whole tiles then the number of tiles used must go exactly into each side to the rectangular floor.

So what is the largest number that can go into both sides 840 cm and 720 cm.

Largest number suggests LCM

lets break up the numbers

840 = 7  x 12 x 10

720 = 6 x 12 x 10

so the largest common number = 12 x 10 = 120

The minimum number of tiles to be used would be 42 since area of floor divided by area of a tile = 840 x 720 / (120 x 120)= 42

Answer = Ms Rivera would need 42 tiles with dimensions 120 cm by 120 cm to cover the floor.

Step 5 – Check your answer against initial information.

The floor was 8.4 m by 7.2 m and the tiles are 1.2 m x 1.2 m squares so 42 x 1.2 x 1.2 must be equal to 8.4 x 7.2

42 x 1.2 x 1.2 = 8.4 x 7.2 = 60.48 square meters

So the answer is correct.