Unit 1: Fractions and Decimals. ACTIVITIES 3 Mathematics - 3º ESO

IES Albayzín (Granada) Page 1

UNIT 1: Fractions and Decimals

Guidelines for problem solving reading

George Polya (1887-1985) was educated in Europe and taught at Stanford University. In his book How to Solve It, Polya outlines (resume) four steps in problem solving. We will use Polya’s four steps as guidelines (orientaciones) for problem solving.

1) Understand the problem

• Read the problem carefully at least twice. In the first reading, get a general overview of the problem. In the second reading, determine exactly what you are been asked to find and what information the problem provides.

• Try to make a sketch to illustrate the problem. Label the information given.

• Make a list of the given facts that are pertinent to the problem • Determine if the information you are given is sufficient to solve the

problem.

2) Device a plan to solve the problem

• Have you seen the problem or a similar problem before? • Can you express the problem in terms of an algebraic equation? • Look for patterns or relationships in the problem that may help in

solving it. • Will listing the information in a table help in solving the

problem? • Sometimes if you know an approximate solution, you can work

backward and eventually determine the correct procedure to solve the problem.

3) Carry out the plan

• Use the plan you devised in step 2 to solve the problem

4) Check the results

• Ask yourself, “Does the answer make sense?” and “is the answer reasonable?”

Unit 1: Fractions and Decimals. ACTIVITIES 3 Mathematics - 3º ESO

IES Albayzín (Granada) Page 2

Percentage Problems

1) Fill in the chart. Percentage 20 % Fraction 3/10 Decimal 0.1

2) Fifty-two of a hospital’s beds are occupied. This is 13% of the total number of beds. How many beds does the hospital have?

3) A certain country has a population of eight million, and a study shows that 28% of the population is diabetic. How many diabetics does the country have?

4) The statistics of two players in a basketball tournament are as follows: Player A: 85 shots and 68 baskets Player B: 94 shots and 72 baskets What percentage of the shots taken by each player was successful? Which of the two players is more reliable?

5) A car is sold for 5225 pounds after a depreciation of 45% of the original purchase price. Calculate the original purchase price of the car.

6) A company with 1,675 employees cuts its staff by 8%. How many employees does it have after the cut? Give your answer to the nearest hundred.

7) At the beginning of spring a reservoir contains 2,800 cubic decameters of water, but recent rainfall has increased its water content by 40%. How much water does the reservoir contain now?

8) The population of the United States on July 4, 1776, was about 2.5 million people. In June 2008, the population had increased to about 304 million. Find the percent increase in population in population. Round to the nearest percent.

9) A sum of $5000 is invested at 7% p.a. (per annum) simple interest. How long will it be before the amount equals $5875? Hint: with simple interest, the interest paid is not reinvested, whereas with compound interest, the amount of interest paid is reinvested and earns interest itself.

10) A sum of 2000 pounds is invested for 2 years at 6% per annum compound interest. Calculate the total amount at the end of that period. Give your answer to the nearest penny.