UNIT 3 PROPORTIONS

UNIT 3: Proportions

Objectives

1. To identify directly proportional magnitudes and construct the corresponding tables of values.

2. To know and use the concept of proportion.

3. To resolve problems of direct proportionality, applying the unitary method and the rule of three method.

4. To understand and use concepts related to percentages.

5. To calculate percentages.

6. To know and apply models to solve the different types of problems involving percentages.

Evaluation Criteria

1.1. To differentiate directly proportional magnitudes from those that are not.

1.2. To construct tables of values, related to directly proportional magnitudes.

2.1. To identify whether two fractions form a proportion.

2.2. To construct proportions from a table of directly proportional values.

2.3. To calculate the unknown term of a proportion.

3.1. To resolve simple problems of direct proportionality using the unitary method.

3.2. To apply the rule of three to solve problems of direct proportionality. 

4.1. To prepare and interpret information in the form of percentages.

4.2. To identify certain percentages with simple fractions.

5.1. To mentally calculate simple percentages.

5.2. To use automated procedures and resources for the calculation of percentages.

6.1. To solve problems of direct percentages (calculation of the part, knowing the total and the percentage).

6.2. To solve inverse percentage problems (calculation of the total, calculation of the percentage).

6.3. To solve problems of percentage increases and decreases.

Contents

DIRECTLY PROPORTIONAL MAGNITUDES

• Identification of the relations of proportionality between different magnitudes.

• Tables of values. Relations.

CONCEPT OF PROPORTION

• Construction of proportions from the values of a table of direct proportionality.

• Calculating the unknown term of a proportion.

SOLVING PROBLEMS OF DIRECT PROPORTIONALITY

• Unitary method.

• Rule of three. 

PERCENTAGES

• The concept of the percentage.

• Calculation of percentages.

– Automation of the calculation of percentages.

– Rapid calculation of some percentages (50%, 25%, 10%).

– Mental calculation of simple percentages.

SOLVING PROBLEMS WITH PERCENTAGES

• Direct percentage problems (calculation of the part, knowing the total).

• Inverse percentage problems.

– Calculation of the total, knowing the part.

– Calculation of the percentage, knowing the total and the part.

• Problems of percentage increases and decreases.

Competencies

• Language skills

• Learning to learn

– Curiosity and interest in numerical relations.

– Interest in the clear presentation of processes and results in calculations with arithmetic expressions.

• Autonomous learning skills

– Appreciation of procedures related to proportionality as tools to solve problems.

– Tenacity and constancy in tackling a problem. Confidence in their own abilities and resources. 

PROBLEMS ABOUT PROPORTIONS 

 PROBLEMS ABOUT FRACTIONS1