Mathematics Grade 7 Competencies

GRADE 7

Table of Competencies: Numbers and Number Sense

Performance Standard: The learners are able to explore set concepts and set operations.

·         Describe and illustrate well-defined sets, universal set, subsets and the null set

·         Define and describe the union and intersection of sets and the complement of a set

Performance Standard: The learners are able to apply various procedures and manipulations on the different subsets of the set of real numbers.

·         Describe and illustrate the absolute value of a number on a number line as the distance of the number from 0

·         Perform fundamental operations on integers: addition, subtraction, multiplication, division

·         State and illustrate the different properties of the operations on integers (commutative, associative, distributive, identity, inverse)

·         Define and illustrate rational numbers and arrange them on a number line

·         Express rational numbers (both repeating and terminating/non-repeating and non-terminating) from fraction form to decimal form and vice versa

·         Perform operations on rational numbers and illustrate their properties

·         Describe principal roots and tell whether they are rational or irrational

·         Determine between what two integers the square root of a number is

·         Illustrate and graph irrational numbers (square roots) on a number line without and with appropriate technology

·         Describe, represent and compare the different subsets of real numbers

·         Find the union, intersection and complement of the set of real numbers and its subsets

·         Arrange real numbers in increasing or decreasing order

·         Determine the significant digits in a given situations

·         Write very large or very small numbers in scientific notation

·         Describe and represent real-life situations which involve integers, rational numbers, square roots of a rational numbers and irrational numbers

·         Solve problems involving real numbers

Table of Competencies: Measurement

Performance Standard: The learners are able to extend concepts of measurements to include different types of measures and all the subsets of the set of real numbers to solve measurement problems.

·         Describe the development of measurement from the primitive to the present international system of units

·         Describe what it means to measure

·         Estimate or approximate the measures of quantities particularly length, weight/mass, volume, time, angle and temperature

·         Use appropriate instruments to measure quantities such as length, weight/mass, volume, time, angle and temperature

·         Convert measurements from one unit to another for each type of measurement

·         Solve real-life problems involving measurements such as perimeter, area, weight, time, speed, temperature, volume/capacity and utilities usage (meter reading)

·         Derive inductively the areas for perimeter, area and volume

Table of Competencies: Algebra

Performance Standard: The learners are able to simplify and evaluate algebraic expressions.

·         Translate verbal phrases to mathematical phrases and vice-versa

·         Differentiate between constants and variables in a given algebraic expression

·         Evaluate algebraic expressions for given values of the variables

Performance Standard: The learners are able to explore the concept of and manipulate polynomials and multinomials.

·         Define and give examples of polynomials, monomial, binomial, trinomial, multinomial

·         Identify the base, coefficient, terms and exponents in a given polynomial

·         Illustrate the laws of exponents

·         Add and subtract polynomials

·         Multiply and divide polynomials using the laws of exponents

·         Find inductively by using models the (a) product of two binomials; (b) product of a sum and difference of two terms; (c) square of a binomial; (d) cube of a binomial; (e) product of a binomial and a trinomial

·         Derive inductively the Laws of Exponents:

Performance Standard: The learners are able to solve equations and inequalities.

·         Differentiate between mathematical expressions and mathematical equations

·         Translate English sentences to mathematical sentences and vice versa

·         Differentiate between equations and inequalities

·         Find the solution of an equation or inequality involving one variable, including one that involves absolute value (a) from a given replacement; (b) intuitively by guess and check; (c) by algebraic procedures (applying the properties of equalities and inequalities); (d) graphing

·         Solve real-life problems that use equations and inequalities

·         Define and illustrate the meaning of

Table of Competencies: Geometry

Performance Standard: The learners are able to analyze and investigate in a more formal environment the basic concepts in geometry.

·         Represent a point, line and plane using concrete and pictorial models

·         Define, identify and name the subsets of a line

·         Illustrate, name, identify and define the different kinds of angles

·         Derive relationships of geometric figures using measurements and by inductive reasoning: supplementary angles, complementary angles, congruent/equal angles, adjacent angles, linear pairs, perpendicular lines and parallel lines

·         Derive relationships between vertical angles and among angles formed by parallel lines cut by a transversal using measurement and by inductive reasoning

Performance Standard: The learners are able to analyze and investigate the different kinds of triangles, quadrilaterals convex polygons and circles.

·         Use a compass and straightedge to bisect line segments and angles and perpendiculars

·         Classify triangles according to their angles and according to their sides

·         Illustrate, name and identify different kinds of triangle and define the terms associated with a triangle

·         Derive relationships among the sides and angles of a triangle using measurement and by inductive reasoning

·         Illustrate, name and identify the different kinds of quadrilaterals

·         Derive relationships among the angles and among the sides of a quadrilateral using measurement and by inductive reasoning

·         Define and illustrate convex polygons

·         Derive the relationship of exterior and interior angles of any convex polygon using measurement and by inductive reasoning

·         Illustrate a circle and define the terms related to it: radius, diameter, center, arc and central angle

Table of Competencies: Probability and Statistics

Performance Standard: The learners are able to engage in statistical investigations.

·         Explain the basic concepts, uses and importance of Statistics

·         Pose questions and problems that may be answered using Statistics

·         Collect or gather statistical data and organize the data in a frequency table according to some systematic considerations

·         Use appropriate graphs to represent organized data: pie chart, bar graph, line graph and a histogram

·         Find the mean, median and mode of ungrouped statistical data

·         Describe the data using information from the mean, median and mode

·         Analyze, interpret accurately and draw conclusions from graphic and tabular presentations of statistical data

• Curriculum Guide