Revised Curriculum Guide Grade 7 Mathematics

7/28/2019 Revised Curriculum Guide Grade 7 Mathematics

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Republic of the PhilippinesDepartment of Education

DepEd Complex, Meralco AvenuePasig City

July 9-13, 2012


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K TO 12 MATHEMATICS

CONCEPTUAL FRAMEWORK

Mathematics is one subject that pervades life at any age, in any circumstance. Thus, its value goes beyond the classroom andthe school. Mathematics as a school subject, therefore, must be learned comprehensively and with much depth.

The twin goals of mathematics in the basic education levels, K-10 are Critical Thinking and Problem Solving. We adopt the definition of

critical thinking by Scriven and Paul (1987):

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/orevaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief

and action.

On the other hand, we define Problem Solving in mathematics using Polyas (1945 & 1962) definition:

Mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown.

These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills andprocesses, desirable values and attitudes, and appropriate tools, recognizing as well the different contexts of Filipino learners.

There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers andNumber Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics.

The specific skills and processes to be developed are: Knowing and Understanding; Estimating, Computing and Solving; Visualizingand Modelling; Representing and Communicating; Conjecturing, Reasoning, Proving and Decision-making, and: Applying and Connecting.

The following values and attitudes are to be honed as well: Accuracy, Creativity, Objectivity, Perseverance, and Productivity.

We recognize that the use of appropriate tools is needed in teaching mathematics. These include: manipulative objects,measuring devices, calculators and computers, Smartphones and tablet PCs, and the Internet.


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We define context as a locale, situation or set of conditions of Filipino learners that may influence their study and use of mathematics todevelop critical thinking and problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions andpractices, and learners prior knowledge and experiences.

The framework is supported by the following underlying learning principles and theories: Experiential and Situated Learning,

Reflective Learning, Constructivism, Cooperative Learning and Discovery and Inquiry-based Learning. The mathematics curriculum is

grounded in these theories.

Experiential learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experientiallearning theory defines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results fromthe combination of grasping and transforming experience" (Kolb, 1984, p. 41). Situated learning, theorized by Lave and Wenger, is learning inthe same context on which concepts and theories are applied.

Reflective learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations.Deeper learning

occurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and

meaning of theirexperiences.

Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his own experiencesand connects them to new ideas that are encountered.

Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task.

The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery and Inquiry-based learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationshipsand concepts.


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Figure 1. The Conceptual Framework of Mathematics Education


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K TO 12 MATHEMATICS

BRIEF COURSE DESCRIPTION

Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic and reasoning.Mathematics is also a tool of science and a language complete with its own notations and symbols and grammar rules, with which conceptsand ideas are effectively expressed.

The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics andProbability. Numbers and Number Sense as a strand includes concepts of numbers, properties, operations, estimation and their applications.

Measurement as a strand includes the use of numbers and measures to describe, understand and compare mathematical and concreteobjects. It focuses on attributes such as length, mass and weight, capacity, time, money and temperature among others, as well as applicationsinvolving perimeter, area, surface area, volume and angle measure.

Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoningand geometric modeling and proofs.

Patterns and Algebra as a strand studies patterns, relationships and changes among shapes and quantities and includes the use ofalgebraic notations and symbols, equations and most importantly, functions, to represent and analyze relationships.

Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables and graphs,understanding, analyzing and interpreting data, dealing with uncertainty and making predictions and outcomes.

The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it provides

necessary concepts and life skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens ofour beloved country, the Philippines.


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K TO 12 MATHEMATICS

LEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematics

as applied, using appropriate technology, in problem solving, critical thinking, communicating, reasoning, making connections,representations, and decisions in real life.

KEY STAGE STANDARDS:

K 3 4 6 7 10

At the end of Grade 3, the learnerdemonstrates understanding and appreciationof key concepts and skills involving numbersand number sense, measurement, geometry,patterns and algebra, statistics and probabilityas applied, using appropriate technology, incritical thinking, problem solving, reasoning,communicating, making connections,representations and decisions in real life.

At the end of Grade 6, the learnerdemonstrates understanding and appreciationof key concepts and skills involving numbersand number sense, measurement, geometry,patterns and algebra, statistics and probabilityas applied, using appropriate technology, incritical thinking, problem solving, reasoning,communicating, making connections,representations and decisions in real life.

At the end of grade 10, the learnerdemonstrates understanding and appreciationof key concepts and skills involving numbersand number sense, measurement, patterns andalgebra, geometry, probability and statistics,and trigonometry as applied, using appropriatetechnology, in critical thinking, problem solving,communicating, reasoning, makingconnections, representations, and decisions inreal life.


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K TO 12 MATHEMATICS

GRADE LEVEL STANDARDS:

GRADE LEVEL GRADE LEVEL STANDARDS

K

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to20, space and measurement, simple geometric figures, pre-algebra concepts and data collection as applied, usingappropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections,representations and decisions in real life.

GRADE 1

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to100, fractions, measurement, simple geometric figures, pre-algebra concepts, data collection and representation asapplied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.

GRADE 2

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to1 000, fractions, measurement and geometric figures, pre-algebra concepts, data collection, representation and

analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating,making connections, representations and decisions in real life.

GRADE 3

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to10 000, fractions, measurement, geometric figures, pre-algebra concepts, data collection, representation andanalysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating,making connections, representations and decisions in real life.

GRADE 4

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to100 000, fractions, decimals including money, ratio, angles, plane figures like square, rectangle, and triangle,measurement (perimeter, area of triangle, parallelogram and trapezoids, volume of cubes and rectangular prisms,pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in

critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions inreal life.

GRADE 5

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to10 000 000, fractions, decimals including money, ratio, percent, geometry (circles and five or more-sided polygons),measurement (circumference, area of circle, volume of cubes and rectangular prisms, temperature) ,pre-algebraconcepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking,problem solving, reasoning, communicating, making connections, representations and decisions in real life.


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GRADE 6

The learner; demonstrates understanding and appreciation of key concepts and skills involving fractions, decimalsincluding money, ratio and proportion, percent, rate, integers, geometry (spatial figures), measurement (surface

area, volume, meter reading), pre-algebra concepts, data collection, representation and analysis, probability,

expressions and equations as applied, using appropriate technology, in critical thinking, problem solving, reasoning,communicating, making connections, representations and decisions in real life.

GRADE 7 The learner demonstrates understanding of key concepts and principles of number sense, measurement, algebra,geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving,reasoning, communicating, making connections, representations and decisions in real life.

GRADE 8

The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability andstatistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating,

making connections, representations, and decisions in real life.

GRADE 9The learner demonstrates understanding of key concepts and principles of algebra, geometry, and trigonometry asapplied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.

GRADE 10

The learner demonstrates understanding of key concepts and principles of number sense, algebra, geometry,probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning,

communicating, making connections, representations and decisions in real l ife.


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K TO 12 MATHEMATICS

GRADE 7

CONTENT CONTENT STANDARDS PERFORMANCE STANDARDS LEARNING COMPETENCIES

Numbers and Number Sense The learner demonstratesunderstanding of key concepts ofsets and the real number system.

The learner is abletoformulateintellectually challenging situationsinvolving sets and real numbersand solve these in a variety ofstrategies

The learnero describes and illustrates well-

defined sets, subsets, universalsets and the null set andcardinality of sets

o describes the union andintersection of sets and thecomplement of a set.

o uses Venn Diagrams torepresent sets, subsets and setoperations

o solves problems involving sets.

o describes and illustrates theabsolute value of a number ona numberline as the distance ofa number from 0.

o performs fundamentaloperations on integers.

o states and illustrates thedifferent properties ofoperations on the sets ofintegers.

o illustrates rational numbers andarrange them on a numberline.

o expresses rational numbers


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(both repeating andterminating/non-repeating andnon-terminating) from fractionform to decimal form and viceversa.

o performs operations on rationalnumbers and illustrate theirproperties.

o describes principal roots andtells whether they are rationalor irrational.

o determines between what twointegers the square root of anumber is.

o estimates the square root of anumber to the nearest tenth.

o illustrates and graphs irrationalnumbers (square roots) on anumberline with and withouttechnology.***

o describes, represents andcompares the different subsetsof real numbers.

o finds the union, intersectionand complement of the set ofreal numbers and its subsets.

o arranges real numbers inincreasing or decreasing order.

o determines the significantdigits in a given situation.

o writes very large and very


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small numbers in scientificnotation.

o describes and represents real-life situations which involveintegers, rational numbers,

square root of rational andirrational numbers.

o solves problems involving realnumbers.

Measurement The learner demonstratesunderstanding of the key conceptsof measurement

The learner is able to formulatereal life problems and solve theseusing a variety of strategies.

The learner

o describes what it means tomeasure. (2nd Quarter)

o describes the development ofmeasurement from theprimitive to the present

international system of units.***o estimates or approximates the

measures of quantitiesparticularly length ,weight/mass, volume, time,angle and temperature.

o uses appropriate instrumentsto measure quantities such aslength, weight/mass, volume,time, angle and temperature***

o converts measurements from

one unit to another for eachtype of measurement includingthe English system.***

o solves problems involvingmeasurements such asperimeter, area, weight/mass,


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time, speed, temperature,volume/capacity and utilitiesusage.***

Algebra The learner demonstratesunderstanding of key concepts

algebraic expressions, theproperties of real numbers asapplied in linear equations andinequalities in one variable.

The learner is able to modelsituations using oral, written,

graphical and algebraic methods insolving problems involvingalgebraic expressions, linearequations and inequalities in onevariable.

The learner

o translates verbal phrases to

mathematical phrases andvice versa.

o differentiates betweenconstants and variables in agiven algebraic expression.

o evaluates algebraicexpressions for given valuesof the variables.

o gives examples of algebraicexpressions which are

polynomials and classifiesthese as to number of terms.

o adds and subtractspolynomials

o interprets the meaning of anwhere n is a positive integer.

o multiplies and dividespolynomials

o derives the laws of exponent.

o finds inductively using models

the (a) product of twobinomials; (b) product of thesum and difference of twoterms; (c) square of abinomial; (d) cube of abinomial; (e) product of a


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binomial and a trinomial.

o finds algebraically the (a)product of two binomials; (b)product of the sum anddifference of two terms; (c)

square of a binomial; (d) cubeof a binomial; (e) product of abinomial and a trinomial. ***

o differentiates betweenmathematical expressions andmathematical equations. (3rdQuarter)

o translates English sentencesto mathematical sentencesand vice versa.

o differentiates between

equations and inequalities.

o illustrates the meaning ofabsolute value.

o finds the solution of anequation or inequalityinvolving one variable,including one that involvesabsolute value (a) from agiven replacement; (b)intuitively by guess and check;(c) by algebraic procedures(applying properties ofequalities and inequalities); (d)graphing.

o solves problems that useequations and inequalities.


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Geometry The learner demonstratesunderstanding of key concepts ofgeometry of shapes and sizes, andgeometric relationships.

The learner is able to createartistically models of plane figures,formulate and solve with accuracyauthentic problems involvinggeometric shapes and sizes.

The learner ..

o presents point, line andplane using concrete andpictorial models.

o

names the subsets of aline.

o illustrate and classify thedifferent kinds of angles.

o derives relationships ofgeometric figures usingmeasurements and byinductive reasoning;supplementary angles,complementary angles,equal angles, vertical

angles, adjacent angles,linear pairs, perpendicularlines and parallel lines.***

o derives relationshipsbetween vertical anglesand among angles formedby parallel lines cut by atransversal usingmeasurement and byinductive reasoning.

o uses a compass and

straight edge to bisect linesegments and angles andconstruct perpendicularsand parallels.


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o classifies trianglesaccording to their anglesand according to theirsides. (4th Quarter)

o illustrates and names

different kinds of triangles.

o derives relationshipsamong the sides andangles of a triangle usingmeasurement andinductive reasoning.

o illustrates and namesdifferent kinds ofquadrilaterals.

o derives relationships

among the sides andangles of a quadrilateralusing measurement andinductive reasoning.

o illustrates convex polygons.

o derives the relationship ofexterior and interior anglesof any convex polygonusing measurement andinductive reasoning.

o illustrates a circle and the

terms related to it; radius,diameter, center, arc andcentral angle.


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Statistics and Probability The learner demonstratesunderstanding of key concept,uses and importance of Statistics,data collection/gathering and the

different forms of datarepresentation.

The learner is able to collect andorganize data systematically andmake the necessaryrepresentation to solve problems in

research, business, education,technology, science, economics,etc.

The learner

o explains the basic concepts,uses and importance of

Statistics.o poses questions and

problems that may beanswered using Statistics.

o collects or gathers statisticaldata and organizes the data ina frequency table according tosystematic consideration.

o uses appropriate graphs torepresent organized data: piechart, bar graph, line graph

and a histogram.***

o finds the mean, median andmode of statistical data.***

o describes the data usinginformation from the mean,median and mode.

o analyzes, interprets accuratelyand draws conclusions fromgraphic and tabular data.

*** Suggestion for ICT enhanced lesson when available and where appropriate

Revised Curriculum Guide Grade 7 Mathematics

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