MATHEMATICS II (Gifted)

Content

Content Standards Performance Standards Learning Competencies

Numbers and Number Sense A. Comprehension of whole

numbers demonstrates understanding of the relationships between numbers and place value of whole numbers up to 1000 and beyond and of ordinal numbers up to 20th and beyond.

number notation and place value, cardinal and ordinal numbers, and comparing and ordering numbers up to 10,000.

explores the concepts of numbers up to 1000 and beyond

reads and writes these numbers

The learner…

visualizes and identifies numbers from 1000 and beyond

explore the concept of cardinal numbers up to 1,000 and beyond and compare these numbers in various contexts

Explore the concept of ordinal numbers from 31st to 100th and beyond

associates numbers with sets having 100 objects and beyond

associates numbers with sets having 501 up to 1000 objects and give the number of objects.

1.1 Associates numbers with sets having 1,001 up to 10,000 objects/things.

counts and groups objects in ones, tens, and hundreds. (lifted from K to 12)

counts numbers by 10s, 50s and 100s.

1.2 Skip counts by 3s, 4s through 1000 1.3 Skip counts by 50s through 10,000

reads and writes numbers from 101 through 1000 in symbols and in words.

2. Reads and writes numbers from 1,001 through 10,000 in symbols and in words

reads and writes numbers through 1000 in symbols and in words.

2.1 Reads numbers from 1,001 through 10,000 in symbols and in words 2.2 Writes numbers from 1,001- 10,000 in symbols and in words

gives the place value of each digit in a three-digit number.

2.3 Gives the place value and value of each digit in a 3 to 5 digit number 2.3.1 From the smallest/biggest to 5 digit number 2.3.2 Round numbers to nearest 10s, 100s, 1000s and 10,000s

writes three-digit numbers in expanded

identify ordinal numbers through 100th.

form.

2.4 Writes 3-5 digit numbers in expanded form 2.4.1 Writes the missing digits of numbers in the expanded forme.g 354= 300 + 50 + 4= 300 + 40 + ____ = 300 + _____ + 4

compares numbers using >, < and =.

orders numbers up to 10,000 from least to greatest and vice versa. (lifted from K to 12 & enhanced)

2.5 Compares numbers using >, < and = 2.6 Rounds number to the 2.6.1 nearest tens, hundreds and thousands 2.6.2 nearest ten thousands 2.7 Differentiates odd from even numbers with 2 to 4- digit numbers 2.8 Identifies odd/even 2-4- digit numbers

visualizes and identifies the 1st through the 20th object of a given set from a given point of reference. (lifted from K to 12)

3. Reads and writes ordinal numbers through 100th in symbols and words

compute sums and solve addition problems involving numbers of up to 1000.

reads and writes ordinal numbers from 1st through the 20th.

3.1 Identifies 31st through 100th object in given sets from a given point of reference 3.2 Identifies ordinal numbers up to the 100th

identifies and uses the pattern of naming ordinal numbers from 1st to the 20th.

3.3 Identifies the pattern of naming ordinal numbers e.g 21st, 22nd, 23rd, 24th, etc. 3.4 Uses the pattern of naming ordinal numbers beyond100th

4. Reads and writes centavos and pesos through 1,0005. Tells how many P100 bills are in P1,000; P50 bills are in P1,0006. Compares values of different denominations of Philippine coins and paper bills through P1,000 using the relation symbols7. Expresses Roman numbers in equivalent Hindu-Arabic through C and vice versa 7.1 Reads and writes Roman Numerals through C in Hindu-Arabic numbers and vice-versa through: a. repetition (e.g II) b. subtraction (e.g IV) c. addition (VI)

the concept of the four operations of whole numbers and the identity and zero properties of multiplication.

7.2 Solves simple addition problems using Roman numerals

COMPREHENSION OF ADDITION

adds numbers with sums up to 1000 without and with regrouping: 2 digit and 3-digit.

1. Adds 2-4 digit numbers with sum up to 9,999 without or with regrouping

uses the following properties of addition in computing for sums of up to 1000: zero/identity property of addition, commutative property of addition, associative property of addition.

1.1 Shows the commutative property of addition 1.2 Shows the associative property of addition

adds numbers with sums up to 1000 without and with regrouping: 3 digit and 3-digit.

use mental strategies to find sums to 18 and differences from 18 or less

mentally adds 1- to 2-digit numbers with sums up to 100. (lifted from K to 12)

mentally adds 3-digit numbers by ones (up to 9).

mentally adds 3-digit numbers by tens (multiples of 10 up to 90).

mentally adds 3-digit numbers by hundreds (multiples of 100 up to 900). (lifted from K to 12)

1.3 Adds 3 to 4 digit numbers with sums up to 10,000 with regrouping 1.3.1 without regrouping in short form 1.3.2 with regrouping in tens /hundreds place 1.4 Adds 2-4 addends digit numbers with zero in any of the addends without and with regrouping with sums up to 9,999 1.5 Estimates sums using front-end and rounding off techniques 1.6 Adds quantity of money up to P500 without regrouping 1.7 Adds mentally 1 to 2 digit numbers having 2-3 addends with sums up to 100

2. Application of addition 2.1 Solves word problems involving addition of 2 to 4 digit numbers including money with sums up to 9,999 without and with regrouping 2.1.1 Reads and understand the problem 2.1.1.1 Tells:

- what is asked - what is/are given - the word clue/s - the operation to be used 2.1.2 Plans what to do and do it 2.1.3 Draws a picture to represent the word problem 2.1.4 Transforms word problem into a number sentence 2.1.5 Solves the determined operation 2.1.6 Answers the question 2.1.7 Checks the answer

2.2 Solves mentally 1- step word problems involving addition with sums up to 999

2.3 Creates 1-step word problems involving addition of whole numbers up to 9,999 including money with or without regrouping

analyzes and solves word problems involving addition of whole numbers including money with sums up to 1000 without and with regrouping.

COMPREHENSION OF SUBTRACTION

compute differences and solve subtraction problems involving numbers of up to 1000.

subtracts 2- to 3-digit numbers with minuends up to 999 without and with regrouping.

1. Subtracts 1 to 3 –digit numbers from 3 to 5 digit numbers with minuend up to 9,999 without and with regrouping and with zero difficulty 1.1 Illustrates how subtraction is used when: 1.1.1 taking away from the given set 1.1.2 comparing two sets 1.1.3 finding a missing part 1.2 Subtracts 1 to 3 digit numbers from 3 to 4 digit numbers without regrouping 1.3 Subtracts 1 to 3 digit numbers from 3 to 4 digit numbers with regrouping 1.4 Subtracts 1 to 3 digit numbers from 3 to 4 digit numbers having zero difficulty with regrouping 1.5 Estimates the difference of two numbers without regrouping using the front-end and rounding technique in estimation 1.6 Subtracts quantity of money with minuend through P500.00 1.7 Subtracts mentally 1 to 2 digit numbers with minuends up to 100 without regrouping

mentally subtracts 1-digit numbers from 1 to 2-digit numbers with minuends up to 50.

mentally subtracts 3-digit by ones without regrouping. (lifted from K to 12)

mentally subtracts 3-digit by tens without regrouping. . (lifted from K to 12)

mentally subtracts 3-digit by hundreds without regrouping. . (lifted from K to 12)

2. Application of Subtraction 2.1 Solves 1-step word problems involving subtraction of 4-digit numbers including money with minuends up to 9,999 Tell:

- What is asked- What are given- The word clue/s- The operation to be used

Draws a picture/diagram/table/graph to represent the word problem

- Transforms the word problem into a number sentence

- States the complete answer- Does the answer make sense?

Why?

analyzes and solves one-step word problems involving subtraction of whole numbers including money with minuends up to1000 without and with regrouping.

compute for sums and differences and solve problems involving both addition and subtraction of numbers.

performs order of operations involving addition and subtraction of small numbers.

3. Application of addition and subtraction 3.1 Solves 2-step word problems involving addition and subtraction of whole numbers including money Tells:

- What is asked- What are given- The word clue/s- The operation to be used

Draws a picture /diagram/table/graph to represent the word problem

- Transforms the word problem into a number sentence

- States the complete answer 3.2 Creates 1 to 2-step word problems including money

solves two-step word problems involving addition and subtraction of 2- to 3-digit numbers including money using appropriate procedures.

explore and illustrate the concept of multiplication of whole numbers.

COMPREHENSION OF MULTIPLICATION

illustrates multiplication as repeated addition, arrays, counting by multiples, and equal jumps on the number line. (lifted from K to 12)

writes a related equation for each type of multiplication: repeated addition, array, counting by multiples, and equal jumps on the number line. (lifted from K to 12)

1. Multiplies 1 to 2 digit numbers by 1-digit numbers up to 9 without and with regrouping in all places with products up to 81 1.1 Transforms an addition sentence with a multiplication sentence and vice-versa 1.2 Identifies the parts of a multiplication sentence

illustrates the property of multiplication that any number multiplied by one (1) is the same number.

illustrates the property of multiplication that zero multiplied by any number is zero.

1.3 Shows that a number multiplied by 1 is the same number

illustrates the commutative property of multiplication. (lifted from K to 12)

1.4 Shows that zero multiplied by a number is zero 1.5 Multiplies 1 to 2 digit numbers by 1-digit numbers up to 9 without regrouping 1.6 Multiplies 1 to 2 digit numbers by 1-digit numbers up to 9 with regrouping

1.7 Gives the pairs of factors of a given number up to 99 1.8 Identifies the multiples of a given number 1.9 Gives the least common multiple (LCM) of two numbers 1.10 Multiplies mentally 1-2 digit numbers with products up to 81 with correction 1.11 Multiplies 1-digit numbers up to 9 by multiples of 10 and 100.

compute products of numbers involving 2, 3, 4, 5 and 10 and solve problems involving multiplication of these numbers.

constructs and fills up the multiplication tables of 2, 3, 4, 5 and 10. (lifted from K to 12)

multiplies mentally to fill up multiplication tables of 2, 3, 4, 5 and 10. (lifted from K to 12)

2. Application of multiplication

analyzes and solves one-step word problems involving multiplication of whole numbers including money.

.

2.1 Solves 1-step word problems involving multiplication of whole numbers including money with products through 81.

Tells: - What is asked- What are given- The word clue/s- The operation to be used

Draws a picture /diagram/table/graph to represent the word problem

- Transforms the word problem into a number sentence

- States the complete answer 2.2 Creates word problems involving multiplications of whole numbers including money

3. Application of multiplication and any of the fundamental operations

analyzes and solves two-step word problems involving multiplication of whole numbers as well as addition and subtraction including money

3.1 Solves 2-step word problems involving multiplication of whole numbers including money and any of the fundamental operations learned 3.1.1 Tells: - What is asked

- What are given- The word clue/s- The operation to be used

Draws a picture /diagram/table/graph to represent the word problem

- Transforms the word problem into a number sentence

- States the complete answer 3.2 Creates a 2-step word problems involving multiplication of whole number including money and any one of the two fundamental operations learned.

explore and model the concept of division of whole numbers.

COMPREHENSION OF DIVISION1. Divides whole numbers with dividends through 81 by 1 digit divisor

represents division as equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects.

1.1 Shows division as repeated subtraction 1.2 Identifies the parts of a division sentence namely, dividend, divisor, and quotient

models and describes division situations in which sets are separated into equal parts. (lifted from K to 12)

1.3 Illustrates division- By partition (dividing a number

into equal parts)

- By distribution (finding how many times a number is contained in a given number

- As inverse of multiplication-

writes a related equation for each type of situation: equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects.

1.4 Relates multiplication sentence to a division sentence 1.5 Transforms a division sentence into a multiplication sentence and vice versa

2. Divides 2 to 3 digit numbers with zero/s in the dividend by 1-digit number without remainder3. Divides 2 to 3 digit numbers by multiples of 10 up to 904. Divides 2 to 3 digit numbers by 1 digit numbers with remainder

compute quotients of numbers found in the multiplication tables involving 2, 3, 4, 5 and 10 and solve problems involving division of these numbers.

5. Application of Division

divides numbers found in the multiplication tables of 2, 3, 4, 5, and 10.(lifted from K to 12)

mentally divides numbers found in the multiplication tables of 2, 3, 4, 5 and 10. (lifted

from K to 12)

5.1 Solves 1-step word problems involving division of whole numbers including money with dividends up to 81. analyzes and solves one-step word problems involving division of numbers found in the multiplication tables of 2, 3, 4, 5, and 10. (lifted from K to 12)

6. Application of Division and any 1 of the 3 fundamental operations learned. 6.1 Solves 1-step word problems involving division of whole numbers including money and any 1 of the other fundamental operations learned. 6.1.1 Tells: - What is asked

- What are given- The word clue/s- The operation to be used

Draws a picture or a diagram to represent the word problem

- Transforms the word problem into a number sentence

- States the complete answer

.

Rational Numbers unit fractions, proper fractions explore the concept of unit COMPREHENSION OF FRACTIONS

and similar fractions, and identification of money value through 100.

fractions and other fractions less than 1 and compare these fractions

visualizes and identifies unit fractions with denominators 10 and below. (lifted from K to 12)

visualizes and identifies other fractions less than one with denominators 10 and below.

visualizes and identifies similar fractions (using group of objects and number line).

reads and writes similar fractions.

compares similar fractions using relation symbols. orders similar fractions.

reads and writes unit fractions. (lifted from K to 12)

compares unit fractions using relation symbols. (lifted from K to 12)

orders unit fractions. (lifted from K to 12)

1.Names some or all equal parts of a wholee.g 1/3, 2/3, 3/3; ¼, 2/4, ¾, 4/4

2. Separates a whole or group of objects into

halve, thirds, fourths, fifths, sixths, eights

3. Compares fractions with similar denominators by different numerators using relation symbols

e.g 2/3 < 3/3, ¾ > ¼, 2/5 < 4/5

4. Visualizes fractional parts of a number from halves to eights through 50

e.g 2/3 of 6 - 2/3 X 6 = 2 X 6 = 12 = 4 3 3

How many parts are shaded = 12 = 4 parts 3

3 of 8 -- 3 X 8 = 3 X 8 = 24 = 6 4 4 4 4

5. Finds the fractional parts of a number6. Solves word problems involving finding fractional part of a given sets/numbers including money7. Creates word problems involving finding fractional part of a given number including money

Enrichment

Reduces fractions to simplest forms

e.g 2/4 / 2/2 = ½ Divide both numbers by

their GCF

apply number concepts on problem situations involving money.

reads and writes money with value through 1000. (lifted from K to 12 and enhanced)

counts and tells the value of a set of bills or a set of coins through 1000 in peso ( coins only, bills only and coins and bills). (lifted from K to 12 and enhanced)

counts and tells the value of a set of bills or a set of coins through 1000 in centavo (coins). (lifted from K to 12 and enhanced)

counts and tells the value of a set of bills or a set of coins through 1000 in combinations of pesos and centavos (Peso and centavo coins only, bills and centavo coins, coins and bills). (lifted from K to 12 and enhanced)

reads and writes money in symbols and in words through 1000. (lifted from K to 12 and enhanced)

compares values of different denominations of coins and paper bills through 1000 using relation symbols >, < and =. (lifted from K to

12 and enhanced)

Geometry the basic properties of geometric shapes, simple tessellations and symmetry.

visualize and model half-circles and quarter circles as well as other common shapes.

Comprehension of Geometry visualizes, identifies, classifies and describes half-circles and quarter circles. (lifted from K to 12)

1. Identifies different shapes common in the home and in school2. classifies shapes according to number of sides and corners constructs squares, rectangles, triangle, circles, half-circles and quarter circles using cut-outs and square grids. (lifted from K to 12)

4. Forms simple symmetrical designs from given shapes

identifies shapes/figures that show symmetry in a line.

4.1 Identifies lines of symmetry 4.2 Identifies figures with lines of symmetry

explore the concept of symmetry. creates figures that show symmetry in a

line. (lifted from K to 12)

visualize, model and represent tessellations.

recognizes shapes that can tessellate. (lifted from K to 12)

tessellates a surface using triangles and squares. (lifted from K to 12)

3. Tessellates a surface using triangles and squares

explore the concept of lines, curves and surface on 3-dimensional objects.

identifies straight lines and curves, flat and curved surfaces in a 3-dimenional object. (lifted from K to 12)

explains the differences between straight lines and curved lines, flat surfaces and curved surfaces. (lifted from K to 12)

Patterns and Algebra patterns on numbers and geometric objects.

argue and justify patterns. identifies and explains simple repeating patterns.

determines the next term (figure/number) in a given sequence and give a reason.

apply their understanding and strategies in completing patterns.

finds and completes patterns according to one or two of the following attributes: shape, size, color, orientation.

Measurement A.1 Comprehension of Time Measure

the concept and application of time and of using standard units in measuring length, mass, area and capacity.

compute for measures of time and solve problems involving time.

1.1 Indicates the time to the nearest minute and second 1.2 Tells time when the minute hand is at 5 minute position e.g 1:05, 1:35, 1:55

1.3 Reads time as shown on the different kinds of time pieces (wristwatches, clocks) in figures and words

1.4 Converts measures of timee.g hours to minutes; minutes to hours; seconds to minutes

2. Application of time measure 2.1 Solves 1-step word problem involving time measure such as determining elapsed time and ending time using the steps in problem solving 2.2 Creates word problems involving time measures

B-1. Comprehension of linear measures

1.1 Measures object using standard units of linear measure i.e centimetre, meter

1.1.1 Approximates and measures the length, width, height and distance of objects in metres and centimetres

1.1.2 Tells the relationship between metres and centimetres

1.2 Finds the perimeter of a given figure using grid

2. Application of linear measure 2.1 Solve 1- step word problems involving linear measure using any of the fundamental operations 2.2 Create word problems involving linear measure

C-1 Comprehension of Area1. Visualizes area of plane figures in square

units2. Finds the area of plane figures in square

units

D-1 Comprehension of mass measure1.1 Measures mass of object using

standard units of mass measure such as gram and kilogram

1.2 Converts standard units of mass measure to lower or higher units

1.3 Approximates measurement of mass1.4 Investigates accuracy in measuring

mass and quantity of things boughte.g weighing sack of rice

2. Application of Mass Measures 2.1 Solves word problems involving mass measures using any of the four fundamental operations

E.1 Comprehension of Capacity 1.1 Makes measurement using standard units of capacity measure e.g litre,

millilitre1.2Converts standard units of capacity

measures from lower to higher units1.3 Approximates capacity of containers

2.Application of Capacity Measures 2.1 Solves word problems involving units of capacity using the steps in problem solving

F-1 Comprehension of Temperature Measure1.1 Identifies the parts of a thermometer1.2 Reads body/weather thermometer using

Celsius degrees2.Application of temperature measure 2.1 Solves word problems involving body/weather temperature

tells and writes the time in minutes including a.m. and p.m. using analog and digital clocks.

finds the duration of time elapsed using calendar, analog and digital clocks.

solves simple word problems involving time.

identify and compare the standard units centimeter and meter.

shows and uses the appropriate unit of length to measure a particular object and their abbreviations cm and m.

compares length in meters or centimeters.

estimate and compute for lengths of objects and solve problems involving lengths using centimeter and meter.

measures objects using appropriate measuring tools in m or cm.

estimates and measures length using meter or centimeter.

solves simple word problems involving length.

identify, use and compare the standard units gram and kilogram.

shows and uses the appropriate unit of mass to measure a particular object or situation and their abbreviations g and kg.

compares mass in grams or kilograms.

estimate and compute for the mass/weight of an object and solve problems involving mass/weight.

measures objects using appropriate measuring units in g or kg.

estimates and measures mass using gram or kilogram.

solves simple word problems involving mass.

explore and illustrate the concept of area.

illustrates area as a measure of how much surface is covered or occupied by plane figure.

shows the area of a given figure using square tile units, i.e. number of square tiles needed.

estimate and compute for the area of a plane figure.

estimates the area of a given figure using any shape.

finds the area of a given figure using square tile units i.e. number of square tiles needed.

measure capacity. shows and finds capacity using appropriate measuring tools, e.g. amount of liquid needed.

Statistics and Probability pictographs with scale representations and the idea of likelihood.

organize and interpret data. collects and organizes data using tables and pictures.

reads and interprets data in a given pictograph.

represent data using scales forms scale representation of objects from the data collected.

makes pictographs using scale representation.

make conjectures and educated guesses about the likelihood of events

makes a guess on whether an event is less likely, more likely, equally likely or unlikely to happen based on facts.

Maps and Graphs

F1 collect and organize dataF2 interpret and create concrete and picture graphsF3 interpret and create pictographs and symbolic graphsF4 pose oral questions in relation to conducting surveys and/or interpreting data

A. Comprehension of graphs 1. Reads and interprets data on a bar graph and a pictograph 1.1 Names the parts of a pictograph and bar graph a. title b. legend c. label 1.2 Tells the function of each part 2. Collects and organizes data for graphs 3. Reads and interprets data presented in pictograph and bar graph

B. Comprehension of maps 1. Tells the position of certain object or place using the primary and secondary directions 1.1. Names the secondary directions 1.2 Locates the secondary directions