Wednesday, January 19, 2011

New Budget of Work in Mathematics for Grade Four


Grade Four

Expectation:    At the end of Grade IV, the child is expected to demonstrate understanding of concepts and perform skills of whole numbers up to millions and billions including money, decimals, fractions, geometry and graphs; exact and estimated computation on the four fundamental operations; and apply the concepts learned to solve problems.

I.   WHOLE NUMBERS

Standard:   The child shows mastery of the concept of whole numbers and enjoys giving the place value and rounding numbers.

A.    Comprehension of Whole Numbers

   1.   Read and write      numbers through millions in symbols and in words
1.1                  Identify numbers from 100 001 through millions/ billions
1.2                  Give the place value of each digit in a six or more digit numbers
1.3                  Read and write numbers through millions/billions in symbols
1.4                  Read and write numbers through millions/billions in words
2.   Round off numbers to the nearest
2.1                  tens, hundreds, thousands 
2.2                  ten thousands, hundred thousands
2.3                  millions, billions

Standard:   The child shows mastery of the four operations, estimation and involving mental computations involving whole numbers and exhibits confidence in solving problems

B.  Comprehension of Addition
1.   Add six or more digit numbers with four or more addends with sums through billions
1.1         without regrouping       
1.2     with regrouping in any two or more places
2.   Estimate the sum of six or more digit addends
3.   Add mentally two to three-digit numbers with sums up to 300 without regrouping
4.   Application of Addition
 4.1    Solve word problems involving addition of whole numbers including money with sums through millions and billions without and with regrouping following the steps in problem solving
 4.2    Solve mentally one-step word problems involving addition with sums up to 300 without regrouping
C.  Comprehension of Subtraction
1.       Subtract five or more digit numbers from six or more digit numbers without and with regrouping in any or all places and involving three or more zeros both in the minuend and subtrahend
                    Subtract five or more digit numbers from six or more digit numbers without regrouping
                    Subtract five or more digit numbers from six or more digit numbers with three continuous or non-continuous zeros in both minuends and subtrahend and with regrouping in any or all places
                    Estimate the difference of numbers with four to six digits
2.       Subtract mentally numbers with minuends up to 300 without regrouping
3.       Application of Subtraction
3.1         Solve one-step word problems involving subtraction of whole numbers including money without and with regrouping following the steps in problem-solving
3.2         Solve mentally one-step word problems involving subtraction without regrouping following the steps in problem solving
4.       Application of Addition and Subtraction    
4.1     Solve two-step word problems involving addition and subtraction including money following the steps in solving 2-step problems     
D.  Comprehension of Multiplication
1.                             Show the properties of multiplication
§  Zero Property
§  Identity Property
§  Distributive Property of Multiplication over Addition                      
2.       Multiply five or more factors by three to five-digit factors without and with regrouping and with zero in any of the factors
            Multiply five or more digit factors by three- to five-digit factors without regrouping
            Multiply five or more digit factors by three- to five-digit factors with regrouping
            Multiply five or more digit factors having one to three zeros in both factors without and with regrouping
            Multiply five or more digit factors by multiples of 10, 100 and 1,000
3.       Estimate the products of five or more digits by two to three-digit numbers
4.       Multiply mentally two-digit numbers with products up to 200 without regrouping
5.       Application of Multiplication
5.1     Solve word problems involving multiplication of whole numbers including money following the steps in problem solving
5.2     Solve two-step word problems involving multiplication and any of addition/ subtraction following the steps in solving two-step problems
E. Comprehension of Division
1.     Divide five or more digit numbers by three or more digit numbers without or with remainder and with zero difficulty.
                  Divide five or more digit number by three or more digit numbers without remainder 
                  Divide five or more digit numbers by three or more digit numbers with remainder
                  Divide five or more digit numbers by three or more digit numbers with zeros in the middle or continuous zeros in the dividend
2.       Divide multiples of 10 by 10 or 100 or 1000
3.       Estimate the quotient of five or more digit dividends by three or more digit divisors
4.       Divide mentally two to three-digit numbers by one-digit numbers without remainder
5.       Application of Division
                      Solve one-step word problems involving division of five or more digit numbers by three or more digit numbers including money following the steps in problem solving
                      Solve two to three-step word problems involving division and any one or two of the other fundamental operations learned including money following the steps in solving two-step problems
II.  RATIONAL NUMBERS
           
Standard:   The child understands the concept of decimals and money and enjoys reading and writing, rounding, renaming and giving the place value of decimals.

A.    Comprehension of Decimals and Money

1.  Read and write common fractions in decimal form through hundredths
1.1         Visualize common fractions as decimals using models like blocks, grid and money
1.2         Write common fractions in decimal form
1.3         Read and write decimal numbers through hundredths
1.4         Rename fractions whose denominators are 10 and 100 in decimal form and vice versa
1.5         Give the place value of each digit of a given decimal through hundredths
2.   Express money as pesos/centavos
3.   Round decimal to the nearest tenths

Standard:   The child demonstrates understanding of addition and subtraction of decimals and applies them in problem solving.

B.    Comprehension of Addition and Subtraction of Decimals
1.   Add and subtract decimals through hundredths without and with regrouping  
1.1         Add decimals through hundredths without and with regrouping
1.2         Subtract decimals through hundredths without or with regrouping
2.   Add and subtract mixed decimals with regrouping
2.1         Add mixed decimals with regrouping
2.2         Subtract mixed decimals with regrouping
3.  Application of addition and subtraction of decimals
3.1     Solve word problems involving either addition or subtraction of decimals including money following the steps in problem solving
3.2     Solve one to two-step word problems involving addition and subtraction of decimals including money following the steps in solving two-step problems
C.    Comprehension of Fractions

Standard:   The child understands differentiating, ordering and renaming fractions and enjoys using the knowledge in everyday life situation.

1.       Differentiate fractions including those with denominators of 10 and 100
                  Identify proper fraction/ improper fraction/mixed forms from a given set of fractions including those with denominators of 10 and 100
1.1.1           Identify fractions using regions, sets and number line
1.1.2           Use fraction to represent division
                  Identify similar and dissimilar fractions from a given set of fractions
2.       Order similar fractions written in different forms from least to greatest and vice versa
3.       Change improper fraction to mixed forms and vice versa
4.       Change one (1) to fraction form and vice versa
5.       Rename decimals to fractions

D.    Comprehension of Addition and Subtraction of Fraction

Standard:   The child performs addition, subtraction and multiplication of fractions and applies them to solve everyday life problems.

1.       Add similar fractions and whole numbers without regrouping
                  Visualize addition of similar fractions
                  Add similar fractions
                  Add a fraction and a whole number
                  Add mentally similar fractions
2.       Subtract similar fractions without regrouping
                  Visualize subtraction of similar fractions
                  Subtract similar fractions
                  Subtract a fraction from a whole number
                  Subtract mentally similar fractions
3.       Application of Addition and Subtraction of Fractions
                  Solve word problems involving addition of similar fractions without         regrouping following the steps in problem solving
                  Solve word problems involving subtraction of similar fractions without regrouping following the steps in problem solving

E.  Comprehension of Multiplication of Fractions
1.  Multiply fractions
1.1         Visualize multiplication of fractions (visual models)
1.2         Find a fractional part of a number
1.2.1          Translate expressions such as:
    of ,
    of  
1.3         Multiply a fraction by another fraction
2.  Application of Multiplication
2.1         Solve word problems involving multiplication of fractions following the steps in problem solving
III.     GEOMETRY

Standard:   The child describes and classifies angles and plane figures like square, rectangle and triangles; enjoys constructing and exploring similar objects around him/her.

A.     Comprehension of Angles and Plane Figures
1.   Describe different kinds of angles
1.1     Visualize different kinds of angles
1.2   Identify parts of an angle
1.2   Name different kinds of angles such as right angle, acute angle and obtuse angle
1.3     Classify angles as right, acute or obtuse
1.4     Identify congruent angles
1.5     Draw congruent angles
2.  Describe plane figures according to their sides, corners and their functional use
2.1         square
2.2         rectangle
2.3         triangle
2.3.1                      parts
2.3.2                      types according to sides
2.3.3                      types according to angles
3.  Illustrate three or four-sided plane figures using ruler and protractor
IV.    MEASUREMENT

Standard:    The child understands the attributes of perimeter, area and volume and enjoys measuring, comparing approximating and applying the formulas in solving variety of problems.

A.  Comprehension of Perimeter
1.  Find the perimeter of regular polygons
1.1          triangle
1.2          quadrilateral
1.3          pentagon, etc.
2.   Derive a formula for finding the perimeter of regular polygons
3.   Find the perimeter of irregular polygons
3.   Application of Perimeter
3.1         Solve word problems involving perimeter measures following the steps in problem solving                 

B.    Comprehension of Area

1.                                                         Find the area of parallelogram and triangle in square metre/centimetre
1.1         Derive a formula for finding the area of a:
1.1.1          parallelogram
1.1.2          triangle
1.2         Find the area of parallelogram and triangle
2.   Solve word problems involving the area of parallelogram and triangle following the steps in problem solving
C.    Comprehension of Volume  
1.   Make measurement using non-standard units:
§  cubes
§  marbles       
2.       Compare among the non-standard units of measuring volume in terms of  consistency and accuracy
3.   Approximate measurement of volume




IV.  Graphs

Standard:   The child shows appreciation of the bar graph through reading, interpreting, constructing and finding average of data.

A.    Comprehension of Bar Graph

1.       Read and interpret data presented in a bar graph
1.1         Read the following parts of a bar graph
   a.  title
   b.  legend
       c.  labels
1.2         Interpret bar graphs
2.       Construct bar graphs
2.1         Organize data in a bar graph
3.       Find the average of data presented in a bar graph

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