New Budget of Work in Mathematics for Grade Six

Grade Six

Expectation:  At the end of Grade VI, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on decimals, fractions, ratio and proportion, percent, geometry, measurement, and graphs; understood concept of probability and simple algebra; exact and estimated computation of the four fundamental operations involving decimals, money, fractions and measurement, and apply the concepts learned in solving problems.

I.    WHOLE NUMBERS

Standard:   The learner understands the concept of the order of operations (PEMDAS) of whole numbers and enjoys relating it to a variety of problem situation.

A.   Comprehension of Whole Numbers

   

1.   Perform operations on whole numbers following the correct order (PEMDAS)        

1.1     Give the meaning of exponent and base

1.2     Give the value of numbers involving exponents

1.3     Interpret PEMDAS rule correctly

1.4     Perform two different operations on whole numbers

a.   with or without exponents

b.   with or without parenthesis or other grouping symbols

1.5     Perform more than two operations on whole numbers

a.   with or without exponents

b.   with or without parenthesis or other grouping symbols

2    Apply the order of operations in solving two to three-step word problems

2.1     Solve two to three-step word problems involving whole numbers following the steps in solving two-step problems     

II.   RATIONAL NUMBERS

A.   Comprehension of Decimals

Standard:   The learner enriches his/her understanding of decimals by translating them in expanded and scientific notation.

1.  Visualize thousandths and ten thousandths        

1.1     Name a decimal for a given model (region/blocks, money, number line, grid)

1.2     Use different models to show a given decimal (region/block, money, number line, grid)

2.  Rename fractions whose denominators are powers of 10 in decimal form 

3.  Read and write decimals through ten thousandths 

3.1     Identify the value/place value of each digit in a given decimal 

3.2     Read decimals through ten thousandths 

3.3     Write decimals through ten thousandths in different notations

§  Standard Notation

§  Expanded Notation

§  Scientific Notation

4.   Compare and order decimals through ten thousandths 

5.   Round decimals through thousandths

Standard:    The learner shows mastery in performing the operations involving decimals and enjoys using various strategies in solving problems.

B.   Comprehension of Addition and Subtraction of Decimals

1.   Add and subtract decimals and mixed decimals through ten thousandths without or with regrouping  

1.1     Estimate sums and differences of decimals and mixed decimals

1.2     Add and subtract whole numbers and decimals

1.3     Add and subtract decimals through ten thousandths without and with regrouping

1.4     Add and subtract mixed decimals with regrouping

1.5     Apply the different properties of addition to compute sums mentally

1.6     Application of addition and subtraction of decimals

1.6.1     Solve one to three-step word problems involving addition and subtraction of decimals including money following the steps in solving problems  

A.    Comprehension of Multiplication of Decimals

1.   Multiply decimals and mixed decimals through thousandths without and with regrouping and with zero difficulty 

1.1     Estimate products of whole numbers and decimals 

1.2     Multiply one to three-digit factors by one to two-digit factors of whole numbers and decimals without and with regrouping and with zero difficulty 

1.3     Multiply hundredths by hundredths 

1.4     Multiply mixed decimals by mixed decimals with hundredths 

1.5     Multiply mentally decimals by 10, 100 and 1,000 

1.6     Multiply mentally decimals by 0.1, 0.01 and 0.001 

2.   Apply the properties of multiplication to compute products 

2.1     Commutative property of multiplication

2.2     Associative property of multiplication 

2.3     Distributive property of multiplication over addition 

3.   Application of multiplication of decimals

3.1     Solve word problems involving multiplication of decimals including money following the steps in solving problems

3.2     Solve two to three-step word problems involving addition, subtraction and multiplication of decimals including money following the steps in solving two-step problems

B.    Comprehension of Division of Decimals

1.   Estimate quotients of whole numbers and decimals 

2.   Divide 

2.1     whole numbers (two to five-digit dividends) by decimals (one to two- digit divisors) 

2.2     Differentiate between terminating and repeating from non-terminating decimal quotients

2.3     mixed decimals by whole numbers 

2.3.1     Visualize division using money as model

2.4     whole numbers by decimals and mixed decimals

2.5     mixed decimals by mixed decimals

3.   Divide decimals by 10, 100, 1,000 mentally

4.   Divide decimals by 0.1, 0.01, 0.001 mentally

5.   Application of division of decimals

5.1     Solve word problems involving division of decimals including money following the steps in solving problems

5.2     Solve two to three-step word problems involving decimals including money following the steps in solving two-step problems

E.     Comprehension of Fractions

Standard:   The learner shows clear understanding of equivalent fractions, finding the LCD and comparing and ordering fractions.

1.   Write the fraction described by a region, set and number line 

2.  Rename fractions as decimals and vice versa 

3.  Form equivalent fractions 

4.  Solve for the missing terms in a pair of equivalent fractions        

5.  Reduce fractions to lowest terms 

6.   Change mixed numbers to improper fractions and vice versa 

7.   Estimate fractions close to 0,  or 1 

8.   Find the least common denominator (LCD) of a set of fraction 

9.   Compare fractions and mixed forms using

9.1     fraction sense, visual reasoning, renaming to like forms 

9.2     cross products method 

9.3     LCD method 

10.  Order fractions in simple and mixed forms in ascending or descending order

Standard:  The learner shows mastery of performing the basic operations of fraction and find satisfaction in applying them in everyday problems.

F.    Comprehension of Addition and Subtraction of Fractions

1.   Visualize addition and subtraction of fractions (using concrete and visual/ pictorial models) 

2.   Estimate sums and differences of fractions in simple and mixed forms 

3.   Add and subtract similar fractions in simple or mixed forms without regrouping 

4.   Add and subtract similar fractions in simple or mixed forms with regrouping 

5.   Add and subtract dissimilar fractions in simple or mixed forms without regrouping 

6.   Add and subtract dissimilar fractions in simple or mixed forms with regrouping 

7.   Add mentally similar fractions using the properties of addition 

8.   Application of addition and subtraction of fractions 

8.1     Solve word problems involving addition or subtraction of fractions in simple or mixed forms with or without regrouping following the steps in solving problems

8.2     Solve two-step word problems involving addition and subtraction of fractions in simple and mixed forms without and with regrouping following the steps in solving two-step problems

G.  Comprehension of Multiplication of Fractions

1.   Simplify factors by cancellation method before multiplying 

2.   Multiply fractions in simple and mixed forms 

3.   Show that multiplying a fraction by its reciprocal is equal to 1 

4.   Application of Multiplication of Fractions 

4.1     Solve word problems involving multiplication of numbers in mixed forms following the steps in solving problems

5.2     Solve two to three-step word problems involving addition, subtraction, and multiplication of numbers in mixed forms following the steps in solving two-step problems 

H.   Comprehension of Division of Fractions 

1.   Visualize division of a whole number by a fraction; a fraction by another fraction

2.   Divide a fraction by a fraction

3.   Divide a whole number by a fraction and vice versa

4.   Divide mixed number by a fraction and vice versa

5.   Divide mixed number by a whole number and vice versa

6.   Divide mixed number

7.   Application of Division of Fraction

7.1     Solve word problems involving division of fractions following the steps in solving problems

7.2     Solve two to three-step word problems involving all operations on fractions following the steps in solving two-step problems 

I.    Comprehension of Ratio and Proportion

1.   Form ratio and proportion for groups of objects/numbers

1.1     Visualize the meaning of proportion

1.2     Tell whether two ratios make a proportion  

1.3     Find a missing term in a proportion 

2.   Application of Ratio and proportion 

2.1     Set up a proportion for a given situation

2.2     Solve word problems with: 

§  Direct proportion 

§  Partitive proportion 

§  Inverse proportion   

J.    Comprehension of Percent

 1.  Give the meaning of the elements used in solving percentage problems 

1.1     Percentage

1.2     Rate or Percent

1.3     Base

2.   Determine the percentage, rate and base in a given problem 

2.1     Set up a proportion to solve problems  

2.2     Solve the three types of percentage problems 

2.2.1     Find the percentage when the rate and base are given

2.2.2     Find the rate or percent when the percentage and base are given 

2.2.3     Find the base when the percentage or rate are given  

3.   Compute common percentage problems mentally

4.   Solve word problems involving finding the percentage/rate/base 

4.4.1     Percent of increase/decrease

§  Discounts

§  Original Price

§  Rate of Discount

§  Sale Price

§  Marked-up Price 

4.4.2     Commission

§  Rate of Commission

§  Total Sales

§  Total Income 

4.4.3     Sales Tax

§  Rate of Sales

§  Tax

§  Selling Price 

4.4.4     Simple Interest

§  Principal Rate

§  Time

  III.      GEOMETRY

Standard:   The learner shows understanding of the attributes of spatial figures and enjoys their functional use in their daily life

A.   Comprehension of Spatial Figures 

1.   Describe different spatial figures

1.1     Visualize the different spatial figures, cube, prism, cylinder, sphere,            pyramid, cone, etc.

1.2     Identify the different spatial figures and their functional use

1.3     Illustrate the different spatial figures

IV.     Measurement

Standard:   The learner extends his understanding of area through surface area, volume and meter reading and applies them in real-life situations.

A.   Comprehension of Surface Area 

1.   Find the surface area of cubes, prisms, and cylinders

1.1     Identify the faces of solid     

1.2     Name the unit of measure used for measuring the surface area of solids 

1.3     Derive a formula for finding the surface area of:

§  cubes

§  prisms

§  cylinders 

2.   Application of Measurement of Surface Area 

2.1     Solve the word problems involving measurement of surface area following the steps in solving problems

B.   Comprehension of Volume

 1.  Find the volume of a solid 

1.1     Name the unit of measure used for measuring the volume of solids

1.2     Convert one cubic unit of measure to a larger or smaller unit 

1.3     Derive a formula for finding the volume of solids like:

§  cylinders

§  pyramids

§  cones

2.   Application of Measurement of Volume 

2.1     Solve word problems involving measurement of volume following the steps in solving problems

C.   Comprehension of Meter Reading

 1.        Read and interpret readings from:

1.1 electric meters

1.2 water meters

2.   Solve word problems involving electric and water consumptions

V.   Graphs

Standard:   The learner shows appreciation of circle graph through reading, interpreting, constructing and finding average of data.

A.   Comprehension of Circle Graph 

1.   Read and interpret data presented in a circle graph 

2.   Construct a circle graph

2.1     Organize data in a circle graph 

VI.  Simple Probability

Standard:   The learner understands the basic concept of probability and enjoys making simple predictions and telling favorable outcomes as applied to real life situations.

1.   Make simple predictions  

2.   Tell the number of favorable outcomes/chances

VII. Introduction to Algebra

Standard:    The learner begins to understand the concept of expression, equation and integers.

            A.   Comprehension of Integers

1.   Visualize integers in their order on a number line 

2.   Compares integers 

3.   Order integers in increasing/decreasing order

            B.   Expressions and Equations

1.   Give the meaning of expression and equation

2.   Differentiate expression from equation