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MATHEMATICS VI

I. WHOLE NUMBERS

A. Comprehension of Whole Numbers

1. Comprehend the order of operations on whole numbers 1.1 Follow the correct order of operations (PEMDAS Rule) when

evaluating expressions having more than one operations 1.1.1 Give the meaning of:

- Expression - Equation - Exponent - Base

1.1.2 Evaluate an expression involving exponents 1.1.3 Evaluate an expression with two different operations with or

without exponents and parenthesis/grouping symbols 1.1.4 Evaluate an expression with more than 2 operations with or

without exponents and parenthesis/grouping symbols 1.2 Apply the order of operations in solving 2-3 step word problems

1.2.1 Solve 2-3 step word problems involving whole numbers following the steps in solving 2-step problems

II. RATIONAL NUMBERS

A. Comprehension of Decimals

1. Visualize ones, tenths, hundredths and thousandths 1.1 Name a decimal for a given model (region/blocks, money, number

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

number line) 2. Rename fractions whose denominators are power of 10 in decimal form 3. Read and write decimals through ten thousandths

3.1 Identify the value/place value of a 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

4. Compare and order decimals through ten thousandths 5. Round decimals through ten thousandths

B. Comprehension of Addition and Subtraction of Decimals

1. Add and subtract decimals and mixed decimals through the thousandths

without or with regrouping 1.1 Estimate sums and differences of whole numbers and decimals 1.2 Add and subtract whole numbers and decimals

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1.3 Add and subtract decimals through ten thousandths without and with regrouping (with concrete/visual models)

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 1 to 3-step word problems involving addition and subtraction of decimals including money following the steps in solving problems

C. 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 up to 3 digit factors by 1 to 2 digit factors 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 .01, 0.01 and 0.001 1.7 Apply the properties of multiplication to compute products

1.7.1 Commutative property of multiplication 1.7.2 Associative property of multiplication 1.7.3 Distributive property of multiplication over addition

1.8 Application of multiplication of decimals 1.8.1 Solve word problems involving multiplication of decimals

including money following the steps in solving problems 1.8.2 Solve 2 to 3 step word problems involving addition, subtraction

and multiplication of decimals including money following the steps in solving 2-step problems

D. Comprehension of Division of Decimals

1. Estimate problems of whole numbers and decimals 2. Divide

2.1 Whole numbers (2-5 digit dividends by decimals (1-2 digit divisions) 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 2 to 3 step word problems involving decimals including money following the steps in solving 2-step problems

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E. Comprehension of Fractions

1. Write the fraction described by a region, set and numberline 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, 21

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

11. Solve mentally word problems involving fractions

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 or subtract similar fractions in simple or mixed forms without

regrouping 4. Add or subtract similar fractions in simple or mixed forms with regrouping 5. Add or subtract dissimilar fractions in simple or mixed forms without

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

regrouping 7. Add mentally similar and dissimilar fractions using the properties of

addition 8. Application of addition and subtraction of fractions

8.1 Write an equation to solve word problems 8.2 Make drawings or diagrams to better understand the given problem 8.3 Solve word problems involving addition or subtraction of fractions in

simple or mixed forms with or without regrouping following the steps in solving problems

8.4 Solve 2-step word problems involving addition and subtraction of fractions in simple and mixed forms without and with regrouping following the steps in solving 2-step problems

G. Comprehension of Multiplication of Fractions

1. Multiply a fraction by another fraction (with visual models) 2. Simplify factors by cancellation method before multiplying 3. Multiply fractions in simple and mixed forms 4. Show that multiplying a fraction by its reciprocal is equal to 1 5. Application of Multiplication of Fractions

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

5.2 Solve 2 to 3 step word problems involving addition, subtraction, and multiplication of numbers in mixed forms following the steps in solving 2-step problems

H. Comprehension of Division of Fractions

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

fraction 2. Divides a whole number by a fraction; a fraction by another fraction 3. Divide fractions in different forms 4. Application of Division of Fraction

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

4.2 Solve 2 to 3-step word problems involving all operations on fractions following the steps in solving 2-step problems

I. Comprehension of Ratio and Proportion

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

1.1 Use colon (:) and fractions in writing ratios and proportions 1.2 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:

2.2.1 Direct proportion 2.2.2 Partitive proportion 2.2.3 Inverse proportion

J. Comprehension of Percent

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

1.1 Percentage 1.2 Ratio or Percent 1.3 Base

2. Determine the percentage, rate and base in a given problem 3. Application of Percent

3.1 Set up an equation or proportion to solve problems 3.2 Solve the three types of percentage problems

3.2.1 Find the percentage when the rate and base are given 3.2.2 Find the rate or percent when the % age and base are given 3.2.3 Find the base when the percentage or rate are given

3.3 Compute common percentage mentally 3.4 Solve word problems involving finding the percentage/rate/base

3.4.1 Percent of increase/decrease - Discounts - Original Price - Rate of Discount - Sale Price

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- Mark-up Price 3.4.2 Commission

- Rate of Commission - Total Sales - Total Income

3.4.3 Sales Tax - Rate of Sales - Tax - Selling Price

3.4.4 Simple Interest - Principal Rate - Time

K. Simple Probability

1. Make simple predictions 2. Tell the number of favorable outcomes/chances

L. Comprehension of Integers

1. Visualize integers in their order on a number line 2. Compares integers 3. Order integers in increasing/decreasing order

III. GEOMETRY

A. Comprehension of Spatial Figures

1. Describe different spatial figures 1.1 Visualize the different spatial figures, cube, rectangular prism,

cylinder, sphere, pyramid, cone, etc. 1.2 Draw the different spatial figures

IV. Measurement

A. Comprehension of Surface Area

1. Tell the surface area of solids 2. Tell the unit of measure used for measuring the surface area of solids 3. Find the area formula of the following plane figures:

- parallelograms - triangles - trapezoids - circles

4. Derive a formula for finding the surface area of: - cubes - prisms - cylinders

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5. Application of Measurement of Surface Area 5.1 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 Tell 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:

- prism - cylinders - pyramid - 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 meter 1.2 water meter

V. Graphs

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