Grade Five
Expectation: At the end of Grade V, the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on fractions, decimals including money, ratio, percent, geometry, measurement and graphs; exact and estimated computation of the four fundamental operations on rational numbers including money and measurement and apply the concepts learned in solving problems.
I. WHOLE NUMBERS
A. Comprehension of Whole Numbers
REVIEW
1. Properties of Whole Numbers
§ Addition
§ Multiplication
2. Operations of Whole Numbers through Problem Solving:
§ Addition
§ Subtraction
§ Multiplication
§ Division
3. Subset of Whole Numbers
3.1 Differentiate prime and composite numbers
3.2 Give the common factors of given numbers
3.3 Find prime factors of a number
II. RATIONAL NUMBERS
Standard: The learner shows understanding of fraction through renaming, ordering dissimilar fractions as well as estimating.
A. Comprehension of Fraction
1. Change dissimilar fractions to similar fractions
1.1 Visualize changing dissimilar fractions to similar fractions
2. Identify equal fractions using the cross product method
3. Change fractions to lowest/higher term (LCM/GCF)
4. Order dissimilar fractions written in different forms from least to greatest and vice versa
5. Estimate fractions close to 0, 
, or 1
, or 1 A. Comprehension of Addition of Fractions
Standard: The learner performs addition, subtraction and multiplication of fractions and makes use of this knowledge to solve everyday problems.
1. Add similar and dissimilar fractions in mixed forms without and with regrouping
1.1 Add two to four similar fractions
1.2 Visualize addition of dissimilar fractions (using concrete and visual/pictorial models)
1.3 Add dissimilar fractions
1.4 Add dissimilar fractions and whole numbers
1.5 Add whole numbers and mixed forms
1.6 Add mixed forms and dissimilar fraction
1.7 Add mixed forms
1.8 Estimate sum
1.9 Add mentally two fractional units with similar denominators
2. Application of Addition of Fractions
2.1 Solve word problems involving addition of similar and dissimilar fractions without or with regrouping following the steps in problem solving
C. Comprehension of Subtraction of Fractions
1. Subtract fractions and mixed forms with common denominators without and with regrouping
1.1 Visualize subtraction of fraction and mixed form (using concrete and visual/pictorial models)
1.2 Subtract whole numbers from mixed forms without and with regrouping
1.3 Subtract fractions from whole numbers
1.4 Subtract fractions from mixed numbers without and with regrouping
1.5 Subtract mixed numbers from whole numbers
1.6 Subtract mixed numbers from mixed numbers (with similar fractions)
2. Subtract dissimilar fractions without and with regrouping
2.1 Visualize subtraction of dissimilar fractions
2.2 Subtract fractions from mixed numbers without and with regrouping
2.3 Subtract mixed numbers from mixed numbers without and with regrouping
3. Subtract mentally similar fractions
4. Application of Subtraction of Fractions
4.1 Solve word problems involving subtraction of fractions following the steps in problem solving
4.2 Solve two-step word problems involving addition and subtraction of fraction following the steps in solving 2-step problems
D. Comprehension of Multiplication of Fractions
1. Multiply fractions by whole number, mixed form by a fraction
1.1 fraction by a whole number
1.2 mixed form by a fraction
1.3 mixed form by a mixed form
2. Multiply mentally fractional units
3. Application of multiplication of fractions
3.1 Solve word problems involving multiplication of fractions following the steps in problem solving
3.2 Solve two-step word problems involving multiplication and any of addition and subtraction following the steps in solving two-step problems
E. Comprehension of Ratio
Standard: The learner understands the concept of ratio and applies knowledge in reducing/expressing to lower/higher terms and appreciates its application to daily life.
1. Express the ratio of two quantities
1.1 Visualize the ratio of two given sets of objects
1.2 Express the ratio of two numbers by using either colon (:) or a fraction
2. Reduce ratios to lowest terms.
3. Identify equivalent ratios
4. Application of Ratios
4.1 Solve word problems involving ratio following the steps in solving problems
F. Comprehension of Decimals
Standard: The learner understands the concept of renaming, rounding and giving the place value of decimals.
1. Read and write decimals through thousandths
1.1 Rename fractions whose denominators are powers of 10 in decimal form and vice versa
1.2 Give the place value of each digit of a given decimal
2. Round decimals to the nearest tenths and hundredths
G. Comprehension of Addition and Subtraction of Decimals
Standard: The learner understands and appreciates the basic operations on decimals and its application to real-world and mathematical situations.
1. Add and subtract decimals through thousandths without and with regrouping
2. Add and subtract mixed decimals without and with regrouping
3. Add and subtract mixed decimals from whole numbers without and with regrouping
4. Application of addition and subtraction of decimals
4.1 Solve word problems involving either addition or subtraction of decimals including money following the steps in problem solving
4.2 Solve two-step word problems involving addition and subtraction of decimals money following the steps in solving two-step problems
H. Comprehension of Multiplication of Decimals
1. Multiply decimals
1.1 Visualize multiplication of decimals using models
1.2 Multiply tenths by another tenth
1.3 Multiply hundredths by tenths and vice versa
2. Multiply mixed decimals with tenths and hundredths by whole numbers
3. Multiply mixed decimals by mixed decimals with tenths and hundredths
4. Multiply decimals by 10 and 100
5. Multiply decimals mentally by 0.1, and 0.01
6. Application of Multiplication of Decimals
6.1 Solve word problems involving multiplication of decimals including money following the steps in solving problems
I. Comprehension of Division of Decimals
1. Divides decimals through hundredths
1.1 Visualize division of decimals using models
1.2 Divide decimals by decimals through hundredths
1.3 Divide decimals by whole numbers
2. Application of Division of Decimals
2.1 Solve word problems involving division of decimals following the steps in problem solving
J. Comprehension of Percent
Standard: The learner extends his understanding of percent (%) to fractions, ratios and decimals to show relationship to one another.
1. Relate fractions, ratios, decimals and percent
1.1 Visualize the meaning of percent (%)
1.2 Give the relationship
§ between fractions, ratios and percents (with visual models)
§ between percent and decimal (with visual models)
§ among fractions, ratios, decimals and percents
III. Geometry
Standard: The learner understands the attributes of circle and 5 or more sided polygons and recognizes and appreciates similar things around him.
A. Comprehension of Polygons
1. Describe five or more sided polygons
1.1 Identify five or more sided polygons
1.2 Illustrate five or more sided polygons
2. Describe similar and congruent polygons
2.1 Visualize congruent polygons
2.2 Identify congruent polygons
2.3 Illustrate congruent polygons
2.4 Visualize similar polygons
2.5 Identify similar polygons
2.6 Illustrate similar polygons
3. Describe a circle
3.1 Visualize circle
3.2 Identify the parts of a circle (radius and diameter)
3.3 Illustrate circles with different radii
IV. Measurement
Standard: The learner extends his/her understanding on concept of circumference, area, volume and temperature measure and enjoys making and using measurement in everyday life.
A. Comprehension of Circumference of a Circle
1. Find the circumference of a circle in centimeter/ meter
1.1 Visualize the circumference of a circle
1.2 Derive a formula for finding the distance around a circle
1.3 Find the circumference of the given circle
2. Application of Circumference
2.1 Solve word problems involving circumference measure following the steps in problem solving
B. Comprehension of Area
1. Find the area of trapezoid and circle in square metres/centimetres
1.1 Visualize the area of trapezoid and circle
1.2 Derive a formula for finding the area of trapezoid and circle
1.3 Find the area
2. Application of Measurement of Area
2.1 Solve word problems involving area of trapezoid and circle following the steps in problem solving
C. Comprehension of Volume
1. Find the volume of cube/ rectangular prism
1.1 Name the unit of measure used for measuring the volume of cube/ rectangular prism
1.2 Convert one cubic unit of measure to a larger or smaller unit
1.3 Derive a formula for finding the volume of cube/rectangular prism
2. Application of Measurement of Volume
2.1 Solve word problem involving measurement of volume following the steps in problem solving
D. Comprehension of Temperature Measure
1. Give body/weather temperature using degree Celsius
1.1 Identify the parts of a thermometer
1.2 Read a thermometer
2. Application of Temperature Measure
2.1 Solve word problem involving body/weather temperature following the steps in problem solving
V. Graphs
Standard: The learner shows appreciation of line graph through reading, interpreting, constructing and finding average of data.
A. Comprehension of Line Graph
1. Read/Interpret data presented in a line graph
2. Construct a line graph
2.1 Organize data in a line graph
3. Find the average of data presented in a line graph
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