PASIG CATHOLIC COLLEGE Grade School Department...

PASIG CATHOLIC COLLEGE Grade School Department

MATHEMATICS 5 FOURTH QUARTER Activity Sheet No. 1

TYPE OF ACTIVITY: Concept Development

TOPIC : Percentage, Base and Rate LEARNING OBJECTIVE : Identify the elements of percent in a give problem. REFERENCE : Soaring 21st Century Mathematics Kotah, Manuel T., et al. Math for Life 5 Revised Edition Wright, Amelia C. and Villamayor, Adelia C. CONCEPT NOTES :

Percentage is part of the base determined by the rate. Base is the whole on which the rate operates.

Rate is the number of hundredths part taken and is written with percent symbol (%).

PASIG CATHOLIC COLLEGE Grade School Department School Year 2015-2016

MATHEMATICS 5

FOURTH QUARTER Activity Sheet No. 2

TYPE OF ACTIVITY: Computational Skills

TOPIC : Finding Percentage LEARNING OBJECTIVES : Solve for the percentage in a worded problem. REFERENCE : Math for Life 5 Revised Edition, 218-219 Wright, Amelia C. and Villamayor, Adelia C. CONCEPT NOTES :

In finding the percentage, base or rate from a given problem, we use the PBR Triangle in obtaining the formula for each situation.

To find the percentage, multiply the base and the rate. P = B × R.

Example 1 What is 30% of 500? R = 30% B = 500 P = ? P = 500 × 30% (change percent to decimal) P = 500 × 0.3 P = 150

Example 2 15% of the fruits in the basket are apples. If there are 60

fruits in the basket, how many are apples? R = 15% B = 60 P = ? P = 60 × 15% (change percent to decimal) P = 60 × 0.15 P = 9, therefore, there are 9 apples in the basket.

P

B × R

PASIG CATHOLIC COLLEGE Grade School Department School Year 2015-2016

MATHEMATICS 5 FOURTH QUARTER Activity Sheet No. 3


TOPIC : Finding the Base LEARNING OBJECTIVES : Solve for the base in a worded problem. REFERENCE : Math for Life 5 Revised Edition, 206-207 Wright, Amelia C. and Villamayor, Adelia C. CONCEPT NOTES :

To find the base, divide the percentage by the rate. B = P ÷ R

Example 1: 24 is 60% of what number? P = 24 R = 60% B = ? B = P ÷ R B = 24 ÷ 60% (change percent to decimal) B = 24 ÷ 0.6 B = 40

Example 2: 20% of the class are non-Catholics. If there are 7

non-Catholics, how many students are there in the class? P = 7 R = 20% B = ? B = P ÷ R B = 7 ÷ 20% (change percent to decimal) B = 7 ÷ 0.2 B = 35, therefore there are 35 students in the class.

PASIG CATHOLIC COLLEGE

Grade School Department School Year 2015-2016

MATHEMATICS 5

FOURTH QUARTER Activity Sheet No. 4


TOPIC : Finding the Rate LEARNING OBJECTIVES : Solve for the rate in a worded problem. REFERENCE : Math for Life 5 Revised Edition, 212-213 Wright, Amelia C. and Villamayor, Adelia C. CONCEPT NOTES :

To find the rate, divide the given percentage by the base or rewrite the number as a fraction.

R = P ÷ B Example 1: 56 is what percent of 80?

P = 56 B = 80 B = ? R = P ÷ B R = 56 ÷ 80 R = 0.7 (change decimal to percent) R = 70%

Example 2: Czarina’s score in her exam is 38. If there are

40 items in the exam, what is the rate of her score? P = 38 B = 40 B = ? R = P ÷ B R = 38 ÷ 40 R = 0.95 (change decimal to percent) R = 95%

P

B R

P

B R

Pasig Catholic College Grade School Department

PCC @ 103: Be with Jesus, Be with the Poor S.Y. 2015 – 2016

Math 5 FOURTH QUARTER

DLA No. 5

TYPES OF ACTIVITY: Concept Development Name_______________________________________________CN___________

Grade & Section_____________________________________Date___________ TOPIC : Point and Lines LEARNING OBJECTIVES : Recognizes Point and Lines Identify Points and Lines REFERENCE : Simplifying Mathematical Challenges 5 Erminda E. De Leon Math for Life 5 Revised Edition Amelia C. Wright and Adelia C. Villamayor CONCEPT NOTES : Geometry Geometry means earth measure. Point is represented by a dot or a point. It is usually named with capital letter. Example: . A is read as point A. Plane is represented by any flat surface and extends indefinitely in all directions. Example: S R

T A

Plane STAR or Plane M. Line is a set of points which go on endlessly in both directions. Example: A B

Read as: Line AB or Line BA Written as: AB or BA Line Segment is a part of a line. It has two endpoints. There are no arrow head/s. Example:

C D E Read as: line segment or segment ___ ___ ___ ___ ___ ___ Written as: CD, DC, CE, EC, DE, ED Ray is a part of a line that has one end point and an arrowhead on the other way. In a ray , the end point is always named first. Example: F G I H Read as : Ray FG and Ray HI Written as: FG HI

Concept Notes Completeness:______ Neatness: ______ Activities Activity 1: ______ Activity 2: ______ Reflection: ______ TOTAL _________

M

KINDS OF LINE PAIRS C 1. Intersecting Lines are lines that are coplanar and K meet at exactly one point. Intersecting lines maybe B CE intersects AK at point B. E 2. Perpendicular Lines are intersecting lines that form square N corners or right angles. The symbol is Example: LM NO is read “ line LM is perpendicular to line NO”. L M O 3. Parallel Lines are lines that are coplanar and do not intersect. E The symbol for parallel lines is T ME IT is read as “ line ME is parallel to line IT” M I

M




DLA No. 6


Grade & Section_____________________________________Date___________ TOPIC : Angles LEARNING OBJECTIVES : Classify angles according to measure. Draw different kinds of angles. REFERENCE : Realistic Math Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : An angle is a figure formed by two rays having the same end points. The endpoint is called vertex . C A R

The names of the angles are written as : CAR, RAC or A.

Angles are classified according to their measure. A. Right angle measures 90º.

90º

B. Acute angle measures less than 90º.

C. Obtuse angle Measures more than 90º . D. Straight angles measure exactly 180º.

E. Reflex angle measures more than 180º but less than 360º

• When two lines cross or intersect, they form two pairs of opposite angles. These opposite angles are called vertical angles. Vertical angles have equal measures. R S

T N

• Angle with the same measure are called congruent angles. • When the sum of the two angles is equal to 90º, they are said to be

complementary angles. • When the sum of the two angles is equal to 180º, they are called

supplementary angles.

Concept Notes Completeness:______ Neatness: ______ Activities Activity 1: ______ Activity 2: ______ Activity 3: ______ Reflection: ______ TOTAL _________

Pasig Catholic College

Grade School Department PCC @ 103: Be with Jesus, Be with the Poor

S.Y. 2015 – 2016


DLA No. 7


Grade & Section_____________________________________Date___________ TOPIC : Triangles and Quadrilaterals LEARNING OBJECTIVES : * Identify the different kinds of triangles and quadrilaterals * Classify triangles and quadrilateral . * Find the measure of a missing angle in a triangle. REFERENCE : Realistic Math Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : Triangle is a polygon with 3 sides and 3 vertices. vertex

leg a hypotenuse

vertex leg b Vertex Triangles can be classified according to angles.

Acute triangle Right triangle Obtuse triangle It has 3 acute angles. It has 1 right angles. It has 1 obtuse angle.

Triangles can be classified according to sides.

Equilateral Isosceles Scalene It has 3 congruent It has 2 congruent It has no congruent sides. sides. sides.


Quadrigons or Quadrilaterals are closed plane figures made up of segments is also called polygons. Kinds of Quadrilaterals 1. Rectangle is a plane figure with four right angles and two pairs of parallel sides. A rectangle is a parallelogram with right angles. 2. Square is a special kind of rectangle that has four right angles and 4 congruent sides. 3. Parallelogram is a quadrilateral with two pairs of parallel sides. In the example the parallelogram has no right angles. 4. Trapezoid has only one pair of parallel sides. A trapezoid may/may not have a right angle. 5. Trapezium has no parallel lines. It may or may not have a right angle

h = 7 dm




DLA No. 8


Grade & Section_____________________________________Date___________ TOPIC : Finding the area of Squares, Rectangles and parallelograms LEARNING OBJECTIVES : * Find the area of square, rectangle and parallelogram. * Find the measure of the missing side of the polygon in a given area. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : Area is a measure of surface, and surface is measured in square units.

A. 9cm ( A= S x S or S2 ) A= 9 x 9 = 81 cm2

11 m B. ( A= L x W ) A = 11 x 6. 5 = 71.5 m2 6.5 m

c. ( A= B x H ) A = 12.6 x 7 = 88.2 dm2 b= 12.6 dm





DLA No. 9

TYPES OF ACTIVITY: Concept/Skill Development Name_______________________________________________CN___________

Grade & Section_____________________________________Date___________

TOPIC : Finding the Area of Triangle LEARNING OBJECTIVES : * Find the area of Triangle. * Derive a formula in finding the area of a triangle. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES :

5m 5m

8m 8m

A= B x H A = ½ x B x H A= 8 x 5 A = ½ x 8 x 5 A= 40 m2 A = 20 m2

The area of a triangle is one – half the area of parallelogram. Thus, the area of triangle , A = ½ bh.





DLA No. 10



TOPIC : Finding the area of Trapezoid LEARNING OBJECTIVES : * Find the area of Trapezoid. * Derive a formula in finding the area of a trapezoid. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : Trapezoid has only one pair of parallel sides. To find its area , multiply the sum of the upper base (b1) and the lower base (b2) by its height . Then divide it by 2. B1 = 2.8 m

h = 3.2 m b2 = 3.6 m Formula

A = !!!!!!

x h A = _2.8 + 3.6_ x 3.2 2 A = _ 6.4 x 3.2_ 2 A = _ 20.48 2 A = 10.24 m2





DLA No. 11



TOPIC : Circumference and Area of Circles LEARNING OBJECTIVES : * Find the circumference of a circle. * Derive a formula in finding the area of a circle. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES :

Radius is the straight line from the center point to the center point to the circle’s edge. Diameter is the line across the end points of the center which passes through the center point. CIRCUMFERENCE The distance around the circle is called circumference. To find the circumference of a circle, use the formula: 1. C = 𝝅 x d ( if diameter is given) Example: 2 dm C = 𝜋 x d C = 3.14 x 2 dm C = 6.28 dm

2. C = 2 x 𝝅 x r ( if radius is given ) Example: C = 2 x 𝜋 x r 4mm C= 2 x 3.14 x 4 mm

C= 25.12 mm


AREA OF A CIRCLE If you cut a circle into pieces then fit them together alternately, a new figure that looks like a rectangle will be formed. The length of the rectangle is ½ the circumference of the circle. The high tog the rectangle is the radius ( r ) of a circle.

Example:

60 m

The diameter of a circular racetrack is 60 m. What is the area of the race track? Since the diameter is 60 m, divide 60 by 2 to obtain the radius. So 60 ÷ 2 = 30 m. We use the formula: A = 𝜋 x r2

A = 3.14 x (30m)2

= 3.14 x 900m2 = 2826 m2 The area of the circular racetrack is 2 826m2.




DLA No. 12



TOPIC : Metric System LEARNING OBJECTIVES : * Tell the importance of the standard units of measure. * Use meter, gram, and liters as standard units of measure. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : Many years ago, there were no standard units of measure. People use some parts of the body in measuring length or distances. Today we use the standard unit of measure in the metric system. The metric system is based on the power of 10. Measures of Length The meter (m) is the basic unit used to measure length.

1 kilometer (km) = 1 000 m 1 hectometer (hm) = 100 m 1 dekametre (dkm) = 10 m 1 decimeter (dm) = 0.1 m

1 centemeter (cm) = 0.01m 1 millimeter (mm) = 0.001m

Measure of Mass The amount of matter that makes up an object is its mass/weight. The kilogram (kg) is the basic unit of mass.

1 kilogram (kg) = 1 000 grams (g) 1 hectogram (hg)= 100g 1 dekagram (dkg) = 10g 1 decigram (dg)= 0.1g

1centigram (cg) = 0.01 g 1 milligram (mg)= 0.001g

Measures of Capacity To measure liquid capacity, we use the liter (L).

1 kiloliter (kL) = 1 000L 1 hectoliter (hL) = 100L 1 dekaliter (dkL)= 10L 1 decileter ( dL)= 0.1 L

1 centiliter= (cL)= 0.01L 1 milliliter (mL)= 0.001L




S.Y. 2014 – 2015


DLA No. 13

TYPES OF ACTIVITY: Concept /Skills Development Name_______________________________________________CN___________


TOPIC : Metric System LEARNING OBJECTIVES : * Covert units of measure from larger unit to smaller unit and vice versa . * Solves word problems involving conversion of units. REFERENCE : Realistic Math 5 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Math for Life 5 Revised Edition Amelia C Wright, Adela C Villamayor CONCEPT NOTES : When converting one metric unit to another , determine first whether the change is from bigger unit to a smaller unit or from smaller unit to bigger unit. Then find out what power of 10 to divide or multiply. Example: kilo-

hecto-

deca-

Meter Gram Liter

deci-

centi-

milli-

To change bigger unit to a smaller unit like km to dkm, we multiply by a power of 10. 5 km = _____dkm Kilo- hecto- deca- There are 2 places from kilo- to deka- and each place is 10 times greater so: 10 x 10 = 100. If 100dkm = 1 km, we need to multiply 100 x 5 = 500 then, 5 km = _500_ dkm


To change smaller unit to bigger unit, like dm to hm, we divide.

583 dm = _____ hectometer

There are 3 places from decimeter to hectometre ,

therefore, !!"

𝑥 !!"𝑥 !!"

= !

!"""

1 dm =

!!"""

hectometer

583 ÷ 1000 = 0. 583

583 dm = 0. 583 hectometer



S.Y. 2015 – 2016


DLA No. 14


Grade & Section_____________________________________Date___________ TOPIC : Measuring Temparature LEARNING OBJECTIVES : 1. Read temperature reading correctly. 2. Uses the thermometer to measure temparature Reference : Math for Life 5 /Simplifying Mathematical Chalenges Author/s : Amelia Celeridad- Wright, Adela C. Villamayor CONCEPT NOTES : Temperature is the process of measuring how cold or how warm an object is. Thermometer is the device use to measure temperature. The Fahrenheit and Celsius scale are composed of units called degrees.


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