PASIG CATHOLIC COLLEGE Grade School Department MATHEMATICS 5 FOURTH QUARTER Activity Sheet No. 1. TYPE OF ACTIVITY: Concept Development

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1 PASIG CATHOLIC COLLEGE MATHEMATICS 5 Activity Sheet No. 1 TYPE OF ACTIVITY: Concept Development : Percentage, Base and Rate LEARNING OBJECTIVE : Identify the elements of percent in a give problem. REFERENCE : Soaring 21 st Century Mathematics Kotah, Manuel T., et al. Wright, Amelia C. and Villamayor, Adelia C. 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 School Year MATHEMATICS 5 Activity Sheet No. 2 TYPE OF ACTIVITY: Computational Skills : Finding Percentage LEARNING OBJECTIVES : Solve for the percentage in a worded problem. REFERENCE :, Wright, Amelia C. and Villamayor, Adelia C. 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. P B R Example 1 What is 30% of 500? R = 30% B = 500 P =? P = % (change percent to decimal) P = 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 = P = 9, therefore, there are 9 apples in the basket.

2 PASIG CATHOLIC COLLEGE School Year MATHEMATICS 5 Activity Sheet No. 3 TYPE OF ACTIVITY: Computational Skills : Finding the Base LEARNING OBJECTIVES : Solve for the base in a worded problem. REFERENCE :, Wright, Amelia C. and Villamayor, Adelia C. To find the base, divide the percentage by the rate. B = P R Example 1: 24 is 60% of what number? P P = 24 R = 60% B =? B = P R B R B = 24 60% (change percent to decimal) B = 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 = B = 35, therefore there are 35 students in the class. PASIG CATHOLIC COLLEGE School Year MATHEMATICS 5 Activity Sheet No. 4 TYPE OF ACTIVITY: Computational Skills : Finding the Rate LEARNING OBJECTIVES : Solve for the rate in a worded problem. REFERENCE :, Wright, Amelia C. and Villamayor, Adelia C. To find the rate, divide the given percentage by the base or rewrite the number as a fraction. R = P B P Example 1: 56 is what percent of 80? P = 56 B = 80 B =? R = P B B R R = 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 = R = 0.95 (change decimal to percent) R = 95%

3 S.Y DLA No. 5 TYPES OF ACTIVITY: Concept Development Activity 1: Activity 2: Reflection: : Point and Lines LEARNING OBJECTIVES : Recognizes Point and Lines Identify Points and Lines REFERENCE : Simplifying Mathematical Challenges 5 Erminda E. De Leon Amelia C. Wright and Adelia C. Villamayor 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 M 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

4 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 ME IT is read as line ME is parallel to line IT M T I

5 S.Y DLA No. 6 TYPES OF ACTIVITY: Concept Development Activity 3: : 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 Amelia C Wright, Adela C Villamayor 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 M 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.

6 S.Y DLA No. 7 TYPES OF ACTIVITY: Concept Development Activity 3: : 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 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.

7 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

8 S.Y DLA No. 8 TYPES OF ACTIVITY: Concept Development Activity 3: : 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 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor Area is a measure of surface, and surface is measured in square units. A. 9cm ( A= S x S or S 2 ) A= 9 x 9 = 81 cm 2 11 m B. ( A= L x W ) A = 11 x 6. 5 = 71.5 m m c. h = 7 dm b= 12.6 dm ( A= B x H ) A = 12.6 x 7 = 88.2 dm 2

9 S.Y DLA No. 9 TYPES OF ACTIVITY: Concept/Skill Development Activity 3: : Finding the Area of Triangle LEARNING OBJECTIVES : * Find the area of Triangle. * Derive a formula in finding the area of a triangle. REFERENCE : Realistic Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor 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 m 2 A = 20 m 2 The area of a triangle is one half the area of parallelogram. Thus, the area of triangle, A = ½ bh.

10 S.Y DLA No. 10 TYPES OF ACTIVITY: Concept/Skill Development : Finding the area of Trapezoid LEARNING OBJECTIVES : * Find the area of Trapezoid. * Derive a formula in finding the area of a trapezoid. REFERENCE : Realistic Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor Trapezoid has only one pair of parallel sides. To find its area, multiply the sum of the upper base (b 1 ) and the lower base (b 2 ) by its height. Then divide it by 2. B1 = 2.8 m h = 3.2 m Formula b2 = 3.6 m A =!!!!!! x h A = _ _ x A = _ 6.4 x 3.2_ 2 A = _ A = m 2

11 S.Y DLA No. 11 TYPES OF ACTIVITY: Concept/Skill Development : 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 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor 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: 4mm C = 2 x π x r C= 2 x 3.14 x 4 mm C= mm

12 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 r 2 A = 3.14 x (30m) 2 = 3.14 x 900m 2 = 2826 m 2 The area of the circular racetrack is 2 826m 2.

13 S.Y DLA No. 12 TYPES OF ACTIVITY: Concept Development : 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 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor 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) = 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) = 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

14 S.Y DLA No. 13 TYPES OF ACTIVITY: Concept /Skills Development : 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 Julio B. Melad, Aurea V. Dela Paz, Aileen G. Tiu Amelia C Wright, Adela C Villamayor 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 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

15 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 = dm = hectometer

16 S.Y DLA No. 14 TYPES OF ACTIVITY: Concept Development : 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 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.